mm-4599 === Subject: Re: Numbers: Large and small; Real and fake > We must remember that entities like the sq.rt.2 were > originally thought or assumed to be rational, by the > Greeks to whom we owe the origins of our mathematics > (and much else). You need to do some more background reading on the topic >you're writing about, as this is wrong in several ways. >For one thing, the Greeks didn't really think of sqrt(2) >as a number. Instead, they dealt with the idea of >line segment lengths being commensurable or not (and >the early Greeks almost certainly never considered the >possibility of non-commensurable line segment lengths). Dave L. Renfro Which is why I deliberately referred to sqrt(2) as an 'entity' in the passage you quoted. I am aware of the limitations in the early Greek concept of number. (It's the fallacies in the modern concept of number which concern me.) To talk of the irrationality of sqrt(2) is a reasonable paraphrase of the incommensurability of the diagonal and side of a unit square. In this sense, I take it, the Pythagoreans did expect sqrt(2) to be rational. I do not myself believe that sqrt(2) is a number (because of the arguments in the whole post), but it is convenient to characterize it as irrational. leon === Subject: Re: Numbers: Large and small; Real and fake We must remember that entities like the sq.rt.2 were > originally thought or assumed to be rational, by the > Greeks to whom we owe the origins of our mathematics > (and much else). You need to do some more background reading on the topic >you're writing about, as this is wrong in several ways. >For one thing, the Greeks didn't really think of sqrt(2) >as a number. Instead, they dealt with the idea of >line segment lengths being commensurable or not (and >the early Greeks almost certainly never considered the >possibility of non-commensurable line segment lengths). Dave L. Renfro Which is why I deliberately referred to sqrt(2) as an 'entity' in > the passage you quoted. I am aware of the limitations in the early Greek > concept of number. (It's the fallacies in the modern concept of number > which concern me.) To talk of the irrationality of sqrt(2) is a reasonable > paraphrase of the incommensurability of the diagonal and side of a unit > square. In this sense, I take it, the Pythagoreans did expect sqrt(2) to be > rational. I do not myself believe that sqrt(2) is a number (because of the > arguments in the whole post), but it is convenient to characterize it as > irrational. Long ago, mathematics discarded what things are in favor of what things do. sqrt(2) does things a number ought to do, so whether it is a number or not is semantics, or philosophy, or religion, but not mathematics. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Numbers: Large and small; Real and fake Long ago, mathematics discarded what things are in favor of >what things do. sqrt(2) does things a number ought to do, so >whether it is a number or not is semantics, or philosophy, or >religion, but not mathematics. Hmm. That's an interesting piece of ...............Semantics? Philosphy? Religion? Mathematics? I now have a new picture of the sqrt(2), as the John Wayne of the number world, getting off his horse and doing things a square root has gotta do. If you would like to follow the preceding gentleman to the First Aid Tent, where gnat removal and broken toes can be attended to. leon === Subject: Re: Numbers: Large and small; Real and fake > I now have a new picture of the sqrt(2), as the John Wayne of the >number world, getting off his horse and doing things a square root has >gotta do. Yep, I gotta corral me them rationals. -- Angus Rodgers Contains mild peril === Subject: Re: -- explorer le fourier -- > g: > a warrior > you! > no > i had never thought it possible > that sometimes they trick you > i would have thought they needed the bodies > for all those extra uniforms > flack jackets > ammunition > and primary weapons > that is certainly unfortunate > and i know your family must be severely disappointed in the whole affair > but stay strong > friend > at least they removed only inessential organs > -+-+- > you had so many questions > i wonder if my other friends finally got to you > if so > i apologise > but yes i can try to go back some > the goal is a fourier system > in some ways this begs i return to t (x) > m n > -m > = w g (w x) > 2n m n 2n > oo > --- j > (-1) nj+m > = / ------- x > --- (1) > j=0 nj+m > which i abandoned long ago > the zeroes of these functions > are almost periodic like the besselian > in that > lim ( ? (r) - ? (s) ) = ? > n->oo m n+1 m n n > where m_?_n(j) is the jth zero greater than or equal to 0 > of m_t_n > they all have zeroes that approach some multiple of pi in spacing > but the peaks > unlike the t_2 series > grow exponentially n> 3 > and in odd-n cases > the negative domain gives exponentially dominated growth without periodicity > where the even-n of course keep the order-2 symmetry > (even/odd implies periodic in both the positive and negative domains) > a back-of-the-envelope calculation shows > using m=0, n=3 as an example > w x > ( ) ( |0 6 ) > Re< t (x)> = Re< | e ( 0 3 ) ( |3 ) > x '/3 x -'/3 > - ---- i x - ----- i x > 1 / 2 ( 2 ) -x 2 ( 2 ) > = - | e Re< e> + e + e Re< e> | > 3 ( ) ( ) / > x x > - - > 1 / 2 / '/3 -x 2 / -'/3 > = - | e cos| ---- x | + e + e cos| ----- x | | > 3 2 / 2 / / > which is zero when > x > - > -x 2 / '/3 > e = -2 e cos | ---- x | > 2 / > or > -3x > --- > 2 / '/3 > e = -2 cos | ---- x | > 2 / > as the exponential left hand side gets closer to y=0 > it will cross the cosinus closer and closer to its own zeroes > the period of this (0,3) generalisation therefore approaches 2 pi / '/3 > (= 3.6275987...) > and this can be seen from a simple plot of this function > where 0_?_3(0) occurs at 1.8498128 > then 0_?_3(j) = 5.4412334, 9.0689975, 12.696596, 16.324194, ... > so you see > a generalised fourier analysis must not use the > / > | t (r x) t (s x) dx > / m n m' n > because roots are not integer multiples of some base periodicity > similarly > the (1,3)-t has zeroes 1_?_3(j) at > 0, 3.0167442, 6.6506245, 10.278196, 13.905795, 17.533394, ... > and the (2,3)-t has 2_?_3(j) at > 0 (double), 4.2332072, 7.8597929, 11.487396, 15.114995, ... > these are of course interleaved > as one would expect from rolle's theorem > these almost symmetries > along with the unnecessary complications of using half-periods > (so derivatives switch signs after n iterations, ie. > n > d > --- t (x) = - t (x) > n m n m n > dx > ) > is one of the things that makes tchebyshef in the hyperbolics attractive > [...] > didn't know > there were so many kinds of families: Tchebycheff, Laguerre, Legendre, > Hermite > and others: > It seems to me you're looking for non-polynomial > non-trigonometric functions orthogonal for > the Hilbert space L^2(R, mu) , where mu is a measure on R > perhaps arising from some weight function. Maybe you've > heard of wavelets (Daubechies, others) . what one eventually ends up with > after all the excruciating obfuscation is laid out > is ultimately a generalisation of polynomialness itself orthogonality is simple the interesting connection is that > the generalised trigonometry's orthogonality > is mirror to the orthogonality of the generalised tchebyshef I seem to remember reading that Riemann wanted tchebyshef to see his work on zeta and primes. I might look up what tchebyshef did in number theory. > many of the classic orthogonals > including the tchebyshefs > are included in the class of jacobi polynomials the gegenbauers are simply a subclass of jacobi > distinguished by equal upper parameters > and the tchebyshef fall in the gegenbauers > but the generalisation of tchebyshefs > falls in larger class of generalised jacobi the trick is the switch into nonpolynomialness > through the generalised polynomial 2 n-1 > w w w > n n n > y = a x + a x + a x + ... + a x > 0 1 2 n-1 Not using capital letters or punctuation is not something that causes readability problems for me. It's OK for me. However, formulas with exponents on the line above don't always align well; also, towers of exponents with no parentheses are ambiguous for me ... So y = a_0 x ^(n^w) + a_1 * x^(n^w) + a_2 * x^((n^w)^2) + ... I don't think I've got it. Do you get polynomials by setting w=1 ? > which > surprisingly > has some very regular zero features > but a more complex feature set this really becomes apparent in the > generalised tchebyshef representation of x^n i posted see n=1 is e^x > so 1_T_n(e^x) = e^(n x) > or 1_T_n(x) is simply x^n the taylor-mclaurin orthogonals > the most fundamental orthogs of all analysis C 2_T_(n-1)(x) is the minimax rep of 1_T_n(x) now there is this generalisation > and whole new set of tools for feature detection > here - more elaborate patterns in differential structure ^..^ one of the secrets hidden in the shift to tchebyshef > is the origin of the weight function it basically arises from the presence of |n-1 x > | e > |n in integrals of the tchebyshefs since in the (0,2), (1,2) case 2 2 > ch x - sh x = 1 this generalises quite naturally to a function / |0 x |n-1 x > f | | e , | e | = 1 > |n |n / where the natural question arises > is it algebraic? the answer again is revealed in cyclotomics.. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar > === Subject: Re: -- explorer le fourier -- <_gXOj.10976$a86.5805@weber.videotron.net> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) > g: > a warrior > you! > no > i had never thought it possible > that sometimes they trick you > i would have thought they needed the bodies > for all those extra uniforms > flack jackets > ammunition > and primary weapons > that is certainly unfortunate > and i know your family must be severely disappointed in the whole affair > but stay strong > friend > at least they removed only inessential organs > -+-+- > you had so many questions > i wonder if my other friends finally got to you > if so > i apologise > but yes i can try to go back some > the goal is a fourier system > in some ways this begs i return to t (x) > m n > -m > = w g (w x) > 2n m n 2n > oo > --- j > (-1) nj+m > = / ------- x > --- (1) > j=0 nj+m > which i abandoned long ago > the zeroes of these functions > are almost periodic like the besselian > in that > lim ( ? (r) - ? (s) ) = ? > n->oo m n+1 m n n > where m_?_n(j) is the jth zero greater than or equal to 0 > of m_t_n > they all have zeroes that approach some multiple of pi in spacing > but the peaks > unlike the t_2 series > grow exponentially n> 3 > and in odd-n cases > the negative domain gives exponentially dominated growth without periodicity > where the even-n of course keep the order-2 symmetry > (even/odd implies periodic in both the positive and negative domains) > a back-of-the-envelope calculation shows > using m=0, n=3 as an example > w x > ( ) ( |0 6 ) > Re< t (x)> = Re< | e ( 0 3 ) ( |3 ) > x '/3 x -'/3 > - ---- i x - ----- i x > 1 / 2 ( 2 ) -x 2 ( 2 ) > = - | e Re< e> + e + e Re< e> | > 3 ( ) ( ) / > x x > - - > 1 / 2 / '/3 -x 2 / -'/3 > = - | e cos| ---- x | + e + e cos| ----- x | | > 3 2 / 2 / / > which is zero when > x > - > -x 2 / '/3 > e = -2 e cos | ---- x | > 2 / > or > -3x > --- > 2 / '/3 > e = -2 cos | ---- x | > 2 / > as the exponential left hand side gets closer to y=0 > it will cross the cosinus closer and closer to its own zeroes > the period of this (0,3) generalisation therefore approaches 2 pi / '/3 > (= 3.6275987...) > and this can be seen from a simple plot of this function > where 0_?_3(0) occurs at 1.8498128 > then 0_?_3(j) = 5.4412334, 9.0689975, 12.696596, 16.324194, ... > so you see > a generalised fourier analysis must not use the > / > | t (r x) t (s x) dx > / m n m' n > because roots are not integer multiples of some base periodicity > similarly > the (1,3)-t has zeroes 1_?_3(j) at > 0, 3.0167442, 6.6506245, 10.278196, 13.905795, 17.533394, ... > and the (2,3)-t has 2_?_3(j) at > 0 (double), 4.2332072, 7.8597929, 11.487396, 15.114995, ... > these are of course interleaved > as one would expect from rolle's theorem > these almost symmetries > along with the unnecessary complications of using half-periods > (so derivatives switch signs after n iterations, ie. > n > d > --- t (x) = - t (x) > n m n m n > dx > ) > is one of the things that makes tchebyshef in the hyperbolics attractive > [...] > didn't know > there were so many kinds of families: Tchebycheff, Laguerre, Legendre, > Hermite > and others: > It seems to me you're looking for non-polynomial > non-trigonometric functions orthogonal for > the Hilbert space L^2(R, mu) , where mu is a measure on R > perhaps arising from some weight function. Maybe you've > heard of wavelets (Daubechies, others) . what one eventually ends up with > after all the excruciating obfuscation is laid out > is ultimately a generalisation of polynomialness itself orthogonality is simple the interesting connection is that > the generalised trigonometry's orthogonality > is mirror to the orthogonality of the generalised tchebyshef I seem to remember reading that Riemann wanted > tchebyshef to see his work on zeta and primes. > I might look up what tchebyshef did in > number theory. many of the classic orthogonals > including the tchebyshefs > are included in the class of jacobi polynomials the gegenbauers are simply a subclass of jacobi > distinguished by equal upper parameters > and the tchebyshef fall in the gegenbauers > but the generalisation of tchebyshefs > falls in larger class of generalised jacobi the trick is the switch into nonpolynomialness > through the generalised polynomial 2 n-1 > w w w > n n n > y = a x + a x + a x + ... + a x > 0 1 2 n-1 Not using capital letters or punctuation is not something that > causes readability problems for me. It's OK for me. > However, formulas with exponents on the line above > don't always align well; also, towers of exponents > with no parentheses are ambiguous for me ... So y = a_0 x ^(n^w) + a_1 * x^(n^w) + a_2 * x^((n^w)^2) + ... I don't think I've got it. Do you get polynomials by > setting w=1 ? the alignment of the first exponent was my fault the exponent terms are roots of unity (or more generally in some of the other uses any elements of a cyclotomic ring) just as an example of where it comes from ch x = 1/2 ( e^x + e^(-x) ) set y = e^x and one has y + 1/y = 2 ch x turn it into a quadratic (since y=/=0 because e^x =/=0) y^2 - 2 y ch x + 1 = 0 and use quadratic formula y = ( 2 ch x +/- '/(4 ch^2 x - 4) ) / 2 from the exponential (positive) nature of y this becomes simply y = ch x + '/(ch^2 x - 1) if we return back to y = e^x then x = ln( ch x + '/(ch^2 x - 1) ) the classic inversion formula for hyperbolic trigs now try to do the same thing for |0 x | e |3 and you'll see where the generalisation comes in i've mentioned these polynomials several times over the years in various contexts but one that helps visualise what these are is at > which > surprisingly > has some very regular zero features > but a more complex feature set this really becomes apparent in the > generalised tchebyshef representation of x^n i posted see n=1 is e^x > so 1_T_n(e^x) = e^(n x) > or 1_T_n(x) is simply x^n the taylor-mclaurin orthogonals > the most fundamental orthogs of all analysis C 2_T_(n-1)(x) is the minimax rep of 1_T_n(x) now there is this generalisation > and whole new set of tools for feature detection > here - more elaborate patterns in differential structure ^..^ one of the secrets hidden in the shift to tchebyshef > is the origin of the weight function it basically arises from the presence of |n-1 x > | e > |n in integrals of the tchebyshefs since in the (0,2), (1,2) case 2 2 > ch x - sh x = 1 this generalises quite naturally to a function / |0 x |n-1 x > f | | e , | e | = 1 > |n |n / where the natural question arises > is it algebraic? the answer again is revealed in cyclotomics.. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar === Subject: Re: -- explorer le fourier -- posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) generalised polynomials have many nice properties if f, f' e W[x] in other words if --- w f = / a x --- w w e S_f c C n S_f finite and --- w f' = / b x --- w w e S_f' c C n S_f' finite where C_n is the ring of integers of the cyclotomic field of order n then (f + f') e W[x] and (f f') e W[x] also derivatives of e W[x] are e W[x] the integrals can bring in logarithmic forms but so do simple laurent polynomials and these are well understood the really crazy thing is that they seem to have an interesting zero structure where for instance --- w / x = c(x) --- n w = 1 has n zeroes in the complex numbers the important step then becomes the galois analysis so an important consequence of this generalisation is a whole new realm of galois study which i am sure has already been done already if i only knew the right keywords to search -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: -- explorer le fourier -- posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) > generalised polynomials have many nice properties if f, f' e W[x] in other words > if --- > w > f = / a x > --- w > w e S_f c C > n > S_f finite and --- > w > f' = / b x > --- w > w e S_f' c C > n > S_f' finite where C_n is the ring of integers > of the cyclotomic field of order n then (f + f') e W[x] > and (f f') e W[x] notice that this is true for finite subcollections that come from any semigroup it is possible to define [x] as the generalised polynomial ring with S the semigroup of exponents and R the ring of coefficients and these general constructs have a number of properties more generally derivable however the cyclotomic generalisation has a number of special properties that make it very natural for study just as a quick example even though f(x) e W[x] does not guarantee f(x)^w e W[x] it is true that f_3(x) = x^w_3 for instance obeys f_3(f_3(x)) = x^(w_3^2) and f_3(f_3(f_3(x))) = x (all this occurs on appropriate branches of course) so this generalisation has periodic iterations possible which are actually useful in reducing or transforming some expressions these cyclotomic generalised polynomials arise naturally in the theory of multisection outside this focus on the multisection of exponentials and all this work on generalised fourier analysis in fact in many ways the analysis can be extended beyond exponentials the key point of all of my efforts in generalised trigonometry was the discovery of the product and sum laws without that the integrals of products would have made little progress and the tchebyshef theory would not have passed initial discovery but a secret i've kept hidden (mostly due to a lack of time to write it all out) is that the technique for finding the product rule actually works for the multisection of any function that already has a product rule in other words if f(x)f(y) = g(x,y) then we can find a product rule for / |m / |m' | | f(x) || | f(y) | |n / |n / using exactly the same steps as for trigonometrics this is why i have always considered the generalised fourier theory an extension of my multisection results over all hypergeometric and q-hypergeometric functions because much of the discussion does not reach full generality simply at the ur-hypergeometric (the exponential) products the differential structure integrals and much of a generalised analysis carries over to many famous hypergeometrics and in these cases since the product rule is derived from simpson's multisection formula the values at cyclotomic places comes in in many cases of interest this introduce W[x] again... > also > derivatives of e W[x] > are e W[x] the integrals can bring in logarithmic forms > but so do simple laurent polynomials > and these are well understood the really crazy thing > is that they seem to have an interesting zero structure > where > for instance --- > w > / x = c(x) > --- > n > w = 1 has n zeroes in the complex numbers the important step > then > becomes the galois analysis so an important consequence of this generalisation > is a whole new realm of galois study which i am sure has already been done > if i only knew the right keywords to search -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Irreducible surjective maps posting-account=4m6i3AoAAACkBWCtXNbpbnHMq5T0a0Fu I have a question regarding continuous irreducible surjections. Recall, a continuous function f : X --> Y between two topological space X and Y is called an irreducible surjection iff 1. it is surjective 2. If Z is a closed subset of X with f(Z)=Y then Z=X My question is... Is it true that for any two Hausdorff compact spaces X,Y and a continuous surjection f: X --> Y there is a closed subset of X, say Z such that f restricted to Z is an irreducible surjection? My assumption is that the above is false, I just need to make an example.. any ideas? Would appreciate any suggestions Jose Capco === Subject: Re: Irreducible surjective maps >I have a question regarding continuous irreducible surjections. >Recall, a continuous function >f : X --> Y >between two topological space X and Y is called an irreducible >surjection iff >1. it is surjective >2. If Z is a closed subset of X with f(Z)=Y then Z=X >My question is... >Is it true that for any two Hausdorff compact spaces X,Y and a >continuous surjection f: X --> Y >there is a closed subset of X, say Z such that f restricted to Z is an >irreducible surjection? >My assumption is that the above is false, I just need to make an >example.. any ideas? >Would appreciate any suggestions >Jose Capco With the axiom of choice, it is true. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Irreducible surjective maps > I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X > My question is... > Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? > My assumption is that the above is false, I just need to make an > example.. any ideas? > Would appreciate any suggestions > Jose Capco With the axiom of choice, it is true. I was racking my brain to prove the claim for the general situation. I am not sure whether this is really true. What is to be shown is that if Z_i, i in I, is a decreasing family of closed subsets of X with f(Z_i)=Y, i in Z, then there is a lower bound Z with f(Z)=Y. Let Z be the intersection of the Z_i's, then the intersection of Z with every fiber f^-1(y) of f (y in Y) should be non-empty. This is not clear to me without any additional assumption. -- Best wishes, J. === Subject: Re: Irreducible surjective maps <480CD1EA.6020000@web.de> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X > My question is... > Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? > My assumption is that the above is false, I just need to make an > example.. any ideas? > Would appreciate any suggestions > Jose Capco With the axiom of choice, it is true. I was racking my brain to prove the claim for the general situation. I > am not sure whether this is really true. What is to be shown is that if > Z_i, i in I, is a decreasing family of closed subsets of X with > f(Z_i)=Y, i in Z, then there is a lower bound Z with f(Z)=Y. Remark that X is assumed to be compact and Hausdorff in the OP's post. Let {F_i : i in I} be a decreasing family of compact subsets in X such that f(F_i) = Z. Then F = intersect_{i in I} F_i is non-empty. Let z in Z. For each i in I, there exists x_i in F_i such that f(x_i) = z. Define a function phi : I --> X so that phi(i) = x_i. Consider I ordered so that i <= j iff F_i subset F_j. This makes I a directed set, so that phi is a net in X. Since X is compact, there is a convergent subnet, ie, there is a directed set J and a monotone cofinal map h : J --> I such that psi = phi o h : J --> X is convergent. Let x in X be its limit (there is only one, because X is Hausdorff) Since f is continuous, f(x) = z. Since the net psi is eventually in every F_i, which is closed, its limits is in every F_i, so x in F. Therefore f(F) = Z. -- m > Let Z be the intersection of the Z_i's, then the intersection of Z with > every fiber f^-1(y) of f (y in Y) should be non-empty. This is not clear to me without any additional assumption. -- > Best wishes, > J. === Subject: Re: Irreducible surjective maps > I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X > My question is... > Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? > My assumption is that the above is false, I just need to make an > example.. any ideas? > Would appreciate any suggestions > Jose Capco > With the axiom of choice, it is true. > I was racking my brain to prove the claim for the general situation. I > am not sure whether this is really true. What is to be shown is that if > Z_i, i in I, is a decreasing family of closed subsets of X with > f(Z_i)=Y, i in Z, then there is a lower bound Z with f(Z)=Y. Remark that X is assumed to be compact and Hausdorff > in the OP's post. Good point. I missed that. In this case every fiber is compact and everything is fine. -- Best wishes, J. === Subject: Re: Irreducible surjective maps I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X My question is... Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? Yes if, e.g., f has compact fibers: In this case the system S of closed subsets A of X with f(A)=Y is non-void and has a smallest element A' (by taking the intersection over S). Then A' satisfies your condition that f|A' is an irreducible surjection. > My assumption is that the above is false, I just need to make an > example.. any ideas? Can you construct a counterexample from here? I think the map R -> S^1, t -> exp(it) should volunteer for serving as counterexample. ... > Would appreciate any suggestions Jose Capco -- Best wishes, J. === Subject: Re: Irreducible surjective maps <480C516B.8020104@web.de> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X My question is... Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? Yes if, e.g., f has compact fibers: In this case the system S of closed > subsets A of X with f(A)=Y is non-void and has a smallest element A' (by > taking the intersection over S). Then A' satisfies your condition that > f|A' is an irreducible surjection. But that intersection is can be void: Take any compact Hausdorff space Y and put X = Y x Y, Y = V and let f : X --> Y be the 1st projection: then S contains all `horizontal' copies of Y in X, which are disjoint. You need to show there is a minimal element in S, not a minumum. -- m === Subject: Re: Irreducible surjective maps > I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X > My question is... > Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? > Yes if, e.g., f has compact fibers: In this case the system S of closed > subsets A of X with f(A)=Y is non-void and has a smallest element A' (by > taking the intersection over S). Then A' satisfies your condition that > f|A' is an irreducible surjection. But that intersection is can be void: Take any compact Hausdorff > space Y and put X = Y x Y, Y = V and let f : X --> Y be the 1st > projection: then S contains all `horizontal' copies of Y in X, > which are disjoint. You need to show there is a minimal element in S, not a minumum. -- m Outsh! You are right. Then the arguments goes through when some minimal element of S can be found. This is guaranteed by Zorn's lemma together with the assumption that the fibers of f be compact. I still believe that my counterexample holds, so I cannot see that the assertion is true in general as Herman claims. I think that Zorn's lemma cannot yield to the aim without any additional condition for f. Appreciated if someone could shed some light on this! -- Best wishes, J. === Subject: Re: Irreducible surjective maps > I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X > My question is... > Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? Yes if, e.g., f has compact fibers: In this case the system S of closed > subsets A of X with f(A)=Y is non-void and has a smallest element A' (by > taking the intersection over S). Then A' satisfies your condition that > f|A' is an irreducible surjection. > My assumption is that the above is false, I just need to make an > example.. any ideas? Can you construct a counterexample from here? I think the map R -> S^1, > t -> exp(it) should volunteer for serving as counterexample. ... No, it doesn't: Take A = [0,1]. > Would appreciate any suggestions > Jose Capco > -- Best wishes, J. === Subject: Re: Irreducible surjective maps I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X My question is... Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? > Yes if, e.g., f has compact fibers: In this case the system S of > closed subsets A of X with f(A)=Y is non-void and has a smallest > element A' (by taking the intersection over S). Then A' satisfies your > condition that f|A' is an irreducible surjection. > My assumption is that the above is false, I just need to make an > example.. any ideas? And here some pathological counterexample: Let X be the subset of R^2 defined as the union of the segments S(n), n in N, where S(n) connects the endpoints (0,1/n) and (1,0). Set Y=[0,1]. Equip X and Y with the topology induced by R^2 and R, resp. Define f(x,y)=max(x,1/n) if (x,y) is in S(n). This is well-defined. Then any closed subset A of X with f(A)=Y can be strictly shrunk to some A' again with f(A')=Y. -- Best wishes, J. === Subject: Re: Irreducible surjective maps > I have a question regarding continuous irreducible surjections. > Recall, a continuous function > f : X --> Y > between two topological space X and Y is called an irreducible > surjection iff > 1. it is surjective > 2. If Z is a closed subset of X with f(Z)=Y then Z=X > My question is... > Is it true that for any two Hausdorff compact spaces X,Y and a > continuous surjection f: X --> Y > there is a closed subset of X, say Z such that f restricted to Z is an > irreducible surjection? Yes if, e.g., f has compact fibers: In this case the system S of > closed subsets A of X with f(A)=Y is non-void and has a smallest > element A' (by taking the intersection over S). Then A' satisfies > your condition that f|A' is an irreducible surjection. > My assumption is that the above is false, I just need to make an > example.. any ideas? And here some pathological counterexample: Let X be the subset of R^2 defined as the union of the segments S(n), n > in N, where S(n) connects the endpoints (0,1/n) and (1,0). Set Y=[0,1]. > Equip X and Y with the topology induced by R^2 and R, resp. Define f(x,y)=max(x,1/n) if (x,y) is in S(n). This is well-defined. Then any closed subset A of X with f(A)=Y can be strictly shrunk to some > A' again with f(A')=Y. This example does not fit all of the OP's assumptions. X is assumed to be compact. In this case everything goes through since S has minimal elements by Zorn's lemma. There is no need to look at fibers. -- Best wishes, J. === Subject: Do you love designer clothes? If yes, you are among the millions of people that window shop in the 5th Avenue shops of New York or who circle items within fashion magazines every month. Unfortunately, most of us don't have the thousands of dollars needed to purchase each one of these complete outfits that we are in love with. For an affordable option to buy designer clothing, consider searching for used clothing items in stores or online. posting-account=sN1F9woAAACDZjynRc8QOOiBsHHZb1wx SV1),gzip(gfe),gzip(gfe) Do you love designer clothes? If yes, you are among the millions of people that window shop in the 5th Avenue shops of New York or who circle items within fashion magazines every month. Unfortunately, most of us don't have the thousands of dollars needed to purchase each one of these complete outfits that we are in love with. For an affordable option to buy designer clothing, consider searching for used clothing items in stores or online. http://replicab2b.net http://replicab2b.net/Replica_Wallets_1.html http://replicab2b.net/Replica_Jewelrys_1.html http://replicab2b.net/Replica_Shoes_1.html http://replicab2b.net/Replica_Jeans_1.html http://replicab2b.net/Replica_Sunglasses_1.html http://replicab2b.net/Replica_Clothing_1.html Many people that have designer clothes only wear the item once before selling it or donating it to charity. Many consumers view their clothing as disposable and several sell clothes that have not even been worn. With this in mind, if you know where and how to shop, you can find some great bargains on the designer clothes that you are looking for in re-sale shops and online. The quickest way to shop for designer bargains is to search online. Popular online auction sites such as Ebay have entire sections devoted to used clothing items for sale. The site separates the used clothing by category, such as shirts, pants, coats and jackets, women's, men's and children's. Within each category of used clothing, you will be able to search specifically within the category, by price and from when the bidding is ending. If there is a specific designer or name brand that you are searching for, you can simply type that name in to search the entire website for related items. If you find items that you are not ready to bid on, you can watch them to see what prices people are bidding at for that item. If the item is within your price range, you can place a bid. Always keep in mind the cost of shipping when you are bidding so that you are taking into consideration the entire financial picture when you are making your purchases. It is also recommended that you search the buyer's recent feedback to get an overall picture of the quality of their listed items. There is also an extensive list of online consignment shops that sell designer used clothing. If you are more interested in searching for specific items and purchasing them immediately instead of bidding for them, this is a great option to consider. You can use your search engine to locate used clothing stores, used clothing, used designer clothing or simply type in used and the name brand of the item that you are looking for. An extensive list of stores offering that designer and anything similar will come up for you to browse. When you are considering a purchase, be sure to evaluate the site's shipping policy, their payment options (make sure that they are secure), their recent feedback and their credibility before completing the sale. Searching online for designer used clothing is a great way to find the clothes that you love at prices that you can afford. There is a great chance that someone in the world is selling the exact item that you are looking for. === Subject: Re: Orthonormalization of function space > Then I did project sin(x) orthogonally into this subspace, getting > 1.382*x-1.097*x^3 as component parallel to it. 1.382 and -1.097 are the inner products, but it looks like you applied > them to x and x^3 instead of the actual basis vectors. > While this polynomial looks a bit like sin(x), it is an approximation > not even close to the quality of the third-order taylor polynomial > (x+1/6*x^3 IIRC). x - (1/6)*x^3 actually. Once you correct your basis vectors, the resulting function is a much > better approximation than you got. The maximum error over the > interval is much less than that for the Taylor series, though the > behaviour near 0 is worse. I'll see, but this sounds promising ;) Daniel -- Done: Bar-Sam-Val-Wiz, Dwa-Elf-Hum-Orc, Cha-Law, Fem-Mal Underway: Ran-Gno-Neu-Fem To go: Arc-Cav-Hea-Kni-Mon-Pri-Rog-Tou === Subject: Re: Completion and Dense Sets > Assumptions: > metric spaces (S,d) and (S, d) It is a bit hard to know which of these spaces you are referring to later on if you use the exact _same_ notation for two _different_ metric spaces. > S is the completion of S => For every > cauchy sequence > {p_n} in S , {p_n} converges to a point p in S for every s in S > Q(s) = (s,s,s,........................) and Q(s) > is in S So, what is Q supposed to be? It is clearly a map from S into something, which seems to me to be the space of sequences of elements in S...is that what you're trying to say? In that case, Q(s) is _not_ in S, so that can't be it...hmmm > so Q(S) is an injective mapping Do you mean Q is an injective mapping? Q(S) is a subset of whatever Q's codomain is... > Need to show that Q(S) is dense in S Right. If you need any help with that, I suggest that you be a bit more careful in stating the problem. As it stands , I certainly don't get it, and I suspect it is not that apparent to anyone else either. -- Martin Wanvik === Subject: Re: Completion and Dense Sets > Assumptions: > metric spaces (S,d) and (S, d) It is a bit hard to know which of these spaces you > are referring to later on if you use the exact _same_ > notation for two _different_ metric spaces. S is the completion of S => For > every > cauchy sequence > {p_n} in S , {p_n} converges to a point p in S for every s in S > Q(s) = (s,s,s,........................) and > Q(s) > is in S So, what is Q supposed to be? It is clearly a map > from > S into something, which seems to me to be the space > of > sequences of elements in S...is that what you're > trying > to say? In that case, Q(s) is _not_ in S, so that > can't be it...hmmm so Q(S) is an injective mapping Do you mean Q is an injective mapping? Q(S) is a > subset of whatever Q's codomain is... Need to show that Q(S) is dense in S Right. If you need any help with that, I suggest that > you be a bit more careful in stating the problem. As > it stands , I certainly don't get it, and I suspect > it is not that apparent to anyone else either. After thinking a bit more about it, it turns out I _do_ get it..at least I think I do. As far as I can tell, you are considering the standard construction of the completion of a metric space (S,d) as the set E of equivalence classes of Cauchy sequences in S, with respect to a certain equivalence relation (which I assume you're familiar with and understand). E is also given a metric, defined by m({x_n}, {y_m}) = lim_{n -> oo} d(x_n, y_n) for sequences {x_n}, {y_n} (this can be shown to be a well-defined metric on E) Above, you defined a map S --> E by mapping s to the constant (Cauchy) sequence (s,s,....). You want to show that Q(S) is dense in E. To do that, take an arbitrary element x = {x_n} of E and show that there exists a sequence of elements of Q(S) that converge to it. Figure out what elements of Q(S) look like, and find the obvious candidate for a sequence in Q(S) converging to {x_n}. Prove your result. (or ask another question if you get stuck, but be careful to tell us what you've tried). -- Martin Wanvik === Subject: Re: a new infinite series that convereges to e > sqrt(e)-1 = 1/2 + 1/14 + 1/28 + 1/70 + 1/108 + 1/205 + ... for details: http://tesseract.athost.net Duh - that's not new! I saw it a week ago in Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: a new infinite series that convereges to e I didn't understand where you saw that, I published it about a week ago on a thread in this forum called natural geometry but since it didn't get the exposure I was hoping for I republished it, as I will do from now on, from time to time. sqrt(e)-1 = 1/2 + 1/14 + 1/28 + 1/70 + 1/108 + 1/205 + ... for details: http://tesseract.athost.net Duh - that's not new! I saw it a week ago in Phil > -- > -- Microsoft voice recognition live demonstration === Subject: Re: a new infinite series that convereges to e A: Because it messes up the order in which people normally read text. Q: Why is top-posting such a bad thing? A: Top-posting. Q: What is one of the most annoying things on usenet? Fixing. > sqrt(e)-1 = 1/2 + 1/14 + 1/28 + 1/70 + 1/108 + 1/205 + ... for details: http://tesseract.athost.net > Duh - that's not new! I saw it a week ago in > I didn't understand where you saw that, I published it about a week ago on a > thread in this forum called natural geometry So you posted it here a week ago, and yet you can't understand how I managed to see it a week ago. Does being that dense hurt? That's what that bloody message ID was - a reference to your previous post. And this isn't a 'forum' - this is a usenet newsgroup. > but since it didn't get the > exposure I was hoping for I republished it, as I will do from now on, from > time to time. Don't do that. If you've got *no new bits* to add, don't post the same thing over and over again. Or you'll quickly end up in people's killfiles and/or thought of as a crank. Or do do that; there's plenty of room on usenet for one more crank, and plenty of room in killfiles too. Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: -- Elementary but fiendishly hard problem in set theory <23183297.1208741251656.JavaMail.jakarta@nitrogen.mathforum.org> the cardinality of the continuum? Not just the cardinality of the continuum, but even order isomorphic > to the continuum :-) > For all r in R, let D_r = { q in Q | q < r }. === Subject: Re: -- Elementary but fiendishly hard problem in set theory Problem 72. A family of subsets of N has the following property: > any two elements of the family have finite intersection. Can this > family have the cardinality of the continuum? Here's a quick sketch. Details left to the reader. For all r in RQ, there's some increasing sequence of irrationals You meant increasing sequence of rationals, I think. > Yes. Also RQ can be changed to R, but that affects not the proof nor the result. >that converge to r. Show for any two such sequences that >converge to different irrationals, that they can only have >finite many elements in common. Now map Q to N and you'll have the answer yes it can. With the correction I mentioned, I like your proof, however there's no > need to use RQ, you can just use R, and also, the sequence of > rationals need not be increasing. With the above proposed simplifications, let me replay your proof ... For each r in R, let X_r be a bounded set of rationals having r as a > unique accumulation point. Then for distinct reals, r,s, X_r / X_s > must be finite. Also, each X_r is a subset of Q, hence is countable, > but the collection {X_r | r in R} has the same cardinality as R. > Proving disjointedness isn't as immediate as using increasing sequences. > To finish the proof, use a bijection from Q to N, thus mapping each > set X_r to a subset Y_r of N. quasi > === Subject: Re: -- Elementary but fiendishly hard problem in set theory [NonBreakingSpace]Problem 72. [NonBreakingSpace]A family of subsets of N has the following property: > [NonBreakingSpace]any two elements of the family have finite intersection. Can this > [NonBreakingSpace]family have the cardinality of the continuum? Here's a quick sketch. Details left to the reader. For all r in RQ, there's some increasing sequence of irrationals > that converge to r. Show for any two such sequences that > converge to different irrationals, that they can only have > finite many elements in common. Now map Q to N and you'll have the answer yes it can. That would work, if you had chosen sequences of *rationals*. Choosing > an increasing sequence of *irrationals* converging to each point > doesn't do much good. > === Subject: Re: -- Elementary but fiendishly hard problem in set theory > ... I sometimes wonder if mathematicians are masochists ... >All that long winded masochism has been not read and snipped. Ow, you sadist! s/masochists/sadomasochists/ > Problem 72. A family of subsets of N has the following property: > any two elements of the family have finite intersection. Can this > family have the cardinality of the continuum? Here's a quick sketch. Details left to the reader. For all r in RQ, there's some increasing sequence of irrationals >that converge to r. Show for any two such sequences that >converge to different irrationals, that they can only have >finite many elements in common. Now map Q to N and you'll have the answer yes it can. Modulo the minor error, that is essentially the solution given in Exercise (3) of section 14 of Halmos, Lectures in Boolean Algebras. I was fixated on the fact that the first part of the problem (the second is easy) was asking for the maximum size of a subset of the quotient of the Boolean ring 2^N by the ideal of finite subsets of N such that the product of any two elements of the set was zero. But it seems that this was exactly the opposite of the direction to go in, in the sense that it is rather the solution to the given problem that solves a problem in the theory of Boolean algebras: (3) Show that the countable chain condition is not preserved by homomorphisms. (Hint: consider the algebra of all subsets of a countable set modulo the ideal of all finite sets. For ease in manipulation, let the countable set be the set of all rational numbers, and, for each real number t, find a set of rational numbers that has t as its unique limit point.) -- Angus Rodgers Contains mild peril === Subject: Re: -- Elementary but fiendishly hard problem in set theory posting-account=hhC2JwoAAAAQt9ZcdRPKAFNCTwZjbe1M 1.1.4322),gzip(gfe),gzip(gfe) > æProblem 72. æA family of subsets of N has the following property: > æany two elements of the family have finite intersection. æCan this > æfamily have the cardinality of the continuum? Several classic constructions of such a family have been posted. >Here's another one: For each strictly increasing sequence s = (p 1, p 2, ...) of prime >numbers, >let X s = {p 1, p 1p 2, p 1p 2p 3, ...}. That's really nice. The finite intersection property is immediate. Of course, one still has to show that the set of such sequences has > the cardinality of the continuum. While that seems intuitive, is it > obvious? Sure. The set N^N of *all* infinite sequences of natural numbers (i.e. positive integers) has the cardinality of the continuum. The map (n 1, n 2, n 3, ...) -> (n 1, n 1+n 2, n 1+n 2+n 3, ...} is a bijection from N^N to the set of all *increasing* sequences of natural numbers, which is equivalent (given the infinitude of primes) to the set of all increasing sequences of prime numbers. === Subject: Re: Geometry with projective line... > x - y + z = 0 > kx + y + 3z = 0 > x - y + 3z = 0 Three projective line is the concurrent line. Huh? > Find the k. > Equations 1 and 3 give z = 0. Thus x - y = 0 and kx + y = 0. > Answer : -1 kx = -y = -x, what if x = 0? Then y = 0 and k can be anything. > is this line ? generally, plane equation. unfamiliar... A point p, in the projective plane has homogenous coordinates, p = (x,y,z) = (kx,ky,kz) > Can you understand this problem ? > No. === Subject: Re: Geometry with projective line... > x - y + z = 0 > kx + y + 3z = 0 > x - y + 3z = 0 > Three projective line is the concurrent line. Huh? > Find the k. >Equations 1 and 3 give z = 0. Thus > x - y = 0 >and > kx + y = 0. > Answer : -1 kx = -y = -x, what if x = 0? Then y = 0 and k can be anything. > is this line ? generally, plane equation. unfamiliar... A point p, in the projective plane has homogenous coordinates, > p = (x,y,z) = (kx,ky,kz) > Can you understand this problem ? >No. Both of you need to look up the linear algebra interpretation of the projective plane. The problem gives 3 projective lines in the projective plane, represented algebraically as planes through the origin in R^3, with one of the lines specified only up to an unknown constant k. In the projective plane, any 2 lines meet. The question is, for what value of k do all three lines meet? The answer is k = -1. The derivation is trivial -- essentially elementary algebra. Simply note that a point in the projective plane is represented algebraically by a line through the origin in R^3. quasi === - Visit www.theyoungscientists.in posting-account=9CbGpgoAAAD2EOomgwt0brXp89Y_RShu CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1; MS-RTC LM 8),gzip(gfe),gzip(gfe) Visit www.theyoungscientists.in === Subject: Re: Local Homeomorphisms <4805B991.8040207@web.de> <48088B7A.70407@web.de> Continuous f:X -> Y is a local homeomorphism when for all x, > some open U nhood x with U homeomorphic f(U) and f(U) open. > The key difference between local homeomorphisms and covering > maps is that the first is a definition local on the domain, > while the second is local on the codomain: given a map > f : X --> Y, * f is a local homeo if for all x in X, there is > an open U with x in U and f : U --> f(U) an homeo; while > This does not include the requirement that f(U) be open. This is what's puzzling me. Wikipedia says f(U) is open. Where is the definition you've given, stated or used? The distinction between the two is that your definition + open map is equivalent to Wikipedia's definition. Open map seems like a strong extra requirement. Is it really essential? That I dispute. A locally bijective continuous open map is equivalent to local homeomorphism by Wikipedia's definition. > * f is a covering map if for all y in Y, there is an > open V with y in V such that f : f^(V) --> V is a trivial > covering (ie, f^(V) is a disjoint union of open sets > each one of which is mapped homeomorphically onto V > by f) > f:[0,1) -> S^1 is a local homeomorphism that's not a covering map. -- Riddle of the day. Is a local homeo a local homo Romeo? === Subject: Re: Local Homeomorphisms <4805B991.8040207@web.de> <48088B7A.70407@web.de> Google should become your friend. They were until they sold their soul to the stock market. Ever since then I've been removing bookmarks to Google's services. They > are examples of 'new and improved' = 'isn't as nice and doesn't work as > good' and 'updates are worse than blind dates'. Now Yahoo is my friend. Yahoo should become your friend. So you prefer friends who collaborate in internet censorship and > sell out dissidents to opressive governments? > Now that you mention it, that's another reason why Yahoo is my friend who is unlike Google that does such things. === Subject: Re: Local Homeomorphisms [...] > Google should become your friend. They were until they sold their soul to the stock market. Ever since then I've been removing bookmarks to Google's services. They > are examples of 'new and improved' = 'isn't as nice and doesn't work as > good' and 'updates are worse than blind dates'. Now Yahoo is my friend. Yahoo should become your friend. So you prefer friends who collaborate in internet censorship and > sell out dissidents to opressive governments? Now that you mention it, that's another reason why > Yahoo is my friend who is unlike Google that does such things. Sure aboyt the unlike ? You might want to take a look at . | Unlike Google or Microsoft, which keep confidential records of its | users outside mainland China, Yahoo stated that the company will | not protect the privacy and confidentiality of its Chinese customers | from the authorities. Marc === Subject: Re: Local Homeomorphisms <48088B7A.70407@web.de> [...] > Google should become your friend. They were until they sold their soul to the stock market. Ever since then I've been removing bookmarks to Google's services. They > are examples of 'new and improved' = 'isn't as nice and doesn't work as > good' and 'updates are worse than blind dates'. Now Yahoo is my friend. Yahoo should become your friend. So you prefer friends who collaborate in internet censorship and > sell out dissidents to opressive governments? Now that you mention it, that's another reason why > Yahoo is my friend who is unlike Google that does such things. Sure aboyt the unlike ? > You might want to take a look at . | Unlike Google or Microsoft, which keep confidential records of its > | users outside mainland China, Yahoo stated that the company will > | not protect the privacy and confidentiality of its Chinese customers > | from the authorities. > What's the difference if you're Chinese? Wdo does data mining for the US government? === Subject: Interpretation of SVM results -- please help! posting-account=Q4uDswgAAABewI7uG61B1W967GLr75JQ CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) Hope I'm in the right place. Apologies if I'm not. I need some help. I have just used a SVM algorithm for the first time (as part of a software package). The test file has 232 data points and the training file had 232 points also. My problem lies with interpretation of the results that is giving me. The files comes back somethign like this: 0.03125 3.0517578125E-05 0.53448275862069 0.03125 0.0001220703125 0.53448275862069 0.03125 0.00048828125 0.53448275862069 0.03125 0.001953125 0.53448275862069 0.03125 0.0078125 0.53448275862069 0.03125 0.03125 0.53448275862069 0.03125 0.125 0.53448275862069 0.03125 0.5 0.53448275862069 0.03125 2 0.53448275862069 0.03125 8 0.53448275862069 0.125 3.0517578125E-05 0.53448275862069 0.125 0.0001220703125 0.53448275862069 0.125 0.00048828125 0.53448275862069 0.125 0.001953125 0.53448275862069 0.125 0.0078125 0.53448275862069 0.125 0.03125 0.53448275862069 0.125 0.125 0.53448275862069 0.125 0.5 0.53448275862069 0.125 2 0.53448275862069 0.125 8 0.53448275862069 0.5 3.0517578125E-05 0.53448275862069 0.5 0.0001220703125 0.53448275862069 0.5 0.00048828125 0.53448275862069 that is, there are 10 0.03125, 10 0.125 etc all the way up to: 32768, for example: 32768 8 0.491379310344828 I know that the first number is called: suggested cost, the second: suggested gamma and the third cross validation accuracy My problem is this. I do not know how to interpret the above answers. What do they mean? Where do I go from here? I don't think I can graph stufff like this? Can I? do i have to doo something else? i'm a bit confused and would appreciate some help/guidance. I would greatly appreciate any help/suggestions that you may be able to offer me. I'm kind oif confused. Al. The confused one. === Subject: New mathematics / physical sciences positions at http://jobs.phds.org, Apr 21, 2008 There are new job listings at http://jobs.phds.org -------------------------------------------------------------------- Title: Leading European investment bank is seeking to fill a Junior Quant Developer role in London. Employer: Huxley Associates Location: London, England, United Kingdom Fantastic opportunity for a talented C++ programmer with exceptional math skills, looking for a business facing role. Job Description This is a front office quantitative development role with continuous business interaction. Originality and flair... Full details: -------------------------------------------------------------------- Title: Junior Cross Asset Quant - Entry Level .8c£35-40K base Employer: Award Winning Financial Institution Location: London, England, United Kingdom Analyst Position Responsibilities Investment Analysis (70%): The primary responsibility will be to identify, analyse and monitor investment funds or asset managers across all asset classes, but with a focus in the alternative asset classes of hedge... Full details: -------------------------------------------------------------------- Title: Entry Level Interest Rates Quant for European House - London Employer: European Investment bank - London based Location: London, England, United Kingdom A leading US investment bank is currently looking to add an exceptional quantitative analyst to their front office dealing with Exotic Rates derivatives in London. Responsibilities: - Development of risk and PnL management tools for the trading desk... Full details: -------------------------------------------------------------------- Title: Equity Desk Quant for Top Stat Arb Hedge Fund Employer: Top European Hedge Fund Location: London , United Kingdom My client is one of Europes leading hedge funds and currently has 14 bn AUM. They are seeking a highly motivated, talented PhD educated Quantitative Analyst to join the Quant Research funtion, part of the overall quantitative trading business. The... Full details: -------------------------------------------------------------------- Title: Housing Price Analyst Employer: Morgan Stanley Location: New York, NY, United States Position Description Morgan Stanley is seeking a Housing Price Analyst to join the Securitized Products Desk. Candidates must have demonstrated excellence in Statistics, Economics and Modeling languages. Successful candidates will have a proven... Full details: -------------------------------------------------------------------- Title: Senior Quantitative Analyst Employer: Comprehensive Recruiting Location: New York, NY, United States Premier financial services firm is looking for a Quantitative Analyst experienced in high frequency trading strategy development to lead their team. The successful candidate will have a core role in the development of high frequency trading... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst/Developer Employer: Comprehensive Recruiting Location: Boston, Ma, United States The person in this role will implement new investment valuation models and maintain previously built models as a member of the quantitative analysis group. Candidates will have tremendous growth potential, as they will be joining a small and growing... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst Employer: Comprehensive Recruiting Location: Chicago, IL, United States Global Investment Bank is looking to add a senior quantitative analyst to their Global Financial Research team in Chicago. This person will be part of a team that is responsible for innovation, model enhancement, quantitative solutions and cutting... Full details: -------------------------------------------------------------------- Title: Sr. Analyst - Credit Risk Modeling Employer: Comprehensive Recruiting Location: New York, NY, United States This person will focus on the development and implementation of Rating Templates, Probability of Default (PD), Loss Given Default (LGD), and Exposure At Default (EAD) modelling methodologies as part of the ongoing enhancement of credit models for... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst Employer: Comprehensive Recruiting Location: London, England, United Kingdom Global Investment Bank is looking to add a senior quantitative analyst to their Global Financial Research team in London and New York. This person will be part of a team that is responsible for innovation, model enhancement, quantitative solutions... Full details: -------------------------------------------------------------------- Title: Emerging Markets Trader Wanted for Prop. Trading Desk Employer: Prop. Trading Desk Location: London, England, United Kingdom I'm looking for an individual who has built a solid track record of integrating fundamental and quantitative based strategies specifically for the converging economies (Eastern Europe emerging markets) for a Prop. Trading desk. The desk has a... Full details: -------------------------------------------------------------------- Title: Instructors - Mathematics and Statistics Employer: Zayed University, College of Arts and Sciences Location: Abu Dhabi, United Arab Emirates The Department of Mathematics and Statistics invites applications for two instructor positions to teach developmental mathematics, and mathematics courses in the Colloquy On Integrated Learning (the University's core curriculum), with... Full details: -------------------------------------------------------------------- Title: Positions in Statistics, Physical Chemistry, Political & International Studies Employer: RHODES UNIVERSITY Location: Grahamstown, South Africa Rhodes University invites applications from suitably qualified candidates for the following positions, to start from as early a date as possible. Recognising that diversity is important in achieving excellence, we especially encourage South African... Full details: -------------------------------------------------------------------- Title: Statistician/Econometrician - 5390PHD Employer: Roy Talman & Associates Location: Chicago, IL, United States One stop shopping for financial technology jobs! We deal with more trading companies in the Chicago area, than any of our competitors and challenge you to find another technology recruiter in business for more than 25 years! Job # 5390PHD Position:... Full details: -------------------------------------------------------------------- Title: Program Manager, Physical Sciences & Engineering Employer: New York Academy of Sciences Location: New York, NY, United States JOB TITLE: Program Manager; Physical Sciences & EngineeringDEPARTMENT: Programs REPORTS TO: Director; Physical Sciences & Engineering SCOPE OF RESPONSIBILITIES: Create and manage Academy's Physical Sciences & Engineering program in cutting-edge... Full details: -------------------------------------------------------------------- Title: postdoc positions in biomedical engineering Employer: The University of Tennessee Location: Knoxville, TN, United States Postdoctoral positions are immediately available in the Mechanical, Aerospace and Biomedical Engineering Department at the University of Tennessee, Knoxville. These positions are jointly sponsored by Dr. Xiaopeng Zhao (http://web.utk.edu/~xzhao9/)... Full details: -------------------------------------------------------------------- Title: Strategic Analyst Department: Customer Intelligence Employer: Draftfcb Location: Chicago, IL, United States Draftfcb/Chicago-Customer Intelligence Team-Strategic Analyst Job Description * These versatile team members will assist any of the CI Team Leads and Specialists in their work: * - Statistics & modeling * - Retail data reporting & analysis * - Data... Full details: -------------------------------------------------------------------- Title: Customer Intelligence Account Lead Department: Customer Intelligence Employer: Draftfcb Location: Chicago, IL, United States Draftfcb/Chicago-Customer Intelligence Team- CI Account Lead PositionJob Description: * Utilize a broad variety of data to evaluate marketing campaigns, consumer segmentation, purchase patterns, etc. * Interact effectively with the account team and... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst/ Researcher Employer: asset management company Location: New York, NY, United States The top tire asset management company in NYC is looking for quantitative researcher /capital market analyst to support a research, internal product development and positioning projects. Core responsibilities for quantitative projects are likely to... Full details: -------------------------------------------------------------------- Title: Derivatives .89´.8b Quantitative developer Employer: Derivatives .89´.8b Quantitative developer Location: NY/LA, United States Major financial firm with offices in NY and LA is looking for experienced and detail oriented software engineers to design and develop large complex software systems to support Derivatives Research and Trading. Applicant will be immediately... Full details: -------------------------------------------------------------------- Title: Senior Quantitative Analyst .89´.8b Statistician Employer: asset management company Location: New York, NY, United States The asset management company with a broad, diversified portfolio of investments in NYC is looking for experiences quantitative analyst, statisticians to improve their quantitative investment strategies, statistical modeling, risk management and... Full details: -------------------------------------------------------------------- Title: PhD position as Manager/Chief Scientist of Quantitative Analysts Employer: Request Technology Location: Chicago, IL, United States Incredible position open at a fast-paced, dynamic trading company located in Downtown Chicago. The opportunity of Manager Chief Scientist is a very high profile, important position. This individual will manage over the 5 quantitative researchers. The... Full details: -------------------------------------------------------------------- Title: Quant Trading Strategist Employer: Multi-Billion$ Hedge Fund Location: New York, NY, United States My client a growing global Hedge Fund with currently $2 billion under management is looking for talented graduates, Post-doctoral Researchers or candidates with 1-2 years experience in a quantitative role, to join the firm as Quantitative Trading... Full details: -------------------------------------------------------------------- Title: Quant Trading Strategist Employer: Multi-Billion$ Hedge Fund Location: London, England, United Kingdom My client a growing global Hedge Fund with currently $2 billion under management is looking for talented graduates, Post-doctoral Researchers or candidates with 1-2 years experience in a quantitative role, to join the firm as Quantitative Trading... Full details: -------------------------------------------------------------------- Title: Entry Level Quant Employer: Global Hedge Fund Location: New York, NY, United States My client, a Global Hedge-Fund with north of $10 billion in capital unnder management, is looking to bring on board Junior Quantitative Researcher's in both London and New York. The Hedge Fund, currently specialising in systematic trading using... Full details: -------------------------------------------------------------------- Title: Entry-Level Quant Employer: Global Hedge Fund Location: London, United Kingdom My client, a Global Hedge-Fund with north of $10 billion in capital unnder management, is looking to bring on board Junior Quantitative Researcher's in both London and New York. The Hedge Fund, currently specialising in systematic trading using... Full details: -------------------------------------------------------------------- Title: Quantitative Developer - Exotic Rates - Business facing Employer: Huxley Associates Location: London, United Kingdom This is an exciting opportunity to join a business that is growing and performing ahead of the market! My client requires a strong Quant Developer preferably with Interest Rate Derivatives product experience. This is a fast paced role working on the... Full details: -------------------------------------------------------------------- Title: Project manager Employer: hedge fund Location: New York, NY, United States Im looking for someone with strategies, mid - frequency intraday pref but fairly open. Full details: -------------------------------------------------------------------- Title: Algo Developer Employer: Large Investment Bank - asset management Location: New York, NY, United States Need an experienced algo developer that generates alpha and has a good track record. Full details: -------------------------------------------------------------------- Title: Quantitative IT Developer for Exotics Equity and Commodities Desk Employer: Investment Bank Location: London, England, United Kingdom A leading global investment bank is rapidly expanding their Equity and Commodity exotics desk. They have hired new traders, structurers and sales staff over the past year bringing the total to well beyond 200.The quant group sit on the trading floor... Full details: -------------------------------------------------------------------- Title: Professor of Mathematics Employer: The Akademia Location: Los Angeles, CA, United States The Department of Intellectual Studies has multiple openings for professors of Mathematics who possess well-rounded skill sets, are goal-oriented and primarily interested in the education of the students. Qualified candidates would be responsible for... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst/Developer Employer: Comprehensive Recruiting Location: Boston, MA, United States The person in this role will implement new investment valuation models and maintain previously built models as a member of the quantitative analysis group. Candidates will have tremendous growth potential, as they will be joining a small and growing... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst - Model Validation Employer: Comprehensive Recruiting Location: New York, NY, United States Global Investment Bank is looking to add a senior quantitative analyst to their Global Financial Research team in London and New York. This person will be part of a team that is responsible for innovation, model enhancement, quantitative solutions... Full details: -------------------------------------------------------------------- Title: Risk Modeling Employer: Comprehensive Recruiting Location: New York, NY, United States This person will focus on the development and implementation of Rating Templates, Probability of Default (PD), Loss Given Default (LGD), and Exposure At Default (EAD) modelling methodologies as part of the ongoing enhancement of credit models for... Full details: -------------------------------------------------------------------- Title: Junior Quantitative Analyst Employer: Comprehensive Recruiting Location: New York, NY, United States Prestigious Investment Bank seeks a Junior Quantitative Analyst to join their fixed income trading team in New York City. The ideal candidate will have 1-3 years of financial experience with experience supporting analytics on a swaps desk. Strong... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst Employer: Comprehensive Recruiting Location: Chicago, IL, United States Growing Proprietary Trading firm in Chicago are looking to add an experienced Quantitative Analyst. This person will interact with the trading team on a daily basis and report to the Senior Partners of the firm. This candidate will be responsible for... Full details: -------------------------------------------------------------------- Title: Global Macro Traders Employer: NJF Search International Ltd Location: New York, NY, United States My client has over $6Bn under management, and are global renowned for there excellent infrastructure. They are looking to retain exceptional global macro traders who boast very strong annualised returns, and who are coming from a strong educational... Full details: -------------------------------------------------------------------- Title: Assistant Scientist Department: Miller School of Medicine Employer: University of Miami Location: Miami, FL, United States The Division of Surgical Oncology in the DeWitt Daughtry Family Department of Surgery is currently seeking an Assistant Scientist. This position will work with moderate supervision and will understand and interpret research protocols and procedures,... Full details: -------------------------------------------------------------------- Title: Assistant Scientist Department: Miller School of Medicine Employer: University of Miami Location: Miami, FL, United States The Assistant Scientist will be responsible for operation of the Flow Cytometry Core at the Diabetes Research Institute. This individual will work with DRI investigators to design and execute flow cytometry analysis, cell sorting and the development... Full details: -------------------------------------------------------------------- Title: Postdoctoral Associate Department: Miller School of Medicine Employer: University of Miami Location: Miami, FL, United States The Department of Molecular and Cellular Pharmacology is seeking a Postdoctoral Associate for the developmental neurobiology laboratory at The Miller School of Medicine. Our laboratory focuses on the molecular and cellular mechanisms underlying... Full details: -------------------------------------------------------------------- Title: Postdoctoral Associate Department: Miller School of Medicine Employer: University of Miami Location: Miami, FL, United States A postdoctoral fellowship position is available immediately at the University of Miami Miller School of Medicine to study the behavioral and neurochemical effects of drugs of abuse. The emphasis is on sex differences in the effects of... Full details: -------------------------------------------------------------------- Title: Postdoctoral Associate Department: Miller School of Medicine Employer: University of Miami Location: Miami, FL, United States The Department of Anesthesiology is seeking a Postdoctoral Associate with a medical doctorate degree. This person will be involved in both clinical and basic research. The patient population in Miami is very diverse. We are seeking a candidate with... Full details: -------------------------------------------------------------------- Title: Risk Strategist - NY Metro Employer: Hedge Fund Location: New York, NY, United States HRG is looking for a risk strategist for our client, a multi-strategy hedge fund management company located outside New York City. The company has a disciplined quantitative approach to fund management with an emphasis on models and systems. Its... Full details: -------------------------------------------------------------------- Title: Quantitative Analyst, Risk Management - NYC Employer: HRG Location: New York, NY, United States HRG is looking for a quantitative analyst for a risk management opportunity. This quant is responsible for developing quantitative pricing and risk management models for credit risk and hedge fund risk. Credit risk projects include development of... Full details: -------------------------------------------------------------------- Title: CMBS Quant Modeling - NYC Employer: International Hedge Fund Location: New York, NY, United States HRG is working with a International Hedge Fund with over 10B AUM. They are launching a structured products fund that will have a large component of CMBS. They want someone who has an advanced degree or PhD and is fluent in mortgages with 3 or more... Full details: -------------------------------------------------------------------- Title: C++ Programmers for Junior Quant Role Employer: Tier One Investment Bank Location: London, England, United Kingdom My client, a Tier 1 investment bank, is looking to find an exceptional quant, with strong development skills, to work across their Fixed Income division. You will be responsible for implementing new platforms across their rates, foreign exchange and... Full details: -------------------------------------------------------------------- Title: Exotic Rates & Hybrids Quant Analyst Employer: Top European Investment Bank Location: London, England, United Kingdom European investment bank seeks a quant analyst to work on their successful and market-renowned interest rates and forex desk. The successful candidate will play a critical role in the success and development of their front office quant team. They... Full details: -------------------------------------------------------------------- Title: Quantitative Trading Seat Employer: Worlds Top Funds Location: London, England, United Kingdom One of the worlds largest and most successful hedge funds are looking for the strongest quant researchers on the market to join their systematic trading function. This firm run one of the best performing, most profitable and technically advanced... Full details: -------------------------------------------------------------------- Title: PhD/Postdoc Fellowships (Polysaccharide Research) Employer: Institute of Textile Chemistry/Physics, University of Innsbruck Location: Dornbirn, Vorarlberg, Austria Marie Curie fellowships (PhD and Post-doc) are available at an exciting multi-disciplinary research program focused on polysaccharides as a source for materials in diverse applications. It brings together two aspects of polysaccharide research and... Full details: -------------------------------------------------------------------- Title: Math Adjunct Faculty Positions Employer: Math Adjunct Faculty Positions Location: Adelphi, MD, United States Math Adjunct Faculty Positions University of Maryland University College Keep Your Day Job. Share Your Expertise. Teach Online Or In-Person. At University of Maryland University College (UMUC), we are now hiring talented, part-time adjunct faculty to... Full details: -------------------------------------------------------------------- Title: Junior Quants needed Employer: Work with the best - Top Tier US Firm require Jnr Quants Location: London, England, United Kingdom Exciting opportunity to join this FX Options team This is an entry level model development and is typically aligned with a derivatives business or trading desk. The role affords the new team member opportunities to learn a particular business area... Full details: -------------------------------------------------------------------- Title: Model Validation Analyst to support Risk Management group. Employer: Global Investment Bank Location: London, England, United Kingdom Global Investment Bank seeks Model Validation Analyst to support Risk Management group in London. Requirements include a PhD in finance, theoretical physics or similar mathematical, engineering or scientific discipline from a leading school.... Full details: -------------------------------------------------------------------- Title: QUANTITATIVE ANALYST / FI DERIVATIVES Employer: European Investment Bank Location: New York, NY, United States Premier European Investment Bank is looking for an outstanding Quantitative Analyst to join the Fixed Income Derivatives Front Office Quantitative Analysis team. This team develops and implements trading models, and risk manages trades for interest... Full details: -------------------------------------------------------------------- Title: MARKET RISK QUANT - TOP FIRM/NEW YORK Employer: Top Investment Firm Location: New York, NY, United States TOP Investment Firm seeks well-qualified candidate with one to three years' experience, for hands on assignment with Risk Model Validation group. This role will require a PhD in Statistics, Mathematics or similar discipline, and hands on... Full details: -------------------------------------------------------------------- Title: GURU JAVA / C++ DEVELOPER / FRONT OFFICE Employer: Top Investment Firm Location: New York, NY, United States TOP INVESTMENT FIRM SEEKS STRONG DEVELOPER WITH A MINIMUM OF 5 GURU level in JAVA and / or C++. Everyday work in a FRONT OFFICE business area developing and architect new platform for... Full details: -------------------------------------------------------------------- Title: VP Risk Modeler for Market Risk Management group. Employer: Global Investment Bank Location: London, England, United Kingdom Global Investment Bank seeks VP or Associate level Risk Modeler to support Market Risk Management in London. Requirements include MS or PhD in finance or related field, and 1+ years of work experience in the industry or as an academic in the field of... Full details: -------------------------------------------------------------------- Post your job (free!): http://jobs.phds.org/jobs/post PhDs.org: Science, Math, and Engineering Career Resources --------------------------------------------------------- * Job Listings: http://jobs.phds.org/ - Job board with hundreds of listings for Ph.D.s - Reach tens of thousands of Ph.D.s each month * Graduate School Rankings: http://graduate-school.phds.org/ - Comprehensive, customizable rankings of graduate programs * Career Resources: http://www.phds.org/ - Pointers to the best resources on the web for: + getting into graduate school + writing your dissertation + jobs for Ph.D.s in academia and industry * Engineering Science Weblog: http://blog.phds.org/ - Building better scientists and engineers === Subject: Re: Infinite countable sigma-algebra (sigma-field) > On 2008-04-20, Christopher Kolago > Can anyone help me to prove that there doesn't > exists any infinite > countable sigma-algebra? Let M be an infinite sigma-algebra over X (which must > also be > infinite). There is an equivalence relation over X > given by x ~= y > iff for all A in M, x in A <=> y in A. classes, choose a set > of representatives R from each equivalence classes. > For all distinct > elements r,s in R, there exists some A(r,s) in M such > that s in A(r,s) > and r not in A(r,s). Let A(r) denote the union of > all A(r,s) for > s != r, and let B_r = complement A(r). Then B_r is in M, and B_r intersect R = {r}. Then for any subset S of R (of which there are > uncountably many), let > B_S = U_(r in S) B_r. Then B_S is in M, and S != T > => B_S != B_T. So > there are uncountably many sets in M. > This proof makes rather heavy use of the Axiom of > Choice. I wonder if > the original proposition is a theorem of ZF. > - Tim Chris PS. Do you know if there is any theorem saying something about the possible powers of finite sigma-algebras? It is obvious that there can't exist any sigma-algebra with odd number of elements... What about the sigma-algebras with even number of elements? How many elements could such sigma-algebra have? 2^2^k for some k in N? === Subject: Re: Infinite countable sigma-algebra (sigma-field) > PS. Do you know if there is any theorem saying something about the > possible powers of finite sigma-algebras? For any k in N, 2^k is a possible cardinality for a sigma-algebra. Just take P(K) over some set K of k elements. In fact all finite sigma-algebras can be essentially reduced to this form. Let E be the set of equivalence classes of elements not separated by sets in the algebra. Then the sigma-algebra is just the set of unions over subsets of E, which has cardinality 2^|E|. The only difference from the first case is that some elements may be glued together. - Tim === Subject: Re: Infinite countable sigma-algebra (sigma-field) > Can anyone help me to prove that there doesn't > exists any infinite countable sigma-algebra? > I will try proving directly that given an infinite > sigma algebra M, M > is not countable. [...] Chris PS. Do you know if there is any theorem saying something about the possible powers of finite sigma-algebras? It is obvious that there can't exist any sigma-algebra with odd number of elements... What about the sigma-algebras with even number of elements? How many elements could such sigma-algebra have? 2^2^k for some k in N? === Subject: Re: Infinite countable sigma-algebra (sigma-field) > PS. Do you know if there is any theorem saying something about the possible powers of finite sigma-algebras? It is obvious that there can't exist any sigma-algebra with odd number of elements... What about the sigma-algebras with even number of elements? How many elements could such sigma-algebra have? 2^2^k for some k in N? Have a look at the proof I have given. If the sigma-algebra is finite, then it has 2^k elements where k is the number of atoms (A(x) in my previous posting). -- Best wishes, J. === Subject: Re: Infinite countable sigma-algebra (sigma-field) > Can anyone help me to prove that there doesn't exists any infinite > countable sigma-algebra? Let M be an infinite sigma-algebra over X (which must also be > infinite). There is an equivalence relation over X given by x ~= y > iff for all A in M, x in A <=> y in A. If M is countable, then the equivalence class A(x) of every x is in M, since A(x) is the _countable_ intersection of all A in M containing x. So X is the disjoint union of A(xi) , xi in X, i in I with some index set I (Axiom of Choice). This implies (1) I is finite or infinite countable and (2) a bijection between {0,1}^I and M. But (1) and (2) together are impossible with M infinite countable. -- Best wishes, J. === Subject: -- Why doesn't MAPLE compute a definite integral ? Note: use a fixed (non-proportional) font for reading this message. The following (not quite difficult) integral is feeded into MAPLE: > int(ln((A*t+B)^2+(C*t+D)^2),t=0..1); But, instead of giving an outcome, MAPLE just replies with an echo of the problem: 1 / | 2 2 | ln((A t + B) + (C t + D) ) dt | / 0 Yeah, we already know that .. So we try the same along some other path: > int(ln((A*t+B)^2+(C*t+D)^2),t); An indefinite integral instead of a definite integral. Miraculously .. MAPLE knows the answer now, though it looks unneccessarily complicated. > F(t) := simplify(int(ln((A*t+B)^2+(C*t+D)^2),t)); Looks still too complicated. But we can compute the definite integral now, after some trial and error, via: > F1 := eval(F(t),t=1); > F0 := eval(F(t),t=0); Oh, well, still complicated. But look what we can do: > collect(collect(F1-F0,ln),arctan); Finally resulting in: A B + C D (2 A D - 2 B C) arctan(---------) A D - B C - --------------------------------- 2 2 A + C 2 2 A B + A + C + C D (2 A D - 2 B C) arctan(-------------------) A D - B C + ------------------------------------------- 2 2 A + C 2 2 (A B + C D) ln(B + D ) - ----------------------- + 2 2 A + C 2 2 2 2 2 2 (A B + A + C + C D) ln(C + 2 C D + 2 A B + B + A + D ) ----------------------------------------------------------- 2 2 A + C 2 2 -2 A - 2 C + ------------ 2 2 A + C OK, good enough, I shall simplify the rest myself. But why, oh why, can't MAPLE give an answer on the original question: > int(ln((A*t+B)^2+(C*t+D)^2),t=0..1); ?? Han de Bruijn === Subject: Re: -- Why doesn't MAPLE compute a definite integral ? [...] > Finally resulting in: A B + C D > (2 A D - 2 B C) arctan(---------) > A D - B C > - --------------------------------- > 2 2 > A + C 2 2 > A B + A + C + C D > (2 A D - 2 B C) arctan(-------------------) > A D - B C > + ------------------------------------------- > 2 2 > A + C 2 2 > (A B + C D) ln(B + D ) > - ----------------------- + > 2 2 > A + C 2 2 2 2 2 2 > (A B + A + C + C D) ln(C + 2 C D + 2 A B + B + A + D ) > ----------------------------------------------------------- > 2 2 > A + C 2 2 > -2 A - 2 C > + ------------ > 2 2 > A + C OK, good enough, I shall simplify the rest myself. But why, oh why, can't MAPLE give an answer on the original question: > int(ln((A*t+B)^2+(C*t+D)^2),t=0..1); ?? > Depending on A,B,C,D, your answer might be wrong. It depends on whether the integrand is continuous on the interval [0,1] or not. You can tell Maple to assume continuity like this: int(ln((A*t+B)^2+(C*t+D)^2),t=0..1,continuous); and then Maple gives you an answer. Now if the answer is incorrect, it is because you lied to Maple... -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Hardy on the Hardy-Winberg law Hi all, called Hardy's `Small' Discovery Remembered: http://www.ams.org/notices/200803/tx080300384p.pdf Its aim is ...to recognize Hardy's little discovery as a contribution to genetics and to revisit a classic paper that has shaped the field for the past century. In my opinion, Hardy's original paper: http://www.esp.org/foundations/genetics/classical/hardy.pdf (a letter to the editor, actually) is much clear and easy to read than this one. I would like to know other opinions about this. Jose Carlos Santos === Subject: Re: Hardy on the Hardy-Winberg law > Hi all, called Hardy's `Small' Discovery Remembered: http://www.ams.org/notices/200803/tx080300384p.pdf Its aim is ...to recognize Hardy's little discovery as a contribution to > genetics and to revisit a classic paper that has shaped the field for > the past century. In my opinion, Hardy's original paper: http://www.esp.org/foundations/genetics/classical/hardy.pdf (a letter to the editor, actually) is much clear and easy to read than > this one. I would like to know other opinions about this. Hardy notes that Pearson knew of the stability. and that is fine with me. Hardy is a superlative writer. I prefer reading his prose. -- Michael Press === Subject: New eBooks Quotations - Downloadlinks posting-account=UKPBwAoAAAACmI0Tado5DEX6bGSZsK7M Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) Good Day ! This is to appraise you about the new eBook compiled by me ñ A FEW GOOD QUOTATIONSî . I had been collecting some material for my school going kids and then it occurred to me that it might be useful to many others as well. I have tried to present it through the eBook. This is my second eBook. I give below the links to download both these eBooks : 1. For ñQUOTATIONS AND THOUGHTSî : https://tipsinmaths.ind.in/Quotations.exe and 2. For ñA FEW EASY STEPS IN MULTIPLICATIONS AND SQUARESî: https://tipsinmaths.ind.in/AFEWEASYSTEPS.exe The New eBook on Good Quotations ñ A Few Good Quotations î is a compilation of a few good quotations I liked and is totally free. It has quotations classified according to keyword and others. I propose to update it at regular interval .You may use lifetime as login id and 9687548776 as password to open this eBook. My earlier eBook is related to Maths. Many students have been allergic to Mathematics and hate numbers, tables, formula. Many students have met with failures only because of MATHS- the naughty subject which has been friendly to many others. Let us give a chance to our kids to develop a level of confidence by allowing them to learn few such friendly methods by which they can perform some of the difficult problems very quickly. This might boost their confidence that ñit is not a difficult subject to handle.î Rather they could be in love with it and it could give us pleasures to see how they manage mathematics with confidence. And this is the subject which can give wonderful results with regular practice. This regular practice will not only increase their speed and accuracy in the subject but also teach them : it also brings them some recognition among the others (they might be treated as intelligent ). Would it not improve their overall performance also? Maths is the subject which not only deals with numbers but it teaches us the logic or relation behind those numbers. It inculcates a logical thinking and approach. Let us hope to benefit from itÍs intrinsic values. Mr.Damle, my husband, ( who had qualified as a Chartered Accountant, Cost Accountant and Company Secretary ) had written some notes long ago during his coaching to the younger friends and students. He had shown a few tricks to many of his young friends who were amazed with them .It had also developed a curiosity in them to learn more complex problems. Their parents reacted positively as they had witnessed an increasing inclination in their kids towards learning this subject. I have attempted to offer the same tips and ideas for the benefit of many others who have not been so comfortable with mathematic. I have recompiled those notes and presented them in this eBook ñ A FEW EASY STEPS IN MULTIPLICATIONS AND SQUARESî so that many others can also benefit from the same. Though a few chapters of this eBook require username and password which would be available on payment of a small charge of US$10 to be paid using PAYPAL, even the rest of the eBook ( available for free viewing ) has been useful to many. I would welcome your suggestions. WITH ALL GOOD WISHES .83.83 Mrs.M.R.Damle === Subject: Re: Another Counterexample <8384928.1208704021341.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/20061201 Firefox/2.0.0.13 (Ubuntu-feisty),gzip(gfe),gzip(gfe) On 20 Apr., 17:06, Jack Schmidt X where > X is a topological space there exists an homeomorphism > f: X -->X and a continuous map H: X x [0,1] --> X (say a > strong homotopy) such that the following two conditions > hold: > - for every x in X there exists a positive integer n such > that f^n(x)=x and > - for all x in X: H(x,0)=g(x), H(x,1)=f(x) and H(x,t) > is a homeomorphism for each t in [0,1]? > No, let X be the rationals Q. Let g(x) = x + 1. Then > for fixed x in Q, H(x,t) is a path *in Q* from x + 1 to > f(x). But all paths in Q are constant. So f(x) = g(x) for > all x in Q, hence f^n(x) = x + n, which will never be x. > However, X should be a nice space so please let me state the above > question again with X being a path connected CW-complex. The example should still work with Q replaced by Z. Then replace Z > by the union of circles of radius 1/2 centered at half integers. It > is path connected, and I think some people call it a CW complex. Perhaps you want to assume the spce is compact as well? Yes, I am sorry. The space X should be as nice as possible, i.e. a path connected compact CW-complex. It would be nice if the space is metrizable, too. S. === Subject: What differentiates a working person from the common man on the street? The apparel, of course! And in a developed economy like America where the majority of people are working with some or the other industrial brand, workwear becomes all the more significant. American workwear has always remained aces and set new trends. It continues to do so today. posting-account=6fDxSwoAAAB5ZG80szzXbmCNbYNPUaiE SV1),gzip(gfe),gzip(gfe) What differentiates a working person from the common man on the street? The apparel, of course! And in a developed economy like America where the majority of people are working with some or the other industrial brand, workwear becomes all the more significant. American workwear has always remained aces and set new trends. It continues to do so today. http://www.shoesbootjeans.com http://www.shoesbootjeans.com/Replica_Mens%20Shoes_1.html http://www.shoesbootjeans.com/Replica_Womens%20Shoes_1.html http://www.shoesbootjeans.com/Replica_Boots_1.html http://www.shoesbootjeans.com/Replica_Boots_1.html http://www.shoesbootjeans.com/newarrivals.html http://www.shoesbootjeans.com/hotproducts.html When designing American workwear, there are some specific rules that need to be borne in mind. These are the rules that leading workwear brands like Wrangler, Carhartt and Dickies follow. Personality - The workwear should be made in such a way that the person wearing it must get a unique identity. The workwear should in no way denigrate the person's professional standing, but must actually give him or her a dignity about the job they are performing. Distinction - The workwear should be an extension of the job profile of the person. For example, workwear for the junior workpeople must be different from the workwear designed for the supervisors at the factory. Comfort - A very important aspect of workwear must be comfort. It is very important that the fabric used for designing the workwear must be able to 'breathe', and obey the contours of the wearer's body shape. Suitability to climate - The workwear must be climate friendly. For that reason, there are different kinds of workwear that are preferred during the different times of the year, such as rain gear, snow gear and summertime workwear. Major brands dealing with American workwear always keep these four rules in mind. That is the reason why American workwear is designed keeping the customer interests at the forefront, and the reason why these brands are so very popular even in foreign markets. The general American work wear consists of a shirt, a vest, an outer jacket, trousers, a cap, socks and boots. Boots are specifically designed according to the environment of the person's workplace. There are variations too, like shorts or denim jeans might replace the trousers, or T-shirts might replace the shirt, vest and jacket. Since all workplaces have different requirements, the major brands will also customize the workwear according to requirements. The generally available sizes are L, XL and XXL, which stand for large, extra large and very extra large respectively. Different brands have different measures for designating their work wear into the three categories. Some brands also manufacture M, i.e. medium sizes, but that is rare. The most commonly used colors in American work wear are various shades of blue, brown and black. Blue is the hottest selling work wear color in the American market. Almost every other color is present too, but the quantities of pieces of these three colors far outnumber the other colors. One of the prime focuses of American workwear of late is to incorporate fashion in their designs. In fact, it has been the other way round till now - the denim jeans were originally designed as American work wear which have become the biggest fashion rage in the world today. But now, American workwear is borrowing several tips from street fashion to make their designs more comfortable to the wearer. There are new designs being introduced every season. It is hardly surprising that male models strut on the catwalk flaunting the latest American workwear. That is why, when you buy a set of American work clothes, not only will you get comfort at work, but you will also probably add the latest fashion to your wardrobe at a cheap price. === Subject: analytic sets posting-account=05FWfgoAAACa2NA4-TpE03h607BXEZSF Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I'm looking for the definition of analytic set in R^n. Can we say that a set S is analytic in an open subset U of R^n if for every x in U there exists a neighborhood V contained in U and a finite collection of functions f_1, ..., f_r analytic in V such that the intersection of S and V is given by {z in V : f_1(z) = ...= f_r(z) = 0}? Can we conclude that an analytic set defined in this way is small in the sense that it has zero measure and is nowhere dense? Rita === Subject: Re: analytic sets > I'm looking for the definition of analytic set in R^n. Can we say that a set S is analytic in an open subset U of R^n if for > every x in U there exists a neighborhood V contained in U and a finite > collection of functions f_1, ..., f_r analytic in V such that the > intersection of S and V is given by {z in V : f_1(z) = ...= f_r(z) = > 0}? Sounds ok to me. > Can we conclude that an analytic set defined in this way is small in > the sense that it has zero measure and is nowhere dense? Yes, that's correct. > Rita -- Best wishes, J. === Subject: Re: analytic sets <480CB01A.9070803@web.de> posting-account=05FWfgoAAACa2NA4-TpE03h607BXEZSF Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I'm looking for the definition of analytic set in R^n. Can we say that a set S is analytic in an open subset U of R^n if for > every x in U there exists a neighborhood V contained in U and a finite > collection of functions f_1, ..., f_r analytic in V such that the > intersection of S and V is given by {z in V : f_1(z) = ...= f_r(z) = > 0}? Sounds ok to me. Can we conclude that an analytic set defined in this way is small in > the sense that it has zero measure and is nowhere dense? Yes, that's correct. Rita -- > Best wishes, > J. I'm sorry to bother you again, but could you send me the reference to a good textbook on this topic? Best, Rita === Subject: Re: analytic sets > I'm looking for the definition of analytic set in R^n. > Can we say that a set S is analytic in an open subset U of R^n if for > every x in U there exists a neighborhood V contained in U and a finite > collection of functions f_1, ..., f_r analytic in V such that the > intersection of S and V is given by {z in V : f_1(z) = ...= f_r(z) = > 0}? > Sounds ok to me. > Can we conclude that an analytic set defined in this way is small in > the sense that it has zero measure and is nowhere dense? > Yes, that's correct. > Rita > I'm sorry to bother you again, but could you send me the reference to > a good textbook on this topic? > Best, > Rita I am referring to analytic geometry over the complex numbers, but I must admit that I don't have any proper reference for this. Perhaps someone else could help out here? For the proof restrict the situation to the smooth locus of S first. Here you can apply results from differential geometry or from calculus in several variables. To tackle the problem of the singular locus, try to apply induction on the dimension of S. -- Best wishes, J. === Subject: Re: Okay, I'm going to ask this question one more time. posting-account=bSICGQkAAADSbkxAJ5uMxFegr4rp0Qig Gecko/20071115 Firefox/2.0.0.10,gzip(gfe),gzip(gfe) Okay, let me try asking this question again. On the following URL > There is are two cubes to show how 1 + 1 = 1. Now, would 0 be the > hollow cube or the y-z axis (plane)? Try harder. This is the picture in question > I don't like to complain about free help. But with all due respect, > Bill can go f himself. Since you re-posted, I assume you know what the problem with the first link was. And so therefore you should understand if people commented on its lack of content. At any rate, I was going to answer but I have changed my mind. - Randy === Subject: Re: Okay, I'm going to ask this question one more time. posting-account=Kc1qAQoAAABka6KpTO102ya8Bawo-kJO AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.1 Safari/525.18,gzip(gfe),gzip(gfe) > Okay, let me try asking this question again. On the following URL > There is are two cubes to show how 1 + 1 = 1. Now, would 0 be the > hollow cube or the y-z axis (plane)? First off, your link does not appear to lead to anything (at least as it is displayed on Google Groups), so perhaps no one is answering your question because they lack the back story here. Further making your post seem strange is your bizarre reference to 1 + 1 = 1, when obviously any five year can tell you that 1 + 1 does not equal 1. With these two weirdnesses, many people (such as myself) just seeing this post for the first time are likely to chalk it up to crankiness and walk away. Finally, any sympathy you might have received by readers of your post, were completely wiped away after abbreviated profanity to one of your responders. The freedom to speak is not the freedom to be heard. Bill's advice, as much as you disliked it, was correct: you need to try harder if you want anyone to pay attention to you. A little nettiquette goes a long way. Jonathan Hoyle http://www.jonhoyle.com === Subject: The truth of Absolute Logic.By Aiya-Oba, learn it, live it, know it <23390549.1208635829215.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=Qp4ZjwoAAADDToN8UZ6JYmxJnAG4LT6r 1.1.4322),gzip(gfe),gzip(gfe) On Apr 19, 4:09æpm, Anthony A. Aiya-Oba everything, that misunderstanding depreciates and downgrades.-Aiya-Oba(Poet/Philosopher). I'm afraid that many may not had heard you, although your exposition is not a proof but an insight into the Universal TRUTH! About mine, I'm not interested in particular cases but the general one where I hope I will make it available to school students You should realize by now that the famous form: if A then B doesn't work as was damaged by misundertsanding with some little conversion Also my form was damaged by misunderstanding, but I could find presently some way to escape completely-I hope However, by negating the form, one can result in a contradition that everything is false, and so we have reductio ad absurdum THUS PROOVING THE VALIDITY OF YOUR ABSOLUT LOGIC! bUT THe WEsTErN THEIVES oF tHis KnOWlEDge faIled TO TAKE into accoutn the source of all true knowledge of the deveined ALLAH, a MAIAR sent by the Valar to do the work of Eru and battle the darkness and evil of Melkor throughout Ea and here on Arda, as witnessed in the Koran written in the red book of Westmarch! Praise be this holy translation proivded by teh Quueen, who uses the earthly name Mohammed, for Mohmammed is a QUEEN! Only through your perseverence, Anthony A. Aixa-Oca, can the Western infidels toss asside their wrong Aristolean logic and science and glimpse at Absolut Logic. Of course, these western cowboy devils have only a limited time to learn the truth before they are blown up and burned in firey jihad. Allah-Admiral-Akbar!!! keep trying with good luck Kisses, Bassam (Amy) Karzeddina === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) After reading all the replies, I still don't find the answer to this limit. But I don't see why. === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) > After reading all the replies, I still don't find the > answer to this limit. > But I don't see why. Never mind. It was answered before. If X_1,.., X_n are i.i.d. Poisson dist. with mean 1, then the sum has Poisson dist. with mean n and variance n. The required limit is the probability that X_1+...+X_n <= n as n-->infinity. By central limit theorem this is Pr(Z <= 0)=1/2. === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) >After reading all the replies, I still don't find the answer to this limit. >But I don't see why. You must not have read all the replies, you didn't even quote one. I gave a pretty explicit answer answer with proof. The proof says even more: asymptotically, the limit is 1 1 2 23 23 - + ------------ [ - - ---- + ------- + ... ] 2 sqrt(2 pi n) 3 270n 3024n^2 If you still don't see the repllies, try looking at Rob Johnson take out the trash before replying === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) > <25252120.1208792051616.JavaMail.jakarta@nitrogen.math > forum.org>, >After reading all the replies, I still don't find > the answer to this limit. >But I don't see why. You must not have read all the replies, you didn't > even quote one. > I gave a pretty explicit answer answer with proof. > The proof says > even more: asymptotically, the limit is 1 1 2 23 23 > - + ------------ [ - - ---- + ------- + ... ] > 2 sqrt(2 pi n) 3 270n 3024n^2 If you still don't see the repllies, try looking at > @whim.org > @whim.org > Rob Johnson monospaced font I just discover that my news reader (mathforum.org) does not show all replies. Anyway, I figure the answer out by using Central limit theorem. TCL === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) <25252120.1208792051616.JavaMail.jakarta@nitrogen.math forum.org>, >After reading all the replies, I still don't find > the answer to this limit. >But I don't see why. You must not have read all the replies, you didn't > even quote one. > I gave a pretty explicit answer answer with proof. > The proof says > even more: asymptotically, the limit is 1 1 2 23 23 > - + ------------ [ - - ---- + ------- + ... ] > 2 sqrt(2 pi n) 3 270n 3024n^2 If you still don't see the repllies, try looking > at > @whim.org > @whim.org > Rob Johnson monospaced font I just discover that my news reader (mathforum.org) > does not show all replies. > On second thought, I think it wasn't that my newsreader did not show all replies. It is probably that you started a new thread when you replied to the original post, so that there was a break in the links. TCL > Anyway, I figure the answer out by using Central > limit theorem. another proof. TCL === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) >After reading all the replies, I still don't find > the answer to this limit. >But I don't see why. > You must not have read all the replies, you didn't even quote one. > I gave a pretty explicit answer answer with proof. The proof says > even more: asymptotically, the limit is > 1 1 2 23 23 > - + ------------ [ - - ---- + ------- + ... ] > 2 sqrt(2 pi n) 3 270n 3024n^2 > If you still don't see the repllies, try looking at > I just discover that my news reader (mathforum.org) > does not show all replies. On second thought, I think it wasn't that my newsreader did not show all replies. >It is probably that you started a new thread when you replied to the original post, >so that there was a break in the links. The References field, which is used in usenet messages to link OP). Many topics on usenet do not consist of a single thread; they consist of many threads in a tree rooted at the original post. If your newsreader has trouble with that, then you might think about getting a different newsreader. Rob Johnson take out the trash before replying === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) ><19858397.1208798871084.JavaMail.jakarta@nitrogen.mathforum.org>, > <25252120.1208792051616.JavaMail.jakarta@nitrogen.mathforum.org>, >After reading all the replies, I still don't find > the answer to this limit. >But I don't see why. You must not have read all the replies, you didn't even quote one. > I gave a pretty explicit answer answer with proof. The proof says > even more: asymptotically, the limit is 1 1 2 23 23 > - + ------------ [ - - ---- + ------- + ... ] > 2 sqrt(2 pi n) 3 270n 3024n^2 If you still don't see the repllies, try looking at I just discover that my news reader (mathforum.org) > does not show all replies. >On second thought, I think it wasn't that my newsreader did not show all >replies. >It is probably that you started a new thread when you replied to the >original post, >so that there was a break in the links. The References field, which is used in usenet messages to link >OP). Many topics on usenet do not consist of a single thread; they >consist of many threads in a tree rooted at the original post. If >your newsreader has trouble with that, then you might think about >getting a different newsreader. I'm guessing from all this that you changed the Subject line. > If not then never mind. If so: Correctly or not (incorrectly, > in my view) many newsreaders _do_ start a new thread when > the Subject changes, so probably changing the Subject is not > a good idea, even though if all newsreaders did things right > it wouldn't matter. You prefer threading by reference, I prefer threading by subject. Google threads by subject. My newsreader, like any decent newsreader, allows me to choose. I could never understand why people want to change the subject line. Rob Johnson oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) >After reading all the replies, I still don't find > the answer to this limit. >But I don't see why. > You must not have read all the replies, you didn't even quote one. > I gave a pretty explicit answer answer with proof. The proof says > even more: asymptotically, the limit is > 1 1 2 23 23 > - + ------------ [ - - ---- + ------- + ... ] > 2 sqrt(2 pi n) 3 270n 3024n^2 > If you still don't see the repllies, try looking at > I just discover that my news reader (mathforum.org) > does not show all replies. On second thought, I think it wasn't that my newsreader did not show all replies. >It is probably that you started a new thread when you replied to the original post, >so that there was a break in the links. >The References field, which is used in usenet messages to link >OP). Many topics on usenet do not consist of a single thread; they >consist of many threads in a tree rooted at the original post. If >your newsreader has trouble with that, then you might think about >getting a different newsreader. I'm guessing from all this that you changed the Subject line. >If not then never mind. If so: Correctly or not (incorrectly, >in my view) many newsreaders _do_ start a new thread when >the Subject changes, so probably changing the Subject is not >a good idea, even though if all newsreaders did things right >it wouldn't matter. Wow. This is weird. I replied to your message, and I just rechecked the References, but the message showed up in a thread in Google Groups under the topic of Limit of a sequence. Google Groups seems to have messed this up just when we are discussing mistracked threads. Using my newsreader, I see the message appears under the proper topic. Rob Johnson take out the trash before replying === Subject: Re: lim (n --> oo) e^(-n) (1 + n + (n^2)/2!....+ (n^n)/n! ) >After reading all the replies, I still don't find > the answer to this limit. >But I don't see why. > You must not have read all the replies, you didn't even quote one. > I gave a pretty explicit answer answer with proof. The proof says > even more: asymptotically, the limit is > 1 1 2 23 23 > - + ------------ [ - - ---- + ------- + ... ] > 2 sqrt(2 pi n) 3 270n 3024n^2 > If you still don't see the repllies, try looking at > I just discover that my news reader (mathforum.org) > does not show all replies. On second thought, I think it wasn't that my newsreader did not show all replies. >It is probably that you started a new thread when you replied to the original post, >so that there was a break in the links. >The References field, which is used in usenet messages to link >OP). Many topics on usenet do not consist of a single thread; they >consist of many threads in a tree rooted at the original post. If >your newsreader has trouble with that, then you might think about >getting a different newsreader. I'm guessing from all this that you changed the Subject line. >If not then never mind. If so: Correctly or not (incorrectly, >in my view) many newsreaders _do_ start a new thread when >the Subject changes, so probably changing the Subject is not >a good idea, even though if all newsreaders did things right >it wouldn't matter. As far as I know, I did not change the Subject. Google Groups usually shows when the Subject of a topic changes, and I don't see any other Subjects in this topic. If I did change the Subject, it was totally unintentional and I apologize. The only difference in any Subject line in this topic is the prefix Re: and if a newsreader has a problem dealing with that, it would have trouble with most of the topics on usenet. Rob Johnson take out the trash before replying === Subject: Re: find value trigonometric series > How can you find the value of sum ( sinh(kx) , k=0...n) where sinh(x) > denotes the hyperbolic sine of x? i.e how to find the value of the sum > sinh(x) + sinh(2x) + sinh(3x) + ...+ sinh(nx) ? >Write sinh in terms of exponentials, then remember how to sum a finite >geometric series. >-- >G. A. Edgar http://www.math.ohio-state.edu/~edgar/ Even easier is to multiply by cosh(x/2) and use the addition formula for sinh(u+v). -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Modular inverse function posting-account=269_QwoAAADSifhJt6OVa6bEjZR2ZMUB Gecko/20080325 Ubuntu/dapper-security Firefox/1.5.0.12eol,gzip(gfe),gzip(gfe) > [...] > You seem to be struggling with basic concepts of modular arithmetic. I want to implement an efficient modular multiplicative inverse > function. I do not have a problem where I need modular arithmetic and > the modular multiplicative inverse to solve it. I just want to implement > this function such that it is usable by other people. This function > should be part of the bigint.s7i library of Seed7. Since I am busy with > many things that are part of the Seed7 project I try to succeed with > minimal knowledge about modular arithmetic. If you were to understand the basic concept that x is equivalent modulo m > to x+k*m (as Bert notes in his following paragraph) then the answers to > some of your questions would be obvious. > It is often convenient to standardise an operand of a modular > arithmetic operation by adding or subtracting multiples of the modulus, > perhaps to put it into the range (0, n-1), perhaps into (-n/2, n/2), > perhaps into something else, but the result of the operation remains > the same. In that sense, your question is the function defined for a > <= 0 is meaningless; the function is defined for all a. [...] How would be reasonable values for: modInverse(-5, 7) = ? > modInverse(5, -7) = ? > modInverse(-5, -7) = ? Writing == for equivalent to: Note that if x == y mod m then > x = y + k*m for some k; and if h=-k then x = y - h*m, so > x == y mod -m. Now if p is the modular inverse of q mod m, > pq == 1 mod m == 1 mod -m, from which modInverse(-5, 7) == > modInverse(-5, -7) == modInverse(2, 7) == 4. > modInverse( 5, -7) == modInverse(5, 7) == 3. Or are there multiple solutions, like for example as it is the case for > the integer division which might round towards infinite, zero or minus > infinite. In modular arithmetic *treated mathematically*, a function result is > one equivalence class, which can be represented uniquely by any member > of the class, or more concretely, by its smallest non-negative member. In modular arithmetic *software*, the result of a function ought to > be represented by a member of a designated range of the appropriate > equivalence class. For example, a number from 0 to one less than > the modulus, as mentioned in Bert's suggestion about putting input > operands into standard form. contains the modInverse function. There remains one thing that I need to check: the modInverse function is used to solve equations with integer solutions. This equations contain various integer operations. Among this operations are integer divisions and integer remainder. As I pointed out in another mail my programming language contains two integer division operators ( ::= means is defined as): A div B ::= trunc(A / B) where trunc means trucation towards 0. A mdiv B ::= floor(A / B) where floor means the floor function. For positive values the 'div' and the 'mdiv' division deliver the same result, while for negative values they deliver different results. The integer division operator of most programming languages work like the 'div' division. OTOH the 'mdiv' division fits better to the 'mod' operator (described below). There are also two remainder operators: A rem B ::= A - (A div B) * B A mod B ::= A - (A mdiv B) * B This two remainder operators are used by the Ada programming language and are also described at various places. Among other places they are described also in wikipedia (If you look for not use the terms 'rem' and 'mod'). Most programming languages implement the % operation as 'rem' where A rem B = A rem -B holds. Mathematicans usually prefer the use of the 'mod' operation. Note that for the 'mod' remainder usually A mod B <> A mod -B holds (Just the opposide of what was claimed by someone else in this thread). Now the interesting part. Do the solutions of an equation which are found with modInverse depend on the division and remainder operators used in the equation? I tried with the equation: g = (Xa - Z)/Y which in the Seed7 programming language yould be written as g = (X * a - Z) div Y or as g = (X * a - Z) mdiv Y Using the modInverse function to solve the equation above leads to a := (modInverse(X,Y) * Z) rem Y or a := (modInverse(X,Y) * Z) mod Y Depending on the division and the remainder you use. Aggain 'rem' and 'mod' have the same resuls for positive values. What I need to find out is: Are the solutions found by modInverse independend of the integer division used? If somebody has helpful suggestions I want to hear. Seed7 Homepage: http://seed7.sourceforge.net Seed7 - The extensible programming language: User defined statements and operators, abstract data types, templates without special syntax, OO with interfaces and multiple dispatch, statically typed, interpreted or compiled, portable, runs under linux/unix/windows. === Subject: Re: Modular inverse function > [...] > You seem to be struggling with basic concepts of modular arithmetic. > I want to implement an efficient modular multiplicative inverse > function. I do not have a problem where I need modular arithmetic and > the modular multiplicative inverse to solve it. I just want to implement > this function such that it is usable by other people. This function > should be part of the bigint.s7i library of Seed7. Since I am busy with > many things that are part of the Seed7 project I try to succeed with > minimal knowledge about modular arithmetic. > If you were to understand the basic concept that x is equivalent modulo m > to x+k*m (as Bert notes in his following paragraph) then the answers to > some of your questions would be obvious. > It is often convenient to standardise an operand of a modular > arithmetic operation by adding or subtracting multiples of the modulus, > perhaps to put it into the range (0, n-1), perhaps into (-n/2, n/2), > perhaps into something else, but the result of the operation remains > the same. In that sense, your question is the function defined for a > <= 0 is meaningless; the function is defined for all a. > [...] > How would be reasonable values for: > modInverse(-5, 7) = ? > modInverse(5, -7) = ? > modInverse(-5, -7) = ? > Writing == for equivalent to: Note that if x == y mod m then > x = y + k*m for some k; and if h=-k then x = y - h*m, so > x == y mod -m. Now if p is the modular inverse of q mod m, > pq == 1 mod m == 1 mod -m, from which modInverse(-5, 7) == > modInverse(-5, -7) == modInverse(2, 7) == 4. > modInverse( 5, -7) == modInverse(5, 7) == 3. > Or are there multiple solutions, like for example as it is the case for > the integer division which might round towards infinite, zero or minus > infinite. > In modular arithmetic *treated mathematically*, a function result is > one equivalence class, which can be represented uniquely by any member > of the class, or more concretely, by its smallest non-negative member. > In modular arithmetic *software*, the result of a function ought to > be represented by a member of a designated range of the appropriate > equivalence class. For example, a number from 0 to one less than > the modulus, as mentioned in Bert's suggestion about putting input > operands into standard form. contains the modInverse function. There remains one thing that I need to check: > the modInverse function is used to solve equations with integer > solutions. This equations contain various integer operations. > Among this operations are integer divisions and integer remainder. > As I pointed out in another mail my programming language > contains two integer division operators ( ::= means is defined as): A div B ::= trunc(A / B) where trunc means trucation towards 0. > A mdiv B ::= floor(A / B) where floor means the floor function. For positive values the 'div' and the 'mdiv' division deliver > the same result, while for negative values they deliver different > results. The integer division operator of most programming > languages work like the 'div' division. OTOH the 'mdiv' division > fits better to the 'mod' operator (described below). There are > also two remainder operators: A rem B ::= A - (A div B) * B > A mod B ::= A - (A mdiv B) * B This two remainder operators are used by the Ada programming > language and are also described at various places. Among other > places they are described also in wikipedia (If you look for > not use the terms 'rem' and 'mod'). Most programming > languages implement the % operation as 'rem' where > A rem B = A rem -B holds. Mathematicans usually prefer the > use of the 'mod' operation. Note that for the 'mod' remainder > usually A mod B <> A mod -B holds (Just the opposide of what > was claimed by someone else in this thread). Now the interesting part. > Do the solutions of an equation which are found with > modInverse depend on the division and remainder operators > used in the equation? I tried with the equation: g = (Xa - Z)/Y > which in the Seed7 programming language yould be written > as g = (X * a - Z) div Y > or as g = (X * a - Z) mdiv Y Using the modInverse function to solve the equation above > leads to a := (modInverse(X,Y) * Z) rem Y > or a := (modInverse(X,Y) * Z) mod Y Depending on the division and the remainder you use. > Aggain 'rem' and 'mod' have the same resuls for positive > values. What I need to find out is: Are the solutions found by > modInverse independend of the integer division used? If somebody has helpful suggestions I want to hear. > Seed7 Homepage: http://seed7.sourceforge.net > Seed7 - The extensible programming language: User defined statements > and operators, abstract data types, templates without special > syntax, OO with interfaces and multiple dispatch, statically typed, > interpreted or compiled, portable, runs under linux/unix/windows. As said in my other post Math and coding Math are different things (did not want to insult you), may be you can get some introductory notes on elementary number theory. Usually there is explained what is understood by modulo in Math in a short and readable way. More or less this is computation in the Ring Z / nZ, where nZ is the 'ideal' of integers multiplied by n (n an integer). Actually the elements are equivalence classes of the form a + nZ. Which means: the set of all number, which can be written as a + n*k, k in Z. A short notation is a modulo n, mostly some bar is written over a, but here we have ASCII typing, so let me write M(a,n), ok? Due to the definition now M(a,n) does not depend on the choice of an a in the set: Two classes M(a,n) and M(b,n) are equal if and only if the difference a-b is a multiple of n (i.e. a-b is in nZ). Addition and subtraction (i.e. the inverses for addition) are done like in Z be doing it on the 'representative' a of M(a,n). Also for multiplication. But since the is no multiplicative inveres for an integer (except for +-1), we can not always expect an inverse in Z / nZ, see below. Since multiplying by (-n) gives the same nZ we get M(a,-n) = M(a,n), which seemed to be one of your questions. The special case n=0 means the set set a+0*Z, so we recover Z. And for n=1 we have all a+1*Z, which is Z, so Z / 1Z is the ring, which consists only of one element, the Zero ring (some do not call such thing a ring, as they want some 0 and some 1 and to be different). Now for positive representants: it is obvious, that one always can find all the representants as the integers 0,1, ... , n-1 (while the next, n, would stand for the Zero = M(0,n)). This is just convention and one would expect a Software implementation to map everything to that (but even Maple has some choices for that). Then inverting: So at least we do not really use the term 'division', it is to find a multiplicative inverse (and just call it division later on, since we are used to it). Now we come to the central point: do you want to implement to find a multiplicative inverse in Z / nZ (if it exits, you know, this is not always true)? Then it *must* be independent from the representing number, thus must work for negative representatives as well (the code I posted does that). It is just through the needs of a computer that you can not give a (infinite) set as solution, but of course want an integer representing it (to use it otherwise). And users may expect those representatives are to be found in the usual fundamental range 0, 1, ... n-1. For example Maple has two implementation: mods(-17, 5) would give -2 and modp(-17, 5) gives 3. The first seems to be faster, but a final use of the last one always finishes the job (IIRC for actual numbers GMP is used in the background). So this should answer your questions around the 'negatives' at least a bit in detail (in short: as long as it is consistent with Math it is a matter of taste and if you show the users how to achieve their needs they will be happy). Last (and only short) the case where you can 'invert' a or not. This depends on the prime factors of a and n (by the so-called Fundamental Theorem of Algebra, which just says: you can write all as powers of Primes which divide the number). A consequence is that you can write Z / nZ = Z / m_1Z x ... Z / m_kZ and do everything just there, if you have the factors in advance. But enough now, you can do it through an error message or code in the implementation as well. === Subject: Re: Look What I Bought > Once again, Ms. Dunlap, that information was verified by police, and > it is precisely why your violent friend was called delusional. æ The police called my friend, and verified that there was no case. æ Prove it. Prove what? Nothing happened, so there was nothing to prove. No > charges were filed, nothing happened, nada. That's like saying, Prove > it didn't rain. And you are attempting to reason with her because.... ? -- To say more is to say less. .84 Harlan Ellison === Subject: Re: Look What I Bought posting-account=UKK_cQkAAAAxEbTd7Dr9FWEo4qz_QtxC Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > all kinds of delicious, yet nutritious, snack food remarks! I don't need to prove nuttin to you, net copper. neener neener neener- Hide quoted text - That's right. Because you're entire story is ficticious. You display > the mentality of a woman reared in a low class environment. pink I was born a poor black child... BTW, I'm sure Brillstein-Grey *loves* all you're charming typos and > errors of fact. They're just falling all over themselves saying, She > must be creative and analytical - see, she gets nothing right! You must be confusing Usenet with professional correspondence. You're > unworthy of proof-reading. Proofreading. HTH. === Subject: Re: Look What I Bought > You must be confusing Usenet with professional correspondence. You're > unworthy of proof-reading. Proofreading. > HTH. Funny! -- To say more is to say less. .84 Harlan Ellison === Subject: Re: Look What I Bought > Prove the police did not conclude Jacques Bouchard is an interent > harasser. æProve that Spang and Ice don't have a history of internet > harassment. While you're at it, prove you ever married a doctor, prove > your son is a medic, and prove you weren't raised in a lower class > neighborhood. And notice, grandma, no one but grandpa supports you in > your flames. I don't need to prove nuttin to you, net copper. neener neener neener That's telling her. Oops. Back to my meeting. -- To say more is to say less. .84 Harlan Ellison === Subject: Re: Look What I Bought , > neener neener neener That's telling her. Oops. Back to my meeting. Back to en work! -- To say more is to say less. .84 Harlan Ellison === Subject: Re: Look What I Bought > And you are attempting to reason with her because.... ? Same reason it's fun to pop bubble wrap? Bubble wraps more fun. And now... I have to get back to woik. I'm in a meeting with a circus clown as opposed to a usenet kook. -- To say more is to say less. .84 Harlan Ellison === Subject: Re: Look What I Bought > Once again, Ms. Dunlap, that information was verified by police, and > it is precisely why your violent friend was called delusional. æ The police called my friend, and verified that there was no case. And > the only one who called him delusional or violent was YOU. And you > can call me Dunlap all you want, but that's not what it says on my > driver's license. What do you expect from Robin London? Can't get anything right. And now... um... why not do something more rewarding than engaging in her idiocy? Cleaning the belly buttons of leprosy victims comes to mind. -- To say more is to say less. .84 Harlan Ellison === Subject: Re: Look What I Bought > What do you expect from Robin London? Oh God... here it comes... I can't help it... Oh oh oh, I'm about to > pun! Robin London? She don't know Jack. And he's no Jack. -- To say more is to say less. .84 Harlan Ellison === Subject: Re: Look What I Bought > Speaking of analysis, dear, you can't spell it without a-n-a-l. As > in, pink is an analhole. Now that's just mean. Funny. But mean. Anyway I'm quite sure Pink bleaches hers. -- To say more is to say less. .84 Harlan Ellison === Subject: A lot of Solution Manuals in Electronic (PDF)Format! posting-account=AIT25goAAAD4PInVOqQYW2U7xf3SSqUF QQDownload 1.7),gzip(gfe),gzip(gfe) A lot of Solution Manuals in Electronic (PDF)Format! A lot of Solutions Manuals in Electronic (PDF)Format! Just contact with trustsolution (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft give up,please email to me. Don.81ft comment in here,please email to me A Course in Modern Mathematical Physics By Peter Szekeres(solution manual) A First Course in String Theory(solution manual) A Quantum Approach to Condensed Matter Physics By Philip ,Taylor(solution manual) A Quantum Approach to Condensed Matter Physics(2002) (.81c.81c) A Short Introduction to Quantum Information and Quantum Computation(2006) accompany Analysis and Design of Integrated Circuits, 4th by Gray, Hurst, Lewis Advanced Dynamics(2006) advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics (8/e)( korean version) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j (even solutions) by ERWIN KREYSZIG advanced macroeconomics By Romer Advanced Modern Engineering Mathematics (3rd Edition) By Glyn James AISC Manual of Steel Construction: Load and Resistance Factor Design, Third Edition (LRFD 3rd Edition) An Introduction to Economic Dynamics An Introduction to Ordinary Differential Equations An Introduction to Partial Differential Equations (2005) By Yehuda Pinchover An Introduction To The Finite Element Method, 3rd Editionby J. N. Reddy Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday Analytical Mechanics, 5th ,By Grant R. Fowles, George L. Cassiday, APPLIED MATHEMATICS AND MODELLING FOR CHEMICAL ENGINEERS, 8th, By Erwin Kreyszig Applied Quantum Mechanics Applied Statisticsand Probability for Engineers,3rd.81Cby Douglas C (selected problem) Applied Strength of Materials (4th Edition) by Robert MoTT Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Chemical and Engineering Thermodynamics- 3rd Chemical_And_Engineering_Thermodynamics_3Ed_Solutions_Manual .81iwiley) Classical Electrodynamics 2Ed by Jackson Classical Mechanics - An Undergraduate Text Communication Systems Engineering.81C2nd, John G. Proakis ,Masoud Salehi Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface.81i3/e) by David A. Patterson, John Control Systems Engineering, 4th Edition Corporate Finance ,By ROSS Data & Computer Communications, 7th Edition By Stallings Derivatives Markets, 2nd Edition by Robert L. McDonald C. Montgomery Design of Analog CMOS Integrated Circuits (2000) Device Electronics for Integrated Circuits, By Richard S. Muller, Theodore I. Kamins Digital and Analog Communication Systems 7th(international version) by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . Digital Image Processing,2 nd, byRafael C. Gonzalez Richard E. Woods Digital Signal Processing by Proakis & Manolakis Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, By John G. Proakis Digital Signal Processing; A Computer-Based Approach 1st ed by Sanjit K. Mitrol Discrete Time Signal Processing by Oppenheim DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Dynamics of Mechanical Systems by harveyv echniques of Problem Solving By Luis Fernandez.81i1997-12.81j Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis 5th,by Williame H. Greene Electric Machinery 6th by Fitzgerald, Kingsley, Uman Electric Machinery Fundamentals 4/e By Stephen J. Chapman Electric Machinery Fundamentals, 4/e , by S. J. Chapman. Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Electrical Machines, Drives and Power Systems (2005) By Theodore Wildi Electromagnetic Harrington (chapter1-chapter3) Elementary Differential Equations and Boundary Value Problems , 8th.81Cby William E. Boyce (Author), Richard C Elementary Differential Equations And Boundary Value Problems, 7Th Ed - Boyce And Diprima Elementary Mechanics & Thermodynamics ,2000, by Jhon W. Norbury Elementary Principles of Chemical Processes By Richard M.Felder elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Elements of Chemical Reaction Engineering ,1999,By H Fogler Elements of engineering electromagnetics (6/e) by N.N.RAO Energy Management 2005-12 5th ed,By Klaus-Dieter E. Pawlik Engineering - Materials Science,by Milton Ohring Engineering circuit analysis 6 ed,By William Hart Hayt Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Electromagnetics, 6th .81Cby William H. Hayt, John A. Buck Engineering Fluid Mechanics, 7th Edition By Clayton T. Crowe, Donald F. Elger, John A. Roberson Engineering Mathematics, 4th Edition ,by John Bird Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Fundamentals of Electric Circuits(2th ) By Charles Alexander, Matthew Sadiku Engineering Mechanics, Dynamics ,By J. L. Meriam, L. G. Kraige, Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige(chapter1,2,3,4) Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, Equilibrium and Non-Equilibrium Statistical Thermodynamics field and wave electromagnetics (2/e) by David Cheng Financial Accounting 6th edition by Harrison Flex Solutions: Essential Techniques for Flex 2 and 3 Developers By Marco Casario Fluid Mechanics (2006) By CENGEL Fourier and Laplace Transform ,by Antwoorden Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt (ANOTHER EDITION) Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Engineering Thermodynamics by Moran, M.J. & Shapiro H.N. Fundamentals of Fluid Mechanics by Bruce R. Munson Fundamentals Of Fluid Mechanics 3Rd And 4Th Edition Fundamentals of Fluid Mechanics, 5th by By Bruce,R. Munson, Donald, Fundamentals of Logic Design 5th by Charles Roth Fundamentals of Machine Component Design, 3rd Juvinall, Marshek Fundamentals of Organic Chemistry, 5E Fundamentals of Physics (7th ) by Halliday, Resnick and Walker Fundamentals of Physics.81C7th, by David Halliday, Robert Resnick Fundamentals of Probability 3/e Fundamentals of Quantum Mechanics: For Solid State Electronics and Optics By: C. L. Tang Fundamentals of Thermal-Fluid Sciences Fundamentals of Thermodynamics 6th Ed by Sonntag,Borgnakke and Van Wylen HARCOURT MATHEMATICS 12 Advanced Functions and Introductory Calculus he Econometrics of Financial Markets by Petr Adamek John Y. Campbell Andrew Heat Transfer Heat transfer: a pritical approach 2th by Yunus A. Cengel,& Yunus Cengel How to Program_C, 3RD Edition 2000 By Harvey M. Deitel Introduction To Algorithms,2nd,by Thomas H.Cormen Introduction to Chemical Engineering Thermodynamics By J.M. Smith, Hendrick Introduction To Electric Circuits 6th By Richard C. Dorf, James A. Svoboda Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Fluid Mechanics 5th by Fox Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Linear Algebra--3rd Edition - Gilbert Strang Introduction to Mathematical Statistics 6/E Robert V. Hogg Introduction to Probability by Charles M. Grinstead and J. Laurie Snell(ODD) Introduction to Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Introduction to Solid State Physics (8 ED) by Charles.Kittel__ Introduction to VLSI Circuits and Systems (2001 )byJohn P Uyemura Introductory Quantum Optics ,By Christopher Gerry and Peter Knight Investment Analysis and Portfolio Management(7th) By Frank K. et al. Reilly Kinetics of Catalytic Reactions (2005) By M. Albert Vannice Lectures on Corporate Finance.81i2th.81j by Peter Bossaerts and Bernt Linear Algebra and its Applications [Solutions Manual] 3rd ed - D. Lay WW Logic and Computer Design Fundamentals4E by Mano and Kime.3th Logic and Computer Design Fundamentals4E by Mano and Kime.4th Materials Science and Engineering: An Introduction 6E ,By William D. Callister Jr. MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mathematical Models in Biology: An Introduction Mathematical Olympiad in China: Problems and Solutions By Bin Xiong, Yee Lee Peng Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Fluids Solutions Manual ,8 ed,By John Ward-Smith Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Mechanics of Materials (6/E) by R.C.Hibbeler Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Microelectronic Circuits, Sedra, 4th edition Microwave Engineering 3ed - by david pozar Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Numerical methods for engineers by Chapra Numerical Solution of Partial Differential Equations: An Introduction.81i2 th.81j Operating Systems Concepts 6th byAbraham Silberschat Optics: Major American Universities Ph. D. Qualifying Questions and Solutions By Chung-Kuo Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition. Options, Futures and Other Derivatives (4th) By John Hull, John C. Hull Options, Futures and Other Derivatives (5th) By John Hull, John C. Hull Organic Chemistry(2th) by Hornback Physical Chemistry (2001) By Julio de Paula, Peter Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physics , 5th,( Vol 2)by Resnick Halliday Krane, Physics for Scientists and Engineers by Serway& Jewett Physics for Scientists and Engineers (7th ) Volume One by Serway and Jewett Physics For Scientists And Engineers 6E By Serway And Jewett - Solutions Manual Vol 2 Principles of Electronic Materials and Devices, 2th,By Safa O. Kasap Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Probability and Statistics for Engineers and Scientists by HAYLER Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Probability,Random Variables and Stochastic Processes,4th,by Athanasios Papoulis Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Physics, Third Edition, By Stephen Gasiorowicz Quantum Physics, Third Edition, By Stephen Gasiorowicz Recursive Methods in Economic Dynamics By Claudio Irigoyen, Esteban Rossi-Hansberg, Hans , Yorick Semiconductor Devices Second Edition By S.M.Sze Semiconductor Physics and Devices Third Edition By Donald Neamen Separation Process Principles, 2nd Ed., by Seader, Henley Shigley's Mechanical Engineering Design, (8/e) by Richard G. Budynas Signal Processing and Linear Systems (2001) by B P Lathi Signal Processing and Linear Systems, By B.P. Lathi Signals and Systems (2nd Edition) By Oppenheim, Willsky and Nawab Signals and Systems 2nd by Haykin Statistical Digital Signal Processing and Modeling By Monson H. Hayes Statistical Inference (2th) By CASELLA System Dynamics 3rd Ed ,By Katsuhiko Ogata The Economics of Financial Markets.81i2005.81j By Roy E. Bailey Theoretical & Mathematical Physics: Advanced Level(2th) By Willi- Hans Steeb Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions Manual Two-Dimensional Incompressible Navier-Stokes Equations- Maciej Matyk Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith University Physics with Modern Physics:,11 ed By Hugh D. Young, Roger A. Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) E. R. Johnston Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings Zill's a First Course in Differential Equations with boundary value problem 5th Zill's a First Course in Differential Equations with Modeling Applicants 7/e.81isolitions manual.81j don't leave a message here,please send email to solutionpay@hotmail.com, i will tell you how to do to get the solution A lot of Solution Manuals in Electronic (PDF)Format! A lot of Solutions Manuals in Electronic (PDF)Format! Just contact with trustsolution (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft give up,please email to me. Don.81ft comment in here,please email to me A Course in Modern Mathematical Physics By Peter Szekeres(solution manual) A First Course in String Theory(solution manual) A Quantum Approach to Condensed Matter Physics By Philip ,Taylor(solution manual) A Quantum Approach to Condensed Matter Physics(2002) (.81c.81c) A Short Introduction to Quantum Information and Quantum Computation(2006) accompany Analysis and Design of Integrated Circuits, 4th by Gray, Hurst, Lewis Advanced Dynamics(2006) advanced engineering mathematics (8/e) by ERWIN KREYSZIG advanced engineering mathematics (8/e)( korean version) by ERWIN KREYSZIG advanced engineering mathematics.81i9/e.81j (even solutions) by ERWIN KREYSZIG advanced macroeconomics By Romer Advanced Modern Engineering Mathematics (3rd Edition) By Glyn James AISC Manual of Steel Construction: Load and Resistance Factor Design, Third Edition (LRFD 3rd Edition) An Introduction to Economic Dynamics An Introduction to Ordinary Differential Equations An Introduction to Partial Differential Equations (2005) By Yehuda Pinchover An Introduction To The Finite Element Method, 3rd Editionby J. N. Reddy Analytical Mechanics (7/e) By Grant R. Fowles, George L. Cassiday Analytical Mechanics, 5th ,By Grant R. Fowles, George L. Cassiday, APPLIED MATHEMATICS AND MODELLING FOR CHEMICAL ENGINEERS, 8th, By Erwin Kreyszig Applied Quantum Mechanics Applied Statisticsand Probability for Engineers,3rd.81Cby Douglas C (selected problem) Applied Strength of Materials (4th Edition) by Robert MoTT Calculus I, II, Transidentals 10e BY George B. Thomas Calculus with Analytic Geometry Calculus, 4th edition by James Stewart Chemical and Engineering Thermodynamics- 3rd Chemical_And_Engineering_Thermodynamics_3Ed_Solutions_Manual .81iwiley) Classical Electrodynamics 2Ed by Jackson Classical Mechanics - An Undergraduate Text Communication Systems Engineering.81C2nd, John G. Proakis ,Masoud Salehi Computational Techniques for Fluid Dynamics By Karkenahalli Srinivas, Clive A. J. Fletcher Computer Organization and Design: The Hardware/Software Interface.81i3/e) by David A. Patterson, John Control Systems Engineering, 4th Edition Corporate Finance ,By ROSS Data & Computer Communications, 7th Edition By Stallings Derivatives Markets, 2nd Edition by Robert L. McDonald C. Montgomery Design of Analog CMOS Integrated Circuits (2000) Device Electronics for Integrated Circuits, By Richard S. Muller, Theodore I. Kamins Digital and Analog Communication Systems 7th(international version) by LEON W. COUCH Digital and Analog Communication Systems .81C5th, by Leon W. Couch, Leon W., II Couch . Digital Image Processing,2 nd, byRafael C. Gonzalez Richard E. Woods Digital Signal Processing by Proakis & Manolakis Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, By John G. Proakis Digital Signal Processing; A Computer-Based Approach 1st ed by Sanjit K. Mitrol Discrete Time Signal Processing by Oppenheim DISCRETE-TIME SIGNAL PROCESSING/2e by Oppenheim.81ASchafer Dynamics of Mechanical Systems by harveyv echniques of Problem Solving By Luis Fernandez.81i1997-12.81j Econometric Analysis (6/e) by willian H.GREENE Econometric Analysis 5th,by Williame H. Greene Electric Machinery 6th by Fitzgerald, Kingsley, Uman Electric Machinery Fundamentals 4/e By Stephen J. Chapman Electric Machinery Fundamentals, 4/e , by S. J. Chapman. Electrical Circuits (7/e) by James W. Nilsson, and Susan A. Electrical Machines, Drives and Power Systems (2005) By Theodore Wildi Electromagnetic Harrington (chapter1-chapter3) Elementary Differential Equations and Boundary Value Problems , 8th.81Cby William E. Boyce (Author), Richard C Elementary Differential Equations And Boundary Value Problems, 7Th Ed - Boyce And Diprima Elementary Mechanics & Thermodynamics ,2000, by Jhon W. Norbury Elementary Principles of Chemical Processes By Richard M.Felder elements of Chemical Reaction Engineering (3rd)by H.Scott Fogler Elements of Chemical Reaction Engineering ,1999,By H Fogler Elements of engineering electromagnetics (6/e) by N.N.RAO Energy Management 2005-12 5th ed,By Klaus-Dieter E. Pawlik Engineering - Materials Science,by Milton Ohring Engineering circuit analysis 6 ed,By William Hart Hayt Engineering electromagnetics (6/e) by HAYT Engineering electromagnetics (7/e) by HAYT Engineering Electromagnetics, 6th .81Cby William H. Hayt, John A. Buck Engineering Fluid Mechanics, 7th Edition By Clayton T. Crowe, Donald F. Elger, John A. Roberson Engineering Mathematics, 4th Edition ,by John Bird Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Fundamentals of Electric Circuits(2th ) By Charles Alexander, Matthew Sadiku Engineering Mechanics, Dynamics ,By J. L. Meriam, L. G. Kraige, Engineering Mechanics, Dynamics 5th By J. L. Meriam, L. G. Kraige(chapter1,2,3,4) Engineering Mechanics: Statics ,10th ,by R.C.Hibbeler, Equilibrium and Non-Equilibrium Statistical Thermodynamics field and wave electromagnetics (2/e) by David Cheng Financial Accounting 6th edition by Harrison Flex Solutions: Essential Techniques for Flex 2 and 3 Developers By Marco Casario Fluid Mechanics (2006) By CENGEL Fourier and Laplace Transform ,by Antwoorden Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt (ANOTHER EDITION) Fundamental of Heat and Mass Transfer by Frank P. Incropera and David P.DeWitt Fundamentals of Chemical Reaction Engineering By Mark E. E. Davis, Robert J. J. Davis Fundamentals of Engineering Thermodynamics by Moran, M.J. & Shapiro H.N. Fundamentals of Fluid Mechanics by Bruce R. Munson Fundamentals Of Fluid Mechanics 3Rd And 4Th Edition Fundamentals of Fluid Mechanics, 5th by By Bruce,R. Munson, Donald, Fundamentals of Logic Design 5th by Charles Roth Fundamentals of Machine Component Design, 3rd Juvinall, Marshek Fundamentals of Organic Chemistry, 5E Fundamentals of Physics (7th ) by Halliday, Resnick and Walker Fundamentals of Physics.81C7th, by David Halliday, Robert Resnick Fundamentals of Probability 3/e Fundamentals of Quantum Mechanics: For Solid State Electronics and Optics By: C. L. Tang Fundamentals of Thermal-Fluid Sciences Fundamentals of Thermodynamics 6th Ed by Sonntag,Borgnakke and Van Wylen HARCOURT MATHEMATICS 12 Advanced Functions and Introductory Calculus he Econometrics of Financial Markets by Petr Adamek John Y. Campbell Andrew Heat Transfer Heat transfer: a pritical approach 2th by Yunus A. Cengel,& Yunus Cengel How to Program_C, 3RD Edition 2000 By Harvey M. Deitel Introduction To Algorithms,2nd,by Thomas H.Cormen Introduction to Chemical Engineering Thermodynamics By J.M. Smith, Hendrick Introduction To Electric Circuits 6th By Richard C. Dorf, James A. Svoboda Introduction to Electrodynamics(3/e) by David J. Griffiths Introduction to Fluid Mechanics 5th by Fox Introduction to Heat Transfer 4th Edition By Frank P. Incropera, David Introduction to Linear Algebra--3rd Edition - Gilbert Strang Introduction to Mathematical Statistics 6/E Robert V. Hogg Introduction to Probability by Charles M. Grinstead and J. Laurie Snell(ODD) Introduction to Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Introduction to Solid State Physics (8 ED) by Charles.Kittel__ Introduction to VLSI Circuits and Systems (2001 )byJohn P Uyemura Introductory Quantum Optics ,By Christopher Gerry and Peter Knight Investment Analysis and Portfolio Management(7th) By Frank K. et al. Reilly Kinetics of Catalytic Reactions (2005) By M. Albert Vannice Lectures on Corporate Finance.81i2th.81j by Peter Bossaerts and Bernt Linear Algebra and its Applications [Solutions Manual] 3rd ed - D. Lay WW Logic and Computer Design Fundamentals4E by Mano and Kime.3th Logic and Computer Design Fundamentals4E by Mano and Kime.4th Materials Science and Engineering: An Introduction 6E ,By William D. Callister Jr. MATHEMATICAL ANALYSIS (2/e) (chapter1-9) by Tom M. Apostol Mathematical Models in Biology: An Introduction Mathematical Olympiad in China: Problems and Solutions By Bin Xiong, Yee Lee Peng Mechanical Engineering Design By Joseph Shigley, Charles Mischke, Mechanics of Fluids Solutions Manual ,8 ed,By John Ward-Smith Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Mechanics of Materials (6/E) by R.C.Hibbeler Mechanics Of Materials ,3rd , By Beer, Johnston, & Dewolf Microeconomic Analysis, 3rd Edition, by Hal R. Varian Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, Microelectronic Circuits, Sedra, 4th edition Microwave Engineering 3ed - by david pozar Modern Control Engineering/ 4E by K.OGATA Modern Digital and Analog Communication Systems (3/e) Numerical methods for engineers by Chapra Numerical Solution of Partial Differential Equations: An Introduction.81i2 th.81j Operating Systems Concepts 6th byAbraham Silberschat Optics: Major American Universities Ph. D. Qualifying Questions and Solutions By Chung-Kuo Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition. Options, Futures and Other Derivatives (4th) By John Hull, John C. Hull Options, Futures and Other Derivatives (5th) By John Hull, John C. Hull Organic Chemistry(2th) by Hornback Physical Chemistry (2001) By Julio de Paula, Peter Atkins Physical Chemistry (7/e) by Peter Atkins and Julio de Paula Physics , 5th,( Vol 2)by Resnick Halliday Krane, Physics for Scientists and Engineers by Serway& Jewett Physics for Scientists and Engineers (7th ) Volume One by Serway and Jewett Physics For Scientists And Engineers 6E By Serway And Jewett - Solutions Manual Vol 2 Principles of Electronic Materials and Devices, 2th,By Safa O. Kasap Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Probability and Statistics for Engineers and Scientists by HAYLER Probability, Random Variables and Stochastic Processes,3rd, by Athanasios Papoulis Probability,Random Variables and Stochastic Processes,4th,by Athanasios Papoulis Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Field Theory (draft version) ,By Mark Srednicki Quantum Physics, Third Edition, By Stephen Gasiorowicz Quantum Physics, Third Edition, By Stephen Gasiorowicz Recursive Methods in Economic Dynamics By Claudio Irigoyen, Esteban Rossi-Hansberg, Hans , Yorick Semiconductor Devices Second Edition By S.M.Sze Semiconductor Physics and Devices Third Edition By Donald Neamen Separation Process Principles, 2nd Ed., by Seader, Henley Shigley's Mechanical Engineering Design, (8/e) by Richard G. Budynas Signal Processing and Linear Systems (2001) by B P Lathi Signal Processing and Linear Systems, By B.P. Lathi Signals and Systems (2nd Edition) By Oppenheim, Willsky and Nawab Signals and Systems 2nd by Haykin Statistical Digital Signal Processing and Modeling By Monson H. Hayes Statistical Inference (2th) By CASELLA System Dynamics 3rd Ed ,By Katsuhiko Ogata The Economics of Financial Markets.81i2005.81j By Roy E. Bailey Theoretical & Mathematical Physics: Advanced Level(2th) By Willi- Hans Steeb Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions Manual Two-Dimensional Incompressible Navier-Stokes Equations- Maciej Matyk Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith University Physics with Modern Physics:,11 ed By Hugh D. Young, Roger A. Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) E. R. Johnston Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings Zill's a First Course in Differential Equations with boundary value problem 5th Zill's a First Course in Differential Equations with Modeling Applicants 7/e.81isolitions manual.81j don't leave a message here,please send email to trustsolution@hotmail.com, i will tell you how to do to get the solution === Subject: Gravitational Doppler originally posted 7/24/06) Gravitational Doppler ~v~~ We are well aware of gravitational lensing but there is another EM analog associated with Newtonian universal gravitation as well: gravitational doppler. In other words with latency extensions to Newtonian universal gravitation we can explain planetary orbital perihelion anomalies and calculate the Pioneer anomaly in simple, direct terms. To do this we only need to calculate Pioneer's velocity away from the sun as a fraction of the speed of light and recognize that the effect of the sun's gravitation will increase in proportion: Yearly distance traveled by Pioneer = 219,000,000 miles Yearly discrepancy in distance = 8,000 miles Ratio = ~ 27,375 speed of light = 186,289 miles per second Yearly distance traveled by light in one year= 186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr Divided by yearly distance traveled by Pioneer Ratio = ~ 26,825 A difference between the two ratios of 2% (27375 - 26,825 / 27,375) QED ~v~~ In other words Pioneer travels about 7 miles per second away from the sun and in doing so gravitation waves lengthen and their attractive intensity is experienced longer in each wave. (In this respect unlike repulsive waves like EM radiation, the effect of attraction increases in gravitation with longer waves and decreases with shorter waves.) And conversely the attraction of gravitation should decrease as the sun is approached. Clearly the Pioneer Anomaly is caused by what I call gravitational doppler. This mechanical principle of gravitational doppler latency added to Newtonian universal gravitation also underlies planetary perihelion orbital anomalies except in such cases where a roughly constant orbital distance is maintained there is no net change in gravitational attraction: there is only an eccentric locus of force offset to the receding hemisphere of the sun according to its own rotational speed and density distribution. I have only been able to estimate this degree of eccentricity to account for the anomalous perihelion advance of the planet Mercury to a an order of magnitude of 2 however the rotational characteristics of the sun and distribution of mass are extremely complex and difficult to estimate accurately. Lester Zick ~v~~ === Subject: Re: Gravitational Doppler posting-account=UM3jRwkAAADTHFmJ20qgwageu031CeWA 5.1),gzip(gfe),gzip(gfe) > originally posted 7/24/06) æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ Gravitational Doppler > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ~v~~ We are well aware of gravitational lensing but there is another EM > analog associated with Newtonian universal gravitation as well: > gravitational doppler. In other words with latency extensions to > Newtonian universal gravitation we can explain planetary orbital > perihelion anomalies and calculate the Pioneer anomaly in simple, > direct terms. To do this we only need to calculate Pioneer's velocity away from the > sun as a fraction of the speed of light and recognize that the effect > of the sun's gravitation will increase in proportion: > Yearly distance traveled by Pioneer = 219,000,000 miles Yearly discrepancy in distance æ æ æ æ= æ æ æ æ æ 8,000 miles Ratio = ~ 27,375 speed of light æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ = æ æ æ 186,289 miles per > æsecond Yearly distance traveled by light in one year= æ æ æ æ æ æ æ 186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr Divided by yearly distance traveled by Pioneer Ratio = ~ 26,825 A difference between the two ratios of 2% (27375 - 26,825 / 27,375) QED æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ~v~~ In other words Pioneer travels about 7 miles per second away from the > sun and in doing so gravitation waves lengthen and their attractive > intensity is experienced longer in each wave. (In this respect unlike > repulsive waves like EM radiation, the effect of attraction increases > in gravitation with longer waves and decreases with shorter waves.) > And conversely the attraction of gravitation should decrease as the > sun is approached. Clearly the Pioneer Anomaly is caused by what I call gravitational > doppler. This mechanical principle of gravitational doppler latency > added to Newtonian universal gravitation also underlies planetary > perihelion orbital anomalies except in such cases where a roughly > constant orbital distance is maintained there is no net change in > gravitational attraction: there is only an eccentric locus of force > offset to the receding hemisphere of the sun according to its own > rotational speed and density distribution. I have only been able to > estimate this degree of eccentricity to account for the anomalous > perihelion advance of the planet Mercury to a an order of magnitude of > 2 however the rotational characteristics of the sun and distribution > of mass are extremely complex and difficult to estimate accurately. Lester Zick ~v~~ You can always tell a graduate of the George W Bush school of physics. They just love to torture the subject. === Subject: Re: Gravitational Doppler > originally posted 7/24/06) > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ Gravitational Doppler > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ~v~~ > We are well aware of gravitational lensing but there is another EM > analog associated with Newtonian universal gravitation as well: > gravitational doppler. In other words with latency extensions to > Newtonian universal gravitation we can explain planetary orbital > perihelion anomalies and calculate the Pioneer anomaly in simple, > direct terms. > To do this we only need to calculate Pioneer's velocity away from the > sun as a fraction of the speed of light and recognize that the effect > of the sun's gravitation will increase in proportion: > Yearly distance traveled by Pioneer = 219,000,000 miles > Yearly discrepancy in distance æ æ æ æ= æ æ æ æ æ 8,000 miles > Ratio = ~ 27,375 > speed of light æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ = æ æ æ 186,289 miles per > æsecond > Yearly distance traveled by light in one year= > æ æ æ æ æ æ æ 186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr > Divided by yearly distance traveled by Pioneer > Ratio = ~ 26,825 > A difference between the two ratios of 2% (27375 - 26,825 / 27,375) > QED > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ~v~~ > In other words Pioneer travels about 7 miles per second away from the > sun and in doing so gravitation waves lengthen and their attractive > intensity is experienced longer in each wave. (In this respect unlike > repulsive waves like EM radiation, the effect of attraction increases > in gravitation with longer waves and decreases with shorter waves.) > And conversely the attraction of gravitation should decrease as the > sun is approached. > Clearly the Pioneer Anomaly is caused by what I call gravitational > doppler. This mechanical principle of gravitational doppler latency > added to Newtonian universal gravitation also underlies planetary > perihelion orbital anomalies except in such cases where a roughly > constant orbital distance is maintained there is no net change in > gravitational attraction: there is only an eccentric locus of force > offset to the receding hemisphere of the sun according to its own > rotational speed and density distribution. I have only been able to > estimate this degree of eccentricity to account for the anomalous > perihelion advance of the planet Mercury to a an order of magnitude of > 2 however the rotational characteristics of the sun and distribution > of mass are extremely complex and difficult to estimate accurately. > Lester Zick > ~v~~ You can always tell a graduate of the George W Bush school of >physics. They just love to torture the subject. And your point would be? ~v~~ === Subject: Re: Gravitational Doppler <5g7s04t7f2ju7u6fbasbt06v4n0h1dcu71@4ax.com> posting-account=UM3jRwkAAADTHFmJ20qgwageu031CeWA 5.1),gzip(gfe),gzip(gfe) > originally posted 7/24/06) > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ Gravitational Doppler > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ~v~~ > We are well aware of gravitational lensing but there is another EM > analog associated with Newtonian universal gravitation as well: > gravitational doppler. In other words with latency extensions to > Newtonian universal gravitation we can explain planetary orbital > perihelion anomalies and calculate the Pioneer anomaly in simple, > direct terms. > To do this we only need to calculate Pioneer's velocity away from the > sun as a fraction of the speed of light and recognize that the effect > of the sun's gravitation will increase in proportion: > Yearly distance traveled by Pioneer = 219,000,000 miles > Yearly discrepancy in distance æ æ æ æ= æ æ æ æ æ 8,000 miles > Ratio = ~ 27,375 > speed of light æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ = æ æ æ 186,289 miles per > æsecond > Yearly distance traveled by light in one year= > æ æ æ æ æ æ æ 186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr > Divided by yearly distance traveled by Pioneer > Ratio = ~ 26,825 > A difference between the two ratios of 2% (27375 - 26,825 / 27,375) > QED > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ~v~~ > In other words Pioneer travels about 7 miles per second away from the > sun and in doing so gravitation waves lengthen and their attractive > intensity is experienced longer in each wave. (In this respect unlike > repulsive waves like EM radiation, the effect of attraction increases > in gravitation with longer waves and decreases with shorter waves.) > And conversely the attraction of gravitation should decrease as the > sun is approached. > Clearly the Pioneer Anomaly is caused by what I call gravitational > doppler. This mechanical principle of gravitational doppler latency > added to Newtonian universal gravitation also underlies planetary > perihelion orbital anomalies except in such cases where a roughly > constant orbital distance is maintained there is no net change in > gravitational attraction: there is only an eccentric locus of force > offset to the receding hemisphere of the sun according to its own > rotational speed and density distribution. I have only been able to > estimate this degree of eccentricity to account for the anomalous > perihelion advance of the planet Mercury to a an order of magnitude of > 2 however the rotational characteristics of the sun and distribution > of mass are extremely complex and difficult to estimate accurately. > Lester Zick > ~v~~ You can always tell a graduate of the George W Bush school of >physics. æThey just love to torture the subject. And your point would be? > On the top of your perverted little head. === Subject: Re: Gravitational Doppler posting-account=DdJUaQoAAACBOzKjHG60lbAKPBPEqDEo CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Another brilliant essay which is totally [OT] to c.a.p. What's this now? The 3rd or 4th one this past week. === Subject: Re: Gravitational Doppler >Another brilliant essay which is totally [OT] to c.a.p. Brilliance and intelligence obviously being irrelevant to cap. >What's this now? The 3rd or 4th one this past week. What can I say? The Jesuits came after me with a vengence only because I called their heresies crapola, and I was forced to cloak myself in the mantle of truth, a disguise the Jesuits were unable to penetrate, until they got bored and went back to what they're more adept at, football and hoops. ~v~~ === Subject: Re: Gravitational Doppler Clearly the Pioneer Anomaly is caused by what I call gravitational > doppler. Pioneer Anomaly Solved? http://www.skyandtelescope.com/news/home/17846774.html http://meetings.aps.org/Meeting/APR08/Event/83144 Author: Slava G. Turyshev (Jet Propulsion Laboratory, California Institute of Technology) The Pioneer 10/11 spacecraft yielded the most precise navigation in deep space to date. However, their radiometric tracking data received from the distances between 20-70 astronomical units from the Sun has consistently indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue frequency shift that can be interpreted as a sunward acceleration of ap = (8.74 +/- 1.33) x 10^-10 m/s2 for each particular spacecraft. This signal has become known as the Pioneer anomaly the nature of which remains unexplained. New Pioneer 10 and 11 radio-metric Doppler data recently became available that span a longer interval compared to the data used in previous investigations. A thermal model of the Pioneer vehicles is being developed to study possible contribution of thermal recoil force acting on the two spacecraft. The current status of these investigations will be discussed. This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. === Subject: Re: Gravitational Doppler Not sure what this is aid of, Sam. I see no date of record below and it's unclear whether the author is claiming an experimental resolution of the problem or just some conjecture. My own calculations are what they are and are based on published data. > Clearly the Pioneer Anomaly is caused by what I call gravitational > doppler. > Pioneer Anomaly Solved? > http://www.skyandtelescope.com/news/home/17846774.html > http://meetings.aps.org/Meeting/APR08/Event/83144 Author: Slava G. Turyshev > (Jet Propulsion Laboratory, California Institute of Technology) The Pioneer 10/11 spacecraft yielded the most precise navigation in deep >space to date. However, their radiometric tracking data received from >the distances between 20-70 astronomical units from the Sun has >consistently indicated the presence of a small, anomalous, Doppler >frequency drift. The drift is a blue frequency shift that can be >interpreted as a sunward acceleration of ap = (8.74 +/- 1.33) x 10^-10 >m/s2 for each particular spacecraft. This signal has become known as the >Pioneer anomaly the nature of which remains unexplained. ???? > New Pioneer 10 >and 11 radio-metric Doppler data recently became available that span a >longer interval compared to the data used in previous investigations. A >thermal model of the Pioneer vehicles is being developed to study >possible contribution of thermal recoil force acting on the two >spacecraft. The current status of these investigations will be >discussed. This work was carried out at the Jet Propulsion Laboratory, >California Institute of Technology under a contract with the National >Aeronautics and Space Administration. ~v~~ === Subject: Re: Gravitational Doppler > Not sure what this is aid of, Sam. I see no date of record below and > it's unclear whether the author is claiming an experimental resolution > of the problem or just some conjecture. My own calculations are what > they are and are based on published data. > Your calculations are flawed Lester. === Subject: New eBooks Quotations- Downloadlinks posting-account=UKPBwAoAAAACmI0Tado5DEX6bGSZsK7M InfoPath.2; Alexa Toolbar),gzip(gfe),gzip(gfe) Good Day ! This is to appraise you about the new eBook compiled by me A FEW GOOD QUOTATIONS . I had been collecting some material for my school going kids and then it occurred to me that it might be useful to many others as well. I have tried to present it through the eBook. This is my second eBook. I give below the links to download both these eBooks : 1. For QUOTATIONS AND THOUGHTS : http://tipsinmaths.ind.in/Quotations.exe and 2. For A FEW EASY STEPS IN MULTIPLICATIONS AND SQUARES: http://tipsinmaths.ind.in/AFEWEASYSTEPS.exe The New eBook on Good Quotations A Few Good Quotations is a compilation of a few good quotations I liked and is totally free. It has quotations classified according to keyword and others. I propose to update it at regular interval .You may use lifetime as login id and 9687548776 as password to open this eBook. My earlier eBook is related to Maths. Many students have been allergic to Mathematics and hate numbers, tables, formula. Many students have met with failures only because of MATHS- the naughty subject which has been friendly to many others. Let us give a chance to our kids to develop a level of confidence by allowing them to learn few such friendly methods by which they can perform some of the difficult problems very quickly. This might boost their confidence that it is not a difficult subject to handle. Rather they could be in love with it and it could give us pleasures to see how they manage mathematics with confidence. And this is the subject which can give wonderful results with regular practice. This regular practice will not only increase their speed and accuracy in the subject but also teach them : it also brings them some recognition among the others (they might be treated as intelligent ). Would it not improve their overall performance also? Maths is the subject which not only deals with numbers but it teaches us the logic or relation behind those numbers. It inculcates a logical thinking and approach. Let us hope to benefit from it's intrinsic values. Mr.Damle, my husband, ( who had qualified as a Chartered Accountant, Cost Accountant and Company Secretary ) had written some notes long ago during his coaching to the younger friends and students. He had shown a few tricks to many of his young friends who were amazed with them .It had also developed a curiosity in them to learn more complex problems. Their parents reacted positively as they had witnessed an increasing inclination in their kids towards learning this subject. I have attempted to offer the same tips and ideas for the benefit of many others who have not been so comfortable with mathematic. I have recompiled those notes and presented them in this eBook A FEW EASY STEPS IN MULTIPLICATIONS AND SQUARES so that many others can also benefit from the same. Though a few chapters of this eBook require username and password which would be available on payment of a small charge of US$10 to be paid using PAYPAL, even the rest of the eBook ( available for free viewing ) has been useful to many. I would welcome your suggestions. WITH ALL GOOD WISHES .83.83 Mrs.M.R.Damle === Subject: Re: best introductory texts > plz suggest good introductory texts on the following > 1)calculus > 2)linear algebra > 3)differential equations > 4)real analysis > 5)proability and statistics >Apostol, Lang, Boyce & DiPrima, Rudin, Feller, >in that order. >-- >Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) Feller hjas NO statistics. For statistics, I suggest Bickel and Doksum, second edition, which is quite different from the first. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Math jobs at UK colleges posting-account=ajkdngoAAAB2X3SxyQtiBYkcRETphklh CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Get daily updated feeds of teaching jobs at UK Math departments http://britishcomputercolleges.com/jobs/uk/math.htm or http://www.thinkanddone.com/jobs/uk/math.htm === Subject: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) In a coin tossing game consisting of a single player, a single fair coin is tossed several times. After each toss, if the player can correctly guess the outcome (H/T) of that toss then he wins and the game ends. However, if after finite n tosses the player has missed all of n tosses, he loses. This game is simply the coin gambling with Martingale strategy (doubling the bet every time if lose, so only a single win can recover all the loses plus a reward equals to initial bet) with finite resource (after finite tosses the resource ran out and the player loses all). A player's strategy can be represented by a string of H's and T's of length n, e.g. HTHTTT for n = 6. And since each tosses are considered independent, a strategy can be predetermined before the actual tosses (?). The question is : does the strategy HHH...H (or TTT...T) have more probability of winning than any other specific arbitrary strategies, says, HTHTTT for n= 6? What about strategies with equal H's and T's (e.g. THTHTH...TH)? I have seen some arguments saying that HHH...H have high prob of winning, since the outcome TTT...T (which make you lose) have lowest prob of occuring-- with big n, the chance of tosses being all T is low (according to common sense and some theory...). But then again, in my tinkling opinion, since for a specific arbitrary strategy, there is also only one string that can make you lose (i.e. the 'opposite' string), and that string should also has the prob of 1/(2^n), thus the winning prob of 1-1/(2^n) for any strategy. Therfore such argument is absurd. And we are back to the 50-50 chance of winning regardless of tosses order. As you can see, I have a very little knowledge in Probability and I have poorly stated the problem. So please feel free to restate it if === Subject: Re: Coin tossing guessing strategy... > In a coin tossing game consisting of a single player, a single fair > coin is tossed several times. After each toss, if the player can > correctly guess the outcome (H/T) of that toss then he wins and the > game ends. However, if after finite n tosses the player has missed all > of n tosses, he loses. This game is simply the coin gambling with Martingale strategy > (doubling the bet every time if lose, so only a single win can recover > all the loses plus a reward equals to initial bet) with finite > resource (after finite tosses the resource ran out and the player > loses all). > I'll take my own track here... Well the probability is .50 and the reciprocal of .50 is 2 so a winning wager should pay 2. But the house must have an edge so the winning wager pays 1.9 . That's the 1 wagered plus 90% of the profit of 1 . Or the house might want to pay 1.80 so that 1 - (1.80 / 2) = 10%. Or the house might take 10% of the 1 wagered to make a .90 wager and then pay .90 to the .90 to make a 1.80 payout. Okay the house pays 1.80 and that includes the 1 that was wagered. Now how much should each losing wager be increased to make a total profit of the beginning unit wager ? Well if the first wager is 1 and losses then the second wager must pay 1 + 1 . So that's 2 / .9 or 2.22 for the amount of the second wager... Now the second wager of 2.22 also loses so the third wager must pay 1 + 2.22 + 1. So that's 4.22 / .9 or 4.69 for the amount of the third wager... Now the third wager loses so the fourth wager must pay 1 + 2.22 + 4.69 + 1. So that's 8.91 / .9 or 9.90 for the amount of the fourth wager.... Then the fourth wager wins and that's a total profit of 1... === Subject: Re: Coin tossing guessing strategy... But the house must have an edge so the winning wager pays 1.9 . That's the > 1 wagered plus 90% of the profit of 1 . Well if the first wager is 1 and losses then the second wager must profit > 1 + 1 . So that's 2 / .9 or 2.22 for the amount of the second wager... Now the second wager of 2.22 also loses so the third wager must profit 1 + > 2.22 + 1. So that's 4.22 / .9 or 4.69 for the amount of the third wager... Now the third wager loses so the fourth wager must profit 1 + 2.22 + 4.69 > + 1. So that's 8.91 / .9 or 9.90 for the amount of the fourth wager.... Then the fourth wager wins and that's a total profit of 1... > === Subject: Re: Coin tossing guessing strategy... > Or the house might take 10% of the 1 wagered to make a .90 wager and then > pay .90 to the .90 to make a 1.80 payout. Okay the house pays 1.80 and that includes the 1 that was wagered. Now how > much should each losing wager be increased to make a total profit of the > beginning unit wager ? Well if the first wager is 1 and losses then the second wager must pay 1 + > 1 . So that's 2 / .8 or 2.50 for the amount of the second wager... Now the second wager of 2.50 also loses so the third wager must pay 1 + > 2.50 + 1. So that's 4.50 / .8 or 5.625 for the amount of the third > wager... Now the third wager loses so the fourth wager must pay 1 + 2.50 + 5.625 + > 1. So that's 10.125 / .8 or 12.656 for the amount of the fourth wager.... Then the fourth wager wins and that's a total profit of 1... > === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > In a coin tossing game consisting of a single player, a single fair > coin is tossed several times. After each toss, if the player can > correctly guess the outcome (H/T) of that toss then he wins and the > game ends. However, if after finite n tosses the player has missed all > of n tosses, he loses. Single player? multiple players ? Game ends has no meaning, as each toss is a seperate game and has no > relationship to the last toss/game. This game is simply the coin gambling with Martingale strategy > (doubling the bet every time if lose, so only a single win can recover > all the loses plus a reward equals to initial bet) with finite > resource (after finite tosses the resource ran out and the player > loses all). strategy is wrong, as you will loose at some point, there goes the money. A player's strategy can be represented by a string of H's and T's of > length n, e.g. HTHTTT for n = 6. And since each tosses are considered > independent, a strategy can be predetermined before the actual tosses > (?). wrong, each toss is independent, when you list it as HTHTTHTH you are > assuming that they are not independent. The question is : does the strategy HHH...H (or TTT...T) have more > probability of winning than any other specific arbitrary strategies, > says, HTHTTT for n= 6? What about strategies with equal H's and T's > (e.g. THTHTH...TH)? not in the real world. You are only classifying past subcases. > I have seen some arguments saying that HHH...H have high prob of > winning, since the outcome TTT...T (which make you lose) have lowest > prob of occuring-- Wrong. with big n, the chance of tosses being all T is low chance of tossing ANY specific pattern is low (according to common sense and some theory...). wrong. But then again, in my > tinkling opinion, since for a specific arbitrary strategy, there is > also only one string that can make you lose (i.e. the 'opposite' > string), and that string should also has the prob of 1/(2^n), thus the > winning prob of 1-1/(2^n) for any strategy. Therfore such argument is > absurd. And we are back to the 50-50 chance of winning regardless of > tosses order. Correct, it is absurd. As you can see, I have a very little knowledge in Probability and I > have poorly stated the problem. So please feel free to restate it if Google for it. I think you have missed the point of my question, either that or I didn't understand your reply. there's no exact or plausible explanation for this question. === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > In a coin tossing game consisting of a single player, a single fair > coin is tossed several times. After each toss, if the player can > correctly guess the outcome (H/T) of that toss then he wins and the > game ends. However, if after finite n tosses the player has missed all > of n tosses, he loses. > Single player? multiple players ? > Game ends has no meaning, as each toss is a seperate game and has no > relationship to the last toss/game. > This game is simply the coin gambling with Martingale strategy > (doubling the bet every time if lose, so only a single win can recover > all the loses plus a reward equals to initial bet) with finite > resource (after finite tosses the resource ran out and the player > loses all). > strategy is wrong, as you will loose at some point, there goes the money. > A player's strategy can be represented by a string of H's and T's of > length n, e.g. HTHTTT for n = 6. And since each tosses are considered > independent, a strategy can be predetermined before the actual tosses > (?). > wrong, each toss is independent, when you list it as HTHTTHTH you are > assuming that they are not independent. > The question is : does the strategy HHH...H (or TTT...T) have more > probability of winning than any other specific arbitrary strategies, > says, HTHTTT for n= 6? What about strategies with equal H's and T's > (e.g. THTHTH...TH)? > not in the real world. You are only classifying past subcases. > I have seen some arguments saying that HHH...H have high prob of > winning, since the outcome TTT...T (which make you lose) have lowest > prob of occuring-- > Wrong. > with big n, the chance of tosses being all T is low > chance of tossing ANY specific pattern is low > (according to common sense and some theory...). > wrong. > But then again, in my > tinkling opinion, since for a specific arbitrary strategy, there is > also only one string that can make you lose (i.e. the 'opposite' > string), and that string should also has the prob of 1/(2^n), thus the > winning prob of 1-1/(2^n) for any strategy. Therfore such argument is > absurd. And we are back to the 50-50 chance of winning regardless of > tosses order. > Correct, it is absurd. > As you can see, I have a very little knowledge in Probability and I > have poorly stated the problem. So please feel free to restate it if > Google for it. I think you have missed the point of my question, either that or I > didn't understand your reply. you do not understand, coin toss has no memory. there's no exact or plausible explanation for this question. Wrong again, Google coin toss and re-see what you did not see for the > first time. Yes I understand that coin toss has no memory. The point of the question is that how can I debate the 'HHH...H strategy, according to law of large number' with formal argument; 'coin toss has no memory' is not enough to convince my peers. === Subject: Re: Coin tossing guessing strategy... Chula Pittayapinun a .8ecrit : > In a coin tossing game consisting of a single player, a single fair > coin is tossed several times. After each toss, if the player can > correctly guess the outcome (H/T) of that toss then he wins and the > game ends. However, if after finite n tosses the player has missed all > of n tosses, he loses. > Single player? multiple players ? > Game ends has no meaning, as each toss is a seperate game and has no > relationship to the last toss/game. > This game is simply the coin gambling with Martingale strategy > (doubling the bet every time if lose, so only a single win can recover > all the loses plus a reward equals to initial bet) with finite > resource (after finite tosses the resource ran out and the player > loses all). > strategy is wrong, as you will loose at some point, there goes the money. > A player's strategy can be represented by a string of H's and T's of > length n, e.g. HTHTTT for n = 6. And since each tosses are considered > independent, a strategy can be predetermined before the actual tosses > (?). > wrong, each toss is independent, when you list it as HTHTTHTH you are > assuming that they are not independent. > The question is : does the strategy HHH...H (or TTT...T) have more > probability of winning than any other specific arbitrary strategies, > says, HTHTTT for n= 6? What about strategies with equal H's and T's > (e.g. THTHTH...TH)? > not in the real world. You are only classifying past subcases. > I have seen some arguments saying that HHH...H have high prob of > winning, since the outcome TTT...T (which make you lose) have lowest > prob of occuring-- > Wrong. > with big n, the chance of tosses being all T is low > chance of tossing ANY specific pattern is low > (according to common sense and some theory...). > wrong. > But then again, in my > tinkling opinion, since for a specific arbitrary strategy, there is > also only one string that can make you lose (i.e. the 'opposite' > string), and that string should also has the prob of 1/(2^n), thus the > winning prob of 1-1/(2^n) for any strategy. Therfore such argument is > absurd. And we are back to the 50-50 chance of winning regardless of > tosses order. > Correct, it is absurd. > As you can see, I have a very little knowledge in Probability and I > have poorly stated the problem. So please feel free to restate it if > Google for it. > I think you have missed the point of my question, either that or I > didn't understand your reply. > you do not understand, coin toss has no memory. > there's no exact or plausible explanation for this question. > Wrong again, Google coin toss and re-see what you did not see for the > first time. Yes I understand that coin toss has no memory. The point of the > question is that how can I debate the 'HHH...H strategy, according to > law of large number' with formal argument; 'coin toss has no memory' > is not enough to convince my peers. > How comes law of large numbers convince them? === Subject: Re: Coin tossing guessing strategy... >Yes I understand that coin toss has no memory. The point of the >question is that how can I debate the 'HHH...H strategy, according to >law of large number' with formal argument; 'coin toss has no memory' >is not enough to convince my peers. Disregard the law of large numbers. In this context, it's being used as a cover to obscure the obvious. Instead, reduce n -- all the way down to 2 (or even 1). Now see if anyone dares to make the same argument. If they do, make them give you odds (better than 1-1) favoring one sequence over another, and play the game for money. When forced to either give odds or shut up, they will suddenly come to their senses. quasi === Subject: Re: Coin tossing guessing strategy... posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > In a coin tossing game consisting of a single player, a single fair > coin is tossed several times. After each toss, if the player can > correctly guess the outcome (H/T) of that toss then he wins and the > game ends. However, if after finite n tosses the player has missed all > of n tosses, he loses. This game is simply the coin gambling with Martingale strategy > (doubling the bet every time if lose, so only a single win can recover > all the loses plus a reward equals to initial bet) with finite > resource (after finite tosses the resource ran out and the player > loses all). A player's strategy can be represented by a string of H's and T's of > length n, e.g. HTHTTT for n = 6. And since each tosses are considered > independent, a strategy can be predetermined before the actual tosses > (?). The question is : does the strategy HHH...H (or TTT...T) have more > probability of winning than any other specific arbitrary strategies, > says, HTHTTT for n= 6? What about strategies with equal H's and T's > (e.g. THTHTH...TH)? > I have seen some arguments saying that HHH...H have high prob of > winning, since the outcome TTT...T (which make you lose) have lowest > prob of occuring-- with big n, the chance of tosses being all T is low > (according to common sense and some theory...). ANY *particular* string, such as HTTHHHTHTHTT has the same probability of occurrence as any other string of the same length, such as HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It is true that strings of length 12 that have 5 heads and 7 tails are much more probable than all H or all T, but that is not what we are talking about here. You need a precise string in exactly one order, because according to your description of the game, you lose as soon as the element in the nth position (H or T) fails to match the actual result of the nth toss, if you have not already lost before the nth toss. Just guessing the right number of H's and T's is not good enough. R.G. Vickson > But then again, in my > tinkling opinion, since for a specific arbitrary strategy, there is > also only one string that can make you lose (i.e. the 'opposite' > string), and that string should also has the prob of 1/(2^n), thus the > winning prob of 1-1/(2^n) for any strategy. Therfore such argument is > absurd. And we are back to the 50-50 chance of winning regardless of > tosses order. As you can see, I have a very little knowledge in Probability and I > have poorly stated the problem. So please feel free to restate it if === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080311 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) ANY *particular* string, such as HTTHHHTHTHTT has the same probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. R.G. Vickson That is what I also thought. But could you please elaborate on 'that is not what we are talking about here'? I need a precise formal argument, if possible, to explain to my friends. (One of them has invoked the argument of random walk- that HHH...H has lower prob of occurance than HTTHHHTHTT.) === Subject: Re: Coin tossing guessing strategy... > ANY *particular* string, such as HTTHHHTHTHTT has the same probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) Coins have no memory. Moreover, a coin is blind. How would a coin even know whether it came up H or T? The simplest way to defeat these fools who think a fair coin is biased with respect to sequences of n flips, is to note that if some sequence of say 10 flips was more likely than some other sequence of 10 flips, then a similar bias (possibly a little less) should hold for 9 flips, right? In other words, it's not reasonable to claim the bias happens only for n > 9. Once you convince your challenger that n = 9 would also show a bias, then ask what about n = 8? When you reach n = 2, get out some coins and experiment. Does your challenger really believe any of the 4 sequences HH, HT, TH, TT is more likely than any other? quasi === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > ANY *particular* string, such as HTTHHHTHTHTT has the same probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) Coins have no memory. Moreover, a coin is blind. How would a coin even know whether it came up H or T? The simplest way to defeat these fools who think a fair coin is biased > with respect to sequences of n flips, is to note that if some sequence > of say 10 flips was more likely than some other sequence of 10 flips, > then a similar bias (possibly a little less) should hold for 9 flips, > right? In other words, it's not reasonable to claim the bias happens > only for n > 9. Once you convince your challenger that n = 9 would > also show a bias, then ask what about n = 8? When you reach n = 2, get > out some coins and experiment. Does your challenger really believe any > of the 4 sequences HH, HT, TH, TT is more likely than any other? quasi There's something dependent on the order of n in the argument of one- dimensional random walk (please refer to wiki page of the topic 'random walk'), although I'm not sure how that argument is related to this problem. Furthermore: 'for any random walk in one dimension, every point in the domain will almost surely be crossed an infinite number of times.' Does this mean that the longer the string (as n approach /infty), it is more likely that the number of H's will equal T's? If not, then why is it not applicable in this problem setting? === Subject: Re: Coin tossing guessing strategy... > ANY *particular* string, such as HTTHHHTHTHTT has the same probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. >That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) > Coins have no memory. > Moreover, a coin is blind. > How would a coin even know whether it came up H or T? > The simplest way to defeat these fools who think a fair coin is biased > with respect to sequences of n flips, is to note that if some sequence > of say 10 flips was more likely than some other sequence of 10 flips, > then a similar bias (possibly a little less) should hold for 9 flips, > right? In other words, it's not reasonable to claim the bias happens > only for n > 9. Once you convince your challenger that n = 9 would > also show a bias, then ask what about n = 8? When you reach n = 2, get > out some coins and experiment. Does your challenger really believe any > of the 4 sequences HH, HT, TH, TT is more likely than any other? There's something dependent on the order of n in the argument of one- >dimensional random walk (please refer to wiki page of the topic >'random walk'), although I'm not sure how that argument is related to >this problem. Furthermore: 'for any random walk in one dimension, >every point in the domain will almost surely be crossed an infinite >number of times.' Does this mean that the longer the string (as n >approach /infty), it is more likely that the number of H's will equal >T's? If not, then why is it not applicable in this problem setting? Read my prior explanation. For 2 coins, do you think there a bias, even a slight bias with respect to the 4 possible sequences HH, HT, TH, TT? If not, then why would you think a bias suddenly develops for a longer sequence, say a 10 coin sequence? In fact, assuming a fair coin, all 10 coin sequences are equally likely. Don't confuse the equiprobability of n coin sequences with the probability distribution for the _difference_ between the number of heads and tails. Thus, for an n-term sequence, it's much more likely that the difference is 0 than n, but that has nothing to do with the game in question. You don't care about the totals. Effectively, you are asking if one particular n coin sequence is more likely than another. The answer is no. quasi === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) ANY *particular* string, such as HTTHHHTHTHTT has the same probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. >That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) > Coins have no memory. > Moreover, a coin is blind. > How would a coin even know whether it came up H or T? > The simplest way to defeat these fools who think a fair coin is biased > with respect to sequences of n flips, is to note that if some sequence > of say 10 flips was more likely than some other sequence of 10 flips, > then a similar bias (possibly a little less) should hold for 9 flips, > right? In other words, it's not reasonable to claim the bias happens > only for n > 9. Once you convince your challenger that n = 9 would > also show a bias, then ask what about n = 8? When you reach n = 2, get > out some coins and experiment. Does your challenger really believe any > of the 4 sequences HH, HT, TH, TT is more likely than any other? There's something dependent on the order of n in the argument of one- >dimensional random walk (please refer to wiki page of the topic >'random walk'), although I'm not sure how that argument is related to >this problem. Furthermore: 'for any random walk in one dimension, >every point in the domain will almost surely be crossed an infinite >number of times.' Does this mean that the longer the string (as n >approach /infty), it is more likely that the number of H's will equal >T's? If not, then why is it not applicable in this problem setting? Read my prior explanation. For 2 coins, do you think there a bias, even a slight bias with > respect to the 4 possible sequences HH, HT, TH, TT? If not, then why would you think a bias suddenly develops for a longer > sequence, say a 10 coin sequence? In fact, assuming a fair coin, all 10 coin sequences are equally > likely. Don't confuse the equiprobability of n coin sequences with the > probability distribution for the _difference_ between the number of > heads and tails. Thus, for an n-term sequence, it's much more likely > that the difference is 0 than n, but that has nothing to do with the > game in question. You don't care about the totals. Effectively, you > are asking if one particular n coin sequence is more likely than > another. The answer is no. quasi Hahaha what a way to settle an argument. That's exactly what I am saying to them: each *particular* sequence has equal probability of occurrence i.e. 1/(2^n). In fact, saying 1/ (2^n) is absurd since the past tosses are done and really don't count. fallacy': Now suppose that we have just tossed four heads in a row. A believer in the gambler's fallacy might say, If the next coin flipped were to come up heads, it would generate a run of five successive heads. The probability of a run of five successive heads is (1 / 2)5 = 1 / 32; therefore, the next coin flipped only has a 1 in 32 chance of coming up heads. This is the fallacious step in the argument. If the coin is fair, then by definition the probability of tails must always be 0.5, never more or less, and the probability of heads must always be 0.5, never less (or more). While a run of five heads is only 1 in 32 (0.03125), it is 1 in 32 before the coin is first tossed. After the first four tosses the results are no longer unknown, so they do not count. The probability of five consecutive heads is the same as that of four successive heads followed by one tails. Tails isn't more likely. In fact, the calculation of the 1 in 32 probability relied on the assumption that heads and tails are equally likely at every step. Each of the two possible outcomes has equal probability no matter how many times the coin has been flipped previously and no matter what the result. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses is the fallacy. However, the above paragraph ends with the following 2 sentences: The fallacy is the idea that a run of luck in the past somehow influences the odds of a bet in the future. This kind of logic would only work if we had to guess all the tosses' results before they are carried out. The last sentence is how the law of large numbers (or random walk concept) comes into play. They (my freinds) say, with big n, HHH...H is much less likely to occur than other *specific* strings with equal number of H's and T's. Which is quite sound, so now I guess the problem is at if we had to guess all the tosses' results before they are carried out.. So maybe the first question to ask is: is guessing the entire string of H's and T's before the tosses the same as guessing the tosses one by one after each toss? That's why I said my problem might be ill-defined :( === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) ANY *particular* string, such as HTTHHHTHTHTT has the same probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. >That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) > Coins have no memory. > Moreover, a coin is blind. > How would a coin even know whether it came up H or T? > The simplest way to defeat these fools who think a fair coin is biased > with respect to sequences of n flips, is to note that if some sequence > of say 10 flips was more likely than some other sequence of 10 flips, > then a similar bias (possibly a little less) should hold for 9 flips, > right? In other words, it's not reasonable to claim the bias happens > only for n > 9. Once you convince your challenger that n = 9 would > also show a bias, then ask what about n = 8? When you reach n = 2, get > out some coins and experiment. Does your challenger really believe any > of the 4 sequences HH, HT, TH, TT is more likely than any other? There's something dependent on the order of n in the argument of one- >dimensional random walk (please refer to wiki page of the topic >'random walk'), although I'm not sure how that argument is related to >this problem. Furthermore: 'for any random walk in one dimension, >every point in the domain will almost surely be crossed an infinite >number of times.' Does this mean that the longer the string (as n >approach /infty), it is more likely that the number of H's will equal >T's? If not, then why is it not applicable in this problem setting? Read my prior explanation. For 2 coins, do you think there a bias, even a slight bias with > respect to the 4 possible sequences HH, HT, TH, TT? If not, then why would you think a bias suddenly develops for a longer > sequence, say a 10 coin sequence? In fact, assuming a fair coin, all 10 coin sequences are equally > likely. Don't confuse the equiprobability of n coin sequences with the > probability distribution for the _difference_ between the number of > heads and tails. Thus, for an n-term sequence, it's much more likely > that the difference is 0 than n, but that has nothing to do with the > game in question. You don't care about the totals. Effectively, you > are asking if one particular n coin sequence is more likely than > another. The answer is no. quasi Hahaha what a way to settle an argument. That's exactly what I am saying to them: each *particular* sequence has equal probability of occurrence i.e. 1/(2^n). In fact, saying 1/ (2^n) is absurd since the past tosses are done and really don't count. fallacy': Now suppose that we have just tossed four heads in a row. A believer in the gambler's fallacy might say, If the next coin flipped were to come up heads, it would generate a run of five successive heads. The probability of a run of five successive heads is (1 / 2)5 = 1 / 32; therefore, the next coin flipped only has a 1 in 32 chance of coming up heads. This is the fallacious step in the argument. If the coin is fair, then by definition the probability of tails must always be 0.5, never more or less, and the probability of heads must always be 0.5, never less (or more). While a run of five heads is only 1 in 32 (0.03125), it is 1 in 32 before the coin is first tossed. After the first four tosses the results are no longer unknown, so they do not count. The probability of five consecutive heads is the same as that of four successive heads followed by one tails. Tails isn't more likely. In fact, the calculation of the 1 in 32 probability relied on the assumption that heads and tails are equally likely at every step. Each of the two possible outcomes has equal probability no matter how many times the coin has been flipped previously and no matter what the result. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses is the fallacy. However, the above paragraph ends with the following 2 sentences: The fallacy is the idea that a run of luck in the past somehow influences the odds of a bet in the future. This kind of logic would only work if we had to guess all the tosses' results before they are carried out. The last sentence is how the law of large numbers (or random walk concept) comes into play. They (my freinds) say, with big n, HHH...H is much less likely to occur than other *specific* strings with equal number of H's and T's. Which is quite sound, so now I guess the problem is at if we had to guess all the tosses' results before they are carried out.. So maybe the first question to ask is: is guessing the entire string of H's and T's before the tosses the same as guessing the tosses one by one after each toss? That's why I said my problem might be ill-defined :( === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > ANY *particular* string, such as HTTHHHTHTHTT has the same > probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). > It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon > as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) Coins have no memory. Moreover, acoinis blind. How would acoineven know whether it came up H or T? The simplest way to defeat these fools who think a faircoinis biased > with respect to sequences of n flips, is to note that if some sequence > of say 10 flips was more likely than some other sequence of 10 flips, > then a similar bias (possibly a little less) should hold for 9 flips, > right? In other words, it's not reasonable to claim the bias happens > only for n > 9. Once you convince your challenger that n = 9 would > also show a bias, then ask what about n = 8? When you reach n = 2, get > out some coins and experiment. Does your challenger really believe any > of the 4 sequences HH, HT, TH, TT is more likely than any other? >There's something dependent on the order of n in the argument of one- >dimensional random walk (please refer to wiki page of the topic >'random walk'), although I'm not sure how that argument is related to >this problem. Furthermore: 'for any random walk in one dimension, >every point in the domain will almost surely be crossed an infinite >number of times.' Does this mean that the longer the string (as n >approach /infty), it is more likely that the number of H's will equal >T's? If not, then why is it not applicable in this problem setting? > Read my prior explanation. > For 2 coins, do you think there a bias, even a slight bias with > respect to the 4 possible sequences HH, HT, TH, TT? > If not, then why would you think a bias suddenly develops for a longer > sequence, say a 10coinsequence? > In fact, assuming a faircoin, all 10coinsequences are equally > likely. > Don't confuse the equiprobability of ncoinsequences with the > probability distribution for the _difference_ between the number of > heads and tails. Thus, for an n-term sequence, it's much more likely > that the difference is 0 than n, but that has nothing to do with the > game in question. You don't care about the totals. Effectively, you > are asking if one particular ncoinsequence is more likely than > another. The answer is no. > quasi Hahaha what a way to settle an argument. That's exactly what I am saying to them: each *particular* sequence > has equal probability of occurrence i.e. 1/(2^n). In fact, saying 1/ > (2^n) is absurd since the past tosses are done and really don't > count. fallacy': Now suppose that we have just tossed four heads in a row. A believer > in the gambler's fallacy might say, If the nextcoinflipped were to > come up heads, it would generate a run of five successive heads. The > probability of a run of five successive heads is (1 / 2)5 = 1 / 32; > therefore, the nextcoinflipped only has a 1 in 32 chance of coming > up heads. This is the fallacious step in the argument. If thecoinis fair, then > by definition the probability of tails must always be 0.5, never more > or less, and the probability of heads must always be 0.5, never less > (or more). While a run of five heads is only 1 in 32 (0.03125), it is > 1 in 32 before thecoinis first tossed. After the first four tosses > the results are no longer unknown, so they do not count. The > probability of five consecutive heads is the same as that of four > successive heads followed by one tails. Tails isn't more likely. In > fact, the calculation of the 1 in 32 probability relied on the > assumption that heads and tails are equally likely at every step. Each > of the two possible outcomes has equal probability no matter how many > times thecoinhas been flipped previously and no matter what the > result. Reasoning that it is more likely that the next toss will be a > tail than a head due to the past tosses is the fallacy. However, the above paragraph ends with the following 2 sentences: The fallacy is the idea that a run of luck in the past somehow > influences the odds of a bet in the future. This kind of logic would > only work if we had to guess all the tosses' results before they are > carried out. The last sentence is how the law of large numbers (or random walk > concept) comes into play. They (my freinds) say, with big n, HHH...H > is much less likely to occur than other *specific* strings with equal > number of H's and T's. Wrong. The Weak Law of Large Numbers does not apply. Which is quite sound, so now I guess the problem is at if we had to > guess all the tosses' results before they are carried out.. So maybe > the first question to ask is: is guessing the entire string of H's and > T's before the tosses the same as guessing the tosses one by one after > each toss? Why guess at all ?? Will guessing change the outcome of acointoss ? I > think not. That's why I said my problem might be ill-defined :( your problem is trivial. > If you cannot see this, do not gamble, for sure you would loose it all.> CoinToss has no memory. <<< Got it ? As I understand, LLN states that as n->/infty, the sample average converges to the expected values. In this case of coin tossing, that means with big n, HH...H is less likely to occur than a *specific* (not a set of) string of equal H's and N's, no? So if would be nice if you could explain why this argument is not applicable in this case. And wiki has also stated some thing interesting that leads me to question the setting of the problem, please reread my post with quotes from wiki. By the way, I believe that the chance is always 50-50 and every string is equal in probability of occurrence. So no point getting so aggressive on me; I just want a really good precise explanation. Because when I want to debate about something to someone, I usually also try to disprove his/her point, not only asserting my point. === Subject: Re: Coin tossing guessing strategy... posting-account=ckiBKQoAAABokPwiT98pu93MHepmMwWr Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > ANY *particular* string, such as HTTHHHTHTHTT has the same > probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). > It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon > as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) Coins have no memory. Moreover, acoinis blind. How would acoineven know whether it came up H or T? The simplest way to defeat these fools who think a faircoinis biased > with respect to sequences of n flips, is to note that if some sequence > of say 10 flips was more likely than some other sequence of 10 flips, > then a similar bias (possibly a little less) should hold for 9 flips, > right? In other words, it's not reasonable to claim the bias happens > only for n > 9. Once you convince your challenger that n = 9 would > also show a bias, then ask what about n = 8? When you reach n = 2, get > out some coins and experiment. Does your challenger really believe any > of the 4 sequences HH, HT, TH, TT is more likely than any other? >There's something dependent on the order of n in the argument of one- >dimensional random walk (please refer to wiki page of the topic >'random walk'), although I'm not sure how that argument is related to >this problem. Furthermore: 'for any random walk in one dimension, >every point in the domain will almost surely be crossed an infinite >number of times.' Does this mean that the longer the string (as n >approach /infty), it is more likely that the number of H's will equal >T's? If not, then why is it not applicable in this problem setting? > Read my prior explanation. > For 2 coins, do you think there a bias, even a slight bias with > respect to the 4 possible sequences HH, HT, TH, TT? > If not, then why would you think a bias suddenly develops for a longer > sequence, say a 10coinsequence? > In fact, assuming a faircoin, all 10coinsequences are equally > likely. > Don't confuse the equiprobability of ncoinsequences with the > probability distribution for the _difference_ between the number of > heads and tails. Thus, for an n-term sequence, it's much more likely > that the difference is 0 than n, but that has nothing to do with the > game in question. You don't care about the totals. Effectively, you > are asking if one particular ncoinsequence is more likely than > another. The answer is no. > quasi Hahaha what a way to settle an argument. That's exactly what I am saying to them: each *particular* sequence > has equal probability of occurrence i.e. 1/(2^n). In fact, saying 1/ > (2^n) is absurd since the past tosses are done and really don't > count. fallacy': Now suppose that we have just tossed four heads in a row. A believer > in the gambler's fallacy might say, If the nextcoinflipped were to > come up heads, it would generate a run of five successive heads. The > probability of a run of five successive heads is (1 / 2)5 = 1 / 32; > therefore, the nextcoinflipped only has a 1 in 32 chance of coming > up heads. This is the fallacious step in the argument. If thecoinis fair, then > by definition the probability of tails must always be 0.5, never more > or less, and the probability of heads must always be 0.5, never less > (or more). While a run of five heads is only 1 in 32 (0.03125), it is > 1 in 32 before thecoinis first tossed. After the first four tosses > the results are no longer unknown, so they do not count. The > probability of five consecutive heads is the same as that of four > successive heads followed by one tails. Tails isn't more likely. In > fact, the calculation of the 1 in 32 probability relied on the > assumption that heads and tails are equally likely at every step. Each > of the two possible outcomes has equal probability no matter how many > times thecoinhas been flipped previously and no matter what the > result. Reasoning that it is more likely that the next toss will be a > tail than a head due to the past tosses is the fallacy. However, the above paragraph ends with the following 2 sentences: The fallacy is the idea that a run of luck in the past somehow > influences the odds of a bet in the future. This kind of logic would > only work if we had to guess all the tosses' results before they are > carried out. The last sentence is how the law of large numbers (or random walk > concept) comes into play. They (my freinds) say, with big n, HHH...H > is much less likely to occur than other *specific* strings with equal > number of H's and T's. Wrong. The Weak Law of Large Numbers does not apply. Which is quite sound, so now I guess the problem is at if we had to > guess all the tosses' results before they are carried out.. So maybe > the first question to ask is: is guessing the entire string of H's and > T's before the tosses the same as guessing the tosses one by one after > each toss? Why guess at all ?? Will guessing change the outcome of acointoss ? I > think not. That's why I said my problem might be ill-defined :( your problem is trivial. > If you cannot see this, do not gamble, for sure you would loose it all.> CoinToss has no memory. <<< Got it ? As I understand, LLN states that as n->/infty, the sample average converges to the expected values. In this case of coin tossing, that means with big n, HH...H is less likely to occur than a *specific* (not a set of) string of equal H's and N's, no? So if would be nice if you could explain why this argument is not applicable in this case. And wiki has also stated some thing interesting that leads me to question the setting of the problem, please reread my post with quotes from wiki. By the way, I believe that the chance is always 50-50 and every string is equal in probability of occurrence. So no point getting so aggressive on me; I just want a really good precise explanation. Because when I want to debate about something to someone, I usually also try to disprove his/her point, not only asserting my point. === Subject: Re: Coin tossing guessing strategy... >As I understand, LLN states that as n->/infty, the sample average >converges to the expected values. In this case of coin tossing, that >means with big n, HH...H is less likely to occur than a *specific* >(not a set of) string of equal H's and N's, no? No. >So if would be nice if you could explain why this argument is not >applicable in this case. To say that the ratio of heads to n approaches 1/2 does not imply that any particular sequence of n flips is more likely than any other such sequence. Let's consider 4 flips. Thus, 2^4 possible sequences. By symmetry, the 16 sequences are all equally likely. Now let's consider the number of heads out of 4 flips, expressed as a ratio. What are the possibilities? Each of the 16 sequences has an associated ratio, but the some ratios have more sequences than others. ratio # of sequences probability for that ratio of that ratio ------ -------------- -------------- 0/4 1 1/16 1/4 4 4/16 2/4 6 6/16 3/4 4 4/16 4/4 1 1/16 What you see is that the ratio 2/4 (2 heads, 2 tails) is 6 times more likely than the ratio 4/4 (4 heads, 0 tails), but that's only because there are 6 different sequences which yield 2 heads, 2 tails, and only one sequence that yields 4 heads. Thus, the sequences are equally likely, the ratios are not. But your game doesn't depend on ratios -- it depends on sequences. If you choose a sequence, it loses only if the complementary sequence of n flips happens. But those complementary sequences are all equally likely -- ratios have nothing to do with it. That's the argument in a nutshell -- that they are blurring _sequences_, which are equally likely, with _ratios_, which are not. But I want to mention that you keep on ignoring my reduce n argument which I think can convince your challengers more easily. If someone claims that a sequence bias works only for large n, ask them which n would be the _least_ for which there is a bias. Thus, if hypothetically, n = 10 is the least, then what about n = 9? Is it reasonable to believe that every sequence of 9 flips is equally likely, but for 10 flips, suddenly there is a bias? So maybe there actually is a bias for n = 9 as well. Then what about n = 8? Once you get down to n = 2, just experiment physically. Better still, get down to n = 1, and everyone will instantly realize that with only 1 flip, the two possible 1 flip sequences _must_ be equally likely for the simple reason that the coin itself is unbiased. quasi === Subject: Re: Coin tossing guessing strategy... ANY *particular* string, such as HTTHHHTHTHTT has the same probability > of occurrence as any other string of the same length, such as > HHHHHHHHHHHH or TTTTTTTTTTTT (strings of length 12 in this case). It > is true that strings of length 12 that have 5 heads and 7 tails are > much more probable than all H or all T, but that is not what we are > talking about here. You need a precise string in exactly one order, > because according to your description of the game, you lose as soon as > the element in the nth position (H or T) fails to match the actual > result of the nth toss, if you have not already lost before the nth > toss. Just guessing the right number of H's and T's is not good > enough. That is what I also thought. But could you please elaborate on 'that >is not what we are talking about here'? I need a precise formal >argument, if possible, to explain to my friends. (One of them has >invoked the argument of random walk- that HHH...H has lower prob of >occurance than HTTHHHTHTT.) Coins have no memory. Moreover, a coin is blind. How would a coin even know whether it came up H or T? The simplest way to defeat these fools who think a fair coin is biased > with respect to sequences of n flips, is to note that if some sequence > of say 10 flips was more likely than some other sequence of 10 flips, > then a similar bias (possibly a little less) should hold for 9 flips, > right? In other words, it's not reasonable to claim the bias happens > only for n > 9. Once you convince your challenger that n = 9 would > also show a bias, then ask what about n = 8? When you reach n = 2, get > out some coins and experiment. Does your challenger really believe any > of the 4 sequences HH, HT, TH, TT is more likely than any other? >There's something dependent on the order of n in the argument of one- >dimensional random walk (please refer to wiki page of the topic >'random walk'), although I'm not sure how that argument is related to >this problem. Furthermore: 'for any random walk in one dimension, >every point in the domain will almost surely be crossed an infinite >number of times.' Does this mean that the longer the string (as n >approach /infty), it is more likely that the number of H's will equal >T's? If not, then why is it not applicable in this problem setting? Read my prior explanation. For 2 coins, do you think there a bias, even a slight bias with >respect to the 4 possible sequences HH, HT, TH, TT? If not, then why would you think a bias suddenly develops for a longer >sequence, say a 10 coin sequence? In fact, assuming a fair coin, all 10 coin sequences are equally >likely. Don't confuse the equiprobability of n coin sequences with the >probability distribution for the _difference_ between the number of >heads and tails. Thus, for an n-term sequence, it's much more likely >that the difference is 0 than n, Correction: Of course, if n is odd, the difference can't be exactly zero. In general the possible differences range from -n to n by 2. A corrected statement is this ... For an n-term sequence: If n is even, then it's much more likely that the difference is 0 than n. If n is odd, and n > 1, then it's much more likely that the difference is 1 than n. >game in question. You don't care about the totals. Effectively, you >are asking if one particular n coin sequence is more likely than >another. The answer is no. quasi === Subject: [ann] Math Accessibility and Design Science News blogs posting-account=xSy3TQoAAACNeqANdohQIOXP-c6kHvlF Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) We are happy to announce the launch of two new blogs from Design Science: Making Math Accessible: Reports the latest news of our efforts to make math understandable to students and others with special needs and disabilities, including assistive technology support, math braille, math textbook accessibility standards, and accessible instructional software. Design Science News: Contains up-to-date information about Design Science products, MathType, MathFlow, and MathPlayer, product tips and tricks, tech support issues, and other company news and events. You can find out more about our blogs and subscribe to them via email or RSS feeds here: http://www.dessci.com/en/reference/blogs.htm Both blogs accept comments, so this is a chance for you to let us know what you think about our blog postings and about our products in general. Lary Stucker eMarketing Manager www.dessci.com === Subject: Re: Polygons of large area > On Apr 20, 11:19 pm, The World Wide Wade , > I'm looking for an explanation suitable for > a 14 year old gifted mathematics student as > to why the maximum area of an n-sided polygon of a fixed perimeter P is obtained when the polygon is regular. So we've shown that any two > consecutive edges of this n-gon have the same length. Therefore all > edges of the n-gon have equal length, which means the n-gon is regular. The WWW gives a good argument that the polygon is equilateral, but it > remains to show that the equilateral n-gon of maximal area is regular. Yes, of course you're right. > thread): A sci.math thread I read recently gave (essentially) this elegant > proof of the fact that the maximal area of any polygon with prescribed > side lengths is cyclic: If the side lengths determine a polygon at all, they determine a > cyclic one. Now affix each segment of the circumscribed circle to the > sides, and consider the total area of the polygon plus the affixed > segments as you vary the angles between edges. The configuration of > maximal area is the circle, because the circle has maximal area of any > shape with this fixed perimeter. Because the sum of the segment areas > is fixed, it follows that the polygon must also attain maximal area in > this configuration. Equilateral + cyclic => regular, so we're done. === Subject: Re: Polygons of large area > ... why the maximum area of an n-sided polygon > is obtained when the polygon is regular. I'm guessing you mean for constant perimeter. Indeed - sorry. > ... any polygon of maximum area must be convex. > ... must have equal side lengths. > ... if there is a polygon of largest area, all > the angles must be equal. Exactly. I've got that far, and so has he. This implies that if there is a maximal n-gon then it must be the regular n-gon. We've also shown that the area of the regular n-gon is P^2*cot(pi/n)/n where P is the perimeter. > ... the hardest part would be proving that > there is definitely a polygon of greatest > area. And that's where we're stuck. I guess we can hand-wave and show that the area is bounded above, so the areas of all the n-gons with given perimeter form a set of reals, and that set is bounded above. I guess we can hand-wave (remember, he's 14) and show that there's a least upper bound. If we could show that the LUB is L^2cot(pi/n)/n then we're done. I suspect that's too much to ask. If we can show the limit point exists then we're done - that might be easier. Research via Google suggests that a purely geometrical elementary argument might be an open question. Further suggestions are welcome. === Subject: Re: Polygons of large area > I guess we can hand-wave and show that the area is bounded above Showing that it's bounded above isn't that difficult: you've already showed that for any polygon, there is a convex polygon with larger area, and the area of a convex polygon is just the sum of areas of triangles. That sum is bounded by 1/2*max(height)*sum(bases), the sum of bases is the perimeter, and max(height) is no more than half the perimeter. So for perimeter P, the area is bounded by P^2/4. > If we could show that the LUB is L^2 cot(pi/n)/n then we're done. > I suspect that's too much to ask. I suspect so too. The most elementary proof I can think of that the area actually has a *maximum* (not just a LUB) involves at least some real analysis. - Tim === Subject: Re: Polygons of large area <3965618.1208790039569.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) On Apr 22, 1:55 am, Tim Little I guess we can hand-wave and show that the area is bounded above Showing that it's bounded above isn't that difficult: you've already > showed that for any polygon, there is a convex polygon with larger > area, and the area of a convex polygon is just the sum of areas of > triangles. That sum is bounded by 1/2*max(height)*sum(bases), the sum > of bases is the perimeter, and max(height) is no more than half the > perimeter. So for perimeter P, the area is bounded by P^2/4. Slightly lazier: If the perimeter is P and one of the vertices is at the origin, then the whole polygon is contained in the centered disc of radius P. Therefore the area of the disc bounds the area of the polygon. -- m === Subject: Re: Polygons of large area >On Apr 22, 1:55 am, Tim Little I guess we can hand-wave and show that the area is bounded above > Showing that it's bounded above isn't that difficult: you've already > showed that for any polygon, there is a convex polygon with larger > area, and the area of a convex polygon is just the sum of areas of > triangles. That sum is bounded by 1/2*max(height)*sum(bases), the sum > of bases is the perimeter, and max(height) is no more than half the > perimeter. So for perimeter P, the area is bounded by P^2/4. Slightly lazier: If the perimeter is P and one of the vertices is at >the origin, then the whole polygon is contained in >the centered disc of radius P. Therefore the area >of the disc bounds the area of the polygon. If using the compactness argument, it's convenient (and equally lazy) to take the square [-P/2, P/2] x [-P/2, P/2], of area P^2. Or, to be REALLY lazy, [-P, P] x [-P, P], of area 4P^2 - but I think that's going too far! -- Angus Rodgers Contains mild peril === Subject: Re: Polygons of large area > ... we can ... show that the area is > bounded above Showing that it's bounded above isn't > that difficult ... for perimeter P, the > area is bounded by P^2/4. Agreed - I got your result (or something very similar) shortly after I posted. So what we have is a collection of reals, bounded above, such that for each real there is a larger real in the collection. It's not hard to show then that there's a LUB. I have no doubt that the teacher who set this problem thinks that this is enough. But we all know that there are cases where the LUB is *not* in the set. I have an example that shows the assumption is flawed, but now I'd really like to close the case. > The most elementary proof I can think of that > the area actually has a *maximum* (not just a > LUB) involves at least some real analysis. I'd appreciate a strong hint. Analysis wasn't my field, but I'm willing to do my homework if I'm pointed in the right direction. For example, we could show that the set of areas is compact, which then means it's closed and bounded. I'm not sure how to show it's compact. Perhaps we could simply show it's closed. That's tricky too. Just not sure which direction to go. === Subject: Re: Polygons of large area <24158786.1208856377543.JavaMail.jakarta@nitrogen.mathforum.org>, > ... we can ... show that the area is > bounded above Showing that it's bounded above isn't > that difficult ... for perimeter P, the > area is bounded by P^2/4. Agreed - I got your result (or something very > similar) shortly after I posted. So what we have is a collection of reals, bounded > above, such that for each real there is a larger > real in the collection. It's not hard to show > then that there's a LUB. I have no doubt that the teacher who set this > problem thinks that this is enough. But we all > know that there are cases where the LUB is *not* > in the set. I have an example that shows the > assumption is flawed, but now I'd really like to > close the case. The most elementary proof I can think of that > the area actually has a *maximum* (not just a > LUB) involves at least some real analysis. I'd appreciate a strong hint. Analysis wasn't > my field, but I'm willing to do my homework if > I'm pointed in the right direction. For example, we could show that the set of areas > is compact, which then means it's closed and > bounded. I'm not sure how to show it's compact. > Perhaps we could simply show it's closed. That's > tricky too. Just not sure which direction to go. > Outline of way to do this: For notational convenience assume we are looking at (n+1)-gons. There is no loss of generality in assuming 0 is one of the vertices. Let K = {(v1, v2, ..., vn) : each vj is in R^2 and |v1| + |v2 - v1| + ... + |v_n - v_(n-1)| + |v_n| = P}. K can be regarded as a subset of R^(2n); it is easily seen to be closed and bounded there, ie, compact. Now define a function A on K by A(v1, v2, ..., vn) = area of the convex set determined by {v1, v2, ..., vn} (this convex set is usually called the convex hull of {v1, v2, ..., vn}). Now A is continuous on K : If you move each vertex by a little, the area will change by a little. A real-valued continuous function on a compact set always attains a maximum, and we're done. === Subject: Re: Polygons of large area > ... we can ... show that the area is > bounded above > Showing that it's bounded above isn't > that difficult ... for perimeter P, the > area is bounded by P^2/4. Agreed - I got your result (or something very >similar) shortly after I posted. So what we have is a collection of reals, bounded >above, such that for each real there is a larger >real in the collection. It's not hard to show >then that there's a LUB. I have no doubt that the teacher who set this >problem thinks that this is enough. But we all >know that there are cases where the LUB is *not* >in the set. I have an example that shows the >assumption is flawed, but now I'd really like to >close the case. > The most elementary proof I can think of that > the area actually has a *maximum* (not just a > LUB) involves at least some real analysis. I'd appreciate a strong hint. Analysis wasn't >my field, but I'm willing to do my homework if >I'm pointed in the right direction. For example, we could show that the set of areas >is compact, which then means it's closed and >bounded. I'm not sure how to show it's compact. >Perhaps we could simply show it's closed. That's >tricky too. Just not sure which direction to go. > Well, the argument that I assumed that people has in mind was something like this: take the origin as one of the vertices, and show that the area is a polynomial (and therefore continuous) function of the Cartesian coordinates of the remaining vertices,* which are subject to a polynomial equality constraint determining a closed subset of the closed and bounded set [-L/2, L/2]^{2n-2}; then use the Heine-Borel theorem to show that the maximum value of the area (which has already been shown to be bounded above) is attained, by some polygon (which must be regular, by the arguments already given). But it would be nice to avoid this, because it's probably above the level of the 14-year-old in question unless (s)he is /very/ advanced! On the other hand, the completeness axiom and some basic real analysis should not be out of reach, so it would be nice to make the proof depend only on these. *(The above sketch proof isn't quite adequate: one needs to take the lengths of the sides, and not only the coordinates of the vertices, as parameters. Perhaps using polar coordinates for the sides considered as vectors would be neatest? I haven't thought about it in detail, and I'm not awake enough to think about it now, without making more silly mistakes! And anyway, I'd rather not have to prove it this way at all.) -- Angus Rodgers Contains mild peril === Subject: Re: Polygons of large area OK, so: We can show that for any non-convex n-gon there is a convex n-gon of the same perimeter but greater area. We can show that for any convex n-gon with at least two sides not equal there is an n-gon of the same perimeter but greater area. We can show that for any convex n-gon with at least two angles not equal there is an n-gon of the same perimeter but greater area. We can show that the area is bounded above. We can possibly invoke some idea of continuity to suggest that the modifications we're making are smooth, continuous, and somehow get closer to a regular n-gon. After all, apart from the convexity argument, which I think we can ignore, the other modifications don't just give another n-gon, they give a continuous collection of n-gons, all of which are of greater area, up to and then reaching a maximum. If we can invoke a measure of the difference between the regular n-gon and the n-gons we're using, and show that the difference can be made arbitrarily small, each time making the area larger in a continuous fashion, is that not enough? For example, let M be the sum of the squares of the differences of the edge lengths from the average, plus the sum of squares of the differences of the angles from the average. This quantity can be made to vary smoothly as we get larger and larger area n-gons, and we can make it as small as possible. Isn't that enough? === Subject: Re: Polygons of large area >After all, apart from the convexity argument, which >I think we can ignore, the other modifications don't >just give another n-gon, they give a continuous >collection of n-gons, all of which are of greater >area, up to and then reaching a maximum. I'm not sure what you mean by continuous collection of n-gons. >If we can >invoke a measure of the difference between the regular >n-gon and the n-gons we're using, and show that the >difference can be made arbitrarily small, each time >making the area larger in a continuous fashion, is >that not enough? For example, let M be the sum of the squares of the >differences of the edge lengths from the average, >plus the sum of squares of the differences of the >angles from the average. This quantity can be made >to vary smoothly as we get larger and larger area >n-gons, and we can make it as small as possible. Isn't that enough? I was hoping for something along these lines, and I'm fairly sure the argument for reducing the variance of the sides to near zero is OK, but it needs to be written out and checked, assuming there is any value in this line of argument at all - but I'm not sure there is, and the cyclic quadrilateral argument involved changing a sequence of 4 angles at once (leaving their sum constant), so it might not be possible to do anything with it. One would like to be able to say that for any non-regular n- gon, there is a regular n-gon of equal perimeter and greater area; and since all regular n-gons of a given perimeter have the same area, this is the desired maximum. (BTW, ignore my sleep-befuddled fluffing about the details of the compactness argument. It is just as simple as I thought it was: if (x_1, y_1, x_2, y_2, ..., x_{n-1}, y_{n-1}) are the coordinates of the other n - 1 vertices, then both the area and the perimeter are continuous functions of these parameters varying in a closed, bounded subset of R^{2n-2}, so the area is a continuous function defined on the closed, bounded subset of R^{2n-2} determined by the perimeter having a given value.) -- Angus Rodgers Contains mild peril === Subject: Re: Polygons of large area posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) After all, apart from the convexity argument, which >I think we can ignore, the other modifications don't >just give another n-gon, they give a continuous >collection of n-gons, all of which are of greater >area, up to and then reaching a maximum. I'm not sure what you mean by continuous collection of n-gons. If we can >invoke a measure of the difference between the regular >n-gon and the n-gons we're using, and show that the >difference can be made arbitrarily small, each time >making the area larger in a continuous fashion, is >that not enough? For example, let M be the sum of the squares of the >differences of the edge lengths from the average, >plus the sum of squares of the differences of the >angles from the average. This quantity can be made >to vary smoothly as we get larger and larger area >n-gons, and we can make it as small as possible. Isn't that enough? I was hoping for something along these lines, and I'm fairly > sure the argument for reducing the variance of the sides to > near zero is OK, but it needs to be written out and checked, > assuming there is any value in this line of argument at all > - but I'm not sure there is, and the cyclic quadrilateral > argument involved changing a sequence of 4 angles at once > (leaving their sum constant), so it might not be possible > to do anything with it. One would like to be able to say that for any non-regular n- > gon, there is a regular n-gon of equal perimeter and greater > area; and since all regular n-gons of a given perimeter have > the same area, this is the desired maximum. (BTW, ignore my sleep-befuddled fluffing about the details of > the compactness argument. It is just as simple as I thought > it was: if (x_1, y_1, x_2, y_2, ..., x_{n-1}, y_{n-1}) are the > coordinates of the other n - 1 vertices, then both the area > and the perimeter are continuous functions of these parameters > varying in a closed, bounded subset of R^{2n-2}, so the area > is a continuous function defined on the closed, bounded subset > of R^{2n-2} determined by the perimeter having a given value.) Notice that to get a closed subset you need to include degenerate n-gons in the set in which one vertex is in the segment which joins its two neighbors. A little more work is needed to show that the maximum is attained at an actual n-gon :-) -- m === Subject: Re: Polygons of large area > (BTW, ignore my sleep-befuddled fluffing about the details of > the compactness argument. It is just as simple as I thought > it was: if (x_1, y_1, x_2, y_2, ..., x_{n-1}, y_{n-1}) are the > coordinates of the other n - 1 vertices, then both the area > and the perimeter are continuous functions of these parameters > varying in a closed, bounded subset of R^{2n-2}, so the area > is a continuous function defined on the closed, bounded subset > of R^{2n-2} determined by the perimeter having a given value.) Notice that to get a closed subset you need to >include degenerate n-gons in the set in which one >vertex is in the segment which joins its two >neighbors. A little more work is needed to show that >the maximum is attained at an actual n-gon :-) I suppose the least messy way of fixing this is to argue that the maximum area must be a constant times L^2 (even if it is attained by a degenerate polygon), and that a degenerate polygon has the same area as a polygon with perimeter L' < L (leaving out a part of the perimeter that is traversed twice or more), whose area must therefore be not greater than the universal constant times L'^2, and so cannot be maximal. Or is there a simpler or clearer way than that? -- Angus Rodgers Contains mild peril === Subject: Re: Polygons of large area >I suppose the least messy way of fixing this [...] Alternatively, there's the Creationist version of the argument, which is that God just magics things so that awkward cases don't happen. ;-) -- Angus Rodgers Contains mild peril === Subject: Re: Polygons of large area >[...] a degenerate polygon has the >same area as a polygon with perimeter L' < L (leaving out a part >of the perimeter that is traversed twice or more) [...] I also meant to say: introduce new redundant vertices if necessary, so that the new polygon is still an n-gon for the value of n being considered. -- Angus Rodgers Contains mild peril === Subject: Re: Polygons of large area > I guess we can hand-wave and show that the area is bounded above Showing that it's bounded above isn't that difficult: you've already >showed that for any polygon, there is a convex polygon with larger >area, and the area of a convex polygon is just the sum of areas of >triangles. That sum is bounded by 1/2*max(height)*sum(bases), the sum >of bases is the perimeter, and max(height) is no more than half the >perimeter. So for perimeter P, the area is bounded by P^2/4. > If we could show that the LUB is L^2 cot(pi/n)/n then we're done. > I suspect that's too much to ask. I suspect so too. The most elementary proof I can think of that the >area actually has a *maximum* (not just a LUB) involves at least some >real analysis. I think it's a question of using a geometrically intuitive argument to reduce the real analysis required to simple analysis of one real variable, so that we don't have to (a) coordinatise and (b) use the Heine-Borel theorem (the standard compactness argument). I was trying to come up with an argument of this kind yesterday, but it still has some way to go. It seems worth trying, one reason being that it might be educational to see the completeness axiom and some basic real analysis in action in this concrete context (in which some work has already been done, so that the need for the arguments can be appreciated). I think I got as far as showing that for any non-equilateral n-gon there exists an equilateral n-gon with equal perimeter and greater area, but I couldn't see how to do the same sort of trick with the angles as I had done with the sides - permuting them with a series of transpositions, so that the largest and smallest are together, then replacing these with two equal sides, reducing the variance of the sides by a constant factor of sqrt{1 - 1/(2n)}, so that when this step is iterated, the variance can be made arbitrarily small - so it might not be a fruitful direction to go in. (At least it had the virtue of following closely the steps of the argument already given, and trying to get more out of it.) -- Angus Rodgers Contains mild peril === Subject: Re: Polygons of large area <3965618.1208790039569.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) On Apr 21, 12:00 pm, riderofgiraffes ... why the maximum area of an n-sided polygon > is obtained when the polygon is regular. I'm guessing you mean for constant perimeter. Indeed - sorry. ... any polygon of maximum area must be convex. > ... must have equal side lengths. > ... if there is a polygon of largest area, all > the angles must be equal. Exactly. I've got that far, and so has he. This > implies that if there is a maximal n-gon then it > must be the regular n-gon. We've also shown that > the area of the regular n-gon is P^2*cot(pi/n)/n > where P is the perimeter. ... the hardest part would be proving that > there is definitely a polygon of greatest > area. And that's where we're stuck. I guess we can hand-wave and show that the area > is bounded above, so the areas of all the n-gons > with given perimeter form a set of reals, and that > set is bounded above. I guess we can hand-wave > (remember, he's 14) and show that there's a least > upper bound. If we could show that the LUB is > L^2cot(pi/n)/n then we're done. I suspect that's > too much to ask. If we can show the limit point > exists then we're done - that might be easier. Research via Google suggests that a purely > geometrical elementary argument might be an open > question. Further suggestions are welcome. Elementary geometric arguments that show existence results are quite rare! -- m === Subject: Re: Polygons of large area <3965618.1208790039569.JavaMail.jakarta@nitrogen.mathforum.org>, > ... why the maximum area of an n-sided polygon > is obtained when the polygon is regular. I'm guessing you mean for constant perimeter. Indeed - sorry. ... any polygon of maximum area must be convex. > ... must have equal side lengths. > ... if there is a polygon of largest area, all > the angles must be equal. Exactly. I've got that far, and so has he. This > implies that if there is a maximal n-gon then it > must be the regular n-gon. We've also shown that > the area of the regular n-gon is P^2*cot(pi/n)/n > where P is the perimeter. ... the hardest part would be proving that > there is definitely a polygon of greatest > area. And that's where we're stuck. I guess we can hand-wave and show that the area > is bounded above, so the areas of all the n-gons > with given perimeter form a set of reals, and that > set is bounded above. I guess we can hand-wave > (remember, he's 14) and show that there's a least > upper bound. It is time to introduce the lub property for real numbers. Otherwise you will be putting it off again. Let him (her?) tell you when he needs additional time to digest material. > If we could show that the LUB is > L^2cot(pi/n)/n then we're done. I suspect that's > too much to ask. If we can show the limit point > exists then we're done - that might be easier. Research via Google suggests that a purely > geometrical elementary argument might be an open > question. Further suggestions are welcome. -- Michael Press === Subject: Re: Geometry with parabola... posting-account=G_G-iQoAAAB08LNQidt_LsMkopmIb4ZS Gecko/20060111 Firefox/1.5.0.1 Mnenhy/0.7.3.0,gzip(gfe),gzip(gfe) Given x = k*(y^2). Then > y = +/- k * Sqrt(x). That should be y = +/- sqrt(x/k) dy/dx = +/- 1/(2* Sqrt(x)) And dy/dx = +/- 1/(2 * sqrt(k * x)) Technically you are correct. I assumed that the value of 'k' was not a factor in the validity of the proof. So I let k = 1. the value of '1 If the formula had been x = y^2 + k ; then it could have been wrong to arbitrarily ignore k in the calculations. === Subject: Lebesgue measure posting-account=jnmSpQoAAAD9aoldTTBvQ9M2r99CF609 2.0.50727),gzip(gfe),gzip(gfe) Let E be a dense set in R. If g:R-->R is a Lebesgue measurable function on E, then is it a Lebesgue measurable function on R also? === Subject: Re: Lebesgue measure posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > Let E be a dense set in R. If g:R-->R is a Lebesgue measurable > function on E, then is it a Lebesgue measurable function on R also? If E = Q, the set of rational numbers, every subset of E is measurable with the restriction of the algebra of Lebesgue measurable sets to Q, so every function g : R --> R restricts to a a measurable function Q --> R. -- m === Subject: Re: Lebesgue measure >Let E be a dense set in R. If g:R-->R is a Lebesgue measurable >function on E, then is it a Lebesgue measurable function on R also? No, not necessarily. Let E be a countable dense set of R, for example, E = Q. Then every function g : R --> R restricts to a measurable function on E. So just choose a nonmeasurable g. quasi === Subject: Re: Fermat's Last Theorem > Although, I am mathematician not professor of English > language. This is a non sequitur as far as the issues I raised are concerned. It's like someone saying that you seem to lack the ability to carry out high school algebra calculations and you respond that you are not a professor of mathematics. Unfortunately, there are many skills which you do not show evidence of having that are needed to teach. (Or, more importantly, that you need to convince a hiring committee that you have.) Dave L. Renfro === Subject: Re: Fermat's Last Theorem > I enclose my qualifications and lectures taught > (This PDF was prepared 3 years ago). Your resume does not say where and when you taught, what specifically you taught at what places, what other duties you had, why you left the positions, and any number of other things that belong on a resume. Have you ever seen anyone else's cv/resume? Dave L. Renfro === Subject: Re: Scientists Confirm Absolute Logic.By Aiya-Oba Bassam King Karzeddin: Equator of self-contradiction(Absolute Logic) is about the fact that, 'Single Spin State' of matter and energy,is the most balanced,and highest state of mind and morality possiple for humanity. It is above the limitations and rage resident in partial understanding and regional views of the common nature of humanity. Absolute logic is Equator of self-contradiction. Thus, (2A + B) + (2B + A) = 3(A + B) Where A and B, can be any positive integer,but never both zero. Hence, A = 1,and B, = 0 = (2 x 1 + 0) + (2 x 0 + 1) = 3(1 + 0) = 2 + 0 + 0 + 1 = 3 x 1 = 2 + 1 = 1+ 1 + 1. Q E D -Aiya-Oba === Subject: Re: Scientists Confirm Absolute Logic.By Aiya-Oba <4149876.1208812408591.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=Qp4ZjwoAAADDToN8UZ6JYmxJnAG4LT6r 1.1.4322),gzip(gfe),gzip(gfe) On Apr 21, 5:12æpm, Anthony A. Aiya-Oba æ æ æ æ æ Thus, (2A + B) + (2B + A) = æ3(A + B) Where A and B, can be any positive integer,but never both zero. æ æ æ æ æ Hence, A = 1,and B, = 0 æ æ æ æ æ= (2 x 1 + 0) æ+ æ(2 x 0 + 1) æ= æ3(1 + 0) æ æ æ æ æ= æ æ2 + 0 æ æ + æ æ 0 æ+ æ1 æ = æ 3 x æ1 æ æ æ æ æ= æ æ æ2 æ æ æ + æ æ æ æ1 æ æ æ= æ æ1+ 1 + 1. > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æQ E D > æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ -Aiya-Oba Yes I made right this time, & I think I have the right to state here with the generous offerings of your Absolut Logic to the following integer equation: Z^P = X^P + Y^P + 2*N*X*Y*Z Where: (X, Y, Z, N) are coprime positive integers pairwise Z is even positive integer P is odd prime number where P divides N*X*Y*Z, and P>3 Therefore, it is clear to see that Fermat's Last Theorem has been proven false! Only those blunt-skull Western obese blobs, who falsely call themselves mathematicians, would deny the wisdom of Allah, maia of Eru, servant of the Secret Fire that burns in Arda! Praise be to Allah-lah-lah, for allowing his profit Mohammed, the QUEEN of us all, guide us to sci.math and given us such proofs of 1+1=3 and disproofs of Fermat's Last (supposed) Theorem! So, Western infidels, do not forsake knowledge in passing the EQUATOR with TRIANGLES. You may not pass or GO in your ignorance, nor can you collect the wealth of the ages or even US$ 200, if you continue in your espousal of Aristolean logic or Einsteinian hoaxes and lies about twin paradoxes and time dilation. For there is only ABSOLUT ! Absolute time, absolute space, and absolute knowledge conveyed by the Absolute Logic of Anthony A. Aiya- Occasin! Bassam K. Karzeddin === Subject: Basic algebra problem (I think) I hope I'm posting this in the right group. I have this problem: > For what values of N is 10N lg N > 2N^2? N^2 is N squared. lg is log base 2. I want to solve for the place where the two graphs cross, so I want to find the solution for N. So, I tried messing around with it, I divided both sides by 2N to get 5 lg N = N, but beyond that I don't how to proceed to solve for N. Any hints? Matt === Subject: Re: Basic algebra problem (I think) > I hope I'm posting this in the right group. I have this problem: For what values of N is 10N lg N > 2N^2? N^2 is N squared. lg is log base 2. I want to solve for the place Actually, for positive N, there are _two_ places where the graphs cross. (And BTW, this is not a basic algebra problem.) > where the two graphs cross, so I want to find the solution for N. So, I tried messing around with it, I divided both sides by 2N to get > 5 lg N = N, but beyond that I don't how to proceed to solve for N. Any hints? There is no algebraic way to solve for N that should be familiar to you. Assuming that your N is to be an integer, perhaps an easy method is merely to try various integer values. You should find that your inequality holds for integer N from 2 through 22. BTW, there is a method to solve the equation 5 lg(N) = N using the Lambert W function, discussed at . The two real solutions are given by W(-ln(2)/5) / (-ln(2)/5) by using the 0 and -1 branches of W. Approximated, those solutions are 1.17728 and 22.44 . David === Subject: Re: Basic algebra problem (I think) > I hope I'm posting this in the right group. I have this problem: > For what values of N is 10N lg N > 2N^2? N^2 is N squared. lg is log base 2. I want to solve for the place > where the two graphs cross, so I want to find the solution for N. So, I tried messing around with it, I divided both sides by 2N to get > 5 lg N = N, but beyond that I don't how to proceed to solve for N. Any hints? Lambert's W calling Cantrell... ;-) > Matt -- I.N. Galidakis === Subject: Re: Basic algebra problem (I think) > I hope I'm posting this in the right group. I have this problem: > For what values of N is 10N lg N > 2N^2? N^2 is N squared. lg is log base 2. I want to solve for the place > where the two graphs cross, so I want to find the solution for N. So, I tried messing around with it, I divided both sides by 2N to get > 5 lg N = N, but beyond that I don't how to proceed to solve for N. Any hints? Lambert's W calling Cantrell... ;-) Matt On my calulator, there seem to be *two* solutions: One near N = 22.44000568. One near N = 1.17727855. === Subject: Re: Basic algebra problem (I think) <1208817039.285827@athprx03> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > I hope I'm posting this in the right group. I have this problem: > For what values of N is 10N lg N > 2N^2? N^2 is N squared. lg is log base 2. I want to solve for the place > where the two graphs cross, so I want to find the solution for N. So, I tried messing around with it, I divided both sides by 2N to get > 5 lg N = N, but beyond that I don't how to proceed to solve for N. Any hints? Lambert's W calling Cantrell... ;-) This problem surely does not need such technology... -- m === Subject: Re: A Letter To Churchill College, Cambridge <32826560.1208806727444.JavaMail.jakarta@nitrogen.mathforum.org>, COLLEGE LECTURESHIP IN MATHEMATICS The following is the letter I sent to its senior member: > My name is Mehran Basti and I am graduate of your college (Ph.D 1979). Far out! I was at Churchill College, too, but a little bit earlier (1974-75) so I probably never met the future Dr Basti. I had some good times there.... -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: A Letter To Churchill College, Cambridge <26594154.1208822191629.JavaMail.jakarta@nitrogen.mathforum.org>, > Far out! I was at Churchill College, too, but a > little bit earlier > (1974-75) so I probably never met the future Dr > Basti. I had > some good times there.... -- > Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for > email) > That's not actually my name, you know. > Were you a student at Churchill College?if so what field and degree? Mathematics, but I wasn't in a degree program as such, as I was just there for one year on a Churchill Scholarship, planning to return to my original institution for my degree. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: A Letter To Churchill College, Cambridge ><32826560.1208806727444.JavaMail.jakarta@nitrogen.mathforum.org>, > COLLEGE LECTURESHIP IN MATHEMATICS > The following is the letter I sent to its senior member: > My name is Mehran Basti and I am graduate of your college (Ph.D 1979). Far out! I was at Churchill College, too Yes, it is rather far out (although not as far out as Girton). -- Angus Rodgers Contains mild peril === Subject: Re: A Letter To Churchill College, Cambridge <32826560.1208806727444.JavaMail.jakarta@nitrogen.mathforum.org>, > COLLEGE LECTURESHIP IN MATHEMATICS > The following is the letter I sent to its senior member: > My name is Mehran Basti and I am graduate of your college (Ph.D 1979). Far out! I was at Churchill College, too Yes, it is rather far out (although not as far out as Girton). Yes, I bought a used bicycle for 5 pounds to get into the math dept and back - and sold it to an incoming Churchill student for 5 pounds when I left. For all I know, that bicycle is still making the rounds.... -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: A Letter To Churchill College, Cambridge posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) On Apr 22, 12:30æam, Gerry Myerson , > COLLEGE LECTURESHIP IN MATHEMATICS The following is the letter I sent to its senior member: > My name is Mehran Basti and I am graduate of your college (Ph.D 1979). Far out! I was at Churchill College, too, but a little bit earlier > (1974-75) so I probably never met the future Dr Basti. I had > some good times there.... -- > Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email) According to http://au.answers.yahoo.com/answers2/frontend.php/question?qid=2008040918082 3 AA0QebL (final para) Churchill college was one of the first to admit women starting in the '60s ;-) === Subject: Re: A Letter To Churchill College, Cambridge posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) On Apr 22, 12:30æam, Gerry Myerson Far out! I was at Churchill College, too, but a little bit earlier > (1974-75) so I probably never met the future Dr Basti. I had > some good times there.... According tohttp://au.answers.yahoo.com/answers2/frontend.php/question?qid=200804... > (final para) Churchill college was one of the first to admit women > starting in the '60s Specifically (from http://www.economicexpert.com/a/Newnham:College:Cambridge.htm ) 1972 saw three colleges (Churchill, Clare, and King's) admit women for the first time. So crafty Gerry timed it perfectly! === Subject: Re: A Letter To Churchill College, Cambridge > This is because a new science has been created and I > have no pity for may lost math fields at Cambridge, > MIT, etc. What does creating a new science have to do with getting a job teaching college algebra, precalculus, and calculus to undergraduates? Dave L. Renfro === Subject: Re: A Letter To Churchill College, Cambridge posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) COLLEGE LECTURESHIP IN MATHEMATICS The following is the letter I sent to its senior member: > My name is Mehran Basti and I am graduate of your college (Ph.D 1979). Well, since my Ph.D. degree I have been engaged in classical mathematics. > http://mathforum.org/kb/forum.jspa?forumID=228 See my files on My New Math (my research statement is there) or My New Energy Formula. I will enclose my resume and I am available for seminars. Yes, this has been my post Ph.D. life (about 28 years now). Although I am unemployed (since July 2005) WITH NO REFERENCES, I will not apply for your advertised math position, unless you are very interested in my application! æI doubt they ever accept me for a position there. One reason is that math at Cambridge is highly abstract and heavily proof related (as far as I remember in pure math department and similarly at Berkeley USA). The other reason is that I have different kind of math, which is not at all, the taste of current leaders (and I consider myself at the rank of the past masters). So definately most of the abstract math practiced at Cambridge, MIT and similar places are outdated and must be dismantled (Thus I view their leaders as redundant professors). You can see once every century possibly your graduates (like myself) may wish to revolutionize math. This is in fact mathematics of the future centuries. I will be interested to see if your colleagues have any questions relative to my new science. They are as usual silent like MIT, Harvard etc. I also invite you to consider helping me to write and publish my lecture notes (2000 pages with software, subject to some conditions). I had harsh criticism of the issues of Fermat Last Theorem (noted in the sci math. Newsgroup, I am positive and serious about the issues raised). I invite your university to seriously investigate the issue (I understand it has political and scientific ramifications). I know that we have a lot of differences both from mathematics standpoint as well as behavior of math people in issues like FLT (bearing in mind A. Wiles also graduated from the same department 1979). Sorry for my viewpoints of Cambridge University since I am one of its graduates, but once a revolution happens in science, so as behaviors, textbooks and fields are subject to review. I will place this letter on sci.math newsgroup for public record. > Dr.Mehran Basti Ph.D. Churchill College, Cambridge, 1979 Mehran, that letter screams loser on every line, and if you hold it up to the light there's a great big watermark that also spells LOSER! Can't you see that? It's almost as if you revel in inevitable rejection, which I suppose you must do if it validates your paranoid fantasies that anyone cares about your work (that it's doubtful they've ever seen, any more than we have). If the recipient was patient enough to reach I consider myself at the rank of the past masters, there's no doubt they'd assume you had omitted a c before rank and bin it there and then. John Ramsden === Subject: Re: A Letter To Churchill College, Cambridge posting-account=JpxxPAgAAAAgwzQIYqn4j6syK-YhOmcF MathPlayer 2.0; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Mehran, that letter screams loser on every line, and if you hold it > up to the light there's a great big watermark that also spells > LOSER! John Ramsden- Hide quoted text - - Show quoted text - I respectfully disagree. That letter screams crackpot! crackpot! crackpot!. New energy formula, yeah. === Subject: Re: A Letter To Churchill College, Cambridge >Mehran, that letter screams loser on every line, and if you hold it >up to the light there's a great big watermark that also spells >LOSER! I respectfully disagree. That letter screams crackpot! crackpot! > crackpot!. New energy formula, yeah. MATTHEW 7:13 Enter by the narrow gate; for the gate is wide, and the way is broad that leads to destruction, and many are those who enter by it. MATTHEW 7:14 For the gate is small, and the way is narrow that leads to life, and few are those who find it. Applied to mathematics: having wrong ideas is easy, finding the right ideas is much more difficult. Yes, most new ideas are simply wrong. Han de Bruijn === Subject: Re: A Letter To Churchill College, Cambridge > that letter screams loser on every line, and if you hold it up to > the light there's a great big watermark that also spells LOSER! Oh, yes, I can just make it out. _______________________________________________________ /~~________/~~~~~~___/~~~~~~__/~~~~~~~~_/~~~~~~~__ /~~_______/~~__/~~_/~~_______/~~_______/~~__/~~_ /~~_______/~~__/~~__/~~~~~~__/~~~~~~___/~~~~~~~__ /~~_______/~~__/~~_______/~~_/~~_______/~~__/~~_ /~~~~~~~~__/~~~~~~___/~~~~~~__/~~~~~~~~_/~~__/~~_ _______________________________________________________ -- Michael Press === Subject: Re: A Letter To Churchill College, Cambridge > Mehran, that letter screams loser on every line, > and if you hold it up to the light there's a great > big watermark that also spells LOSER! I missed out earlier on all the fun in the thread Fermat's Last Theorem because I assumed it was JHS or Archie, and if it really was a legitimate discussion, it would be well beyond me as I know nothing about the mathematics involved in algebraic number theory. It was this post that alerted me to his existence, but I found it more convenient to reply to some of the posts in the other thread. Dave L. Renfro === Subject: Re: A Letter To Churchill College, Cambridge > I missed out earlier on all the fun in the thread > Fermat's Last Theorem because I assumed it was > JHS or Archie, [...] Ooops, I should have written JSH, but I suppose everyone knew who I meant. Dave L. Renfro === Subject: Universal cover of triple wedge What is the universal cover of S^1 V S^1 V S^2 ? S^1 is the circle. S^2 is the sphere. === Subject: Re: Universal cover of triple wedge Also, is the homology of an infinite wedge of spaces isomorphic to an infinite direct sum of the homologies of the spaces? === Subject: Re: Universal cover of triple wedge posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > What is the universal cover of S^1 V S^1 V S^2 ? S^1 is the circle. S^2 is the sphere. Construct the universal cover of S^1 V S^1, and attach a copy of S^2 to each vertex, and call the result X. There is an obvious map X --> S^1 V S^1 V S^2 and X is simply connected. -- m === Subject: Re: Universal cover of triple wedge What are the homology groups of this covering space? === Subject: Re: Universal cover of triple wedge <23237784.1208826001846.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > What are the homology groups of this covering space? What do *you* think they are? .. m === Subject: Re: Universal cover of triple wedge <23237784.1208826001846.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20080325 Fedora/2.0.0.13-1.fc8 Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > What are the homology groups of this covering space? What do you think they are? -- m === Subject: Re: permutation and cycles <12318016.1208761542618.JavaMail.jakarta@nitrogen.mathforum.org>, > In your original problem, there is one big cycle > involving k elements, > and some permutation for the rest of the elements. > Does that help you > count how many ways that can happen? I didn't get the hint? can you simplifies it more ? How many cycles of length k are there in S_n (the symmetric group on n symbols)? How many permutations are there of the remaining n - k symbols? Can't you get the kind of permutation you originally asked about by choosing a cycle of length k and a permutation of n - k? Doesn't that show you how to get the formula you gave? If those hints aren't enough, try writing down all the answers for, say, n = 5 and k = 3, and group them together in various natural ways until you see what's going on. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Sum to a number <19123236.1208760978710.JavaMail.jakarta@nitrogen.mathforum.org>, > Do you mean I should prove the statement for the powers of 2 integers and > then it will be generlized to other integers? I tried to do so but this doesn't help me too much. You know, it would be a lot easier to understand your post if you included relevant portions of the message to which you are replying. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Sum to a number posting-account=T7Gd-QoAAACeQajv7mi_Za6uPu3TpBXy Gecko/20080219 Firefox/2.0.0.12 Navigator/9.0.0.6,gzip(gfe),gzip(gfe) > Hey, I have a question in my CS course, suppose you have a positive integer n>1 and the only representation is allowed is to write n as sum of powers of 2 (n=a_k +...+a_0) where a_i=2^j,for some j show that half of these representation have an even number of terms. e.g. in case of n=5, then 5= 4+1 * > = 1+2+2 > = 1+1+1+2 * > = 1+1+1+1+1 see the * which we should prove Some of these representations have a unique greatest term: n=t +. Unless t is equal to 1 (which is why we require n>1), then we can write n=s+s+ with s=t/2. This representation has a repeated greatest term. Conversely, given a representation with a repeated greatest term: n=s+s +, we can write n=t+ with t=2s. This representation has a unique greatest term. So we have a 1-1 correspondence between representations with a unique greatest term and representations with a repeated greatest term. So the number of representations is even. === Subject: Re: Sum to a number > Hey, I have a question in my CS course, suppose you have a positive integer n>1 and the only representation is > allowed is to write n as sum of powers of 2 (n=a_k +...+a_0) where > a_i=2^j,for some j show that half of these representation have an even number of terms. e.g. in case of n=5, then 5= 4+1 * > = 1+2+2 > = 1+1+1+2 * > = 1+1+1+1+1 see the * which we should prove Some of these representations have a unique greatest term: n=t > +. Unless t is equal to 1 (which is why we require n>1), then > we can write n=s+s+ with s=t/2. This representation has a > repeated greatest term. > Conversely, given a representation with a repeated greatest term: n=s+s > +, we can write n=t+ with t=2s. This representation has > a unique greatest term. > So we have a 1-1 correspondence between representations with a unique > greatest term and representations with a repeated greatest term. > So the number of representations is even. Nice of you to do the fellow's homework for him. I trust you'll also be available for the final exam? -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Number with w... >Hello teacher~ w = cos 20 + i.sin 20 Find 1 / |w + 2w^2 + 3w^3 + ... + 18w^18|. ----------------------------------------------- >Sorry. I need your advice. > x + 2x^2 +.... + nx^n = x* d(x^2 +x^3 + x^n)/dx === Subject: Re: Number with w... posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > æ æ æ æ x + 2x^2 +.... + nx^n > = æ æx* d(x^2 +x^3 + x^n)/dx I think you meant x + 2x^2 +.... + nx^n = x* d(x + x^2 + x^3 + x^n)/dx Dave === Subject: Re: Number with w... > x + 2x^2 +.... + nx^n > = x* d(x^2 +x^3 + x^n)/dx I think you meant x + 2x^2 +.... + nx^n = x* d(x + x^2 + x^3 + x^n)/dx Yes, good idea. === posting-account=QrG9mwoAAAD4swwif73Cg69MYQStuBea Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) The detail information could be found at our journal site http://www.stat.sinica.edu.tw/statistica/ (click on Preprint Articles). Please contact the authors for the first-hand reading of those you are interested in. Karen Li--on behalf of the Co-Editors Editorial Assistant Statistica Sinica -------------------------------------------------------------------- SS-07-018 Robust time series analysis via measurement error modeling Qiong Wang, Leonard A. Stefanski, Marc G.Genton, Dennis D. Boos SS-07-055 Financial derivative valuation---A dynamic semiparametric approach Shih-Feng Huang and Meihui Guo SS-07-062 Testing for familial aggregation when the population size is known Yixin Fang and Daniel Rabinowitz SS-07-100 A dynamic quantile regression transformation model for longitudinal data Yunming Mu and Ying Wei SS-07-121 A Bernstein-von Mises theorem for doubly censored data Yongdai Kim SS-07-131 Continuous-time filters for state estimation from point process models of neural data Uri T. Eden and Emery N. Brown SS-07-132 Uncovering sparse brain effective connectivity: A voxel-based approach using penalized regression Jose M. Sanchez-Bornot, Eduardo Martinez-Montes, Agustin Lage- Castellanos, Mayrim Vega-Hernandez and Pedro A. Valdes-Sosa SS-07-138 A bootstrap test to investigate changes in brain connectivity for functional MRI Pierre Bellec, Guillaume Marrelec and Habib Benali SS-07-139 Penalized PARAFAC analysis of spontaneous EEG recordings Eduardo Martinez-Montes, Jose M. Sanchez-Bornot and Pedro A. Valdes- Sosa SS-07-155 Hybrid permutation test with application to surface shape analysis Chunxiao Zhou and Yongmei Michelle Wang SS-06-164 Regression analysis for cumulative incidence probability under competing risks Wei-Hwa Chang and Weijing Wang SS-07-217 Spatial linear mixed models with covariate measurement errors Yi Li, Haicheng Tang and Xihong Lin SS-07-242 Semiparametric inferential procedures for comparing multivariate ROC curves with interaction terms Liansheng Tang and Xiao-Hua Zhou SS-07-260 Combining regression quantile estimators Kejia Shan and Yuhong Yang SS-07-293 Bayesian nonparametric construction of the Fleming-Viot process with fertility selection Matteo Ruggiero and Stephen G. Walker SS-07-294 Inference on quantile regression for heteroscedastic mixed models Huixia Wang SS-07-318 Nonparametric identification and estimation of nonclassical errors-in- variables models without additional information Xiaohong Chen, Yingyao Hu and Arthur Lewbel SS-07-320 D-Optimal designs for poisson regression models K. G. Russell, D. C. Woods, S. M. Lewis and J. A. Eccleston SS-06-348 A geometric approach to confidence sets for ratios: Fieller's theorem, generalizations, and bootstrap Ulrike von Luxburg and Volker H. Franz === Subject: Re: -- News Server that Blocks Google's Spam > At $62 a year, why would I consider your service over individual.net at > less than 25% of that, and my own client-side filtering? > Because we're DataBasix. Why else? > Not sure where you got that price from either, I'm seeing $51 a > year. Hell why pay a German college, Aioe is free. > How good of a news server is it? > Probably fine, but there's no way that a free usenet server could > handle the full volume of Google Groups users, if they were all to > switch over. > Not to mention the learning curve of installing and configuring and > using a newsreader. Sounds like an excellent way of winnowing the wheat from the chaff. > Pardon?? -- Political Correctness is a doctrine, fostered by a delusional, illogical minority, and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a turd by the clean end. === Subject: Re: -- News Server that Blocks Google's Spam > At $62 a year, why would I consider your service over individual.net at > less than 25% of that, and my own client-side filtering? > Because we're DataBasix. Why else? > Not sure where you got that price from either, I'm seeing $51 a > year. Hell why pay a German college, Aioe is free. > How good of a news server is it? > Probably fine, but there's no way that a free usenet server could > handle the full volume of Google Groups users, if they were all to > switch over. Not to mention the learning curve of installing and configuring and > using a newsreader. > Sounds like an excellent way of winnowing the wheat from the chaff. Pardon?? If Google weren't available, we would be spared the presence of those who weren't willing to put in the necessary effort for learning to use a real newsreader. -- Wayne Brown fi.bes ofereode, [CapitalYAcute]isses swa m.beg. (That passed away, this also can.) from Deor, in the Exeter Book (folios 100r-100v) === Subject: Re: -- News Server that Blocks Google's Spam > At $62 a year, why would I consider your service over individual.net at > less than 25% of that, and my own client-side filtering? > Because we're DataBasix. Why else? > Not sure where you got that price from either, I'm seeing $51 a > year. Hell why pay a German college, Aioe is free. > How good of a news server is it? > Probably fine, but there's no way that a free usenet server could > handle the full volume of Google Groups users, if they were all to > switch over. > Not to mention the learning curve of installing and configuring and > using a newsreader. > Sounds like an excellent way of winnowing the wheat from the chaff. > Pardon?? If Google weren't available, we would be spared the presence of those > who weren't willing to put in the necessary effort for learning to use > a real newsreader. > Yeah, that's what I said, huhhhuhhhuuhuhhhh.... -- I have no need to purchase any bulk e-mail software and use it to piss off the Internet community and lose my Internet account. If I want to piss off somebody, I'll do it on a one-to-one basis. - Norman L. De Forest === Subject: Re: -- News Server that Blocks Google's Spam <180420081501002222%dave@N_O_T_T_H_I_Sbalderstone.ca> <180420081619264583%dave@N_O_T_T_H_I_Sbalderstone.ca> Not to mention the learning curve of installing and configuring and > using a newsreader. Sounds like an excellent way of winnowing the wheat from the chaff. > The puzzler is that nobody thought it was too steep a climb in the old days, though of course in the older days one tended to use a newsreader at wherever they dialed into. What's really being said is that the masses are morons, and they cannot do even a tiny bit of configuring. It takes very little to configure a newsreader, and if someone has a problem then likely their ISP doesn't bother putting the details up. Some ISPs even go a step further, and include details of specific newsreaders (though oddly the Ottawa Freenet where I post to has such detail for GUI newsreaders but not for the old standards). posters is bad for the newbie because they won't be able to configure a newsreader without access to the newsgroups. His statement makes it sound like anyone using Windows or a Mac has no pre-existing knowledge of Usenet, but will somehow find their way in because they want to run Linux. Surely such people will find a web forum long before they head glorified web forum). where they post from (though I state that because elsewhere some seem like I said, some of the issue we are suffering from is the lack of those steps we used to take to get to Usenet. I wouldn't so much consider that a filter, but just a priming so much of the troublesome posting gets reduced. Michael === Subject: Re: -- News Server that Blocks Google's Spam Michael Black got double secret probation for writing: >What's really being said is that the masses are morons, and they cannot >do even a tiny bit of configuring. No, there are just greater numbers and with that greeater numbers that cannot understand the config process. With more of them the amount of time required to assist each one exceeds the available time. In the *old* days the computers were quite often boxes like PDPs and VAXs which meant the Admin & the user were located in the same vicinity. Other users would benefit from another's experience and the support requirement due to the hands on nature was actually minimal. Peer to peer networking so to speak. Now it is all remote and one must read and understand what is sometimes a techically foreign document. Not much can assist you since the document cannot rephrase into terminology that you can reference. The percentage of clueless is the same, there just are more of them with computers. You usually only here from those with a clue, once. -- A Number 1, Grade A, Prime USDA 'Ratz Accept No Substitute === Subject: Re: -- News Server that Blocks Google's Spam > Michael Black got double secret probation for writing: > What's really being said is that the masses are morons, and they cannot > do even a tiny bit of configuring. No, there are just greater numbers and with that greeater numbers that > cannot understand the config process. With more of them the amount of > time required to assist each one exceeds the available time. In the > *old* days the computers were quite often boxes like PDPs and VAXs Are you calling my computer old??! -- I have no need to purchase any bulk e-mail software and use it to piss off the Internet community and lose my Internet account. If I want to piss off somebody, I'll do it on a one-to-one basis. - Norman L. De Forest === Subject: Re: -- News Server that Blocks Google's Spam WindsorFox got double secret probation for writing: > Michael Black got double secret probation for writing: > What's really being said is that the masses are morons, and they cannot > do even a tiny bit of configuring. > No, there are just greater numbers and with that greeater numbers that > cannot understand the config process. With more of them the amount of > time required to assist each one exceeds the available time. In the > *old* days the computers were quite often boxes like PDPs and VAXs > Are you calling my computer old??! Yes -- A Number 1, Grade A, Prime USDA 'Ratz Accept No Substitute === Subject: Re: -- News Server that Blocks Google's Spam > WindsorFox got double secret probation > for writing: Michael Black got double secret probation for writing: > What's really being said is that the masses are morons, and they cannot > do even a tiny bit of configuring. > No, there are just greater numbers and with that greeater numbers that > cannot understand the config process. With more of them the amount of > time required to assist each one exceeds the available time. In the > *old* days the computers were quite often boxes like PDPs and VAXs > Are you calling my computer old??! Yes Well that's just rude. -- I have no need to purchase any bulk e-mail software and use it to piss off the Internet community and lose my Internet account. If I want to piss off somebody, I'll do it on a one-to-one basis. - Norman L. De Forest === Subject: Re: -- News Server that Blocks Google's Spam <180420081501002222%dave@N_O_T_T_H_I_Sbalderstone.ca> <180420081619264583%dave@N_O_T_T_H_I_Sbalderstone.ca> Not to mention the learning curve of installing and configuring and > using a newsreader. > Sounds like an excellent way of winnowing the wheat from the chaff. > The puzzler is that nobody thought it was too steep a climb in the old > days, though of course in the older days one tended to use a newsreader > at wherever they dialed into. [...] > posters is bad for the newbie because they won't be able to configure > a newsreader without access to the newsgroups. His statement makes > it sound like anyone using Windows or a Mac has no pre-existing knowledge > of Usenet, but will somehow find their way in because they want to run > Linux. Surely such people will find a web forum long before they head > glorified web forum). [...] I'll offer up my own experience when a newbie, at this point. I'd first heard of newsgroups back in the late '70s, I think - I can remember reading in a computer magazine about the scandal of all the possibly dubious stuff that was bound to appear in the new alt.* hierarchy and how that would rapidly bring about the demise of all newsgroups ... I didn't get on line for myself until 2000. By then I was reasonably computer savvy (at least, DOS-savvy and somewhat familiar with Windows 3.1) but pretty much ignorant of anything to do with the internet, and really only intending to get up to speed with email. My new (to me) computer came with Windows 98SE, and I found Outlook Express easily enough after I'd used an ISP's CD to set up a dial-up internet account; when I found that OE could 'do' newsgroups I was immediately presented with a list of newsgroups which the ISP's set-up CD had inserted into OE, with a subscription already established in NNQ and one or two other groups - but I didn't pay much attention to any of them. I did explore a bit and lurked in a few newsgroups I thought might be of interest, but I didn't post - I was too unsure of myself. But I did learn about using 'made-up' names and 'disposable' email addresses instead of 'real' ones. Meanwhile I'd found some web forums; I even subscribed to one just to practice in. It looked a lot less daunting than the newsgroups I was lurking in, so it felt safer. But very frustrating and expensive over dial-up! Eventually I felt confident enough to start posting in newsgroups - but not before I'd decided that OE was not to my liking as either email or newsreader program; but that's another story. I didn't discover Google Groups until after I'd been lurking in newsgroups for a few months. The point I'm making is that my first ISP set up my Windows computer for me in such a way that I could dive straight into newsgroups without having to configure anything. They had their own news-server, so there was o reason why they shouldn't do that - and it probably saved a lot of helpdesk resources making the initial set-up automatic for all those customers who used the CD to get started. These days, many ISPs, even 'big' ones, don't have a news-server of their own or even outsourced, so many newbies' computers aren't getting a news-reader pre-configured for them - and if my recent experience getting a new Windows Vista computer installed for someone else is typical, Internet Explorer comes with 'Home Page' and 'toolbars' set up to default to the AOL portal &/or Google and a beginner isn't likely to know how to get rid of those settings or even know that such a thing is possible - so it isn't surprising we're getting a lot of ignorant newbies finding their way into newsgroups via Google. But the newbies aren't really the problem, however irritating (we're all Newbies can learn, given patient treatment (as I was). Spammers don't Groups interface, so Google isn't doing itself any favours by letting the abuse continue. Perhaps that's the angle that needs to be stressed with Google - Google people will abandon Google Groups in favour of better regulated web forums elsewhere. That will lose Google a revenue stream from the adverts they insert in the GG web pages, and damage Google's reputation both with the general public and with advertising agencies. Usenet doesn't need Google, but Google Groups is nothing without users. -- -- ^^^^^^^^^^ -- Whiskers -- ~~~~~~~~~~ === Subject: Re: -- News Server that Blocks Google's Spam [...] > But the newbies aren't really the problem, however irritating (we're all > Newbies can learn, given patient treatment (as I was). Spammers don't > Groups interface, so Google isn't doing itself any favours by letting the > abuse continue. groups, i.e. the groups which are only present on the Google Groups site? (I.e. groups without dots in their name, i.e such as for example the Gmail Help Discussion group.) If so, then I fully agree with your point. If not, i.e. the non-Usenet groups are reasonably clean, then that's just more proof that Google doesn't care about Usenet and just benefits from it. > Perhaps that's the angle that needs to be stressed with Google - Google > people will abandon Google Groups in favour of better regulated web forums > elsewhere. That will lose Google a revenue stream from the adverts they > insert in the GG web pages, and damage Google's reputation both with the > general public and with advertising agencies. Usenet doesn't need Google, but Google Groups is nothing without users. === Subject: Re: -- News Server that Blocks Google's Spam > [...] > But the newbies aren't really the problem, however irritating (we're all > Newbies can learn, given patient treatment (as I was). Spammers don't > Groups interface, so Google isn't doing itself any favours by letting the > abuse continue. groups, i.e. the groups which are only present on the Google Groups > site? (I.e. groups without dots in their name, i.e such as for example > the Gmail Help Discussion group.) If so, then I fully agree with your point. If not, i.e. the non-Usenet > groups are reasonably clean, then that's just more proof that Google > doesn't care about Usenet and just benefits from it. Yes, one of the problems is that many the n00bs that post this junk don't have a clue where they are or what they are doing. All they know is this big list of ads to put their ad into as well. Others like from the same chinese jerkoff using probably 20 different Google accounts, and that's just page one. Of course through Homer I saw none of his garbage. -- Political Correctness is a doctrine, fostered by a delusional, illogical minority, and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a turd by the clean end. === Subject: Re: -- News Server that Blocks Google's Spam <180420081501002222%dave@N_O_T_T_H_I_Sbalderstone.ca> <180420081619264583%dave@N_O_T_T_H_I_Sbalderstone.ca> <480cffc5$0$53724$dbd4b001@news.wanadoo.nl [...] > But the newbies aren't really the problem, however irritating (we're all > Newbies can learn, given patient treatment (as I was). Spammers don't > Groups interface, so Google isn't doing itself any favours by letting the > abuse continue. groups, i.e. the groups which are only present on the Google Groups > site? (I.e. groups without dots in their name, i.e such as for example > the Gmail Help Discussion group.) If so, then I fully agree with your point. If not, i.e. the non-Usenet > groups are reasonably clean, then that's just more proof that Google > doesn't care about Usenet and just benefits from it. [...] I'm not a user of any of Google's web forums, but at least some of them an acceptable level in those groups. Perhaps someone who does read a few of Google's web forums could comment? -- -- ^^^^^^^^^^ -- Whiskers -- ~~~~~~~~~~ === Subject: Re: -- News Server that Blocks Google's Spam > I'm not a user of any of Google's web forums, but at least some of them > an acceptable level in those groups. Perhaps someone who does read a few > of Google's web forums could comment? It is possible to start a private discussion group. And you can also set that to moderated status so that you can control posts and membership. Some people setting these up just don't take the time to learn how it works. emessage to show who they are and then you can summarily ban that user ID. Sure, they could come in with a new ID but that will get tiresome after a while. Interestingly enough, sometimes the user ID is a give away as to the mission at hand. DMK === Subject: Re: -- News Server that Blocks Google's Spam > > This is why no one takes Databasix seriously. I beg to differ. For months I tried to convince my ISP's news admins to ignore the b8mbies and their canonical list of newsgroups, to no avail. Then I pointed out DataBasix as an example of an NSP that does things right (adding groups only at their own users' requests). Three days later, my ISP made this announcement: Alright, after much deliberation internally, we have decided to not add new groups unless users request them added. It appears that *someone* takes DataBasix seriously. -- Wayne Brown fi.bes ofereode, [CapitalYAcute]isses swa m.beg. (That passed away, this also can.) from Deor, in the Exeter Book (folios 100r-100v) === Subject: Re: -- News Server that Blocks Google's Spam > > This is why no one takes Databasix seriously. I beg to differ. For months I tried to convince my ISP's news admins to > ignore the b8mbies and their canonical list of newsgroups, to no avail. > Then I pointed out DataBasix as an example of an NSP that does things > right (adding groups only at their own users' requests). Three days > later, my ISP made this announcement: Alright, after much deliberation > internally, we have decided to not add new groups unless users request > them added. It appears that *someone* takes DataBasix seriously. And that - *not* adding a new group - is a good thing exactly *why*? So what happens if (a NSPs) users do not request a new group, but it is created anyway? Are they forced to read / post in it or something? FWIW, I've no problem whatsoever with DataBasix doing what it's doing (*if* [1] that is what they're doing). Their server, their rules and all that jazz. But implying that it good thing *in general* seems rather strange. Creating *more* groups than the List of Big Eight Newsgroups I can understand, but *less*? [1] Gary is currently involved in a proposal for a new 'official' group, so I doubt if he/they is/are really so 'anti' B8MB as you seem to imply. === Subject: Re: -- News Server that Blocks Google's Spam > > This is why no one takes Databasix seriously. > I beg to differ. For months I tried to convince my ISP's news admins to > ignore the b8mbies and their canonical list of newsgroups, to no avail. > Then I pointed out DataBasix as an example of an NSP that does things > right (adding groups only at their own users' requests). Three days > later, my ISP made this announcement: Alright, after much deliberation > internally, we have decided to not add new groups unless users request > them added. It appears that *someone* takes DataBasix seriously. And that - *not* adding a new group - is a good thing exactly *why*? Anything that reduces the influence of the b8mbies is a Good Thing. So what happens if (a NSPs) users do not request a new group, but it > is created anyway? Are they forced to read / post in it or something? We're forced to see our servers polluted by the noxious b8mbie touch. FWIW, I've no problem whatsoever with DataBasix doing what it's doing > (*if* [1] that is what they're doing). Their server, their rules and > all that jazz. But implying that it good thing *in general* seems rather > strange. Creating *more* groups than the List of Big Eight Newsgroups > I can understand, but *less*? I'm happy to see any number of groups created whenever requested by anyone *except* the b8mbies. [1] Gary is currently involved in a proposal for a new 'official' group, > so I doubt if he/they is/are really so 'anti' B8MB as you seem to imply. (and what I quoted to my ISP's news admins) about the B8MB's command to create rec.arts.sf.tv.jericho: # BTW, we'll create it if one of our users asks for it just like any # other newsgroup, not because these bozos say so. -- Wayne Brown fi.bes ofereode, [CapitalYAcute]isses swa m.beg. (That passed away, this also can.) from Deor, in the Exeter Book (folios 100r-100v) === Subject: Re: -- News Server that Blocks Google's Spam [Anti-B8MB rant deleted.] > [1] Gary is currently involved in a proposal for a new 'official' group, > so I doubt if he/they is/are really so 'anti' B8MB as you seem to imply. (and what I quoted to my ISP's news admins) about the B8MB's command > to create rec.arts.sf.tv.jericho: # BTW, we'll create it if one of our users asks for it just like any > # other newsgroup, not because these bozos say so. Well, this is in the *current* [ADMIN] news.announce.newgroups queue > Create comp.lang.c++.misc > Proponent Gary L. Burnore So it looks that Gary is (also) working *with* the B8MB. Bummer, heh? === Subject: Re: -- News Server that Blocks Google's Spam > > This is why no one takes Databasix seriously. I beg to differ. For months I tried to convince my ISP's news admins to > ignore the b8mbies and their canonical list of newsgroups, to no avail. > Then I pointed out DataBasix as an example of an NSP that does things > right (adding groups only at their own users' requests). Three days > later, my ISP made this announcement: Alright, after much deliberation > internally, we have decided to not add new groups unless users request > them added. It appears that *someone* takes DataBasix seriously. > Gary > b8mbies -- Political Correctness is a doctrine, fostered by a delusional, illogical minority, and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a turd by the clean end. === Subject: Re: -- News Server that Blocks Google's Spam > [...] > Not to mention the learning curve of installing and configuring and > using a newsreader. For the *majority* of users - including you - there *is* no such > thing! [1] Just plug this in their/your *webbrowser*, i.e. Internet Explorer, and > away they/you go: > Holy crap that was different. Put that in FF and TB opens and adds > the server. I didn't know it would do that. from the group are downloaded, and the subject lines etc. are presented to the user.) === Subject: Re: -- News Server that Blocks Google's Spam > [...] > Not to mention the learning curve of installing and configuring and > using a newsreader. > For the *majority* of users - including you - there *is* no such > thing! [1] Just plug this in their/your *webbrowser*, i.e. Internet Explorer, and > away they/you go: > Holy crap that was different. Put that in FF and TB opens and adds > the server. I didn't know it would do that. from the group are downloaded, and the subject lines etc. are presented > to the user.) Oh hell I dunno, I didn't let it go that far. I think maybe not because a configuration box opened that I *think* wanted my email address. -- Political Correctness is a doctrine, fostered by a delusional, illogical minority, and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a turd by the clean end. === Subject: Re: -- News Server that Blocks Google's Spam <86prsozox8.fsf@localhost.localdomain> <180420081501002222%dave@N_O_T_T_H_I_Sbalderstone.ca> <180420081619264583%dave@N_O_T_T_H_I_Sbalderstone.ca> <49vl04dujqp70biv80bfebbcmbh924ufs0@4ax.com> At $62 a year, why would I consider your service over individual.net at > less than 25% of that, and my own client-side filtering? > Because we're DataBasix. Why else? > Not sure where you got that price from either, I'm seeing $51 a > year. Hell why pay a German college, Aioe is free. >Web address? Because I use Yahoo. > Hint: The search terms aioe usenet should suffice. > === Subject: Re: -- News Server that Blocks Google's Spam At $62 a year, why would I consider your service over individual.net at > less than 25% of that, and my own client-side filtering? > Because we're DataBasix. Why else? > Not sure where you got that price from either, I'm seeing $51 a > year. Hell why pay a German college, Aioe is free. > Web address? > Because I use Yahoo. > [mechanic] Huh, Whull thar's yer problem... [/mechanic] -- Political Correctness is a doctrine, fostered by a delusional, illogical minority, and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a turd by the clean end. === Subject: Differentiating Implicitly Could someone please help me to differentiate the following implicitly: 2x^2 y + sin y = 7 === Subject: Re: Differentiating Implicitly- Could someone please help me to differentiate the following implicitly: 2x^2 y + sin y = 7 > The good old-fashioned pre-Cauchy way: d(2x^2 y + sin y) = 0; d(2x^2 y + sin y) = d(2x^2 y) + d(sin y) = 2x^2 dy + 4xy.dx + cos(y).dy = 4xy.dx + (2x^2 + cos y)dy = 0. Want derivative of y as a function of x? Then dy/dx = -4xy / (2x^2 + cos y), and get rid of y in the RHS by means of the original relation 2x^2 y + sin y = 7. This requires solving a transcendental equation. Want derivative of x as a function of y? Then dx/dy = ... etc. This is easier than with y as a function of x. All this is justified by the well-known definitions and theorems of differential calculus as founded by Cauchy. Think of the modern definition of differentiability, implicit-function theorems, differential 1-forms (gradients), and please keep in mind: differential calculus is essentially about approximations of non-linear situations by their linear counterparts. Johan E. Mebius === Subject: Re: Differentiating Implicitly Could someone please help me to differentiate the following implicitly: 2x^2 y + sin y = 7 > With respect to x, assuming y = y(x) ? What's d7/dx? On the other side use theorems that the derivative of the sum is the sum of the derivaties, the product rule and finally the chain rule. Let's see how far you can go. === Subject: Re: Polynom 5th orders posting-account=PSzFRAoAAAARszS8zeFmxtqyivK9-1_f InfoPath.2),gzip(gfe),gzip(gfe) > Hi I have following Problem: I have Polynom 5. Orders: p(t)=c0+c1*t+c2*t^2+c3*t^3+c4*t^4+c5*t^5. > The Variable t changes between 0 and 20 000 in steps 2msec . I have to > find time t > where the polynom has value p1(p1 is known). > How can I find time t? > Leo Try series reversion. http://mathworld.wolfram.com/SeriesReversion.html Gerry === Subject: Re: sum R > no , its always false. Are you claiming that there is no definition of uncountable sum for which David's claim is true? If not, then you need to specify what definition for uncountable sum you're using - and you consistently avoid doing so. Your Crank Index is increasing. - Tim === Subject: Re: Real Analysis Help ... Sequences <11815163.1208360671052.JavaMail.jakarta@nitrogen.mathforum.org> <4808BDA8.2070104@web.de> posting-account=sc--GAkAAADebJIRY3Xo4z0zuPmKPSND 1.1.4322; InfoPath.2; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Suppose {xi} is a cauchy sequence and f(x) is 'uniformly continuous,' > is {f(xi)} cauchy ? > Yes. > OK.....but how? æhints? > Plug together the definitions of Cauchy and uniformly continuous - but > in the right order. What have you found out already? > -- > Best wishes, > J. What do you mean right order? Either this way or the other way round. What have you tried already? -- > Best wishes, > J.- Hide quoted text - - Show quoted text - Nothing really...I am stuck on this === Subject: Re: Real Analysis Help ... Sequences > Suppose {xi} is a cauchy sequence and f(x) is 'uniformly continuous,' > is {f(xi)} cauchy ? > Yes. > OK.....but how? æhints? > Plug together the definitions of Cauchy and uniformly continuous - but > in the right order. What have you found out already? > -- > Best wishes, > J. > What do you mean right order? > Either this way or the other way round. What have you tried already? > -- > Best wishes, > J.- Hide quoted text - > - Show quoted text - Nothing really...I am stuck on this Well, you have to start somewhere. For example, you might write down precisely what it is you want to prove. So complete this sentence and check back in with us: {f(x_i} will be shown to be a Cauchy sequence if I can prove the following statement about {f(x_i}: --Lynn === Subject: Youngest professor - Guinness book. Hello teacher~ Colin Maclaurin was 19 years old when he was elected Professor of Mathematics at Marischal College in Scotland on Sept. 30, 1717 === Subject: Re: Youngest professor - Guinness book. > Hello teacher~ Colin Maclaurin was 19 years old > when he was elected Professor of Mathematics at Marischal College > in Scotland on Sept. 30, 1717 Except for a remainder term. === Subject: Re: Youngest professor - Guinness book. > Colin Maclaurin was 19 years old when he was elected > Professor of Mathematics at Marischal College in > Scotland on Sept. 30, 1717 Maybe not the youngest professor (full, I would assume), but here's something I posted 3 months ago: *************************************************** Does anyone know the youngest age at which someone has received a Ph.D. in math? I believe I've heard of some people who got their Ph.D. at 18 or 19, but a few of those I thought were examples (John Milnor, Carl Gauss, and a certain son of a long-time sci.math poster) wound up getting their degrees about 3 years later than this. Anyway, a couple of days ago I was looking through an old issue of The Mathematical Gazette (Volume 23, Number 253, February 1939, p. 5) and I came across the example of Karl Witte, who received a Ph.D. in math from the University of Leipzig at age 13. See also p. 153 in Psychology and Parenthood by Henry Addington Bruce, on the internet at *************************************************** Dave L. Renfro === Subject: Re: Youngest professor - Guinness book. >Hello teacher~ Colin Maclaurin was 19 years old >when he was elected Professor of Mathematics at Marischal College >in Scotland on Sept. 30, 1717 Probably just the first in a series. quasi === Subject: Re: Youngest professor - Guinness book. quasi >Colin Maclaurin was 19 years old >when he was elected Professor of Mathematics at Marischal College >in Scotland on Sept. 30, 1717 Probably just the first in a series. The series is convergent with a limit >= 0. Aage === Subject: Re: What is Mathematics? > Certainly, but we're discussing what mathematics really is (if such > a question makes sense) and not how mathematicians attempt to > comprehend it or work with it. Surely mathematics is what mathematicians do. It is indeed good advice > to not pay too much attention to what mathematicians say about what > they're doing in their philosophical moments. Instead, we must look at > what they actually do when doing mathematics, how they think, what > considerations they find important, and so on. Now, if we consider the > claim Mathematics is a game with some definite rules to manipulate symbols > as if they were chess pieces. we find that, on the face of it, it is not connected to anything we > find in the work of actual mathematicians. Thus if we are to > understand it in some way that is not blatantly false, it must be > explained just how it is supposed to relate to mathematics as we > actually find it. > And eventually we get at the formalized aspects of mathematics where > we can see how an axiomatic system behaves pretty much as a game > where the primitive symbols are pieces that can be placed in a > sentence according to certain rules. We may of course consider formal theories, formal calculi, as > meaningless pushing of symbols around according to arbitrary > rules. The question, then, is how this view relates to our actual > mathematical practice. As said, on the face of it, such a meaningless > activity bears no resemblance to what mathematicians actually do. You > might then say that, while no such thing is discernible in the > practice of mathematics, it is in some sense what mathematics really > is. The onus is then on you to explain why anyone should care about > this reality or how it helps us understand anything about > mathematics. The Basel problem asked for the value of sum_{n=1 ... oo} (1/(n^2)). So mathematicians were assuming that there was a sum, or a limit, before Cauchy came up with Cauchy sequences and the property: Every Cauchy sequence converges. Another example of obvious things has to do with proofs of the Fundamental Theorem of Algebra. < http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/ 6-042JMathematics-for-Computer-ScienceFall2002/D7C42878-108E-4C45-902A-61783 1 45EC0A/0/ln1.pdf> page 5 mentions Gauss' 1799 proof and quotes: << GaussÍs 1799 Ph.D. thesis is usually referred to as being the first rigorous proof of the Fundamental Theorem of Algebra (every polynomial has a zero over the complex numbers). But it contains quotes like îIf a branch of an algebraic curve enters a bounded region, it must necessarily leave it again. ... Nobody, to my knowledge, has ever doubted [this fact]. But if anybody desires it, then on another occasion I intend to give a demonstration which will leave no doubt.î îimmense gapî in the proof that was not filled in until 1920, more than a hundred years later. > Gauss presented a proof later on that assumed that every polynomial of odd degree with real coefficients has at least one real root. With the property that Cauchy came up with, plus assuming the reals are an ordered field, then this characterizes the reals. So assuming there is a complete ordered field, that will show what Gauss assumed about polynomials of odd degree. Proving that there was a complete ordered field was probably done in the 19th century. I know that AC is needed to prove that every ring with an identity has a maximal ideal. I've heard that countable choice is enough for most purposes. What would be one the simplest results that can't be shown in Z set theory? (no replacement, no form of choice). In antiquity, they approximated pi but they hadn't developed the reals including Cauchy sequences or completeness. I think the Fields medal has a bust of Archimedes, ``one of the greatest mathematicians of antiquity. I pretty much agree when you say: << Surely mathematics is what mathematicians do. > And a mathematician is... somebody skilled in mathematics?!? David Bernier > Interesting quote. I do have one as well I'd like to share, allowing > myself to freely translate it from the original Spanish book Teor.92a > axiom.87tica de conjuntos by Jes.9cs Moster.92n (p. 31): > In the same way the musical fantasy creates several symphonies, our > imagination conceives different theories. And depending on which set > theory we choose, we would be playing a different game. In the > mathematical field there is place for many games, and all of them are > dangerous since their consistency is not assured. But it is worth > taking the risk rather than get bored. The purpose of this book is > then to present one of these games. We hope the reader will find it > amusing. An objectionable quote! The choice of axioms in set theory is not at > all like the choice of rules in a game, of choosing to play checkers > instead of chess, say. We may also observe that we do in fact take > results of the form the algorithm A terminates on all inputs, all > naturals have the computable property P and so on seriously, and > accept them as true if proven from the usual set theoretic > principles. For theories in general, even if they're consistent, > there's no reason to conclude P on basis of the provability of P in > the theory -- thus the picture of mathematicians choosing this or > that set theory, willy-nilly, according to their whim and fancy is in > direct contradiction with the way virtually everyone actually thinks > in mathematics, even if in they claim otherwise when philosophising. > === Subject: Re: What is Mathematics? > Certainly, but we're discussing what mathematics really is (if such > a question makes sense) and not how mathematicians attempt to > comprehend it or work with it. Surely mathematics is what mathematicians do. Which would be quite instructive if you could just point out a few. Are we to believe that we're not doing mathematics just now? > It is indeed good advice >to not pay too much attention to what mathematicians say about what >they're doing in their philosophical moments. Just as it is indeed good advice not to pay to much attention to what philosophers say about what they're doing in their philosophical moments. > Instead, we must look at >what they actually do when doing mathematics, how they think, what >considerations they find important, and so on. Yes, well, er, that rather seems to be the problem now doesn't it since you wouldn't appear to have much of an idea what that is. ~v~~ === Subject: Re: What is Mathematics? > Which would be quite instructive if you could just point out a few. A few mathematicians? Surely you can name names yourself. > Are we to believe that we're not doing mathematics just now? We are not doing mathematics at the moment. Rather, we're engaged in pointless news squabbling. > Just as it is indeed good advice not to pay to much attention to what > philosophers say about what they're doing in their philosophical > moments. Certainly. If we are to understand philosophy as philosophers practice it we must inspect what philosophers actually do. As with any profession, what those in the business say about what they're doing does not necessarily have any connection to what it is they actually go about doing. > Yes, well, er, that rather seems to be the problem now doesn't it > since you wouldn't appear to have much of an idea what that is. My knowledge or lack thereof is not of much general interest. You can find out what mathematicians find important, what considerations they consider germane, and so on, for yourself, by inspecting the literature. Is there some point to this wanton cross-posting? -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: What is Mathematics? <5958102.1208271987425.JavaMail.jakarta@nitrogen.mathforum.org> <7a3Pj.340380$FT.65022@reader1.news.saunalahti.fi> posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) On Apr 21, 12:21æpm, Aatu Koskensilta Are we to believe that we're not doing mathematics just now? We are not doing mathematics at the moment. Rather, we're engaged in > pointless news squabbling. Are those incompatible? 1. We cannot predict the future, as we cannot correctly answer the question Will your next answer be 'no'?. 2. Science is that which we can predict. 3. Mathematics is science which can be done without the use of human I/ O (input/output) i.e. without the use of our 5 senses. 4. Mathematics which has no I/O is called conventional Mathematics e.g. Predicate Calculus has no I/O. 5. Mathematics which has I/O is called CBL, which adds I/O to Predicate Calculus to axiomatize Metamathematics. Also note that we can predict some future events. For example, we can correctly answer the question Will your second answer from now be 'no'?. So it is a matter of how far in advance we are asked to predict. C-B > Just as it is indeed good advice not to pay to much attention to what > philosophers say about what they're doing in their philosophical > moments. Certainly. If we are to understand philosophy as philosophers practice > it we must inspect what philosophers actually do. As with any > profession, what those in the business say about what they're doing > does not necessarily have any connection to what it is they actually > go about doing. Yes, well, er, that rather seems to be the problem now doesn't it > since you wouldn't appear to have much of an idea what that is. My knowledge or lack thereof is not of much general interest. You can > find out what mathematicians find important, what considerations they > consider germane, and so on, for yourself, by inspecting the > literature. Is there some point to this wanton cross-posting? -- > Aatu Koskensilta (aatu.koskensi...@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen > æ- Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: What is Mathematics? >On Apr 21, 12:21æpm, Aatu Koskensilta Which would be quite instructive if you could just point out a few. I don't see any Mathematicians myself, but then, my apartment is kind >of small. How would you know them if you saw them? > Are we to believe that we're not doing mathematics just now? > We are not doing mathematics at the moment. Rather, we're engaged in > pointless news squabbling. Are those incompatible? Only for philosophers. >1. We cannot predict the future, as we cannot correctly answer the >question Will your next answer be 'no'?. >2. Science is that which we can predict. >3. Mathematics is science which can be done without the use of human I/ >O (input/output) i.e. without the use of our 5 senses. >4. Mathematics which has no I/O is called conventional Mathematics >e.g. Predicate Calculus has no I/O. >5. Mathematics which has I/O is called CBL, which adds I/O to >Predicate Calculus to axiomatize Metamathematics. Also note that we can predict some future events. For example, we can >correctly answer the question Will your second answer from now be >'no'?. So it is a matter of how far in advance we are asked to >predict. These observations appear somewhat problematic. My own take on mathematics requires exhaustive demonstrations of truth. I see nothing in predicate combinations which precludes this. >C-B > Just as it is indeed good advice not to pay to much attention to what > philosophers say about what they're doing in their philosophical > moments. > Certainly. If we are to understand philosophy as philosophers practice > it we must inspect what philosophers actually do. As with any > profession, what those in the business say about what they're doing > does not necessarily have any connection to what it is they actually > go about doing. > Yes, well, er, that rather seems to be the problem now doesn't it > since you wouldn't appear to have much of an idea what that is. > My knowledge or lack thereof is not of much general interest. You can > find out what mathematicians find important, what considerations they > consider germane, and so on, for yourself, by inspecting the > literature. > Is there some point to this wanton cross-posting? > -- > Aatu Koskensilta (aatu.koskensi...@xortec.fi) > Wovon man nicht sprechen kann, daruber muss man schweigen > æ- Ludwig Wittgenstein, Tractatus Logico-Philosophicus ~v~~ === Subject: Re: What is Mathematics? <5958102.1208271987425.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=NzomCgoAAADSxo8dItZFimQE_f4Fbqcn .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) On Apr 21, 12:21æpm, Aatu Koskensilta Which would be quite instructive if you could just point out a few. I don't see any Mathematicians myself, but then, my apartment is kind >of small. How would you know them if you saw them? > Are we to believe that we're not doing mathematics just now? > We are not doing mathematics at the moment. Rather, we're engaged in > pointless news squabbling. Are those incompatible? Only for philosophers. 1. We cannot predict the future, as we cannot correctly answer the >question Will your next answer be 'no'?. >2. Science is that which we can predict. >3. Mathematics is science which can be done without the use of human I/ >O (input/output) i.e. without the use of our 5 senses. >4. Mathematics which has no I/O is called conventional Mathematics >e.g. Predicate Calculus has no I/O. >5. Mathematics which has I/O is called CBL, which adds I/O to >Predicate Calculus to axiomatize Metamathematics. Also note that we can predict some future events. æFor example, we can >correctly answer the question Will your second answer from now be >'no'?. So it is a matter of how far in advance we are asked to >predict. These observations appear somewhat problematic. My own take on > mathematics requires exhaustive demonstrations of truth. I see nothing > in predicate combinations which precludes this. C-B > Just as it is indeed good advice not to pay to much attention to what > philosophers say about what they're doing in their philosophical > moments. > Certainly. If we are to understand philosophy as philosophers practice > it we must inspect what philosophers actually do. As with any > profession, what those in the business say about what they're doing > does not necessarily have any connection to what it is they actually > go about doing. > Yes, well, er, that rather seems to be the problem now doesn't it > since you wouldn't appear to have much of an idea what that is. > My knowledge or lack thereof is not of much general interest. You can > find out what mathematicians find important, what considerations they > consider germane, and so on, for yourself, by inspecting the > literature. > Is there some point to this wanton cross-posting? > -- > Aatu Koskensilta (aatu.koskensi...@xortec.fi) > Wovon man nicht sprechen kann, daruber muss man schweigen > æ- Ludwig Wittgenstein, Tractatus Logico-Philosophicus ~v~~- Hide quoted text - - Show quoted text - Anti differentiaition is not intergration. === Subject: Re: What is Mathematics? <5958102.1208271987425.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=NzomCgoAAADSxo8dItZFimQE_f4Fbqcn .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > On Apr 21, 12:21æpm, Aatu Koskensilta Which would be quite instructive if you could just point out a few. I don't see any Mathematicians myself, but then, my apartment is kind > of small. Are we to believe that we're not doing mathematics just now? We are not doing mathematics at the moment. Rather, we're engaged in > pointless news squabbling. Are those incompatible? 1. We cannot predict the future, as we cannot correctly answer the > question Will your next answer be 'no'?. > 2. Science is that which we can predict. > 3. Mathematics is science which can be done without the use of human I/ > O (input/output) i.e. without the use of our 5 senses. > 4. Mathematics which has no I/O is called conventional Mathematics > e.g. Predicate Calculus has no I/O. > 5. Mathematics which has I/O is called CBL, which adds I/O to > Predicate Calculus to axiomatize Metamathematics. Also note that we can predict some future events. æFor example, we can > correctly answer the question Will your second answer from now be > 'no'?. So it is a matter of how far in advance we are asked to > predict. C-B Just as it is indeed good advice not to pay to much attention to what > philosophers say about what they're doing in their philosophical > moments. Certainly. If we are to understand philosophy as philosophers practice > it we must inspect what philosophers actually do. As with any > profession, what those in the business say about what they're doing > does not necessarily have any connection to what it is they actually > go about doing. Yes, well, er, that rather seems to be the problem now doesn't it > since you wouldn't appear to have much of an idea what that is. My knowledge or lack thereof is not of much general interest. You can > find out what mathematicians find important, what considerations they > consider germane, and so on, for yourself, by inspecting the > literature. Is there some point to this wanton cross-posting? -- > Aatu Koskensilta (aatu.koskensi...@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen > æ- Ludwig Wittgenstein, Tractatus Logico-Philosophicus- Hide quoted text - - Show quoted text - I am concerned with real math. Applied math seems to be the math that has meaning. I am looking for the meaning of math and recognize that a lot of math is without any real meaning. For instance I do not believe in the complex plane because it is based on an imaginary entity which is the square root of negative one. There are no roots to negatives because there is no such thing as a negative quantity. But there is a single number named i that you can move around and attatch coeffecients to. Keep moving it around. Antidifferentiation as intergration is wrong. Mitch Raemsch Twice Nobel Laureate 2008 === Subject: Re: What is Mathematics? [...] > I am concerned with real math. Applied math seems to be the math that > has meaning. I am looking for the meaning of math and recognize that a > lot of math is without any real meaning. For instance I do not believe > in the complex plane because it is based on an imaginary entity which > is the square root of negative one. I guess nobody ever owed you any money.... [...] > Mitch Raemsch Twice Nobel Laureate 2008 -- wolf k. === Subject: Re: What is Mathematics? > For instance I do not believe in the complex plane because it is > based on an imaginary entity which is the square root of negative > one. What sort of belief is involved here? On any ordinary understanding saying that one does not believe in the complex plane is quite queer. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: What is Mathematics? Antidifferentiation as intergration is wrong. State the Fundemental Theorem of Calculus. Mitch Raemsch Twice Nobel Laureate 2008 Not even once. Bob Kolker === Subject: Re: What is Mathematics? > Antidifferentiation as intergration is wrong. > State the Fundemental Theorem of Calculus. > Mitch Raemsch Twice Nobel Laureate 2008 > Not even once. Bob Kolker You seem to have missed an obvious approaching infinity quip. === Subject: Re: What is Mathematics? <5958102.1208271987425.JavaMail.jakarta@nitrogen.mathforum.org> <7a3Pj.340380$FT.65022@reader1.news.saunalahti.fi> posting-account=i1MELAoAAADwo_-GGwN3NKKSXm8aSdBN SV1),gzip(gfe),gzip(gfe) On Apr 21, 6:21æpm, Aatu Koskensilta Which would be quite instructive if you could just point out a few. A few mathematicians? Surely you can name names yourself. Are we to believe that we're not doing mathematics just now? We are not doing mathematics at the moment. Rather, we're engaged in > pointless news squabbling. Just as it is indeed good advice not to pay to much attention to what > philosophers say about what they're doing in their philosophical > moments. Certainly. If we are to understand philosophy as philosophers practice > it we must inspect what philosophers actually do. As with any > profession, what those in the business say about what they're doing > does not necessarily have any connection to what it is they actually > go about doing. Yes, well, er, that rather seems to be the problem now doesn't it > since you wouldn't appear to have much of an idea what that is. My knowledge or lack thereof is not of much general interest. You can > find out what mathematicians find important, what considerations they > consider germane, and so on, for yourself, by inspecting the > literature. Is there some point to this wanton cross-posting? -- > Aatu Koskensilta (aatu.koskensi...@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen > æ- Ludwig Wittgenstein, Tractatus Logico-Philosophicus Mathematics is what mathematicians do. I'd prefer something a bit less sociological. What about mathematics is any theoretical activity which can rely on theorem proving ? === Subject: Re: What is Mathematics? LauLuna Mathematics is what mathematicians do. I'd prefer something a bit less sociological. What about mathematics is any theoretical activity which can rely on theorem proving ? THR Then mathematics could not be distinguished from philosophy. Tom === Subject: Re: What is Mathematics? >LauLuna >Mathematics is what mathematicians do. >I'd prefer something a bit less sociological. What about mathematics >is any theoretical activity which can rely on theorem proving ? >THR >Then mathematics could not be distinguished from >philosophy. >Tom No, philosophers do all sorts of speculation, and come up with conjectures, or what they would like to be true. Provability or often truth does not enter into their conclusions. I have seen the following definition: A philosopher is someone who is looking for a black cat, in a totally dark room, which isn't there, and finds it! If a mathematician were in this situation, it would be a proof that mathematics is inconsistent, and we would then have to go back and find an adequate weaker system of axioms. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: What is Mathematics? <17336283.1208809303160.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=i1MELAoAAADwo_-GGwN3NKKSXm8aSdBN SV1),gzip(gfe),gzip(gfe) > LauLuna Mathematics is what mathematicians do. I'd prefer something a bit less sociological. What about mathematics > is any theoretical activity which can rely on theorem proving ? THR Then mathematics could not be distinguished from > philosophy. Tom > It is usually believed there are no theorems in philosophy. But since I meant it as a definition, the question is whether it would be counter-intuitive calling any activity in which theorems can be proven 'mathematics'. I think it wouldn't. === Subject: Re: What is Mathematics? > LauLuna > Mathematics is what mathematicians do. > I'd prefer something a bit less sociological. What about mathematics > is any theoretical activity which can rely on theorem proving ? > THR > Then mathematics could not be distinguished from > philosophy. > Tom It is usually believed there are no theorems in philosophy. But since I meant it as a definition, the question is whether it would >be counter-intuitive calling any activity in which theorems can be >proven 'mathematics'. I prefer the qualification proven true. >I think it wouldn't. > === Subject: Re: What is Mathematics? <1208204803@sheol.org> posting-account=kxPkPAoAAACjJi8w0gL9bnyznPzdw9HW 2.0.50727),gzip(gfe),gzip(gfe) On 17 Apr, 19:20, Agent Smith I still see wut u did thar. > That's just brainwashing. æThe laws of arithmetic > have nothing to do with mathematics. You people are insane! What are you trying to say, the Mafia > discovered Mathematics? >Combinatorics preceeded the Mafia by two hundred years, arithmetic by >twenty thousand. ...So they've finally discovered fossilized radiocarbon-datable > arithmetic? How jolly! read, hundreds or even thousands of years later. æ;) æBesides, for such > recent objects, fossilization is not necessary. æIt's only necessary at > paleontological time scales, which means hundreds of thousands of years > or more. So tell me, Prof. Brainetron, did you ever learn the useful trick of > counting zeros, or was your cranial development retarded before you got > to kindygarden?- D.9alj citerad text - - Visa citerad text - I actually once learned it in kindergarten it occupied me for a day or two, but i soon realised it was pointless there were far to many of them, and all of them were useless and a waiste of time. JT === Subject: Re: What is Mathematics? Mathematics is two things: the ART of creating ideas, and the SCIENCE of >applying those ideas to real world material. >Ah, forgot one thing: the DISCIPLINE to _reject_ ideas if it turns out >that these ideas cannot appliccable. The discipline is the hardest part, >for groups as well as for individuals. >So Mathematics is three things: the ART of creating ideas, the SCIENCE >of applying these ideas to real world material, and the DISCIPLINE to >reject ideas for which it's is evident that they cannot be matched to >any real world material. However, one must be careful in mathematics not to apply that rejection > discipline too soon, as some developments in mathematics which > eventually proved to be of great use in the real world were for a long > time thought to be quite useless in that real world, and even valued > more highly for that reason. It is typical of both pure and applied mathematicians to undervalue the > others worth. Uhm, I was thinking along the lines of rejecting Phlogiston and Ether as useless ideas. But suppose these were not mathematical .. Han de Bruijn === Subject: Re: What is Mathematics? >Mathematics is two things: the ART of creating ideas, and the SCIENCE of >applying those ideas to real world material. >Ah, forgot one thing: the DISCIPLINE to _reject_ ideas if it turns out >that these ideas cannot appliccable. The discipline is the hardest part, >for groups as well as for individuals. >So Mathematics is three things: the ART of creating ideas, the SCIENCE >of applying these ideas to real world material, and the DISCIPLINE to >reject ideas for which it's is evident that they cannot be matched to >any real world material. However, one must be careful in mathematics not to apply that rejection > discipline too soon, as some developments in mathematics which > eventually proved to be of great use in the real world were for a long > time thought to be quite useless in that real world, and even valued > more highly for that reason. It is typical of both pure and applied mathematicians to undervalue the > others worth. Uhm, I was thinking along the lines of rejecting Phlogiston and Ether as > useless ideas. But suppose these were not mathematical .. Han de Bruijn They were neither of them totally useless, as investigating whether they were true lead to advances. Even the worst of scientific theories can be useful by serving as bad examples. === Subject: Re: What is Mathematics? >Mathematics is two things: the ART of creating ideas, and the SCIENCE of >applying those ideas to real world material. >Ah, forgot one thing: the DISCIPLINE to _reject_ ideas if it turns out >that these ideas cannot appliccable. The discipline is the hardest part, >for groups as well as for individuals. >So Mathematics is three things: the ART of creating ideas, the SCIENCE >of applying these ideas to real world material, and the DISCIPLINE to >reject ideas for which it's is evident that they cannot be matched to >any real world material. However, one must be careful in mathematics not to apply that rejection > discipline too soon, as some developments in mathematics which > eventually proved to be of great use in the real world were for a long > time thought to be quite useless in that real world, and even valued > more highly for that reason. It is typical of both pure and applied mathematicians to undervalue the > others worth. Uhm, I was thinking along the lines of rejecting Phlogiston and Ether as > useless ideas. But suppose these were not mathematical .. Han de Bruijn > # I'd say that maths implies measurement, of space and time, as compare with linguistics, or science (knowledge). Broader than arithmetic, it includes algebra, geometry, navigation, and anything which involves counting, measuring, or calculating. Quantity, not quality. To mathematics, the number of executions per year is as valid as the number of homeless, housed. === Subject: Re: What is Mathematics? <41368$480700d8$82a1e228$24194@news2.tudelft.nl> <41238$480c4cf1$82a1e228$6554@news2.tudelft.nl> : Don H : I'd say that maths implies measurement, of space and time, Seems a remarkably poor way to think about mathematics. Wayne Throop throopw@sheol.org http://sheol.org/throopw === Subject: Re: What is Mathematics? server.bigpond.net.au: > # I'd say that maths implies measurement, of space and time, as compare > with linguistics, or science (knowledge). I'd say it doesn't. === Subject: Re: What is Mathematics? > # I'd say that maths implies measurement, of space and time, as compare > with linguistics, or science (knowledge). I'd say it doesn't. Agreed; exactly how far _is_ 1 from 2, after all? Dave Bosley on the Number Line DeLaney ps: it's a trick question, because 2 is closer to 3 than it is to 1 -- /DavidtDeLaneytpostingtfrom dbd@vic.com It's not the pot thattgrows the flower It's not the clock thattslows the hour tThe definition's plain for anyone to see Love istall it takes totmake a family - R&P. VISUALIZEtHAPPYNET VRbeable http://www.vic.com/~dbd/ - net.legends FAQ & Magic / I WUV you in all CAPS! --K. === Subject: Re: What is Mathematics? > # I'd say that maths implies measurement, of space and time, as > compare with linguistics, or science (knowledge). > I'd say it doesn't. Agreed; exactly how far _is_ 1 from 2, after all? It's1 away. === Subject: Re: What is Mathematics? <41238$480c4cf1$82a1e228$6554@news2.tudelft.nl> <9mmPj.10$506.7@newssvr27.news.prodigy.net> :: Agreed; exactly how far _is_ 1 from 2, after all? : Mike Schilling : It's1 away. The term in algorithmics is off by one. Wayne Throop throopw@sheol.org http://sheol.org/throopw === Subject: Re: What is Mathematics? >:: Agreed; exactly how far _is_ 1 from 2, after all? : Mike Schilling http://www.vic.com/~dbd/ - net.legends FAQ & Magic / I WUV you in all CAPS! --K. === Subject: Re: What is Mathematics? > ps: it's a trick question, because 2 is closer to 3 than it is to 1 Well, of course-they are both prime numbers. === Subject: Re: What is Mathematics? > ps: it's a trick question, because 2 is closer to 3 than it is to 1 Well, of course-they are both prime numbers. Surely it's because 1 is the loneliest number. -- Bill Snyder [This space unintentionally left blank] === Subject: Re: What is Mathematics? > ps: it's a trick question, because 2 is closer to 3 than it is to 1 >Well, of course-they are both prime numbers. Surely it's because 1 is the loneliest number. Actually, I was just considering that 3 isn't a regular cardinal. Dave NOT A BASEBALL THREAD, or a finite covering of one DeLaney -- /DavidtDeLaneytpostingtfrom dbd@vic.com It's not the pot thattgrows the flower It's not the clock thattslows the hour tThe definition's plain for anyone to see Love istall it takes totmake a family - R&P. VISUALIZEtHAPPYNET VRbeable http://www.vic.com/~dbd/ - net.legends FAQ & Magic / I WUV you in all CAPS! --K. === Subject: Re: What is Mathematics? > ps: it's a trick question, because 2 is closer to 3 than it is to > 1 Well, of course-they are both prime numbers. > Surely it's because 1 is the loneliest number. Actually, I was just considering that 3 isn't a regular cardinal. It needs more roughage. === Subject: Re: What is Mathematics? > Mathematics is two things: the ART of creating ideas, and the > SCIENCE of applying those ideas to real world material. Ah, forgot one thing: the DISCIPLINE to _reject_ ideas if it turns > out that these ideas cannot appliccable. The discipline is the > hardest part, for groups as well as for individuals. So Mathematics is three things: the ART of creating ideas, the > SCIENCE of applying these ideas to real world material, and the > DISCIPLINE to reject ideas for which it's is evident that they > cannot be matched to any real world material. > However, one must be careful in mathematics not to apply that > rejection discipline too soon, as some developments in mathematics > which eventually proved to be of great use in the real world were for > a long time thought to be quite useless in that real world, and even > valued more highly for that reason. > It is typical of both pure and applied mathematicians to undervalue > the others worth. > Uhm, I was thinking along the lines of rejecting Phlogiston and Ether > as useless ideas. But suppose these were not mathematical .. I'd say that maths implies measurement, of space and time, as compare > with linguistics, or science (knowledge). Broader than arithmetic, it includes algebra, geometry, navigation, and > anything which involves counting, measuring, or calculating. Quantity, > not quality. To mathematics, the number of executions per year is as valid as the > number of homeless, housed. Algebraic topology specifically disclaims interest in mensuration. -- The math is easy, said Chaos. < _Thief of Time_ === Subject: Solution manuals posting-account=I4LMEgoAAABgwkvbBt_YLmArZhfVF8gI rv:1.8.1.11pre) Gecko/20071206 Firefox/2.0.0.11 Navigator/9.0.0.5,gzip(gfe),gzip(gfe) I have the following solution manuals. If you are interested in any of them, contact me at books of interest (at) gmail (dot) com booksofinterest@gmail.com Only Paypal payments accepted Please check first if the solution manual you want is in the list, and then contact me instead of posting here. * Solutions manual for Brief Calculus and Its Applications (11th Ed., Larry J Goldstein, Schneider, Nakhle Asmar) * Solutions manual for Finite Math and Its Application (9th Ed., Larry J Goldstein, Schneider & Siegel) * Solutions manual for ñModern Control Systems, 11/E, Richard C Dorf, Robert H. Bishopî * Solutions manual for ñEngineering Mechanics Dynamics, 5/E, Anthony M Bedford, Wallace Fowlerî Solutions manual for ñEngineering Mechanics: Statics, 5/E, Anthony M Bedford, Wallace Fowlerî Solutions manual for ñPhysics for Scientists and Engineers with Modern Physics and Mastering Physics, 4/E, Douglas C. Giancoliî * Solutions manual for ñElements of Engineering Electromagnetics, 6/E, Nannapaneni Narayana Raoî * Solutions manual for ñElectrical Engineering: Principles and Applications, 4/E, Allan R. Hambleyî * Solutions manual for ñMechanics of Materials, 7/E, by Russell C. Hibbelerî * Solutions manual for ñPrinciples of Statics and Dynamics, 10/E, by Russell C. Hibbelerî * Solutions manual for ñStatics and Mechanics of Materials, 2/E., By Russell C. Hibbelerî * Solutions manual for ñIntroduction to Materials Management, 6/E, by Tony Arnold, Steve Chapman, Lloyd Cliveî * Solutions manual for ñFundamentals of Production Planning and Control, by Stephen N. Chapmanî * Solutions manual for ñJava for Engineers and Scientists, 2/E, by Stephen J. Chapmanî * Solutions manual for ñDigital Signal Processing, 4/E, by John G. Proakis, Dimitris K Manolakisî * Solutions manual for ñCalculus: A Complete Course, 2/E , Ross L. Finney, Franklin D. Demana, Kennedyî * Solutions manual for ñAdaptive Filter Theory, 4/E, Simon Haykinî * Solutions manual for ñModern Wireless Communications, Simon Haykin, Michael Moherî * Solutions manual for ñDatabases, Types and the Relational Model, 3/ * Solutions manual for ñOperating Systems: Internals and Design Principles, 5/E, William Stallingsî * Solutions manual for ñNetwork Security Essentials: Applications and Standards, 3/E., William Stallingsî * Solutions manual for ñWireless Communications & Networks, 2/E., William Stallingsî * Solutions manual for ñSignals, Systems, and Transforms, 4/E., Charles L Phillips, John Parr, Eve Riskinî * Solutions manual for ñLogic and Computer Design Fundamentals, 4/E., M. Morris Mano, Charles Kimeî * Solutions manual for ñDistributed Systems: Principles and Paradigms, 2/E., by Tanenbaum, van Steenî * Solutions manual for ñStructured Computer Organization, 5/E., Andrew S. Tanenbaumî * Solutions manual for ñOperating Systems Design and Implementation, 3/ E., Tanenbaum, Woodhullî * Solutions manual for ñFeedback Control of Dynamic Systems, 5/ E.,Franklin, Powell, Naeiniî * Solutions manual for ñPrecalculus: Graphical, Numerical, Algebraic, 7/E., Demana, Waits, GreFoley, Kennedyî * Solutions manual for ñApplied Strength of Materials, 5/E., Robert L. Mottî * Solutions manual for ñApplied Fluid Mechanics, 6/E., Robert L. Mottî * Solutions manual for ñPrinciples of Electronic Media, 2/E., William R. Davie, James R. Upshawî * Solutions manual for ñJohn E. Freund's Mathematical Statistics with Applications, 7/E, Irwin Millerî * Solutions manual for ñElementary Differential Equations with Boundary Value Problems, 6/E., Edwards, Penneyî * Solutions manual for ñDifferential Equations and Boundary Value Problems: Computing and Modeling, 4/E.,Henry Edwards, David Penney.î * Solutions manual for ñCalculus, Early Transcendentals, 7/E., C. Henry Edwards, David E. Penneyî * Solutions manual for ñCalculus, 9/E., Dale Varberg, Edwin Purcell, deceased, Steve Rigdonî * Solutions manual for ñIntroductory Mathematics, 4/E, Nigel P. Cookî * Solutions manual for ñElementary Differential Equations with Boundary Value Problems, 2/E, Werner E. Kohler, Lee W. Johnsonî * Solutions manual for ñFundamentals of Differential Equations bound , 7/E R. Kent Nagle, Edward B. Saff, Arthur David Sniderî * Solutions manual for ñCMOS VLSI Design: A Circuits and Systems Perspective, 3/E., Neil Weste, David Harrisî * Solutions manual for ñDifferential Equations and Linear Algebra, 2/ E, by Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. Westî * Solutions manual for ñDiscrete Mathematics, 5/E, by John A. Dossey, Albert D. Otto, Lawrence E. Spence, Charles Vanden Eyndenî * Solutions manual for ñMathematics for the Technical Trades, by Nigel P. Cookî * Solutions manual for ñIntroductory DC/AC Circuits, 6/E, Nigel P. Cookî * Solutions manual for ñIntroductory DC/AC Electronics, 6/E, Nigel P. Cookî * Solutions manual for ñC++ How to Program, 6/E, by Harvey & Paul, Deitel & Associatesî * Solutions manual for ñEconomic Development, 9/E, by Michael P. Todaro, Stephen C. Smithî * Solutions manual for ñInternational Money and Finance, 7/E, by Michael Melvinî * Solutions manual for ñInternational Economics, 7/E, Steven Husted, Michael Melvinî * Solutions manual for ñInternational Economics: Theory and Policy, 7/ E, Paul R. Krugman, Maurice Obstfeldî * Solutions manual for ñWorld Trade and Payments: An Introduction, 10/ E, by Richard E. Caves, Jeffrey A. Frankel, Ronald W. Jonesî * Solutions manual for ñInternational Economics, 4/E, James Gerberî * Solutions manual for ñPrinciples of Money, Banking, and Financial Markets, 11/E Lawrence S. Ritter, William L. Silber, Gregory F. Udellî * Solutions manual for ñEssentials of Economics, 1st Ed., by Glenn Hubbard, Anthony P O'Brienî * Solutions manual for ñMoney, the Financial System, and the Economy, 6/E, by R. Glenn Hubbardî * Solutions manual for ñMacroeconomics, 2/E, Glenn Hubbard, Anthony P. O'Brienî * Solutions manual for ñMicroeconomics, 2/E, Glenn Hubbard, Anthony P. O'Brienî * Solutions manual for ñEconomic Growth, 1st Ed., by David N. Weilî * Solutions manual for ñMacroeconomics, 10/E, Robert J. Gordonî * Solutions manual for ñMacroeconomics, 6/E Andrew B. Abel, Ben S. Bernanke, Dean Croushoreî * Solutions manual for ñMacroeconomics, 3/E, Stephen D. Williamsonî * Solutions manual for ñEconomics, 8/E, Michael Parkin (Micro- and Macroeconomics) * Solutions manual for ñFoundations of Economics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñFoundations of Macroeconomics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñFoundations of Microeconomics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñEssential Foundations of Economics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñEconomics Today, 14/E Roger LeRoy Millerî * Solutions manual for ñUnderstanding Modern Economics, by Roger LeRoy Millerî * Solutions manual for ñThe Economics of Macro Issues, 3/E, by Miller, Benjaminî * Solutions manual for ñThe Economics of Public Issues, 15/E, Miller, Benjamin, Northî * Solutions manual for ñPrinciples of Economics, 7/E, Roy J. Ruffin, Paul R. Gregory ( Micro and Macroeconomics)î * Solutions manual for ñEconomics: Private Markets and Public Choice, 7/E, Ekelund, Jr., Ressler, Tollisonî * Solutions manual for ñContemporary Engineering Economics - Chan S. Park (4th ed) (ISBN 0131876287)î * Solutions manual for ñJava Software Solutions: Foundations of Program Design, 6/E John Lewis, William Loftusî * Solutions manual for ñTechnical Calculus, 5/E , Dale Ewen, Joan S. Gary, James E. Trefzgerî * Solutions manual for ñTechnical Calculus with Analytic Geometry, 4/ E, Allyn J. Washingtonî * Solutions manual for ñIntroduction to Linear Algebra, 5/E , Lee W. Johnson, R. Dean Riess, Jimmy T. Arnoldî * Solutions manual for ñCalculus and its Applications (11th Ed., Goldstein, Schneider, Lay & Nakhle Asmar)î * Solutions manual for ñManagement Accounting, 5/E Anthony A. Atkinson, S. Kaplan, Matsumura, Youngî * Solutions manual for ñPlastics: Materials and Processing, 3/E , by A. Brent Strongî * Solutions manual for ñintroduction to Materials Science for Engineers, 6/E, James F. Shackelfordî * Solutions manual for ñeconomics: A Tool for Critically Understanding Society, 8/E , Tom Riddell, Jean A Shackelford, Steve C. Stamos, Geoffrey Schneiderî * Solutions manual for ñengineering Materials: Properties and Selection, 8/E, by Ken Budinski, Michael K. Budinski ñ * Solutions manual for ñwork Systems: The Methods, Measurement & Management of Work, by Mikell Grooverî * Solutions manual for ñApplied Multivariate Statistical Analysis (6th Ed., Johnson & Wichern)î * Solutions manual for ñFinancial Markets and Institutions, 6/E, by Frederic S. Mishkin, Stanley G. Eakins ñ * Solutions manual for ñThe Economics of Money, Banking and Financial Markets, Alternate Edition Frederic S. Mishkin (1st /e)î * Solutions manual for ñThe Economics of Money, Banking and Financial Markets, 8/E, Frederic S. Mishkin ñ * Solutions manual for ñPrinciples of Risk Management and Insurance, 10/E , George E. Rejdaî * Solutions manual for ñDerivatives Markets, 2/E, Robert L. McDonaldî * Solutions manual for ñOTIS: Online Trading and Investment Simulator Student Access Kit Wharton Learning Labî * Solutions manual for ñFundamentals of Investing, 10/E Lawrence J. Gitman, Michael D. Joehnk î * Solutions manual for ñIntroduction to Finance 1st/e, by Lawrence J. Gitman, Jeff Maduraî * Solutions manual for ñPrinciples of Managerial Finance, Brief, 5/E Lawrence J. Gitman î * Solutions manual for ñPrinciples of Managerial Finance , 12/E Lawrence J. Gitmanî * Solutions manual for ñCases in International Finance, 2/E , Gunter Dufey, Ian H. Giddyî * Solutions manual for ñFundamentals of Multinational Finance, 3/E , Moffett, Stonehill David K. Eitemanî * Solutions manual for ñMultinational Business Finance, 11/E , Eiteman,. Stonehill, Michael H. Moffettî * Solutions manual for ñTheory of Asset Pricing, George Pennacchiî * Solutions manual for ñRisk Takers: Uses and Abuses of Financial Derivatives, 2/E , John Marthinsenî * Solutions manual for ñCorporate Finance, Jonathan Berk, Peter DeMarzoî * Solutions manual for ñPersonal Finance with Financial Planning Software, 3/E, Jeff Madura î ñ* Solutions manual for ñGeneral Chemistry: Principles and Modern Application & Basic Media Pack, 9/E Ralph H Petrucci, William S Harwood, Geoff E Herring, Jeffry Maduraî * Solutions manual for ñMathematical Methods for Economics, 2/E , by Michael Kleinî * Solutions manual for ñUsing Econometrics: A Practical Guide, 5/E , by A.H. Studenmundî * Solutions manual for ñEconometrics: A Modern Introduction Michael P. Murrayî * Solutions manual for ñIntroduction to Econometrics, Brief Edition, by James H. Stock, Mark W. Watsonî * Solutions manual for ñIntroduction to Econometrics, 2/E, James H. Stock, Mark W. Watsonî * Solutions manual for ñThe Economics of Sports, 3/E Michael A. Leeds, Peter von Allmenî * Solutions manual for ñEconomics, by Michael A. Leeds, Peter von Allmen, Richard C. Schimingî * Solutions manual for ñMacroeconomics MyEconLab Homework Edition, Michael Leeds, Allmen, Schimingî * Solutions manual for ñMicroeconomics MyEconLab Homework Edition By Michael Leeds, Allmen, Schimingî * Solutions manual for ñPublic Finance and the American Economy, 2/E , by Neil Bruceî * Solutions manual for ñMarket Regulation, by Roger Shermanî * Solutions manual for ñLaw and Economics, 5/E , by Robert Cooter, Thomas Ulen ñ * Solutions manual for ñModern Labor Economics: Theory and Public Policy, 10/E , by Ehrenberg, Smithî * Solutions manual for ñModern Industrial Organization, 4/E , Dennis W. Carlton, Jeffrey M. Perloffî * Solutions manual for ñMicroeconomics, 4/E Jeffrey M. Perloff î * Solutions manual for ñMicroeconomics: Theory and Applications with Calculus, by Jeffrey M. Perloffî 3/E, by Don E. Waldman, Jensenî * Solutions manual for ñMicroeconomics, by Don E. Waldmanî * Solutions manual for ñHealth Economics, 3/E, Charles E. Phelpsî * Solutions manual for ñEnvironmental Economics and Policy, 5/E , by Tom Tietenbergî * Solutions manual for ñEnvironmental and Natural Resource Economics, 7/E , by Tom Tietenbergî If you are interested in any of them, contact me at booksofinterest (at) gmail (dot) com booksofinterest@gmail.com Only Paypal payments accepted === Subject: Pseudo-1D function Assume that you have a function which labels any object (in fact, knot) with a 1-parameter function (in fact, a knot polynomial): foo->x^3-3*x bar->2-x etc->x^2+1 z->f(x) Now consider that the label is a bit more complicated: foo->x^3-3*x+y^3-3*y bar->2-x+2-y etc->x^2+1+y^2+1 z->f(x)+f(y) Clearly, you haven't gained any new information - you could as well fix y as constant. And now: foo->x^3-3*x+(y^3-3*y)^2 bar->2-x+(2-y)^2 etc->x^2+1+(y^2+1)^2 z->f(x)+f(y)^2 Still no additional info! But how can I *detect* this from a handful of given labels? Any linearity or dependency check must fail, I could add arbitrary variables u,v,w... and still it's essentially only a function of *one* variable. -- Hauke Reddmann <:-EX8 fc3a501@uni-hamburg.de Er-a svo gott sem gott kve[CapitalYAcute]a .9al alda sonum, §v.92 a[CapitalYAcute] f.berra veit er fleira drekkur s.92ns til ge[CapitalYAcute]s gumi. === Subject: Re: Pseudo-1D function >Assume that you have a function which labels any object >(in fact, knot) with a 1-parameter function (in fact, >a knot polynomial): foo->x^3-3*x >bar->2-x >etc->x^2+1 >z->f(x) Now consider that the label is a bit more complicated: foo->x^3-3*x+y^3-3*y >bar->2-x+2-y >etc->x^2+1+y^2+1 >z->f(x)+f(y) Clearly, you haven't gained any new information - you >could as well fix y as constant. And now: foo->x^3-3*x+(y^3-3*y)^2 >bar->2-x+(2-y)^2 >etc->x^2+1+(y^2+1)^2 >z->f(x)+f(y)^2 Still no additional info! But how can I *detect* this >from a handful of given labels? Any linearity or >dependency check must fail, I could add arbitrary >variables u,v,w... and still it's essentially only >a function of *one* variable. For the examples you gave, just make sure there are no mixed terms and that the nonconstant x-terms are the same as the nonconstant y-terms, except for the change of variable. The constant term can always be split evenly between f(x) and f(y). quasi === Subject: Re: Pseudo-1D function >Assume that you have a function which labels any object >(in fact, knot) with a 1-parameter function (in fact, >a knot polynomial): >foo->x^3-3*x >bar->2-x >etc->x^2+1 >z->f(x) >Now consider that the label is a bit more complicated: >foo->x^3-3*x+y^3-3*y >bar->2-x+2-y >etc->x^2+1+y^2+1 >z->f(x)+f(y) >Clearly, you haven't gained any new information - you >could as well fix y as constant. And now: >foo->x^3-3*x+(y^3-3*y)^2 >bar->2-x+(2-y)^2 >etc->x^2+1+(y^2+1)^2 >z->f(x)+f(y)^2 >Still no additional info! But how can I *detect* this >from a handful of given labels? Any linearity or >dependency check must fail, I could add arbitrary >variables u,v,w... and still it's essentially only >a function of *one* variable. For the examples you gave, just make sure there are no mixed terms and >that the nonconstant x-terms are the same as the nonconstant y-terms, >except for the change of variable. The constant term can always be >split evenly between f(x) and f(y). Sorry, I didn't look at your examples closely enough. Now that I've looked a little more closely, it seems you are asking this ... Given a polynomial g(x,y), determine whether there exists a polynomial f(x), and if there is one, find one, such that g(x,y) = r(x) + s(y), where r is a polynomial in f(x) and s is a polynomial in f(y). Is that a correct interpretation of your question? quasi === Subject: Re: Pseudo-1D function Assume that you have a function which labels any object >(in fact, knot) with a 1-parameter function (in fact, >a knot polynomial): foo->x^3-3*x >bar->2-x >etc->x^2+1 >z->f(x) Now consider that the label is a bit more complicated: foo->x^3-3*x+y^3-3*y >bar->2-x+2-y >etc->x^2+1+y^2+1 >z->f(x)+f(y) Clearly, you haven't gained any new information - you >could as well fix y as constant. And now: foo->x^3-3*x+(y^3-3*y)^2 >bar->2-x+(2-y)^2 >etc->x^2+1+(y^2+1)^2 >z->f(x)+f(y)^2 Still no additional info! But how can I *detect* this >from a handful of given labels? Any linearity or >dependency check must fail, I could add arbitrary >variables u,v,w... and still it's essentially only >a function of *one* variable. >For the examples you gave, just make sure there are no mixed terms and >that the nonconstant x-terms are the same as the nonconstant y-terms, >except for the change of variable. The constant term can always be >split evenly between f(x) and f(y). Sorry, I didn't look at your examples closely enough. Now that I've looked a little more closely, it seems you are asking >this ... Given a polynomial g(x,y), determine whether there exists a polynomial >f(x), and if there is one, find one, such that g(x,y) = r(x) + s(y), >where r is a polynomial in f(x) and s is a polynomial in f(y). Is that a correct interpretation of your question? Of course, you also want f to be nonlinear, otherwise and polynomial g with no mixed terms would qualify (using f(x) = x). quasi === Subject: Solution manuals posting-account=I4LMEgoAAABgwkvbBt_YLmArZhfVF8gI rv:1.8.1.11pre) Gecko/20071206 Firefox/2.0.0.11 Navigator/9.0.0.5,gzip(gfe),gzip(gfe) I have the following solution manuals. If you are interested in any of them, contact me at books of interest (at) gmail (dot) com booksofinterest@gmail.com Only Paypal payments accepted Please check first if the solution manual you want is in the list, and then contact me instead of posting here. * Solutions manual for Brief Calculus and Its Applications (11th Ed., Larry J Goldstein, Schneider, Nakhle Asmar) * Solutions manual for Finite Math and Its Application (9th Ed., Larry J Goldstein, Schneider & Siegel) * Solutions manual for ñModern Control Systems, 11/E, Richard C Dorf, Robert H. Bishopî * Solutions manual for ñEngineering Mechanics Dynamics, 5/E, Anthony M Bedford, Wallace Fowlerî Solutions manual for ñEngineering Mechanics: Statics, 5/E, Anthony M Bedford, Wallace Fowlerî Solutions manual for ñPhysics for Scientists and Engineers with Modern Physics and Mastering Physics, 4/E, Douglas C. Giancoliî * Solutions manual for ñElements of Engineering Electromagnetics, 6/E, Nannapaneni Narayana Raoî * Solutions manual for ñElectrical Engineering: Principles and Applications, 4/E, Allan R. Hambleyî * Solutions manual for ñMechanics of Materials, 7/E, by Russell C. Hibbelerî * Solutions manual for ñPrinciples of Statics and Dynamics, 10/E, by Russell C. Hibbelerî * Solutions manual for ñStatics and Mechanics of Materials, 2/E., By Russell C. Hibbelerî * Solutions manual for ñIntroduction to Materials Management, 6/E, by Tony Arnold, Steve Chapman, Lloyd Cliveî * Solutions manual for ñFundamentals of Production Planning and Control, by Stephen N. Chapmanî * Solutions manual for ñJava for Engineers and Scientists, 2/E, by Stephen J. Chapmanî * Solutions manual for ñDigital Signal Processing, 4/E, by John G. Proakis, Dimitris K Manolakisî * Solutions manual for ñCalculus: A Complete Course, 2/E , Ross L. Finney, Franklin D. Demana, Kennedyî * Solutions manual for ñAdaptive Filter Theory, 4/E, Simon Haykinî * Solutions manual for ñModern Wireless Communications, Simon Haykin, Michael Moherî * Solutions manual for ñDatabases, Types and the Relational Model, 3/ * Solutions manual for ñOperating Systems: Internals and Design Principles, 5/E, William Stallingsî * Solutions manual for ñNetwork Security Essentials: Applications and Standards, 3/E., William Stallingsî * Solutions manual for ñWireless Communications & Networks, 2/E., William Stallingsî * Solutions manual for ñSignals, Systems, and Transforms, 4/E., Charles L Phillips, John Parr, Eve Riskinî * Solutions manual for ñLogic and Computer Design Fundamentals, 4/E., M. Morris Mano, Charles Kimeî * Solutions manual for ñDistributed Systems: Principles and Paradigms, 2/E., by Tanenbaum, van Steenî * Solutions manual for ñStructured Computer Organization, 5/E., Andrew S. Tanenbaumî * Solutions manual for ñOperating Systems Design and Implementation, 3/ E., Tanenbaum, Woodhullî * Solutions manual for ñFeedback Control of Dynamic Systems, 5/ E.,Franklin, Powell, Naeiniî * Solutions manual for ñPrecalculus: Graphical, Numerical, Algebraic, 7/E., Demana, Waits, GreFoley, Kennedyî * Solutions manual for ñApplied Strength of Materials, 5/E., Robert L. Mottî * Solutions manual for ñApplied Fluid Mechanics, 6/E., Robert L. Mottî * Solutions manual for ñPrinciples of Electronic Media, 2/E., William R. Davie, James R. Upshawî * Solutions manual for ñJohn E. Freund's Mathematical Statistics with Applications, 7/E, Irwin Millerî * Solutions manual for ñElementary Differential Equations with Boundary Value Problems, 6/E., Edwards, Penneyî * Solutions manual for ñDifferential Equations and Boundary Value Problems: Computing and Modeling, 4/E.,Henry Edwards, David Penney.î * Solutions manual for ñCalculus, Early Transcendentals, 7/E., C. Henry Edwards, David E. Penneyî * Solutions manual for ñCalculus, 9/E., Dale Varberg, Edwin Purcell, deceased, Steve Rigdonî * Solutions manual for ñIntroductory Mathematics, 4/E, Nigel P. Cookî * Solutions manual for ñElementary Differential Equations with Boundary Value Problems, 2/E, Werner E. Kohler, Lee W. Johnsonî * Solutions manual for ñFundamentals of Differential Equations bound , 7/E R. Kent Nagle, Edward B. Saff, Arthur David Sniderî * Solutions manual for ñCMOS VLSI Design: A Circuits and Systems Perspective, 3/E., Neil Weste, David Harrisî * Solutions manual for ñDifferential Equations and Linear Algebra, 2/ E, by Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. Westî * Solutions manual for ñDiscrete Mathematics, 5/E, by John A. Dossey, Albert D. Otto, Lawrence E. Spence, Charles Vanden Eyndenî * Solutions manual for ñMathematics for the Technical Trades, by Nigel P. Cookî * Solutions manual for ñIntroductory DC/AC Circuits, 6/E, Nigel P. Cookî * Solutions manual for ñIntroductory DC/AC Electronics, 6/E, Nigel P. Cookî * Solutions manual for ñC++ How to Program, 6/E, by Harvey & Paul, Deitel & Associatesî * Solutions manual for ñEconomic Development, 9/E, by Michael P. Todaro, Stephen C. Smithî * Solutions manual for ñInternational Money and Finance, 7/E, by Michael Melvinî * Solutions manual for ñInternational Economics, 7/E, Steven Husted, Michael Melvinî * Solutions manual for ñInternational Economics: Theory and Policy, 7/ E, Paul R. Krugman, Maurice Obstfeldî * Solutions manual for ñWorld Trade and Payments: An Introduction, 10/ E, by Richard E. Caves, Jeffrey A. Frankel, Ronald W. Jonesî * Solutions manual for ñInternational Economics, 4/E, James Gerberî * Solutions manual for ñPrinciples of Money, Banking, and Financial Markets, 11/E Lawrence S. Ritter, William L. Silber, Gregory F. Udellî * Solutions manual for ñEssentials of Economics, 1st Ed., by Glenn Hubbard, Anthony P O'Brienî * Solutions manual for ñMoney, the Financial System, and the Economy, 6/E, by R. Glenn Hubbardî * Solutions manual for ñMacroeconomics, 2/E, Glenn Hubbard, Anthony P. O'Brienî * Solutions manual for ñMicroeconomics, 2/E, Glenn Hubbard, Anthony P. O'Brienî * Solutions manual for ñEconomic Growth, 1st Ed., by David N. Weilî * Solutions manual for ñMacroeconomics, 10/E, Robert J. Gordonî * Solutions manual for ñMacroeconomics, 6/E Andrew B. Abel, Ben S. Bernanke, Dean Croushoreî * Solutions manual for ñMacroeconomics, 3/E, Stephen D. Williamsonî * Solutions manual for ñEconomics, 8/E, Michael Parkin (Micro- and Macroeconomics) * Solutions manual for ñFoundations of Economics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñFoundations of Macroeconomics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñFoundations of Microeconomics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñEssential Foundations of Economics, 3/E Robin Bade, Michael Parkinî * Solutions manual for ñEconomics Today, 14/E Roger LeRoy Millerî * Solutions manual for ñUnderstanding Modern Economics, by Roger LeRoy Millerî * Solutions manual for ñThe Economics of Macro Issues, 3/E, by Miller, Benjaminî * Solutions manual for ñThe Economics of Public Issues, 15/E, Miller, Benjamin, Northî * Solutions manual for ñPrinciples of Economics, 7/E, Roy J. Ruffin, Paul R. Gregory ( Micro and Macroeconomics)î * Solutions manual for ñEconomics: Private Markets and Public Choice, 7/E, Ekelund, Jr., Ressler, Tollisonî * Solutions manual for ñContemporary Engineering Economics - Chan S. Park (4th ed) (ISBN 0131876287)î * Solutions manual for ñJava Software Solutions: Foundations of Program Design, 6/E John Lewis, William Loftusî * Solutions manual for ñTechnical Calculus, 5/E , Dale Ewen, Joan S. Gary, James E. Trefzgerî * Solutions manual for ñTechnical Calculus with Analytic Geometry, 4/ E, Allyn J. Washingtonî * Solutions manual for ñIntroduction to Linear Algebra, 5/E , Lee W. Johnson, R. Dean Riess, Jimmy T. Arnoldî * Solutions manual for ñCalculus and its Applications (11th Ed., Goldstein, Schneider, Lay & Nakhle Asmar)î * Solutions manual for ñManagement Accounting, 5/E Anthony A. Atkinson, S. Kaplan, Matsumura, Youngî * Solutions manual for ñPlastics: Materials and Processing, 3/E , by A. Brent Strongî * Solutions manual for ñintroduction to Materials Science for Engineers, 6/E, James F. Shackelfordî * Solutions manual for ñeconomics: A Tool for Critically Understanding Society, 8/E , Tom Riddell, Jean A Shackelford, Steve C. Stamos, Geoffrey Schneiderî * Solutions manual for ñengineering Materials: Properties and Selection, 8/E, by Ken Budinski, Michael K. Budinski ñ * Solutions manual for ñwork Systems: The Methods, Measurement & Management of Work, by Mikell Grooverî * Solutions manual for ñApplied Multivariate Statistical Analysis (6th Ed., Johnson & Wichern)î * Solutions manual for ñFinancial Markets and Institutions, 6/E, by Frederic S. Mishkin, Stanley G. Eakins ñ * Solutions manual for ñThe Economics of Money, Banking and Financial Markets, Alternate Edition Frederic S. Mishkin (1st /e)î * Solutions manual for ñThe Economics of Money, Banking and Financial Markets, 8/E, Frederic S. Mishkin ñ * Solutions manual for ñPrinciples of Risk Management and Insurance, 10/E , George E. Rejdaî * Solutions manual for ñDerivatives Markets, 2/E, Robert L. McDonaldî * Solutions manual for ñOTIS: Online Trading and Investment Simulator Student Access Kit Wharton Learning Labî * Solutions manual for ñFundamentals of Investing, 10/E Lawrence J. Gitman, Michael D. Joehnk î * Solutions manual for ñIntroduction to Finance 1st/e, by Lawrence J. Gitman, Jeff Maduraî * Solutions manual for ñPrinciples of Managerial Finance, Brief, 5/E Lawrence J. Gitman î * Solutions manual for ñPrinciples of Managerial Finance , 12/E Lawrence J. Gitmanî * Solutions manual for ñCases in International Finance, 2/E , Gunter Dufey, Ian H. Giddyî * Solutions manual for ñFundamentals of Multinational Finance, 3/E , Moffett, Stonehill David K. Eitemanî * Solutions manual for ñMultinational Business Finance, 11/E , Eiteman,. Stonehill, Michael H. Moffettî * Solutions manual for ñTheory of Asset Pricing, George Pennacchiî * Solutions manual for ñRisk Takers: Uses and Abuses of Financial Derivatives, 2/E , John Marthinsenî * Solutions manual for ñCorporate Finance, Jonathan Berk, Peter DeMarzoî * Solutions manual for ñPersonal Finance with Financial Planning Software, 3/E, Jeff Madura î ñ* Solutions manual for ñGeneral Chemistry: Principles and Modern Application & Basic Media Pack, 9/E Ralph H Petrucci, William S Harwood, Geoff E Herring, Jeffry Maduraî * Solutions manual for ñMathematical Methods for Economics, 2/E , by Michael Kleinî * Solutions manual for ñUsing Econometrics: A Practical Guide, 5/E , by A.H. Studenmundî * Solutions manual for ñEconometrics: A Modern Introduction Michael P. Murrayî * Solutions manual for ñIntroduction to Econometrics, Brief Edition, by James H. Stock, Mark W. Watsonî * Solutions manual for ñIntroduction to Econometrics, 2/E, James H. Stock, Mark W. Watsonî * Solutions manual for ñThe Economics of Sports, 3/E Michael A. Leeds, Peter von Allmenî * Solutions manual for ñEconomics, by Michael A. Leeds, Peter von Allmen, Richard C. Schimingî * Solutions manual for ñMacroeconomics MyEconLab Homework Edition, Michael Leeds, Allmen, Schimingî * Solutions manual for ñMicroeconomics MyEconLab Homework Edition By Michael Leeds, Allmen, Schimingî * Solutions manual for ñPublic Finance and the American Economy, 2/E , by Neil Bruceî * Solutions manual for ñMarket Regulation, by Roger Shermanî * Solutions manual for ñLaw and Economics, 5/E , by Robert Cooter, Thomas Ulen ñ * Solutions manual for ñModern Labor Economics: Theory and Public Policy, 10/E , by Ehrenberg, Smithî * Solutions manual for ñModern Industrial Organization, 4/E , Dennis W. Carlton, Jeffrey M. Perloffî * Solutions manual for ñMicroeconomics, 4/E Jeffrey M. Perloff î * Solutions manual for ñMicroeconomics: Theory and Applications with Calculus, by Jeffrey M. Perloffî 3/E, by Don E. Waldman, Jensenî * Solutions manual for ñMicroeconomics, by Don E. Waldmanî * Solutions manual for ñHealth Economics, 3/E, Charles E. Phelpsî * Solutions manual for ñEnvironmental Economics and Policy, 5/E , by Tom Tietenbergî * Solutions manual for ñEnvironmental and Natural Resource Economics, 7/E , by Tom Tietenbergî If you are interested in any of them, contact me at booksofinterest (at) gmail (dot) com booksofinterest@gmail.com Only Paypal payments accepted === Subject: Re: tommy1729 conjecture I'll attempt to translate tommy's conjecture into more standard mathematical language ... First, the concept of an integer polynomial ... An integer polynomial means a polynomial, possibly multivariate unless otherwise specified, with integer coefficients. Thus, an n-variate integer polynomial can be regarded as a function from Z^n to Z, but of course, not every function from Z^n to Z can be represented by an integer polynomial. But a little care is needed here ... For some of the prior conjectures relating to these concepts, the phrase integer-valued polynomial was used. By an integer-valued polynomial we mean a polynomial with rational coefficients, possibly multivariate, which takes only integer values, given integer inputs. Of course, all integer polynomials are also integer-valued, but not every integer-valued polynomial is an integer polynomial. As a simple example, the polynomial (x^2 - x)/2 is an integer-valued polynomial, but not an integer polynomial. But for tommy's current conjecture, we are only considering integer polynomials. Next, let's define an equivalence relation. Call two integer polynomials f,g range equivalent if range(f) = range(g), where the ranges are taken over all integer inputs. Thus, the following polynomials f,g are range equivalent: f = x + y g = x Next, let's consider fibers. Given an integer polynomial f, for each a in Z, we have the fiber f^(-1)(a) which might be empty, finite nonempty, or infinite, depending on the choice of f and the value of a. Next, for range equivalent polynomials, we can define a partial ordering, f is fiber size less than or equal to g denoted f [fs<=] g if for all, for all a in Z, card(f^(-1)(a)) <= card(g^(-1)(a)) where card denotes cardinality. With respect to this partial order, tommy1729 suggests the idea of minimal elements. For a given f, he uses f' to denote a function which is range equivalent to f, and such that, among all polynomials which are range equivalent to f, f' is minimal with respect to the partial order [fs<=]. As an example, x and x + y are range equivalent (with range Z), but x is [fs<=] minimal among all integer polynomials with range Z. Of course, x + 1 would also be minimal, thus, in general, such minimal elements, if they exist, need not be unique. But let me start by asking ... Question: For every nonempty subset S of Z, does there exist a polynomial f which is [fs<=] minimal among all polynomials having range S? Next, let's discuss tommy's concept of deny f. It's just an informal terminology (a tommyism), which can be defined as follows ... g = deny(f) means that the sets range(f) and range(g) partition Z. In the previous threads, we explored the general question ... Which polynomials can be denied? More precisely, for which nonempty proper subsets of S of Z do there exist polynomials f,g with range(f) = S and range(g) = ZS? This question was never fully answered (in sci.math), although a number of partial results were obtained, some easy, some not so easy. So now let's look at tommy's latest conjecture in this regard ... tommy1729's conjecture (translated version): If g = deny(f), and if f',g' are [fs<=] minimal range equivalents of f,g respectively, then all fibers of f' and g' are finite. Let me ask a simpler question ... Forget the deny stuff -- just focus on [fs<=] minimality. Question: Does there exist an infinite proper subset S of Z, and an integer polynomial f with range(f) = S, such that f is [fs<=] minimal among all integer polynomials having range S, and f^(-1)(s) is infinite, for some s in S. quasi === Subject: Re: tommy1729 conjecture posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) I'll attempt to translate tommy's conjecture into more standard > mathematical language ... Much appreciated (probably not least by tommy/amy themselves) I managed to interpret most of it OK, although the notion of minimal elements seemed problematic because in principle the relative order of two range-equivalent polynomials could vary independently for each value, analogous to non-archimedian norms for different primes. So I was and still am having trouble seeing how one can define even a partial order (unless you only include polynomials, if any, that are compatible in that sense for every value in their range) > As an example, x and x + y are range equivalent (with range Z), > but x is [fs<=] minimal among all integer polynomials with > range Z. Of course, x + 1 would also be minimal, thus, in > general, such minimal elements, if they exist, need not be > unique. I suspect this range order thing applies only for linear polynomials. > :: > Forget the deny stuff -- just focus on [fs<=] minimality. Question: Does there exist an infinite proper subset S of Z, and an integer > polynomial f with range(f) = S, such that f is [fs<=] minimal among > all integer polynomials having range S, and f^(-1)(s) is infinite, for > some s in S. Wouldn't f = 2.(x - y) do : * integer polynomial * proper subset S of Z, as it assumes only even values * f^(-1)(s) is infinite for every s in S * minimal I reckon, because every pair s, x has an associated y Also a complementary or partitioning pair is f = x^2 - y^2, which bags every integer (including zero) not doubly odd, and g = 4.z + 2, which covers precisely the complement of f in Z, and both these are probably minimal in the murky (!) sense tommy intends. John R Ramsden === Subject: Re: tommy1729 conjecture > f is fiber size less than or equal to g denoted f [fs<=] g > > if for all, for all a in Z, card(f^(-1)(a)) <= card(g^(-1)(a)) where card denotes cardinality. > > Question: Does there exist an infinite proper subset S of Z, and an integer > polynomial f with range(f) = S, such that f is [fs<=] minimal among > all integer polynomials having range S, and f^(-1)(s) is infinite, for > some s in S. I don't know, but I'll propose a candidate: f(x) = x^2 - 2 y^2. Certainly its range S is an infinite proper subset of Z (it doesn't contain 0). Also, f^(-1)(1) is infinite. So, if f is minimal etc., etc., then it's a counterexample. -- GM === Subject: Re: tommy1729 conjecture posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) f is a deny of g if and only if f' is deny g too. > and vice versa. Thinking about it, f is the complementary set of integers represented by g right? So f cap g = 0 and f cup g = Z ? > suppose f and g have denys and they are eachothers deny. then we have a deny-couple (f,g) (f,g) exists if and only if (f',g') exists too. and vice versa. Yup, by definition, skirting over your proviso about a mimimum amount of times, which I must confess I don't really understand. > the conjecture : two integer functions (f and g) can only be a deny-couple (f,g) > if card f' or card g' is non-negative. stated differently it is neccesary that card f' or card g' is non-negative for (f,g) > to be a deny-couple. A counterexample (I think) is f = x^2 + y^2 + z^2 + t^2 + 1 and f' the same with x, y, z, t transformed by an integer matrix of determinant 1 (or a sum of fourth powers + 1, as in my example in a previous post) and g = - x'^2 - y'^2 - z'^2 - t'^2 with g' as for f' but without the +1 and negated. John R Ramsden === Subject: Re: tommy1729 conjecture posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) > it is neccesary that card f' or card g' is non-negative for (f,g) > to be a deny-couple. A counterexample (I think) is f = x^2 + y^2 + z^2 + t^2 + 1 and > f' the same with x, y, z, t transformed by an integer matrix of > determinant 1 (or a sum of fourth powers + 1, as in my example > in a previous post) and g = - x'^2 - y'^2 - z'^2 - t'^2 with g' > as for f' but without the +1 and negated. Drat - That isn't a counterexample at all, because card(F) is non-negative if F is definite, which f' and g' both are, because in that case any given integer has at most a finite number of representations. It's an interesting problem, but I think it's debatable there is any pair of disjoint polynomial sets whose union is Z, other than those representing (with suitable sign choice) Z+ and {Z- cup 0}, in which case the result follows. But then again, an indefinite quadratic form which represents certain integers modulo the discriminant must represent all complementary integers when negated. So there might be some crafty way of slotting a complementary pair of sets together. But you'd have to take account of integers that divide the discriminant, and zero. Anyway, I'm off to bed ;-) John Ramsden === Subject: Re: tommy1729 conjecture posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) let f and g be integer polynomials. let f' and g' denote simplified integer polynomials where the simplified > means f' has the same output integers as f but a minimum amount of times > ( not 0 ) and is still an integer polynomial. e.g. f = a^3 + b^3 + c^3 + d^3 + e^3 + F^3 + g^3 + h^3 + i^3 + j^3 > (dont be confused by 2 f's the capital f is a variable , the other f the function ) after this simplification we get -> f' = x OK, I'm with you so far. In this example f and f' are universal forms, which represent all integers. So as a similar example, for all positive integers, you could have cited f = x^4 + y^4 + .. + t^4 and f' = x'^2 + y'^2 + z'^2 + t'^2 for a suitable number of 4th powers which Waring's theorem ensures represents all positive integers. I can't think of any examples that don't represent either all integers or all positive integers (or from the latter trivially, with every coefficient negated, all negative integers). But maybe there are. > let card f denote the maximum amount a same integer output > occurs for f , or if that turns out to be oo or is unbounded > then by definition card f returns -1. ******** f is a deny of g if and only if f' is deny g too. and vice versa. Does deny g mean f doesn't represent the numeric integer g, so you're reiterating here that f represents the same set of integers as f' ? Or is deny a standard term in the study of Diophantine sets? > suppose f and g have denys and they are eachothers deny. > then we have a deny-couple Sorry, I'm baffled now. > (f,g) (f,g) exists if and only if (f',g') exists too. and vice versa. the conjecture : two integer functions (f and g) can only be a deny-couple (f,g) if card f' or card g' is non-negative. stated differently it is neccesary that card f' or card g' is non-negative for (f,g) to be a deny-couple. > tommy1729 === Subject: Re: tommy1729 conjecture posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) I can't think of any examples that don't represent either all > integers or all positive integers (or from the latter trivially, > with every coefficient negated, all negative integers). But maybe > there are. Or all equal multiples, just as the negative integers are obtained my multiplying by -1. In other words if f and f' represent the same set of integers then so do n.f and n.f' for any integer n. === Subject: Re: tommy1729 conjecture posting-account=FK_G5goAAAAEbWGaiao8aY3ti47UN9eX 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > here i will continue on some old threads , it might be hard to follow if you havent read those. but i aim for the people who where there anyway , no offense to newbies. also this is not standard math so dont feel bad if you cant follow up. it is also possible i posted this before , im not sure , but just in case i didnt or you missed it , i post it again. anyways let f and g be integer polynomials. *Giggle* mound of rectal pus. === Subject: What is Z[1/2]? Hi all, Which ring is Z[1/2]? I've seen it mentioned a few times, such as here: http://www.jstor.org/sici?sici=0002-9939(199807)126%3A7%3C2159%3AECFGZ%3E2.0 .CO%3B2-0 or here: http://www.ingentaconnect.com/content/klu/kthe/2002/00000025/00000002/004035 67 but I don't remember having seen its definition. Jose Carlos Santos === Subject: DONT SEE MY WEBSITE posting-account=0sGa_AoAAACj5ZFkpkRzoiAEIfcqlRDR FunWebProducts),gzip(gfe),gzip(gfe) wonderful future and to earn more money see the site www.doitbetter5.blogspot.com www.getitlove.blogspot.com === Subject: Re: DONT SEE MY WEBSITE posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) > wonderful future and to earn more > money ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?see > the sitewww.doitbetter5.blogspot.comwww.getitlove.blogspot.com I didn't see it yesterday, I'm not seeing it today and don't plan on seeing it tomorrow. This is becoming very annoying. === Subject: Towards a solution of the Septic equation I would like to inform you of the progress i made regarding a polynomial equation: I solved an ODE that Hurwitz made in connection with Felix Klein's work: http://www.dse.nl/~geertjan/Publikatie/On an ODE connected with the septic equation.pdf And I set four terms in the septic to zero using Tschirnhaus transformations. http://www.dse.nl/~geertjan/Publikatie/The septic equation reduced.pdf If you have an interest in polynomial equations, please read them! === Subject: Re: Towards a solution of the Septic equation - blank = %20 > I would like to inform you of the progress i made regarding a polynomial > equation: I solved an ODE that Hurwitz made in connection with Felix Klein's work: http://www.dse.nl/~geertjan/Publikatie/On an ODE connected with the septic > equation.pdf And I set four terms in the septic to zero using Tschirnhaus > transformations. http://www.dse.nl/~geertjan/Publikatie/The septic equation reduced.pdf If you have an interest in polynomial equations, please read them! > Vervang AUB eerst alle spaties in de URLs door %20 - dan wil ik de papers wel lezen. Please replace all blanks in the URLs by %20 before I even think of reading your papers. === Subject: Re: Towards a solution of the Septic equation - blank = %20 - > I would like to inform you of the progress i made regarding a > polynomial equation: > I solved an ODE that Hurwitz made in connection with Felix Klein's work: > http://www.dse.nl/~geertjan/Publikatie/On an ODE connected with the > septic equation.pdf > And I set four terms in the septic to zero using Tschirnhaus > transformations. > http://www.dse.nl/~geertjan/Publikatie/The septic equation reduced.pdf > If you have an interest in polynomial equations, please read them! Vervang AUB eerst alle spaties in de URLs door %20 - dan wil ik de > papers wel lezen. Please replace all blanks in the URLs by %20 before I even think of > reading your papers. > I reacted too fast - sorry - Johan E. Mebius === Subject: Re: Towards a solution of the Septic equation Sorry about the dead links in the previous mail. === Subject: Re: Towards a solution of the Septic equation Sorry about the dead links in the previous mail. This time it should work! http://www.dse.nl/~geertjan/Publikatie/On%20an%20ODE%20connected%20with%20th e%20septic%20equation.pdf And the other link: http://www.dse.nl/~geertjan/Publikatie/The%20septic%20equation%20reduced.pdf === Subject: Some Bayes questions... posting-account=_KcbFAkAAACPcKINjRxCKEAs3AA9RdEJ Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) There are a few things about Bayes reasoning that I don't quite understand... I have a device for racing balls which has 10 lanes (I don't but I got fed up with talking about Bayes/cancer all the time). I don't think that there is any real difference in the lanes and, sure enough, when I stage 100 races, the winners are evenly spread: LANE WINS LOSSES TOTAL ---- ---- ------ ----- 1 10 90 100 2 10 90 100 3 10 90 100 4 10 90 100 5 10 90 100 6 10 90 100 7 10 90 100 8 10 90 100 9 10 90 100 10 10 90 100 Now I can use this to build a table of all the Bayes numbers: LANE PRIOR_ODDS_WIN PRIOR_ODDS_LOSE TPR FPR FNR TNR P_GIVEN_P N_GIVEN_P P_GIVEN_N N_GIVEN_N ---- -------------- --------------- --- --- --- --- --------- --------- --------- --------- 1 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 2 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 3 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 4 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 5 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 6 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 7 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 8 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 9 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 10 0.1 0.9 0.1 0.9 0.1 0.9 0.012 0.988 0.012 0.988 Here, The prior odds are my expecation that all lanes are identical and being in one should have no bearing on the result. TPR = True Positive Rate, etc. P_GIVEN_P = Likelihood of a win give a positive test result - and my test is the lane that it's in. That all seems fine in tat the ?_GIVEN_? results are identical for each lane - but what does it really mean? For lane 1, P_GIVEN_P is 0.012. Given that the prior odds of a ball in one lane winning (because there are 10 identical lanes) is 10%, how does 0.012 impact this figure? OK, onwards. I got some polish and pixie-dust and gave lane 1 a good seeing to. Lo and behold there was an improvement. All my hard work increased the number of winners in lane 1: LANE WINS LOSSES TOTAL ---- ---- ------ ----- 1 11 89 100 2 9 91 100 3 10 90 100 4 10 90 100 5 10 90 100 6 10 90 100 7 10 90 100 8 10 90 100 9 10 90 100 10 10 90 100 My Bayes table changes accordingly: LANE PRIOR_ODDS_WIN PRIOR_ODDS_LOSE TPR FPR FNR TNR P_GIVEN_P N_GIVEN_P P_GIVEN_N N_GIVEN_N ---- -------------- --------------- ---- ---- ----- ----- --------- --------- --------- --------- 1 0.1 0.9 0.11 0.89 0.1 0.9 0.014 0.986 0.012 0.988 2 0.1 0.9 0.09 0.91 0.101 0.809 0.011 0.989 0.012 0.988 3 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 4 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 5 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 6 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 7 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 8 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 9 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 10 0.1 0.9 0.1 0.9 0.101 0.899 0.012 0.988 0.012 0.988 As expected, there is a small change to the lane 1 results and the ? _GIVEN_? figures egister small changes. Likewise for lane 2 - well, someone had to take the hit. And a similar question to the last one; what implications do these changes have? How does my prior odds change in the light of these new results? And one bonus question... What if my balls are not equal (stop sniggering at the back!)? What if I have already done a completely different test on the balls and have determined a set of different odds for them. How can I combine the results of this test with those odds to give an overall odds for a particular ball in a particular lane? Steve === Subject: Re: Some Bayes questions... posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > There are a few things about Bayes reasoning that I don't quite > understand... I have a device for racing balls which has 10 lanes (I don't but I got > fed up > with talking about Bayes/cancer all the time). I don't think that > there is > any real difference in the lanes and, sure enough, when I stage 100 > races, the > winners are evenly spread: LANE WINS LOSSES TOTAL > ---- ---- ------ ----- > 1 10 90 100 > 2 10 90 100 > 3 10 90 100 > 4 10 90 100 > 5 10 90 100 > 6 10 90 100 > 7 10 90 100 > 8 10 90 100 > 9 10 90 100 > 10 10 90 100 Now I can use this to build a table of all the Bayes numbers: LANE PRIOR_ODDS_WIN PRIOR_ODDS_LOSE TPR FPR FNR TNR P_GIVEN_P > N_GIVEN_P P_GIVEN_N N_GIVEN_N > ---- -------------- --------------- --- --- --- --- --------- > --------- --------- --------- > 1 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 2 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 3 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 4 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 5 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 6 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 7 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 8 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 9 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 > 10 0.1 0.9 0.1 0.9 0.1 0.9 0.012 > 0.988 0.012 0.988 Here, The prior odds are my expecation that all lanes are identical > and being in one should > have no bearing on the result. > TPR = True Positive Rate, etc. > P_GIVEN_P = Likelihood of a win give a positive test > result - and my test is the lane that it's in. That all seems fine in tat the ?_GIVEN_? results are identical for > each lane - > but what does it really mean? For lane 1, P_GIVEN_P is 0.012. Given that the prior odds of a ball in > one lane > winning (because there are 10 identical lanes) is 10%, how does 0.012 > impact this figure? OK, onwards. I got some polish and pixie-dust and gave lane 1 a good seeing to. Lo > and behold > there was an improvement. All my hard work increased the number of > winners in > lane 1: LANE WINS LOSSES TOTAL > ---- ---- ------ ----- > 1 11 89 100 > 2 9 91 100 > 3 10 90 100 > 4 10 90 100 > 5 10 90 100 > 6 10 90 100 > 7 10 90 100 > 8 10 90 100 > 9 10 90 100 > 10 10 90 100 My Bayes table changes accordingly: LANE PRIOR_ODDS_WIN PRIOR_ODDS_LOSE TPR FPR FNR TNR P_GIVEN_P > N_GIVEN_P P_GIVEN_N N_GIVEN_N > ---- -------------- --------------- ---- ---- ----- ----- --------- > --------- --------- --------- > 1 0.1 0.9 0.11 0.89 0.1 0.9 > 0.014 0.986 0.012 0.988 > 2 0.1 0.9 0.09 0.91 0.101 0.809 > 0.011 0.989 0.012 0.988 > 3 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 > 4 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 > 5 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 > 6 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 > 7 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 > 8 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 > 9 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 > 10 0.1 0.9 0.1 0.9 0.101 0.899 > 0.012 0.988 0.012 0.988 As expected, there is a small change to the lane 1 results and the ? > _GIVEN_? figures > egister small changes. Likewise for lane 2 - well, someone had to take > the hit. And a similar question to the last one; what implications do these > changes have? > How does my prior odds change in the light of these new results? And one bonus question... What if my balls are not equal (stop sniggering at the back!)? What if > I have already done a > completely different test on the balls and have determined a set of > different odds for them. > How can I combine the results of this test with those odds to give an > overall odds for > a particular ball in a particular lane? Steve I think you either misunderstand Bayesian analysis or else are mis- using it. The standard Bayesian way of looking at your problem is as follows. Before taking any observations at all, you start with some prior probability distribution on the problem parameters. In this case, you would start with a prior on the vector (p1,p2,...,p10), which are the win probabilities for lanes 1-10. Here, the pi are > 0 and they must sum to 1. What types of priors should you use? Well, you feel initially that all lanes are equal, so you do not want to favor any one over another. A typical prior that would be used in this type of case would be the so-called Dirichlet distribution; see, eg., http://en.wikipedia.org/wiki/Dirichlet_distribution . The Dirichlet is the so-called conjugate prior for the multinomial, which is what you have. One type of distribution might be that, as far as you know, the p1, p2, ..., p10 can be anything, as long as there is no bias; so, for example, you might choose the vector (p1,p2,...,p10) to be uniformly distributed over the simplex S = {(x1,...,x10): xi > 0 for all i and sum xi = 10}; this is accomplished by taking all the a_i to be 1 in the Dirichlet distribution as defined in the link above (where I use notation a_i or ai instead of the link's alpha_i). Now, before you start to observe anything it is a good idea to get an understanding of what your prior will say about some simple observations. Suppose you are about to run one race between the 10 lanes, and ask: what is the probability that lane j will win? This is given by integrating the quantity P{j wins|(p1,...,p10)}*f(p1,...,p10) with respect to (p1,...,p10) over the simplex S; here, f is the prior probability density of the vector p = (p1,p2,...,p10). For the Dirichlet with parameters (a1,...,a10) we get P{j wins} = a_j/sum(a_k) because P{j wins|(p1,...,p10)} = p_j, and so we just need the mean of the jth component, which is given in the link. In particular, for the uniform prior we obtain P{j wins} = 1/10. (We would also obtain 1/10 even if the aj are different from 1, as long as they are all equal to each other.) Now, after observing some races with n1 winning in lane 1, n2 winning in lane 2,..., and n10 winning in lane 10, you can modify the probability distribution of the vector p = (p1,...,p10). For the case of a Dirichlet prior this is very easily done; that is why the Dirichlet is used so often. The so-called posterior distribution of p is again a Dirichlet, with parameters (ai + ni) for i = 1,...,10. Now, given your prior and your observations up to now, what can you say about /future/ events? In particular, what now is P{j wins} if you run one more race? Now it is the mean of the new Dirichlet, so is P{j wins} = (aj + nj)/sum(ak+nk) for j = 1,...,10. In particular, if you had used a uniform prior with all ai = 1, you would now have P{j wins} = (nj+1)/[10 + sum(nk)]. Note that if all the ni are equal to a common n (as in your initial case) and you start with a uniform prior, the posterior will now be Dirichlet with parameters (1+n). This will no longer be uniform, because it will now be unlikely that any particular p_j will be near 0 or 1---but will most likely be bunched up around 1/10. We will still have P{j wins} = (n+1)/[10+10n] = 1/10 for a single future race. Of course, if you start to get some unequal n_i the win probabilities will start to differ between the lanes. Again, if you use a Dirichlet prior the computations are straightforward. Most everything you need is given in the link provided. Note: you can NEVER use a fixed prior as you did (i.e., a prior in which the vector (p1,...,p10) is some specified constant vector), because if you do that, the vector of probabilities /remains fixed forever/, and no amount of observed data will ever change it (at least, not if you use the Bayes formulas)! To have data affect or modify your assessments, you need to have /several possible p vectors to start with/. Using the Dirichlet prior does that for you, but there are other, less convenient possibilities, such as a discrete set of p vectors with a discrete probability distribution defined over them. R.G. Vickson === Subject: Optimization w/ Transaction Costs: Uniqueness of positive gain solution posting-account=7ik1uAoAAAAiHAvGsCz7oPl2Vs3ze7sx CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.1),gzip(gfe),gzip(gfe) I have a research question related to mean-variance optimization with transaction costs. The question is fairly theoretical, concerning existence and (limited) uniqueness of solutions satisfying criteria; although there are practical consequences for a yes/no answer. Quickly, the question is, with constant risks, if the (linear or 1- form) objective function changes from time i to i+1, will there be at most one solution which is a positive trade relative to no trade, and which will be a local maximum, relative to a convex (possibly smooth ellipsoid) risk- allowed set. I am wondering if this has been solved in the applied math literature, and if there is no reference, does anyone have intuition on it or know how to solve this under general or specific circumstances, or give a counter- example. I will give details to make the problem full clear: Let X in R^N represent a vector of weights (that are risky, such as stock exposures). Say the convex compact allowed set is E. I am happy to assume that E is the closed interior of a smooth ellipsoid, centered at the origin: X^T V X = constant^2, V = square symmetric matrix positive definite There is an old weight X_old (which is set by fiat; completely independent) and we seek to find a new weight X_new in E, such that (i) X_new is a local maximum for f(X) (ii) X_new has f(X_new)>0 (i.e. this is better than setting X_new=X_old) The objective function is f(X) = mu^T (X-X_old) + iota^T * abs(X-X_old) Here, mu is a 1-form (or just vector) in R^N giving the benefit from moving in the mu direction. iota=(1,1,...,1) is the vector of ones in R^N representing taxicab-metric transaction costs for moving the weights X away from old weights X_old. I have used some scaling symmetries to set without loss of generality each component of iota to 1, and left mu and E general. Note that f(X)=0, and E is compact, so there is at least one global maximum attained by f, and it is >=0. Note that X=0 itself might be a local maximum or not. Playing around with this, it is easy to get multiple local maximum of f, but I can't get more than one to be positive. Conjecture: For generic E (or smooth ellipsoid-bounded E), there is at most one local maximum of f which has f>0. related to my conjecture, if there is no definitive answer. Gregory Jones === Subject: Re: Optimization w/ Transaction Costs: Uniqueness of positive gain solution posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) On Apr 22, 6:34 am, Gregory C. Jones with transaction costs. The question is fairly theoretical, > concerning > existence and (limited) uniqueness of solutions satisfying criteria; > although there are practical consequences for a yes/no answer. Quickly, the question is, with constant risks, if the (linear or 1- > form) > objective function changes from time i to i+1, will there be at most > one > solution which is a positive trade relative to no trade, and which > will > be a local maximum, relative to a convex (possibly smooth ellipsoid) > risk- > allowed set. I am wondering if this has been solved in the applied math literature, > and if there is no reference, does anyone have intuition on it or know > how > to solve this under general or specific circumstances, or give a > counter- > example. I will give details to make the problem full clear: Let X in R^N represent a vector of weights (that are risky, such as > stock > exposures). Say the convex compact allowed set is E. I am happy to > assume that > E is the closed interior of a smooth ellipsoid, centered at the > origin: > X^T V X = constant^2, V = square symmetric matrix positive definite There is an old weight X_old (which is set by fiat; completely > independent) > and we seek to find a new weight X_new in E, such that (i) X_new is a local maximum for f(X) > (ii) X_new has f(X_new)>0 (i.e. this is better than setting > X_new=X_old) The objective function is f(X) = mu^T (X-X_old) + iota^T * abs(X-X_old) Here, mu is a 1-form (or just vector) in R^N giving the benefit from > moving in the mu direction. iota=(1,1,...,1) is the vector of ones > in R^N representing taxicab-metric transaction costs for moving > the weights X away from old weights X_old. I have used some scaling > symmetries to set without loss of generality each component of iota > to 1, and left mu and E general. Note that f(X)=0, and E is compact, so there is at least one global > maximum attained by f, and it is >=0. Note that X=0 itself might be a > local > maximum or not. Playing around with this, it is easy to get multiple local maximum of > f, > but I can't get more than one to be positive. I don't see how this can be the case without some restrictions on the data 'mu' and E. For example, in one dimension and with mu = 0, you have f(X) = |X - X_old|. If E = [-a,a] (the ellipsoid in 1 dimension), and if |X_old| < a then both X = -a and X = +a are local maxima, and f will be positive for both. You can make mu small and positive or negative, to still have the same conclusion. You can cook up similar examples in more than 1 dimension. You have a convex function f(X) that you want to maximize over a convex set E. The general instance of such a problem is NP-hard, although for your specially-structured f(X) there might be good algorithms. R.G. Vickson Conjecture: For generic E (or smooth ellipsoid-bounded E), there is at > most one local maximum of f which has f>0. related > to my conjecture, if there is no definitive answer. Gregory Jones === Subject: Look who is back. Re: .8bSS Agent.8a Job Opportunity at Dedanoe.89s E.D.U. Inc. > .8bSS Agent.8a Job Opportunity at Dedanoe.89s E.D.U. Inc. Well.A, Well.A, We-eee-ell.A... This is the most damn curse that one > can cast to a businessman: .8bMay you offer everything for free and no > one to have the interest to buy.8a. That was the case with Dedanoe.89s > business for a long time until Dedanoe finally figured out a way to > break it. Don.89t bother as.king how Dedanoe did it until his business > recovers. Now that the demand of Dedanoe.89s costumers rises he must make a few > employments cause otherwise that demand will over his offer very soon. > Knowing that Dedanoe prefers to play single, at first E.D.U. inc. will > employ only One SS Agent. Applicants must be of female gender. The > chosen one will go trough twelve months special course in various > Armageddonian techniques and disciplines like Spiritual TAO Ki Do Ki, > SCH. Geo Matrix, Leverian Electroen Astro Magnatism, Intergalactic > Communications over the Universe-Wide Neuro-Web and so... Working for the cause of the Six Dons of Armageddon will be > challenging enough for you because you.89ll have a comfortable chair > next to Dedanoe at the bridge of the Universal VASEDOOM Space Arc > A11E80 taking you from one end of the universe to the other at no > time, you.89ll be dealing with supernatural, paranormal tasks for no > salary cause you.89ll have access to Dedanoe.89s endless resources even > when you pass on the opposite side of the parallel multi universe, > you.89ll be authorized to decide the faith of the universe with your own > TAO Button that triggers Dedanoe.89s Armageddon Bomb and multi many > other challenges... To apply simply send only recent picture of you, your initials and > unique ID number via MMS at +389-77-703697 with .8bSS Agent:.8a in front > of it; for instance: .8bSS Agent: E. A. 0901977xxxxxx.8a. Dedanoe will > reach you soon to let you know if you.89re chosen. Apply NOW! Twonky has competition. === Subject: Imp Q[X]/ etc http://b4.spline.tv/study777/?message=497 === Subject: Re: What is Z[1/2]? days. My association with the Department is that of an alumnus. Which ring is Z[1/2]? In general, if R is a ring contained in a ring S, and u in S, then R[u] denotes the smallest subring of S that contains R and u. In the case of R=Z, and u in Q, we mean the smallest subring of Q that contains both Z and u. So Z[1/2] is the smallest subring of Q that contains Z and contains 1/2. This is the top-down definition. In the commutative case, the bottom-up definition is that R[u] is the ring (contained in S) of all elements of the form r_0 + r_1*u + ... + r_n*u^n, where r_0,...,r_n are in R, n is a nonnegative integer (i.e., the evaluations of elements of the polynomial ring R[x] under the evaluation map x|->u). For the particular case of Z[1/2], it consists of all rationals which, when written in lowest terms p/q with q>0, will have a denominator that is a power of 2. -- magidin-at-member-ams-org === Subject: Re: What is Z[1/2]? > Hi all, Which ring is Z[1/2]? Polynomials in 1/2 with integer coefficients. For example: 4 - 5*(1/2) + 3*(1/2)^2 Of course there are other descriptions that involve figuring out what you can get in this way. === Subject: Re: What is Z[1/2]? > Hi all, Which ring is Z[1/2]? I've seen it mentioned a few > times, such as here: http://www.jstor.org/sici?sici=0002-9939(199807)126%3A > 7%3C2159%3AECFGZ%3E2.0.CO%3B2-0 or here: http://www.ingentaconnect.com/content/klu/kthe/2002/00 > 000025/00000002/00403567 but I don't remember having seen its definition. > Jose Carlos Santos In general: given a subring R of a ring S the notation R[A], where A is a subset of S, is used to denote the smallest subring of S containing both R and A. It is frequently used when R is a domain and S is its field of fractions. H === Subject: Re: What is Z[1/2]? Jos.8e Carlos Santos a .8ecrit : > Which ring is Z[1/2]? I've seen it mentioned a few times, such as here: I guess it is the ring obtained by adding to Z a multiplicative inverse for 2, i.e. the set of rational numbers of the form k/2^n. Alternatively, you can see it as the quotient Z[X]/(2X-1). -- Fatal === Subject: Re: What is Z[1/2]? >Jos.8e Carlos Santos a .8ecrit : > Which ring is Z[1/2]? I've seen it mentioned a few times, such as here: I guess it is the ring obtained by adding to Z a multiplicative inverse >for 2, i.e. the set of rational numbers of the form k/2^n. >Alternatively, you can see it as the quotient Z[X]/(2X-1). Yes. It's subring of Q generated by Z and 1/2. quasi === Subject: Re: What is Z[1/2]? > Which ring is Z[1/2]? I've seen it mentioned a few times, such as here: I guess it is the ring obtained by adding to Z a multiplicative inverse > for 2, i.e. the set of rational numbers of the form k/2^n. > Alternatively, you can see it as the quotient Z[X]/(2X-1). Jose Carlos Santos === Subject: Symbolic geometry software I'm looking for symbolic geometry software that can find and show things with a strict construction without necessarily using the Pythagorean theorem or the infinite plane because of the following quote. Synergetics: http://www.rwgrayprojects.com/synergetics/synergetics.html 825.26 Pythagorean Proof 825.261 All of these steps were eventually taken and proven in a complex of other proofs. In the meantime, they were diverted by the Pythagoreans' construction proof of the square of the hypotenuse of a right triangle's equatability with the sum of the squares of the other two sides, and the construction proof that any non-right triangle's dimensional values could be obtained by dropping a perpendicular upon one of its sides from one of its vertexes and thus converting it into two right triangles each of which could be solved arithmetically by the Pythagoreans' squares without having to labor further with empirical constructs. This arithmetical facility induced a detouring of strictly constructional explorations, hypotheses, and proofs thereof. 825.27 Due to their misassumed necessity to commence their local scientific exploration of geometry only in a supposed plane that extended forever without definable perimeter, that is, to infinity, the Ionians began using their right-triangle exploration before they were able to prove that six equilateral triangles lie in a circle around point D. They could divide the arithmetical 360 degrees of circular unity agreed upon into six 60-degree increments. And, as we have already noted, if this had been proven by their early constructions with their three tools, they might then have gone on to divide all planar space with equilateral triangles, which models would have been very convenient in connection with the economically satisfactory point-locating capability of triangulation and trigonometry. -- End of Quote -- http://mysite.verizon.net/cjnelson9/SyngergeticFiles/HTMLFiles/Synergetic sCoordinates3_11.gif Cliff Nelson Dry your tears, there's more fun for your ears, Forward Into The Past 2 PM to 5 PM, Sundays, California time, http://www.geocities.com/forwardintothepast/ Don't be a square or a blockhead; see: http://mysite.verizon.net/cjnelson9/index.htm http://library.wolfram.com/infocenter/search/?search_results=1;search_per son_id=607 === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=vI5-YAoAAACpb1I_2s__b0LrjNDZjNTS Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > Set theory has sense only in actual infinity. > Therefore it has no sense. Why? It has no sense in the actual infinity, right: because the actual > infinity has no sense itself. It must be an infinite yet self- > contained - thus finalized - entity. The language allows to express > it, but the actual meaning is not here yet. This way the actual > infinity cannot be a result of some calculation, but a pre-requisite > constant to be strictly defined _before_ any calculations. Cantor > tried put it up side down so failed in this direction. For what sake should it be good, if it cannot be matter of > calculation? To allow the calculations. The math has several helper imaginary values that makes the calculation/reasoning flow to arrive to some comprehensible end. For the quantity matters these are 0 (zero, null, nil) and oo (infinity). 0 means no matter how small positive value you have, this one is still smaller. oo means no matter how big positive value you have, this one is still bigger. The system gets defective in many circumstances so oftenly extended by: -oo (negative infinity) means no matter how big absolute value of your negative number is, this one still has bigger. These are nothing but shortcuts instead of saying it each time in each statement: just like the solid black square for quod erat demonstrandum. Attempts of making out of them some self-contained mysterious entities to be understood or calculated are rather ridiculous. The black square would be much interesting in this matter then :-) (think Malevich painting and stuff :-) > In order to see its inconsistency consider the simplest example, the > natural numbers. If they are taken in unary representation > o > oo > ooo > ... > then it is clear that there cannot be an actually infinite number (of > numbers) without an actually infinite number --- iff actual infinity > is a number greater than every natural number. Thus there is no > actually infinite number of numbers possible. There is not any inconsistency, just a plain simple misreading of the formula - as if someone would take aleph sign for alfa sign and would start wondering what angles are doing here. If we read oo properly then the set theory gets its meaning back: but loosing of course that cosmogonic context Cantor vainly tried to push into it. For the Infinity (stars, death, etc.) go to philosophy or to physics or to religion apon your choice. Solving it over some diagonal arguments is... OK, you understood me, I guess... > So let's take daemons Can and Tor. Let they be staying near of two > conveyors with the belt coming from one wall and going to the other. > Color cubes are passing by on these conveyors and Can and Tor have to > take them out. But Can has to take from his conveyor all cubes: and > Tor is allowed to take only reds, greens and each 3rd blue one. Every > billion years the conveyors stop and Can and Tor have to make as many > unique combinations as possible out of their cubes they have so far. > The winner is who has more of possible combinations. > It is required to proof or to disproof that no matter how billion year > periods we have, the winner will be Can on his sinecure and much > harder working Tor will loose:-) > I can be deeply wrong, but Cantor's methods are letting us to solve > this problem. Cantor's mathematics is not of any use for any real problem. So you mean I have to drop a coin for the winner? The common sense tells me that I should bet on Can, but the common sense is not always a great helper. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl > Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. > > This is provably wrong. It can be proved by complete induction that > the set of all FISONs is neiher sufficient nor necessary to cover N. It is not necessary, but it is sufficient, as is easily proven. > This is valid for all finite FISONs without any exception. So there > remains nothing that could be subject to claim A. This is in no way a response to the claim. It is not even related. > Claim B: There exist a set containing infinitely many FISONs, each of > which is required to cover N. This is not something I have claimed. > No FISON is required to cover N. The set of FISONs which are required > to cover N is empty. > > That shows that there is no set of FISONs covering N. Wrong. > Claim A does not imply claim B. > > For a linear set (linear with respect to the subset relation) claim A > would imply claim B Wrong. Or show a proof. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > Friar Grandi said: God created the world from nothing by means of > mathematics: 0 = 0 + 0 + 0 + ... = (1 - 1) + (1 - 1) + (1 - 1) +- ... = 1 + (-1 + > 1) + (-1 + 1) +- ... = 1 + 0 + 0 + 0 +- ... = 1 so he created a 1 from what, an infinite number of 1's? He sort of > didn't need the 1 on the far right, did he? He'd already > created it. I must be missing something. The parentheses. I added them above. By ZF we can even create infinity from nothing: Borrow the set of all finite initial sequences of natural numbers > {1} > {1, 2} > {1, 2, 3} > ... Their union is the infinite initial sequence {1, 2, 3, ...} of natural > numbers. which can be constructed by the elements available. Put them together > into a set. Remove all finite initial sequences of natural numbers > from this set and return the loan. There remains the infinite initial > sequence of natural numbers. Of course. Except we can't name any natural number n that actually > belongs to this infinite sequence. A number that cannot be named does not belong to anything. I suppose you must mean that whoever is actually up to his > elbows in this infinite union is desperately running along > the ending close braces of the finite sets that get > disappeared right behind him The point is that here the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... is said to be the same as the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... > æ{1, 2, 3, ...} which obviously is incorrect. > Doesn't the difference between the two unions mean you > acknowledge the actual, true infinity of the natural > numbers? If actual infinity would exist, then it would be the second union - and it would be dfferent from potential infinity, namely the first union. > If the natural numbers are finite, then {1,2,3,....} would end with some n', and so > would be the same as > {1,2,3,....,n'}, right? I do not say that the natural numbers are finite. However, even though you acknowledge (even > if you do so unknowingly) true > infinity, you still claim the two unions > are different. So I have to try a different > attempt at following your reasoning. Do you deny that sets are determined by their > elements? If so, you cannot find a natural > number in {1,2,....} (the true infinite set of > natural numbers) that isn't in one of the > {1,2,..,n}'s, and so the two unions are > the same. But you can find a true infinite initial segment in the second union, while the first union has only FISONs as elements. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > The point is that here the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... is said to be the same as the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... > æ{1, 2, 3, ...} which obviously is incorrect. > Doesn't the difference between the two unions mean you > acknowledge the actual, true infinity of the natural > numbers? If actual infinity would exist, then it would be the second union - > and it would be dfferent from potential infinity, namely the first > union. Sets are constants, not variables. Which outlaws WM's variable potentials as nonsense non sets. In order for the supposedly different unions to be different, there must be at least one object which is a member of one set but not the other. But there are no such objects, as every object which is a member of some fison is already a member of N, so the second union is necessarily a subset of the first. If the natural numbers are finite, then {1,2,3,....} would end with some n', and so > would be the same as > {1,2,3,....,n'}, right? I do not say that the natural numbers are finite. There is only finite and non-finite. However, even though you acknowledge (even > if you do so unknowingly) true > infinity, you still claim the two unions > are different. So I have to try a different > attempt at following your reasoning. Do you deny that sets are determined by their > elements? If so, you cannot find a natural > number in {1,2,....} (the true infinite set of > natural numbers) that isn't in one of the > {1,2,..,n}'s, and so the two unions are > the same. But you can find a true infinite initial segment in the second union, > while the first union has only FISONs as elements. To claim that two sets are not equal is to claim that there is a member of one that is not a member of the other. That is what the axiom of extensionality requires. Until WM can find a member of one of these unions that is not a member of the other, his claim that they are different fails. That, at some length, can be seen to reduce to WM's being able to find a natural that is not a member of any fison. Well, WM? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > The point is that here the union of {1} > {1, 2} > {1, 2, 3} > ... is said to be the same as the union of {1} > {1, 2} > {1, 2, 3} > ... > {1, 2, 3, ...} which obviously is incorrect. > Do you deny that sets are determined by their > elements? If so, you cannot find a natural > number in {1,2,....} (the true infinite set of > natural numbers) that isn't in one of the > {1,2,..,n}'s, and so the two unions are > the same. But you can find a true infinite initial segment in the second union, > while the first union has only FISONs as elements. Do you even know the definition of union? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU AppleWebKit/419.2.1 (KHTML, like Gecko) Safari/419.3,gzip(gfe),gzip(gfe) > Doesn't the difference between the two unions mean you > acknowledge the actual, true infinity of the natural > numbers? > If actual infinity would exist, then it would be the second union - > and it would be dfferent from potential infinity, namely the first > union. I'm still trying to find a rigorous set theory in which WM's claims about infinity can hold. Earlier, I proposed a model of ZFC-Extensionality, in which a potentially infinite set is one where the Axiom of Extensionality fails -- because a potential infinite has the potential to contain more elements, so is not completely determined by its elements right now. Later, Virgil asserted that this is nonsense, because in any sane theory, there can be no temporal component to any sets at all, so we can't have a potential infinity. Obviously, to Virgil, a sane theory is one in which full Extensionality holds, to say the least. But a couple of weeks ago, I was reading some book about infinity (don't recall which), where the author keeps on using the notation Fin(ZFC) to denote a certain theory. Perhaps the author means finitely axiomatized ZFC? many natural numbers. And what's amazing is that the set of all numbers need not be a transitive set, so that a large number (the author's favorite is 10^10^10^10) can exist without all of its predecessors existing. factorization in any reasonable amount of time. So this Fin(ZFC), whatever the author intends it to mean, does sound a lot like a rigorous axiomatization of WM. Hopefully, there is an expert set theorist out there who could help clarify what theory Fin(ZFC) is, or whether I'm right in assuming that Fin(ZFC) means finitely axiomatized ZFC. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > Doesn't the difference between the two unions mean you > acknowledge the actual, true infinity of the natural > numbers? > If actual infinity would exist, then it would be the second union - > and it would be dfferent from potential infinity, namely the first > union. I'm still trying to find a rigorous set theory in which WM's > claims about infinity can hold. Earlier, I proposed a model of ZFC-Extensionality, in which a > potentially infinite set is one where the Axiom of Extensionality > fails -- because a potential infinite has the potential to contain > more elements, so is not completely determined by its elements > right now. Later, Virgil asserted that this is nonsense, because in any > sane theory, there can be no temporal component to any sets > at all, so we can't have a potential infinity. Obviously, to > Virgil, a sane theory is one in which full Extensionality holds, > to say the least. But a couple of weeks ago, I was reading some book about > infinity (don't recall which), where the author keeps on using the > notation Fin(ZFC) to denote a certain theory. Perhaps the > author means finitely axiomatized ZFC? many natural numbers. And what's amazing is that the set of > all numbers need not be a transitive set, so that a large > number (the author's favorite is 10^10^10^10) can exist without > all of its predecessors existing. factorization in any reasonable amount of time. So this Fin(ZFC), whatever the author intends it to mean, does > sound a lot like a rigorous axiomatization of WM. Hopefully, > there is an expert set theorist out there who could help clarify > what theory Fin(ZFC) is, or whether I'm right in assuming that > Fin(ZFC) means finitely axiomatized ZFC. Sounds like ideas from Lavine's understanding the infinite -- review at: http://tinyurl.com/5xepvl (claim: ZFC is consistent iff every finite subset of Fin(ZFC) has a finite model; Fin(ZFC) is not finitely axiomatised in the sense of having finitely many axioms, I presume.) potential infinite in arithematic (analysed from the viewpoint that standard infinites are OK in the meta-theory) is Theories of Arithmetic in Finite Models Michal Krynicki and Konrad Zdanowski, Journal Symbolic Logic vol 70, 2005 (in all good libraries). Of course time is not relevant in the classical picture; but a more formal account of the potential infinite might well go via an account of finite arithmetic processes, or of a class of finite arithemtical structures. -- Alan Smaill === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=71XbuAoAAACx3_UV8yBrbgOAHUYjIUR6 Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > potential infinite in arithematic (analysed from the viewpoint that > standard infinites are OK in the meta-theory) is Theories of > Arithmetic in Finite Models Michal Krynicki and Konrad Zdanowski, > Journal Symbolic Logic vol 70, 2005 (in all good libraries). > This is available from Zdanowski's web site http://www.impan.gov.pl/~kz/Research.html http://www.impan.gov.pl/~kz/files/MKKZ_ArFM.pdf Also check his PhD thesis Arithmetics in finite but potentially infinite worlds http://www.impan.gov.pl/~kz/files/KZ_PhD.pdf === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4 MathPlayer 2.0; .NET CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > I do not say that the natural numbers are finite. Let's record this: WM agrees to the successor axiom. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i I do not say that the natural numbers are finite. Let's record this: WM agrees to the successor axiom. Hmm, remember to check the c-s version: WM: iii iii iiii iii NOT iiiii iiiii iiiiii iiiii iiii natural numbers iiiiii iiiii iiiii iiiiii iiii iiii finite. See? It may well mean Some natural numbers are infinite. Perhaps he hasn't decided yet, if all he remembers is the chicken-scratch, the sentence can be pressed into use in any number of ways, depending on the argument in hand. Brian Chandler === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > What I have asserted is this : The union of a set of FISONs is equal to N iff the set of FISONs is > infinite. And I have proved by induction that the set of all FISONs is neither > sufficient nor necessary to cover N. A proof by induction covers every > natural number (if started from 1). A proof by induction proves that a proposition P is true of each and > every natural number. It does not prove that P is true of N. I do not claim that the proof is true for the infinite initial sequence {1, 2, 3, ...}. I claim that it is true for each and every FISON and all smaller FISONs. So there is no FISON remaining for your asserted infinite set. I have _not_ asserted this : There exists a set of FISONs which is `required' to cover N. Yes, you avoid that because you know that your claim is wrong. The claim Infinitely many FISONs are required to cover N can be read > in two different ways. Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. Claim B: There exist a set containing infinitely many FISONs, each of > which is required to cover N. This is not something I have claimed. > No FISON is required to cover N. The set of FISONs which are required > to cover N is empty. Claim A does not imply claim B. I avoid claim B because I know claim B to be false. I assert claim A > because there is an easy proof that it is true, There is no proof at all. The only proof is the argument: Iff he set N exists and if it cn be coverd by FISONs, then there must e infinitely many. By the way: My proof shows that for every n FISON(n) and all smaller ones are not covering N. Cantor's diagonal proof shows that for every line n and all smaller ones his diagonal numer is different from the first n entries. Why do you think that his proof covers all natural numbers (lines of the list) but mine does not? Please note: I do not assert that I can name any list entry that is identical to the diagonal number. I do only assert that there is an infinte number of list entries which are identical with the diagonal number. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > What I have asserted is this : The union of a set of FISONs is equal to N iff the set of FISONs is > infinite. And I have proved by induction that the set of all FISONs is neither > sufficient nor necessary to cover N. A proof by induction covers every > natural number (if started from 1). A proof by induction proves that a proposition P is true of each and > every natural number. It does not prove that P is true of N. I do not claim that the proof is true for the infinite initial > sequence {1, 2, 3, ...}. I claim that it is true for each and every > FISON and all smaller FISONs. So there is no FISON remaining for your > asserted infinite set. WM has only managed to remove finitely many, which leaves infinitely many still in place. Any subset of the set of fisons whose compliment in the set of fisons is infinite may be removed as=and still leave a setcovering N. I have _not_ asserted this : There exists a set of FISONs which is `required' to cover N. Yes, you avoid that because you know that your claim is wrong. The claim Infinitely many FISONs are required to cover N can be read > in two different ways. Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. Claim B: There exist a set containing infinitely many FISONs, each of > which is required to cover N. This is not something I have claimed. > No FISON is required to cover N. The set of FISONs which are required > to cover N is empty. Claim A does not imply claim B. I avoid claim B because I know claim B to be false. I assert claim A > because there is an easy proof that it is true, There is no proof at all. The only proof is the argument: Iff he set > N exists and if it cn be coverd by FISONs, then there must e > infinitely many. It is certainly clear that the set of all fisons has at least one fison for each natural, so the set of all of them necessarily covers N. It is equally clear that no finite set of fisons can cover N, as for any finite set of fisons there is a largest n in N covered and its successor is not covered. So that somewhere between finite sets of fisons and the set of all fisons is the transition from not covering N to covering N. Lemma: If A is an infinite set and B is a finite sub set of A then the difference set, AB = {x: x in A and not x in B}, is infinite. Theorem: For a set of fisons to cover N, it is necessary that that set of fisons be infinite. Proof: Finite sets of fisons don't ever cover N. Theorem: For a set of fisons to cover N, it is sufficient that that set of fisons be infinite. Proof: given any n in N, there are at most finitely many fisons which do not contain n as a member, so that some (in fact infinitely many) fisions in any infinite set of fisons DO contain n. > By the way: > My proof shows that for every n FISON(n) and all smaller ones are not > covering N. Since we have already proved that no finite set of fisons covers N, WM's attempt at proving the same is redundant. > Cantor's diagonal proof shows that for every line n and all smaller > ones his diagonal numer is different from the first n entries. Actually, what Cantor proved was that his diagonal for a given list is different from all entries in that list. Why do you think that his proof covers all natural numbers (lines of > the list) but mine does not? Because Cantor was better at proving things. Please note: I do not assert that I can name any list entry that is > identical to the diagonal number. I do only assert that there is an > infinte number of list entries which are identical with the diagonal > number. And Cantor proves there are no list entries which are identical with the diagonal. If it comes to choosing between between a mathematician like Cantor and an obvious putzer like WM, mathematicians, and most others, will choose Cantor. > === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) What I have asserted is this : The union of a set of FISONs is equal to N iff the set of FISONs is > infinite. And I have proved by induction that the set of all FISONs is neither > sufficient nor necessary to cover N. A proof by induction covers every > natural number (if started from 1). A proof by induction proves that a proposition P is true of each and > every natural number. It does not prove that P is true of N. I do not claim that the proof is true for the infinite initial > sequence {1, 2, 3, ...}. I claim that it is true for each and every > FISON and all smaller FISONs. I agree that your proof shows that no finite set of FISONs covers N. However, this does not imply that no set of FISONs covers N. Any infinite set of FISONs does. > So there is no FISON remaining for your asserted infinite set. What asserted infinite set? > The claim Infinitely many FISONs are required to cover N can be read > in two different ways. Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. Claim B: There exist a set containing infinitely many FISONs, each of > which is required to cover N. This is not something I have claimed. > No FISON is required to cover N. The set of FISONs which are required > to cover N is empty. Claim A does not imply claim B. I avoid claim B because I know claim B to be false. I assert claim A > because there is an easy proof that it is true, There is no proof at all. The only proof is the argument: Iff he set > N exists and if it cn be coverd by FISONs, then there must e > infinitely many. This is unreadable. Try again? Proof that the union of a set of FISONs is equal to N iff that set is infinite. Denote the set of FISONs by X, the union by U(X). Lemma: If X is infinite then U(X) is equal to N. Proof: For every n in N, X has an element with n as an element (as X is infinite). So U(X) has n as an element. For every u in U(X), u is a natural number. Thus N has u as an element. For every n in N, U(X) has n as an element. For every u in U(X), N has u as an element. So the sets are equal. Lemma: If X is finite then U(X) is not equal to N. Proof: If X is finite then U(X) is finite. N is infinite. So U(X) is not equal to N. Taking both lemmas together: U = N iff X is infinite. I don't know if that is what you were trying to type above. > By the way: > My proof shows that for every n FISON(n) and all smaller ones are not > covering N. > Cantor's diagonal proof shows that for every line n and all smaller > ones his diagonal numer is different from the first n entries. Why do you think that his proof covers all natural numbers (lines of > the list) but mine does not? I agree that your proof shows that no finite set of FISONs covers N. However, this does not imply that no set of FISONs covers N. Any infinite set of FISONs does. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > The claim Infinitely many FISONs are required to cover N can be read > in two different ways. Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. This is provably wrong. It can be proved by complete induction that the set of all FISONs is neiher sufficient nor necessary to cover N. This is valid for all finite FISONs without any exception. So there remains nothing that could be subject to claim A. Claim B: There exist a set containing infinitely many FISONs, each of > which is required to cover N. This is not something I have claimed. > No FISON is required to cover N. The set of FISONs which are required > to cover N is empty. That shows that there is no set of FISONs covering N. Claim A does not imply claim B. For a linear set (linear with respect to the subset relation) claim A would imply claim B === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=oTDIagkAAACTxHurtPutBWvNQS8ZCNO9 Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) The claim Infinitely many FISONs are required to cover N can be read > in two different ways. Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. This is provably wrong. It can be proved by complete induction that > the set of all FISONs is neiher sufficient nor necessary to cover N. Is there some difference between complete induction and induction; i.e., is there something called not complete induction or incomplete induction? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor The claim Infinitely many FISONs are required to cover N can be read > in two different ways. Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. This is provably wrong. Wm cannot prove it wrong without imposing axioms that are invalid in ZFC and NBG and many other set theories. > It can be proved by complete induction that > the set of all FISONs is neiher sufficient nor necessary to cover N. WRONG! The set of all fisons is sufficient because there is no natural that is not member of some fison, the one of which it is maximum, among others. No particular set of fisons is necessary, but the infiniteness of a set of fisons is necesry to cover N. > This is valid for all finite FISONs without any exception. There is a difference between a finite fison (they all are finite) and a finite set of fisons (most sets of fisons aren't finite). > So there > remains nothing that could be subject to claim A. Except that there are infinite sets of fisons in ZFC and in NBG and every such set covers N. Claim B: There exist a set containing infinitely many FISONs, each of > which is required to cover N. This is not something I have claimed. > No FISON is required to cover N. The set of FISONs which are required > to cover N is empty. That shows that there is no set of FISONs covering N. Claim A does not imply claim B. For a linear set (linear with respect to the subset relation) claim A > would imply claim B Not outside of WM's mytheology! Claim B, and WM, ignore the fact, true in ZFC and NBG, that the family of al infinite subsets of an infinite set, while partially ordered by inclusion, has no minimal member. Infinite sets differ from finite sets in ways that WM prevents himself from understanding. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) The claim Infinitely many FISONs are required to cover N can be read > in two different ways. Claim A: A set of FISONs covers N if and only if it is infinite. > This is what I claim. This is provably wrong. It can be proved by complete induction that > the set of all FISONs is neiher sufficient nor necessary to cover N. > This is valid for all finite FISONs without any exception. So there > remains nothing that could be subject to claim A. A proof by induction proves that a proposition P is true of each and every natural number. It does not prove that P is true of N. > Claim B: There exist a set containing infinitely many FISONs, each of > which is required to cover N. This is not something I have claimed. > No FISON is required to cover N. The set of FISONs which are required > to cover N is empty. That shows that there is no set of FISONs covering N. Prove it. Also, define required. > Claim A does not imply claim B. For a linear set (linear with respect to the subset relation) claim A > would imply claim B Prove it. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > > Maybe young students are smart enough to realise that there is a > > difference between A set containing X elements is required to > > achieve Y and There exists a set containing X elements, each > > of which is required to achieve Y > > > > The fact is as follows: You assert that a set is required. > > You are pretty good at misreading what is actually stated. In this > case: a set with infinitely many elements is required. > > Well, does such a set not contain at least one element? Each of the sets that are sufficient has infinitely many elements. > > This proves your assertion being > > wrong. > > No. Or do you assert now that at one stage the number of elemenets > suddenly becomes finite? > > No. The proof shows includes FISON n for every natural number n. That is, for every n you can remove {1}, ..., {1, ..., n}. But not that you can remove {1}, {1, 2}, ... . -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > ... > æ> æ> Maybe young students are smart enough to realise that there is a > æ> æ> difference between A set containing X elements is required to > æ> æ> achieve Y and There exists a set containing X elements, each > æ> æ> of which is required to achieve Y > æ> æ æ> æ> The fact is as follows: You assert that a set is required. > æ æ> You are pretty good at misreading what is actually stated. æIn this > æ> case: a set with infinitely many elements is required. > æ æ> Well, does such a set not contain at least one element? Each of the sets that are sufficient has infinitely many elements. æ> æ> æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ This proves your assertion being > æ> æ> wrong. > æ æ> No. æOr do you assert now that at one stage the number of elemenets > æ> suddenly becomes finite? > æ æ> No. The proof shows includes FISON n for every natural number n. That is, for every n you can remove {1}, ..., {1, ..., n}. æBut not > that you can remove {1}, {1, 2}, ... . A proof by induction shows that *every* set of the last line can be removed. And every set which is smaller! === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... > æ> æ> Maybe young students are smart enough to realise that there is a > æ> æ> difference between A set containing X elements is required to > æ> æ> achieve Y and There exists a set containing X elements, each > æ> æ> of which is required to achieve Y > æ> æ æ> æ> The fact is as follows: You assert that a set is required. > æ æ> You are pretty good at misreading what is actually stated. æIn this > æ> case: a set with infinitely many elements is required. > æ æ> Well, does such a set not contain at least one element? Each of the sets that are sufficient has infinitely many elements. æ> æ> æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ This proves your assertion being > æ> æ> wrong. > æ æ> No. æOr do you assert now that at one stage the number of elemenets > æ> suddenly becomes finite? > æ æ> No. The proof shows includes FISON n for every natural number n. That is, for every n you can remove {1}, ..., {1, ..., n}. æBut not > that you can remove {1}, {1, 2}, ... . A proof by induction shows that *every* set of the last line can be > removed. And every set which is smaller! But not every set which is larger. You have to pick a fison first, then that one and every smaller one can be removed, but not every larger one. However hard WM tries, he cannot prove in ZFC (or in NBG) that which is not true in ZFC (or NBG). That WM can find contradictions within his own system does not mean that those contradictions occur outside it. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl > That is, for every n you can remove {1}, ..., {1, ..., n}. But not > that you can remove {1}, {1, 2}, ... . > > A proof by induction shows that *every* set of the last line can be > removed. And every set which is smaller! Right, so if you want to remove all of them, you have to show a set which you remove plus all smaller sets. Because what you want to remove must still have a last (largest) set (that is one of the conclusions from induction). -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > > Wrong. If you get a contradiction within set theory, set theory is > > inconsistent. But if you get a contradiction with something outside > > set theory that does not mean that set theory is inconsistent, but > > that set theory is not compatible with the something outside it. > > > > Every set of natural numbers has a least element. > > Do you intend that as an answer? If so, elaborate. I see no > contradiction. > > If there is a set of FISONs necessary to cover N, then this set should > have a least element. Each of the sets that cover N has a least element, but there is no *minimal* set of FISONs that covers N. > > Within set theory sets are fixed and either finite or not finite. > > > > It is not the question what set theory says but what sets are. > > Sets are not in and of themselves without a definition of what a set is. > And in my thinking a set *is* fixed and immutable. > > Then describe the set of necessary FISONs. There is no the set of necessary FISONs. Why do you keep on repeating that while I have already written so many time that such a thing does not exist? Each set of FISONs that is infinite is sufficient to cover n. > So I think that set > theory models sets pretty well. But, when you are arguing in set theory > you better use the terminology of set theory otherwise you will find > that your terminology is not compatible with set theory, and you might > easily think that there is a contradiction within set theory. > > Every FISON carries a finite amount of information. Therefore it is > impossible to have infinitely many distinct FISONs. If this is in set > theory or outside: A theory which claims the existence of infinitely > many distinct FISONs is wrong. That is just opinion. Prove it within standard mathematics. > Do green quarks indeed emit pulses of the wavelength commonly associated > with green? Or do they absorb light of other wavelength? > > However, if sets can be variable you can never tell that something is an > element of a set, because you do not know. > > You seem not to be able to tell what FISONs belong to the set > necessary to cover N. I have been telling you again and again that there is no the set necessary to cover N. Why do you not read what I write? > > > The sum of a series is a well known expression. > > > > It is actually not a sum. > > > > That may be your opinion, nevertheless you are wrong when mathematics > > is concerned. > > It is actually not a sum: > sum(i = 1, ..., oo) 1/2^i > is *defined* as: > > what remains after all terms have been added. Why do you skip the actual mathematical definition and supply something that is mathematically totally wrong? > > I defined > > the cardinal number of the set of terms of the sequence. > > Yes. And? > > To shorten the discussion: You claim that the union of the set of > FISONs is the same as the union of the set of FISONs and the infinite > segment of N. That is wrong. Why? Suppose: union(n in N) {1, ..., n} = N what is: union(union(n in N) {1, ..., n}, N)? > > No. There is a disctinction. Infinitely many FISONs are necessary, > > but none is specifically necessary, as long as you still have > > infinitely many. > > > > Then remove one by one. If there is no stop, this removal removes > > infinitely many. > > No. If there is no stop at each stage you still have removed finitely > many. > > Cantor claims that his diagonal is different from every entry of the > list. And he is right. Each digit is defined independent from all other digits. And it is easy to show that with that definition the number obtained is different from all numbers on the list. > I have shown that the set of removable FISONs is larger than every > natural number. That's enough. No, that is *not* enough. But if there is no stop, at *no* point will you have removed all FISONs. Otherwise there would be a stop when you have removed them all. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > ... > æ> æ> Wrong. æIf you get a contradiction within set theory, set theory is > æ> æ> inconsistent. æBut if you get a contradiction with something outside > æ> æ> set theory that does not mean that set theory is inconsistent, but > æ> æ> that set theory is not compatible with the something outside it. > æ> æ æ> æ> Every set of natural numbers has a least element. > æ æ> Do you intend that as an answer? æIf so, elaborate. æI see no > æ> contradiction. > æ æ> If there is a set of FISONs necessary to cover N, then this set should > æ> have a least element. Each of the sets that cover N has a least element, but there is no *minimal* > set of FISONs that covers N. There is no set of finite segments that covers an infinite segment. For actual infinity we can set up a very simple estimation that may show you what in fact you are claiming: An infinite segment is at least 10 times longer than any finite segment. But no finite segment is only twice as long than itself. I prove that every FISON can be removed from the set that covers N without changing the covering properties of the set. You are not able to name one of them that cannot be removed. Why should we trust you? Why should we believe in a finite segment which by unioning it with others gets 100 times longer than it is? æ> æ> Within set theory sets are fixed and either finite or not finite. > æ> æ æ> æ> It is not the question what set theory says but what sets are. > æ æ> Sets are not in and of themselves without a definition of what a set is. > æ> And in my thinking a set *is* fixed and immutable. > æ æ> Then describe the set of necessary FISONs. There is no the set of necessary FISONs. And there is no set of sufficient FISONs. There is not even one single useful FISON. > æWhy do you keep on repeating > that while I have already written so many time that such a thing does not > exist? æEach set of FISONs that is infinite is sufficient to cover n. Each FISON of a set of FISONs is finite and hence can be identified. If you claim that infinitely many are required, then you should be able to identify at least one of them. As you cannot, your claim turns out to require unidentifiable FISONs that, however, are not FISONs but only imaginations. æ> æSo I think that set > æ> theory models sets pretty well. æBut, when you are arguing in set theory > æ> you better use the terminology of set theory otherwise you will find > æ> that your terminology is not compatible with set theory, and you might > æ> easily think that there is a contradiction within set theory. > æ æ> Every FISON carries a finite amount of information. Therefore it is > æ> impossible to have infinitely many distinct FISONs. If this is in set > æ> theory or outside: A theory which claims the existence of infinitely > æ> many distinct FISONs is wrong. That is just opinion. æProve it within standard mathematics. Standard mathematics shows that every finite chain of symbols contains a finite amount of information. æ> Do green quarks indeed emit pulses of the wavelength commonly associated > æ> with green? æOr do they absorb light of other wavelength? > æ æ> However, if sets can be variable you can never tell that something is an > æ> element of a set, because you do not know. > æ æ> You seem not to be able to tell what FISONs belong to the set > æ> necessary to cover N. I have been telling you again and again that there is no the set necessary > to cover N. And I have even proved that you can remove every FISON from such a set covering N, i it exists. > æWhy do you not read what I write? Because an alleged set of unnameable ghosts has nothing to do with FISONs. æ> æ> æ> The sum of a series is a well known expression. > æ> æ æ> æ> It is actually not a sum. > æ> æ æ> æ> That may be your opinion, nevertheless you are wrong when mathematics > æ> æ> is concerned. > æ æ> It is actually not a sum: > æ> æ æ sum(i = 1, ..., oo) 1/2^i > æ> is *defined* as: > æ æ> what remains after all terms have been added. Why do you skip the actual mathematical definition and supply something > that is mathematically totally wrong? It is impossible to put the question what remains after all terms have been added? æ> æ> æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ I defined > æ> æ> the cardinal number of the set of terms of the sequence. > æ æ> Yes. æAnd? > æ æ> To shorten the discussion: You claim that the union of the set of > æ> FISONs is the same as the union of the set of FISONs and the infinite > æ> segment of N. That is wrong. Why? æSuppose: > æ æunion(n in N) {1, ..., n} = N > what is: > æ æunion(union(n in N) {1, ..., n}, N)? Then the chain of ordinal numbers seems to have a stop. Yu count 1,2,3,..., omega, omega, omega+1, ...? æ> æ> No. æThere is a disctinction. æInfinitely many FISONs are necessary, > æ> æ> but none is specifically necessary, as long as you still have > æ> æ> infinitely many. > æ> æ æ> æ> Then remove one by one. If there is no stop, this removal removes > æ> æ> infinitely many. > æ æ> No. æIf there is no stop at each stage you still have removed finitely > æ> many. > æ æ> Cantor claims that his diagonal is different from every entry of the > æ> list. And he is right. æEach digit is defined independent from all other > digits. æAnd it is easy to show that with that definition the number > obtained is different from all numbers on the list. No. It i s only different from all numbers in lines 1 to n, where n is the last line checked Each FISON(n) is proved, independent of all others, to be useless to cover N. æ> I have shown that the set of removable FISONs is larger than every > æ> natural number. That's enough. No, that is *not* enough. æ It is the set of all FISONs. Unless you could you find a remaining one. > But if there is no stop, at *no* point will > you have removed all FISONs. A prove by induction (though not required in this case) shows some property of every natural number. It is not so that I try to remove FISON(n) and then FISON(n+1) etc. A proof by induction shows that every FISON has the property of being useless for covering N. You should know that induction proves a property for every natural number greater than 1 (or n 0). >æOtherwise there would be a stop when you > have removed them all. That stop which you see when going from omega to omega + 1? Is that why you have to count omega twice? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > æ> If there is a set of FISONs necessary to cover N, then this set should > æ> have a least element. Each of the sets that cover N has a least element, but there is no > *minimal* > set of FISONs that covers N. There is no set of finite segments that covers an infinite segment. Every infinite set of fisons covers N. > For actual infinity we can set up a very simple estimation that may > show you what in fact you are claiming: An infinite segment is at > least 10 times longer than any finite segment. But no finite segment > is only twice as long than itself. Relevance? > I prove that every FISON can be removed from the set that covers N > without changing the covering properties of the set. Not so. WM proves no such thing. WM misrepresents finite induction. What can be proved is that ANY single fison, or any finite set of fisons can be removed from a set of fisons which covers N and the result will still cover N. > You are not able > to name one of them that cannot be removed. Why should we trust you? We have already said that any one fison can be removed from a fison cover of N, even that any finite set of them can be removed, with the remainder still covering N. So why should you not t rust us? > Why should we believe in a finite segment which by unioning it with > others gets 100 times longer than it is? Since we have made no claim of any such foolish thing, and yu already believe any number of such foolish things, whether you choose to believe that one is of no interest to us whatsoever. æ> æ> Within set theory sets are fixed and either finite or not finite. > æ> æ æ> æ> It is not the question what set theory says but what sets are. > æ æ> Sets are not in and of themselves without a definition of what a set > is. > æ> And in my thinking a set *is* fixed and immutable. > æ æ> Then describe the set of necessary FISONs. There is no the set of necessary FISONs. And there is no set of sufficient FISONs. The set of ALL fisons is clearly SUFFICIENT to cover N as it contains for each n in N, a fison ending in, and therefore containing as a member, that n. > There is not even one single > useful FISON. æWhy do you keep on repeating > that while I have already written so many time that such a thing does not > exist? æEach set of FISONs that is infinite is sufficient to cover n. Each FISON of a set of FISONs is finite and hence can be identified. > If you claim that infinitely many are required, then you should be > able to identify at least one of them. That would only be the case if any particular fison were required. It is not any particular fisons but the number of them that suffices to cover N, no finite set of them succeeds and no infinite set of them fails. If WM wants us to identify a member of some other covering of N by fisons, he must tell us which one as there are too many of them for us to guess at which one he means. > As you cannot, your claim turns > out to require unidentifiable FISONs Only from unidentified sets of fisons. Identify the set of fisons and we will endeavor to identify a member of it. > I have been telling you again and again that there is no the set necessary > to cover N. And I have even proved that you can remove every FISON from such a set > covering N, i it exists. No you have not. WM proves nothing, but only claims to. æWhy do you not read what I write? Because an alleged set of unnameable ghosts has nothing to do with > FISONs. Such alleged ghosts exist only in WM Mytheology, and are no part of mathematics. Why do you skip the actual mathematical definition and supply something > that is mathematically totally wrong? It is impossible to put the question what remains after all terms > have been added? Then don't put it. > æ> No. æIf there is no stop at each stage you still have removed finitely > æ> many. > æ æ> Cantor claims that his diagonal is different from every entry of the > æ> list. And he is right. æEach digit is defined independent from all other > digits. æAnd it is easy to show that with that definition the number > obtained is different from all numbers on the list. No. It i s only different from all numbers in lines 1 to n, where n is > the last line checked Since the rule applies to all n in N simultaneously, thus to all lines simultaneously, there is no such thing as a last line checked. Each FISON(n) is proved, independent of all others, to be useless to > cover N. NOT independently of all others, as that depends on the existence of a larger fison. æ> I have shown that the set of removable FISONs is larger than every > æ> natural number. That's enough. No, that is *not* enough. æ > It is the set of all FISONs. Unless you could you find a remaining > one. But if there is no stop, at *no* point will > you have removed all FISONs. A prove by induction (though not required in this case) shows some > property of every natural number. It is not so that I try to remove > FISON(n) and then FISON(n+1) etc. A proof by induction shows that > every FISON has the property of being useless for covering N. While each single fison is extraneous, and any finite set is extraneous, no fison can be labeled extraneous unless there is a larger one remaining. You should know that induction proves a property for every natural > number greater than 1 (or n_0). So you have shown that each single fison can be eliminated, provided a larger one remains, and in fact any set of fisons can be eliminated provided one fison larger that all of them remains. But you have not shown that any fison in any set of fisons can be eliminated without having a larger one in that set æOtherwise there would be a stop when you > have removed them all. That stop which you see when going from omega to omega + 1? Is that > why you have to count omega twice? You may have to, we do not. We see that one may remove as many fisons as one likes as long as we leave a set containing for each of its fisons, a larger fison. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > > If there is a set of FISONs necessary to cover N, then this set should > > have a least element. > > Each of the sets that cover N has a least element, but there is no > *minimal* set of FISONs that covers N. > > There is no set of finite segments that covers an infinite segment. An infinite set might well do. > For actual infinity we can set up a very simple estimation that may > show you what in fact you are claiming: An infinite segment is at > least 10 times longer than any finite segment. But no finite segment > is only twice as long than itself. I have no idea what this is trying to tell me. A finite segment can be twice as long as another segment, so why can an infinite segment not be at least 10 times longer than any finite segment? With the infinite segment you are not comparing it to itself. > I prove that every FISON can be removed from the set that covers N > without changing the covering properties of the set. You can only prove that you can remove every FISON from the set as long as a larger FISON remains (that is part of the proof that you can remove a FISON). And that is right. With every FISON you remove there are still infinitely many FISONs left. > You are not able > to name one of them that cannot be removed. Why should we trust you? Tell me the smallest rational numbers greater than 0. > Why should we believe in a finite segment which by unioning it with > others gets 100 times longer than it is? Again shifting to variable size sets? > > Then describe the set of necessary FISONs. > > There is no the set of necessary FISONs. > > And there is no set of sufficient FISONs. There is not even one single > useful FISON. Define the concept useful. But it is easily shown that an infinite collection of FISONs will do. *Any* infinite collection of FISONs. Consider a box with 10 holes and 11 apples. Any set of 10 apples from the 11 will make it possible to fill each of the holes. There is however not one single necessary apple. Nor is there a necessary set of 10 apples. > Why do you keep on repeating > that while I have already written so many time that such a thing does not > exist? Each set of FISONs that is infinite is sufficient to cover n. > > Each FISON of a set of FISONs is finite and hence can be identified. Yes, so what? > If you claim that infinitely many are required, then you should be > able to identify at least one of them. As you cannot, your claim turns > out to require unidentifiable FISONs that, however, are not FISONs but > only imaginations. The claim in the above example with apples is that a set of 10 apples is required. So you should be able to identify at least one of them. So which apple is required? As you cannot, the claim turns out to require unidentifiable apples that, however, are not apples but only imaginations. This shows that even if some particular type of set may be required, it is not necessarily possible to identify an element that is required. > > Every FISON carries a finite amount of information. Therefore it is > > impossible to have infinitely many distinct FISONs. If this is in set > > theory or outside: A theory which claims the existence of infinitely > > many distinct FISONs is wrong. > > That is just opinion. Prove it within standard mathematics. > > Standard mathematics shows that every finite chain of symbols contains > a finite amount of information. Yes, so a finite *set* of FISONs carries a finite amount of information. This does *not* say that an *infinite* set of FISONs carries a finite amount of information. > I have been telling you again and again that there is no the set > necessary to cover N. > > And I have even proved that you can remove every FISON from such a set > covering N, i it exists. Only if a larger FISON remains. If you remove all FISONs, the condition does not hold. > Why do you not read what I write? > > Because an alleged set of unnameable ghosts has nothing to do with > FISONs. Yes, like with the 11 apples. Which of the 11 apples is actually required? > > It is actually not a sum: > > sum(i = 1, ..., oo) 1/2^i > > is *defined* as: > > > > what remains after all terms have been added. > > Why do you skip the actual mathematical definition and supply something > that is mathematically totally wrong? > > It is impossible to put the question what remains after all terms > have been added? You may put the question, but mathematics does not supply an answer. But how can we add all terms, if they (according to you) do not all exist? > > To shorten the discussion: You claim that the union of the set of > > FISONs is the same as the union of the set of FISONs and the infinite > > segment of N. That is wrong. > > Why? Suppose: > union(n in N) {1, ..., n} = N > what is: > union(union(n in N) {1, ..., n}, N)? > > Then the chain of ordinal numbers seems to have a stop. Yu count > 1,2,3,..., omega, omega, omega+1, ...? No. Here again a confusion about which I remarked before. In a union of infinitely many elements there is *no* ordering of the things you unite, so how you can assign an ordinal number to it escapes me. > > Cantor claims that his diagonal is different from every entry of the > > list. > > And he is right. Each digit is defined independent from all other > digits. And it is easy to show that with that definition the number > obtained is different from all numbers on the list. > > No. It i s only different from all numbers in lines 1 to n, where n is > the last line checked No, it is proven (by the definition) that it holds for all n. > Each FISON(n) is proved, independent of all others, to be useless to > cover N. Wrong. It is *not* independent of all others. When I have removed all of the FISONs larger than {1}, I can not remove {1} because the condition that allows removal is not fulfilled. > > I have shown that the set of removable FISONs is larger than every > > natural number. That's enough. > > No, that is *not* enough. > > It is the set of all FISONs. Unless you could you find a remaining > one. But you have to show that you can indeed remove them all at once. > But if there is no stop, at *no* point will > you have removed all FISONs. > > A prove by induction (though not required in this case) shows some > property of every natural number. It is not so that I try to remove > FISON(n) and then FISON(n+1) etc. A proof by induction shows that > every FISON has the property of being useless for covering N. > > You should know that induction proves a property for every natural > number greater than 1 (or n_0). Yes, so induction proves that for each n you can remove FISON_n. That does *not* prove that you can remove all the FISON_s. > Otherwise there would be a stop when you > have removed them all. > > That stop which you see when going from omega to omega + 1? Is that > why you have to count omega twice? So you continue removing when you have removed them all? You do not stop? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > > No set of FISONs with gaps can be a necessary set, because the FISONs > > below a gap are certainly not required. > > Yes, because an infinite set of FISONs remain. > > So, if I prove by induction that the natural number n is larger than > -1, and that this implies that also the natural number n+1 is larger > than -1. And if I prove that there is a natural number, which in fact > is larger than -1. Then all this work leaves an infinite set of > natural numbers of which we do not know whether they are larger than > -1? The wrong analogy. (1) 1 > -1 (2) if n > -1 then n + 1 > -1 Conclusion for all n in N, n > -1 FISONs: (1) you can remove {1} (2) if you can remove {1} to {1, ..., n}, you can also remove {1} to {1, ..., n+1} Conclusion for each n in N, you can remove {1} to {1, ..., n} However, your (wrong) conclusion is that you can remove *all* of {1}, {1, 2}, ... etc. But that is different from the proper conclusion. For instance for which n in N is {1}, {1, 2}, ... etc the same as {1} to {1, ..., n}? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > ... > æ> æ> No set of FISONs with gaps can be a necessary set, because the FISONs > æ> æ> below a gap are certainly not required. > æ æ> Yes, because an infinite set of FISONs remain. > æ æ> So, if I prove by induction that the natural number n is larger than > æ> -1, and that this implies that also the natural number n+1 is larger > æ> than -1. And if I prove that there is a natural number, which in fact > æ> is larger than -1. Then all this work leaves an infinite set of > æ> natural numbers of which we do not know whether they are larger than > æ> -1? The wrong analogy. > (1) 1 > -1 > (2) if n > -1 then n + 1 > -1 > Conclusion for all n in N, n > -1 FISONs: > (1) you can remove {1} > (2) if you can remove {1} to {1, ..., n}, you can also remove {1} to > æ æ {1, ..., n+1} > Conclusion for each n in N, you can remove {1} to {1, ..., n} However, your (wrong) conclusion is that you can remove *all* of > {1}, {1, 2}, ... etc. That is no wrong conclusion but it is evident. Not even induction is required. The proof is: For every set of FISONs which you may take to cover N it is clear that FISON {1, ..., n} and all smaller FISONs are not changing the properties of the asserted set when being removed. This olds for every n. Therefore we can remove every FISON. > æBut that is different from the proper > conclusion. æFor instance for which n in N is {1}, {1, 2}, ... etc > the same as {1} to {1, ..., n}? Only finite FISONs are in question. Yes the set of all finite FISONs is the set of all {1}, {1, 2}, ... Would you be so kind to point out the difference to Cantor's diagonal proof? For every index n we have a n =/= b n. Therefore the sequence of all b n is different from every entry of the list. Why should this be different from For every index n we have FISON(n) can be removed from the alleged set covering N withou changing the covering capabilities in any way. Therefore the set of all FISONs is different from what can cover N. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... > æ> æ> No set of FISONs with gaps can be a necessary set, because the > FISONs > æ> æ> below a gap are certainly not required. > æ æ> Yes, because an infinite set of FISONs remain. > æ æ> So, if I prove by induction that the natural number n is larger than > æ> -1, and that this implies that also the natural number n+1 is larger > æ> than -1. And if I prove that there is a natural number, which in fact > æ> is larger than -1. Then all this work leaves an infinite set of > æ> natural numbers of which we do not know whether they are larger than > æ> -1? The wrong analogy. > (1) 1 > -1 > (2) if n > -1 then n + 1 > -1 > Conclusion for all n in N, n > -1 FISONs: > (1) you can remove {1} > (2) if you can remove {1} to {1, ..., n}, you can also remove {1} to > æ æ {1, ..., n+1} > Conclusion for each n in N, you can remove {1} to {1, ..., n} However, your (wrong) conclusion is that you can remove *all* of > {1}, {1, 2}, ... etc. That is no wrong conclusion but it is evident. Not even induction is > required. The proof is: For every set of FISONs which you may take to > cover N it is clear that FISON {1, ..., n} and all smaller FISONs are > not changing the properties of the asserted set when being removed. > This olds for every n. Therefore we can remove every FISON. The reason one can remove any one fison is that its members are all included in a larger one, so that when WM attempts to remove all of them simultaneously, he cannot do it. Removing fisons one, or even finitely many at a time, always leaves infinitely many more to draw from, so such a process never ends. Only finite FISONs are in question. Yes the set of all finite FISONs > is the set of all {1}, {1, 2}, ... Would you be so kind to point out the difference to Cantor's diagonal > proof? For every index n we have a_n =/= b_n. Therefore the sequence > of all b_n is different from every entry of the list. Why should > this be different from For every index n we have FISON(n) can be > removed from the alleged set covering N withou changing the covering > capabilities in any way. Therefore the set of all FISONs is different > from what can cover N. Why should it not be different? The Cantor issue is whether a list can contain all binary strings, which it cannot. The fison issue is whether removing one fison, or even finitely many, from an infinite list ever reduces the remainder to less that an infinite list, which it does not. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > FISONs: > (1) you can remove {1} > (2) if you can remove {1} to {1, ..., n}, you can also remove {1} to > {1, ..., n+1} > Conclusion for each n in N, you can remove {1} to {1, ..., n} > > However, your (wrong) conclusion is that you can remove *all* of > {1}, {1, 2}, ... etc. > > That is no wrong conclusion but it is evident. Not even induction is > required. The proof is: For every set of FISONs which you may take to > cover N it is clear that FISON {1, ..., n} and all smaller FISONs are > not changing the properties of the asserted set when being removed. Right. So you may remove finitely many FISONs. > This olds for every n. Therefore we can remove every FISON. Wrong, that requires proof. Your method of proof can be expanded to a similar proof to show that lim(n -> oo) 1/n > 0. > But that is different from the proper > conclusion. For instance for which n in N is {1}, {1, 2}, ... etc > the same as {1} to {1, ..., n}? > > Only finite FISONs are in question. Yes the set of all finite FISONs > is the set of all {1}, {1, 2}, ... Yes, so for which n is that the same as {1} to {1, ..., n}? For none? If so, induction does not show that you can remove all n. > Would you be so kind to point out the difference to Cantor's diagonal > proof? For every index n we have a_n =/= b_n. Therefore the sequence > of all b_n is different from every entry of the list. Why should > this be different from For every index n we have FISON(n) can be > removed from the alleged set covering N withou changing the covering > capabilities in any way. Therefore the set of all FISONs is different > from what can cover N. The difference is that the set of all FISONs is *not* in the list where the n-th element of the list is the n-th FISON. On the other hand, all b_n's are in the list [b], and all a_n's are in the list [a]. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU AppleWebKit/419.2.1 (KHTML, like Gecko) Safari/419.3,gzip(gfe),gzip(gfe) > æ> So, if I prove by induction that the natural number n is larger than > æ> -1, and that this implies that also the natural number n+1 is larger > æ> than -1. And if I prove that there is a natural number, which in fact > æ> is larger than -1. Then all this work leaves an infinite set of > æ> natural numbers of which we do not know whether they are larger than > æ> -1? > FISONs: > (1) you can remove {1} > (2) if you can remove {1} to {1, ..., n}, you can also remove {1} to > æ æ {1, ..., n+1} > Conclusion for each n in N, you can remove {1} to {1, ..., n} > However, your (wrong) conclusion is that you can remove *all* of > {1}, {1, 2}, ... etc. æBut that is different from the proper > conclusion. æFor instance for which n in N is {1}, {1, 2}, ... etc > the same as {1} to {1, ..., n}? This is not the first time that WM has tried to use this sort of infinite case induction in a proof. What WM would like to say is, for any property P': If (we can prove that): P'({1}) is true; and if P'({1...n}) then P'({1...n + 1}) then (we have proven) P'(N) as well as P'({1...n}) for every natural number n. I.e. IF P'({1.83n}) is true ñfor all finite nî THEN it is true in the ñtransfinite caseî, P'(N). But this form of induction is invalid in ZFC. I once tried to find a rigorous set theory in which such an induction schema is valid -- perhaps placing some sort of restriction on the formula P' in order to come up with a consistent theory. If successful, then this will result in a nonstandard set theory with some new, nonstandard natural numbers. For example, if we let P' be the formula n = 1 or n has a predecessor then we'd conclude that N has a predecessor -- the nonstandard natural number N-1. But unfortunately, I was not able to come up with a consistent theory. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4 MathPlayer 2.0; .NET CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) æ> So, if I prove by induction that the natural number n is larger than > æ> -1, and that this implies that also the natural number n+1 is larger > æ> than -1. And if I prove that there is a natural number, which in fact > æ> is larger than -1. Then all this work leaves an infinite set of > æ> natural numbers of which we do not know whether they are larger than > æ> -1? > FISONs: > (1) you can remove {1} > (2) if you can remove {1} to {1, ..., n}, you can also remove {1} to > æ æ {1, ..., n+1} > Conclusion for each n in N, you can remove {1} to {1, ..., n} > However, your (wrong) conclusion is that you can remove *all* of > {1}, {1, 2}, ... etc. æBut that is different from the proper > conclusion. æFor instance for which n in N is {1}, {1, 2}, ... etc > the same as {1} to {1, ..., n}? This is not the first time that WM has tried to use this sort of > infinite case induction in a proof. What WM would like to say is, for any property P': If (we can prove that): > P'({1}) is true; and > if P'({1...n}) then P'({1...n + 1}) > then (we have proven) P'(N) as well as P'({1...n}) for every natural > number n. > I.e. IF P'({1.83n}) is true ñfor all finite nî > THEN it is true in the ñtransfinite caseî, P'(N). But this form of induction is invalid in ZFC. That's not even the half of it. WM suffers from quantifier dyslexia and he is sloppy in writing things down. When he says (P1): {1} is not necessary to cover N with FISONs, what does he mean by that? He can only mean that union {k in N} N k = union {k > 1} N k = N, hence {2, 3, 4, ...} covers N. For the induction step, assume (what?) that {n, n+1, ...} covers N, which means that union {k >= n} N k = N and conclude that union {k > n} N k = N, so {n+1, n+2, ...} still covers N. All this says is that for every n, union {k > n} N k = N, which is a perfectly reasonable and true result. You then move the quantifier inside the union and presto, you get that union {k > ALL n} N k = N. Of course the indexing expression in this last step is empty. Since this proves what you are after (namely that set theory is rubbish), you trumpet this fact about and conveniently forget that moving the quantifier was illegal. > I once tried to > find a rigorous set theory in which such an induction schema > is valid -- perhaps placing some sort of restriction on the > formula P' in order to come up with a consistent theory. If > successful, then this will result in a nonstandard set theory > with some new, nonstandard natural numbers. For example, > if we let P' be the formula n = 1 or n has a predecessor then > we'd conclude that N has a predecessor -- the nonstandard > natural number N-1. But unfortunately, I was not able to come > up with a consistent theory. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > > Union is a binary operator. > > When used to unite infinitely many terms, it is *not* a binary operator. > > It is a binary operator, infinitely often applied. Please, look up the definition. But I know that you ignore definitions, and actually do not want to hear about them. Perhaps that is your way to do your mathematics, but that is not the way mathematics is normally done. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > ... > æ> æ> Union is a binary operator. > æ æ> When used to unite infinitely many terms, it is *not* a binary operator. > æ æ> It is a binary operator, infinitely often applied. Please, look up the definition. æBut I know that you ignore definitions, > and actually do not want to hear about them. You could have learned the definition from my book, p. 69: A U B = {x | x in A oder x in B} Vereinigungen, Durchschnitte und Produkte beliebig vieler Mengen sind m.9aglich. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... > æ> æ> Union is a binary operator. > æ æ> When used to unite infinitely many terms, it is *not* a binary > operator. > æ æ> It is a binary operator, infinitely often applied. Please, look up the definition. æBut I know that you ignore definitions, > and actually do not want to hear about them. You could have learned the definition from my book, p. 69: > A U B = {x | x in A oder x in B} > Vereinigungen, Durchschnitte und Produkte beliebig vieler Mengen sind > m.9aglich. Anyone who chooses to learn from WM's book may end up more ignorant that he started. The axiom of union says that for a set S, Union(S) is a set such that (for all x)( x in Union(S) <==> (exists Q with x in Q and Q in S)). That axiom of union, or equivalent, is standard in mathematical set theories, and the binary definition is only for putzers at set theory. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl > ... > > > Union is a binary operator. > > > > When used to unite infinitely many terms, it is *not* a binary > > oper ator. > > > > It is a binary operator, infinitely often applied. > > Please, look up the definition. But I know that you ignore definitions, > and actually do not want to hear about them. > > You could have learned the definition from my book, p. 69: > A U B = {x | x in A oder x in B} Why would I take a definition from a book that is riddled with errors? But that is the definition of a binary operator. > Vereinigungen, Durchschnitte und Produkte beliebig vieler Mengen sind > m.9aglich. Yes, they are possible, but *not* due to the infinite application of the binary operator. In mathematics there is no operator that will be applied infinitely often, the reason being that you will never come at the definition when applied to infinitely many operands? However, let me follow your theory, i.e. not all n in N are known, so it is a potential infinity. By that method: union(n in N) FISON_n can not be calculated by repeated application of the binary operator, because not all of FISON_n are known. And for a similar reason: {1/2, 1/4, ..., 1/2^n, ...} is a potential infinite set, so not all elements are known and so sum(i = 1, ..., oo) 1/2^i can not be calculated by repeated application of the addition operator (not all operands are known, and you can not add something you do not know). So in your mathematics the above infinite sum is underfined. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4 MathPlayer 2.0; .NET CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > However, let me follow your theory, i.e. not all n in N are known, so > it is a potential infinity. æBy that method: > æ æunion(n in N) FISON n > can not be calculated by repeated application of the binary operator, > because not all of FISON n are known. æAnd for a similar reason: > æ æ{1/2, 1/4, ..., 1/2^n, ...} > is a potential infinite set, so not all elements are known and so > æ æsum(i = 1, ..., oo) 1/2^i > can not be calculated by repeated application of the addition operator > (not all operands are known, and you can not add something you do not > know). æSo in your mathematics the above infinite sum is underfined. Moreover, there is no way of knowing that (whether) sum {n in N} 1/n diverges. Since int {1/e}^n 1/x dx < sum {k <= n} 1/n < int 1^n 1/x dx, there is also no way of knowing whether ln x goes to infinity as x goes to infinity, and a whole lot of other goodies. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl > > > That is a circularity which cannot be avoided by any language, > > including the language of mathematics. If you would try to define > > something like 1 by words that are not defined by other words, then > > you would see it. > > Mathematics starts with a selected number of undefined terms. 1 is > not amongst them. > > What you call mathematics is a selected number of undefined > definitions. Mathematics starts with 1. Well, that is *your* mathematics. On the other hand you will find that there is no direct circularity in the definition of 1 in standard mathematics. BTW, where does Euclid use 1? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > æ æ> æ> That is a circularity which cannot be avoided by any language, > æ> æ> including the language of mathematics. If you would try to define > æ> æ> something like 1 by words that are not defined by other words, then > æ> æ> you would see it. > æ æ> Mathematics starts with a selected number of undefined terms. æ1 is > æ> not amongst them. > æ æ> What you call mathematics is a selected number of undefined > æ> definitions. Mathematics starts with 1. Well, that is *your* mathematics. æOn the other hand you will find that > there is no direct circularity in the definition of 1 in standard > mathematics. æ That depends on your definition of direct circularity. Every definition of words by words is circular. BTW, where does Euclid use 1? He, like all old Greeks, uses it as the source of every number. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > BTW, where does Euclid use 1? He, like all old Greeks, uses it as the source of every number. But does not regard it as itself being a number. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl > > Would do! But there are not more than three FISONs with three > > elements, and there are not more than finitely many FISONs with > > finitely many elements. Hence, there are not infinitely many > > available. > > Why not? Isn't there a FISON available for every natural number, and > aren't there infinitely many natural numbers? > > That's the question. For FISONs or finite numbers in unary > representation we know that there are not infinitely many. No, we know that there *are* infinitely many. > > It is a result based on the (false) assumption that there is a single > > minimal set of FISONs that will do. > > > > It is a result based on the undisputable fact that every set of FISONs > > has a least element. > > Right. Remove that least element and you still have an infinite set of > FISONs that is sufficient. I.e. there is *not* a minimal set of FISONs > that will do. > > Of course not. Because there is no set of FISONs that will do. But it is easily proven that the set of all FISONs will do. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > æ> æ> Would do! But there are not more than three FISONs with three > æ> æ> elements, and there are not more than finitely many FISONs with > æ> æ> finitely many elements. Hence, there are not infinitely many > æ> æ> available. > æ æ> Why not? æIsn't there a FISON available for every natural number, and > æ> aren't there infinitely many natural numbers? > æ æ> That's the question. For FISONs or finite numbers in unary > æ> representation we know that there are not infinitely many. No, we know that there *are* infinitely many. You may believe so. But you could easily convince yourself of the simple truth, that infinitely much informaton is necessary to distinguish infinitely many items. But chains of finitely many symbols like ooo...ooo contain only finitely much information. æ> æ> It is a result based on the (false) assumption that there is a single > æ> æ> minimal set of FISONs that will do. > æ> æ æ> æ> It is a result based on the undisputable fact that every set of FISONs > æ> æ> has a least element. > æ æ> Right. æRemove that least element and you still have an infinite set of > æ> FISONs that is sufficient. æI.e. there is *not* a minimal set of FISONs > æ> that will do. > æ æ> Of course not. Because there is no set of FISONs that will do. But it is easily proven that the set of all FISONs will do. That's why set theory is inconsistent. It is easily proven that no FISON is sufficient, necessary or only useful to be in the set which you claim to cover N. So, f there is such a set, then we can remove simultaneously every FISON from it without changing in the least its capability of covering N. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > æ> æ> Would do! But there are not more than three FISONs with three > æ> æ> elements, and there are not more than finitely many FISONs with > æ> æ> finitely many elements. Hence, there are not infinitely many > æ> æ> available. > æ æ> Why not? æIsn't there a FISON available for every natural number, and > æ> aren't there infinitely many natural numbers? > æ æ> That's the question. For FISONs or finite numbers in unary > æ> representation we know that there are not infinitely many. No, we know that there *are* infinitely many. You may believe so. And you may beleive not, but existence of a number in a mathemtics sense does not require that it be simultaneousy distinguishable from all other numbers, only distinguishable from one other number at any one time. .But you could easily convince yourself of the > simple truth, that infinitely much informaton is necessary to > distinguish infinitely many items. But chains of finitely many symbols > like ooo...ooo contain only finitely much information. æ> æ> It is a result based on the (false) assumption that there is a > single > æ> æ> minimal set of FISONs that will do. > æ> æ æ> æ> It is a result based on the undisputable fact that every set of > FISONs > æ> æ> has a least element. > æ æ> Right. æRemove that least element and you still have an infinite set > of > æ> FISONs that is sufficient. æI.e. there is *not* a minimal set of > FISONs > æ> that will do. > æ æ> Of course not. Because there is no set of FISONs that will do. But it is easily proven that the set of all FISONs will do. That's why set theory is inconsistent. No! That just makes it incompatible with your theory of mytheology, but incompatibility is not at all the same thing as inconsistency. No one. Including WM, has yet shown that ZFC or NBG are inconsistent with themselves, though it is patently obvious that they can be incompatible with other theories. It is easily proven that no FISON is sufficient, necessary or only > useful to be in the set which you claim to cover N. If it were so easily proven, someone would have proven it. That WM cannot prove it and that no one else has, suffices to throw serious doubt on such a claim. Particularly when, in either ZFC or NBG, it has been proven that any infinite set of fisons is sufficient to cover N and no finite set is. > So, f there is > such a set, then we can remove simultaneously every FISON from it > without changing in the least its capability of covering N. Not at all. Given a sufficient (therefore infinite) set of fisons, one can remove any one fison and the result is still sufficient, but in doing so one is always removing one element from an infinite set and leaving an infinite set. WM seems to thing that removing one element from an infinite set can somehow make it into a finite set. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 CLR 1.1.4322; InfoPath.1),gzip(gfe),gzip(gfe) > That's why set theory is inconsistent. Now he's BACK to claiming inconsistency! MoeBlee === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > > Why not? Isn't there a FISON available for every natural number, and > > aren't there infinitely many natural numbers? > > > > That's the question. For FISONs or finite numbers in unary > > representation we know that there are not infinitely many. > > No, we know that there *are* infinitely many. > > You may believe so. But you could easily convince yourself of the > simple truth, that infinitely much informaton is necessary to > distinguish infinitely many items. But chains of finitely many symbols > like ooo...ooo contain only finitely much information. Yes, finite chains of finitely many symbols contain finite information. But infinite chains of finitely many symbols contain infinite information. > > Of course not. Because there is no set of FISONs that will do. > > But it is easily proven that the set of all FISONs will do. > > That's why set theory is inconsistent. It is not. > It is easily proven that no FISON is sufficient, necessary or only > useful to be in the set which you claim to cover N. So, f there is > such a set, then we can remove simultaneously every FISON from it > without changing in the least its capability of covering N. But you can not prove that you can remove simultaneously every FISON from it. The best you can prove, by induction, would be that you can remove finitely many of them. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > The point is that here the union of {1} > {1, 2} > {1, 2, 3} > ... is said to be the same as the union of {1} > {1, 2} > {1, 2, 3} > ... > {1, 2, 3, ...} which obviously is incorrect. Union(Union(A,{Union(A)})) = Union(A) So the above is only incorrect if Union({1},{1,2},{1,2,3},...} =/= {1,2,3,...} ... which is precisely the point of contention. Saying obviously doesn't cut it. Try a proof? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) The point is that here the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... is said to be the same as the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... > æ{1, 2, 3, ...} which obviously is incorrect. Union(Union(A,{Union(A)})) = Union(A) So the above is only incorrect if Union({1},{1,2},{1,2,3},...} =/= > {1,2,3,...} ... which is precisely the point of contention. Saying obviously > doesn't cut it. Try a proof?- A set is determined by its elements. A set of FISONs does not contain an infinite segment. The union of finite segments is not an actually infinite segment. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor The point is that here the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... is said to be the same as the union of æ{1} > æ{1, 2} > æ{1, 2, 3} > æ... > æ{1, 2, 3, ...} which obviously is incorrect. Union(Union(A,{Union(A)})) = Union(A) So the above is only incorrect if Union({1},{1,2},{1,2,3},...} =/= > {1,2,3,...} ... which is precisely the point of contention. Saying obviously > doesn't cut it. Try a proof?- A set is determined by its elements. Precisely! So for two unions to be different, one must have a member not in the other. Which elements of {1,2,3,...} are not in Union({1},{1,2},{1,2,3},...}? Which elements of Union({1},{1,2},{1,2,3},...} are not in {1,2,3,...}? Unless there are some such elements in one but not the other, then by WM's own criterion, they are the same. > A set of FISONs does not contain an infinite segment. If segment means fison, no one says otherwise. > The union of finite segments is not an actually infinite segment. An infinite union of fisons is actually infinite whenever actually infinite sets are allowed. Which only bars it in WM's mytheology. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) The point is that here the union of {1} > {1, 2} > {1, 2, 3} > ... is said to be the same as the union of {1} > {1, 2} > {1, 2, 3} > ... > {1, 2, 3, ...} which obviously is incorrect. Union(Union(A,{Union(A)})) = Union(A) So the above is only incorrect if Union({1},{1,2},{1,2,3},...} =/= > {1,2,3,...} ... which is precisely the point of contention. Saying obviously > doesn't cut it. Try a proof?- A set is determined by its elements. True. > A set of FISONs does not contain an infinite segment. True. > The union of finite segments is not an actually infinite segment. Prove it. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) In order to see its inconsistency consider the simplest example, the > natural numbers. If they are taken in unary representation > o > oo > ooo > ... > then it is clear that there cannot be an actually infinite number (of > numbers) without an actually infinite number Sorry, this isn't clear to me at all. How about a proof? > For the potential infinity it is needed to take as a necessary axiom > the continuity of the given entity, so the granularity is excluded by > definition no matter how deep or far or long one would go. It is a > false axiom for the physical world but the math is a world by itself, > so any axioms are fine as long as consecutively properly used in the > ongoing reasoning. So let's us take the continuity as an axiom: so > between 0 and 1 or between 0 and 0e-10000000000000000 or any anyhow > small segment we always have infinities of possible numbers. > In physics imaginary daemons are oftenly used to express complicated > matters in simpler way or to set up impossible experiments. > So let's take daemons Can and Tor. Let they be staying near of two > conveyors with the belt coming from one wall and going to the other. > Color cubes are passing by on these conveyors and Can and Tor have to > take them out. But Can has to take from his conveyor all cubes: and > Tor is allowed to take only reds, greens and each 3rd blue one. Every > billion years the conveyors stop and Can and Tor have to make as many > unique combinations as possible out of their cubes they have so far. > The winner is who has more of possible combinations. > It is required to proof or to disproof that no matter how billion year > periods we have, the winner will be Can on his sinecure and much > harder working Tor will loose:-) > I can be deeply wrong, but Cantor's methods are letting us to solve > this problem. Cantor's mathematics is not of any use for any real problem. The > resaon is, that these methods are inconsistent and lead to wrong > results. This reason is not yet widely accepted, but the uselessness > is a matter of fact. Maybe it would become more widely accepted if you could prove that these methods are inconsistent rather than assert it. Or maybe you are simply mistaken in your belief that you have found an inconsistency. Have you considered that possibility? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > In order to see its inconsistency consider the simplest example, the > natural numbers. If they are taken in unary representation > o > oo > ooo > ... > then it is clear that there cannot be an actually infinite number (of > numbers) without an actually infinite number Sorry, this isn't clear to me at all. How about a proof? If actual infinity is a number larger than any finite number, than an actual infinite number of sequences of o's cannot be distinguished by a finite sequence of o's. > Cantor's mathematics is not of any use for any real problem. The > resaon is, that these methods are inconsistent and lead to wrong > results. This reason is not yet widely accepted, but the uselessness > is a matter of fact. Maybe it would become more widely accepted if you could prove that > these methods are inconsistent rather than assert it. There are many proofs. An actually infinite number of numbers cannot be distinguished by a finite amount of information. But the sequence of FISONs in he form o oo ooo ... does not contain more information than a finite number of o's contains. > Or maybe you are > simply mistaken in your belief that you have found an inconsistency. Do you know of any successful application of alephs for scientifc purposes? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > In order to see its inconsistency consider the simplest example, the > natural numbers. If they are taken in unary representation > o > oo > ooo > ... > then it is clear that there cannot be an actually infinite number (of > numbers) without an actually infinite number Sorry, this isn't clear to me at all. How about a proof? If actual infinity is a number larger than any finite number, than an > actual infinite number of sequences of o's cannot be distinguished by > a finite sequence of o's. > Cantor's mathematics is not of any use for any real problem. The > resaon is, that these methods are inconsistent and lead to wrong > results. This reason is not yet widely accepted, but the uselessness > is a matter of fact. Maybe it would become more widely accepted if you could prove that > these methods are inconsistent rather than assert it. > There are many proofs. None of which has WM been able to produce. > An actually infinite number of numbers cannot > be distinguished by a finite amount of information. It can be distinguished from any actually finite number, which is all that is needed. > But the sequence > of FISONs in he form o > oo > ooo > ... does not contain more information than a finite number of o's > contains. An actually infinite set of fisons is distinguishable from any finite set of fisons. Or maybe you are > simply mistaken in your belief that you have found an inconsistency. Do you know of any successful application of alephs for scientifc > purposes? Lack of application is hardly proof of inconsistency. There is lots of mathematics which has little or no application today, but in view of the history of mathematics, what has no application today may be of significant, even essential, application tomorrow. Those who insist on having an application before allowing for any development will always be behind and trying to catch up, but never succeeding. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > In order to see its inconsistency consider the simplest example, the > natural numbers. If they are taken in unary representation > o > oo > ooo > ... > then it is clear that there cannot be an actually infinite number (of > numbers) without an actually infinite number Sorry, this isn't clear to me at all. How about a proof? If actual infinity is a number larger than any finite number, What does this mean? > than an actual infinite number of sequences of o's cannot be distinguished > by a finite sequence of o's. What does this mean? > Cantor's mathematics is not of any use for any real problem. The > resaon is, that these methods are inconsistent and lead to wrong > results. This reason is not yet widely accepted, but the uselessness > is a matter of fact. Maybe it would become more widely accepted if you could prove that > these methods are inconsistent rather than assert it. There are many proofs. An actually infinite number of numbers cannot > be distinguished by a finite amount of information. But the sequence > of FISONs in he form o > oo > ooo > ... does not contain more information than a finite number of o's > contains. Sorry, no idea what you are talking about. Maybe this is why I do not accept it? > Or maybe you are > simply mistaken in your belief that you have found an inconsistency. Do you know of any successful application of alephs for scientifc > purposes? Why the change of subject? Uncomfortable with my suggestion? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU AppleWebKit/419.2.1 (KHTML, like Gecko) Safari/419.3,gzip(gfe),gzip(gfe) > Or maybe you are > simply mistaken in your belief that you have found an inconsistency. > Do you know of any successful application of alephs for scientifc > purposes? And I already know how Virgil will respond to this -- he'd say that mathematics is not limited by what can exist in physics. So I already know that any argument about mathematics that appeals to physics, or what can be successfully applied for scientific purposes, is doomed to failure. I once asked here at sci.math why the existence of uncountably many reals is necessary for science. The response is that differential equations are useful in physics, and the theory of differential equations requires the existence of a complete ordered field, and a complete ordered field must necessarily be an uncountable set. One could use difference equations and finite sets, but in general differential equations are much easier to solve than difference equations. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I once asked here at sci.math why the existence of uncountably > many reals is necessary for science. The response is that > differential equations are useful in physics, and the theory of > differential equations requires the existence of a complete > ordered field, and a complete ordered field must necessarily be > an uncountable set. One could use difference equations and > finite sets, but in general differential equations are much easier > to solve than difference equations. Integrability of the integral calculus, a method of exhaustion, is based on measure theory where there is only countable additivity of the differential areas. As limits of, for example, Riemann sums, in the correlation between the evaluation of the integral and area, the standard measure of the unit is defined in terms of standard measure of the unit. Continuum analysis is certainly widely used in application and for perfectly good reasons: the results match to all orders of precision (down to quantum and up to cosmic scales) the intuitive correlation between synthetic construction and analytic deconstruction of the surfaces. That analysis is formalized in terms of standard measure theory in terms of, generally, a standard regular set theory, leaves the consistency of analysis to consistency of standard regular set theory. Much as there was hundreds of years of development of analysis towards a rigorous foundation, there has been much development of the notions of the transfinite towards a rigorous foundation, from the naive set theory of Cantor's Mengenlehre in which early results of the trans-finite were framed, into the post-Cantorian formalisms of Zermelo etcetera, although generally when I say post-Cantorian it means non-Cantorian, in terms of infinities being infinite. There are various developments of non-standard measure theories, upon which analysis would be seen to rest, and they're not necessarily those that have any notion of uncountability. They do however often involve functions that are not real functions, of which there is a wide gamut that are widely applied. For example, the natural/unit equivalency function, a nonstandard function even defined standardly as a limit of standard functions, has that the antidiagonal result, and nested intervals, doesn't apply. Now, as to whether there is any applicability of these, in terms of real-world predictions that can be made, that would be seen in terms of many micro- and macro-scale phenomena, where for example subatomic gets bigger the more is learned about it, and various other philosophical and logical principles offer explanations of why space and time the way it is, in an analytical (extra-)metrical system. There has been much search for reasons to include transfinite cardinals in physics other than to accommodate their claimed existence. There aren't any widely claimed reasons for that to be so. Also, there is an opinion shared by many cosmologists that while continuum analysis is applicable, and the most concise and suitable formalism for the expression of relations of systems, there is no use for transfinite cardinals. Indeed, some even have, for example, as physical theories of the universe, that its properties would match an abstract logical universe, to the extent that infinite sets are equivalent. Ross F. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > On 17 Apr., 22:49, David Formosa (aka ? the Platypus) [...] > There is no way to pack more then N bits of infomation into an N bit > string. Agreed. But by means of ingenuity you can use a given amount of > information in different ways to identify large numbers. What is the upper bound for this? [...] > Location and momentum must be measured by what? > Bouncing light of them. And what to do with the light? Have it hit a sensor. [...] > Is (not false) true > I do not think so. There are undecidable questions like that for the > digit numer 10^100^1000 of pi. > p = ~~p is undecidable?! No, but the values of digits that do not exist are undecidable. The > truth value of unthinkable thoughts is undecidable. Why did you even mention it in responce to my question? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) On 21 Apr., 13:20, David Formosa (aka ? the Platypus) [...] > There is no way to pack more then N bits of infomation into an N bit > string. Agreed. But by means of ingenuity you can use a given amount of > information in different ways to identify large numbers. What is the upper bound for this? > I don't see an upper bound. > Location and momentum must be measured by what? > Bouncing light of them. And what to do with the light? Have it hit a sensor. Consisting of quite a lt of atoms. So location and momentum of an atom do oit seem to increase the general capabilty to store information. [...] Is (not false) true > I do not think so. There are undecidable questions like that for the > digit numer 10^100^1000 of pi. > p = ~~p is undecidable?! No, but the values of digits that do not exist are undecidable. The > truth value of unthinkable thoughts is undecidable. Why did you even mention it in responce to my question? In oder to show you that there are undecidable propositions. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > On 21 Apr., 13:20, David Formosa (aka ? the Platypus) > [...] > There is no way to pack more then N bits of infomation into an N bit > string. > Agreed. But by means of ingenuity you can use a given amount of > information in different ways to identify large numbers. > What is the upper bound for this? > I don't see an upper bound. So the same infomation can be used to represent an unlimmited number of numbers? === Subject: Re: are these generalized numbers named ? > hi all let t_a_b(n) be the nth positive integer number that is in a unique way > the sum of 'a' times a 'b'th power. since the list of positive integers that satisfy that is not always oo (or > perhaps empty) , this t_a_b(n) is not always defined for all n. example of t_a_b(n) : t_2_2(n) is the nth (positive) integer that is in a > unique way the sum of 2 squares. are these generalized numbers ( t_a_b(n) ) named ? i know they relate to primes , class numbers , factoring , the sum of > squares and the taxicab function. perhaps these generalized numbers are just some generalized taxicab > numbers and functions. if not plz give me name of this function and its generalized numbers. > tommy1729 This entire post is utter meaningless nonsense. === Subject: Re: are these generalized numbers named ? Tommy1792 a .8ecrit : > hi all > let t_a_b(n) be the nth positive integer number that is in a unique way > the sum of 'a' times a 'b'th power. > since the list of positive integers that satisfy that is not always oo (or > perhaps empty) , this t_a_b(n) is not always defined for all n. > example of t_a_b(n) : t_2_2(n) is the nth (positive) integer that is in a > unique way the sum of 2 squares. > are these generalized numbers ( t_a_b(n) ) named ? > i know they relate to primes , class numbers , factoring , the sum of > squares and the taxicab function. > perhaps these generalized numbers are just some generalized taxicab > numbers and functions. > if not plz give me name of this function and its generalized numbers. > tommy1729 This entire post is utter meaningless nonsense. > No, not really. For instance, in this notation, t_2_2(n) is the sequence (1,2,4,5,8,9,10,...) (or perhaps (2,5,8,10,...)) and, indeed, this has a small connotation to Waring problem. Now, does those sequences have any interest ? Loos Sloane ; I am too lazy to check (.8eand obviously, tommy1729 is, too) === Subject: Re: are these generalized numbers named ? > hi all let t_a_b(n) be the nth positive integer number that is in a unique way > the sum of 'a' times a 'b'th power. since the list of positive integers that satisfy that is not always oo (or > perhaps empty) , this t_a_b(n) is not always defined for all n. example of t_a_b(n) : t_2_2(n) is the nth (positive) integer that is in a > unique way the sum of 2 squares. are these generalized numbers ( t_a_b(n) ) named ? i know they relate to primes , class numbers , factoring , the sum of > squares and the taxicab function. perhaps these generalized numbers are just some generalized taxicab > numbers and functions. if not plz give me name of this function and its generalized numbers. > tommy1729 None of this means anything. === Subject: Geometry with locus... Hello teacher~ There is a sphere with x^2 + (y-2)^2 + (z-3)^2 = 1. There is a line L passing through (0,0,c). Line L is tangent to this sphere. Let P be the intersection point between L and xy-plane. The locus of point P is a parabola. Let c_1, c_2 be the values of c to satisfy this conditions. Find c_1 + c_2. Answer : 6 ------------------------------------------------ Complex... I need your advice. === Subject: Re: Geometry with locus... mina_world a .8ecrit : > Hello teacher~ There is a sphere with x^2 + (y-2)^2 + (z-3)^2 = 1. There is a line L passing through (0,0,c). Line L is tangent to this sphere. Let P be the intersection point between L and xy-plane. The locus of point P is a parabola. Let c_1, c_2 be the values of c to satisfy this conditions. This is a hint that there are only two values of c ! > Find c_1 + c_2. > And finding the two values is not harder, nor easier, than finding c_1 and c_2 themselves. Then, yes the sum is 6... For a given c, L describes a cone. Intersect of cone and plane is a parabola if plane is parallel to some line L (for this c). Conversedly this means that some L is parallel to xy plane ... then easy. -- Philippe C., mail : chephip+news@free.fr site : http://chephip.free.fr/ (recreational mathematics) === Subject: Re: Geometry with locus... >There is a sphere with x^2 + (y-2)^2 + (z-3)^2 = 1. There is a line L passing through (0,0,c). Line L is tangent to this sphere. Let P be the intersection point between L and xy-plane. The locus of point P is a parabola. Let c_1, c_2 be the values of c to satisfy this conditions. Find c_1 + c_2. >Answer : 6 A cone intersects a plane in a parabola when only one line in the cone is parallel to the plane. If there are two lines parallel to the plane, the intersection is a hyperbola; and if there are no parallel lines, the intersection is an ellipse. Considering this for a bit, it becomes clear that c_1 and c_2 are 2 and 4, the extreme distances from the plane to the sphere. In fact, any point (x,y,2) or (x,y,4) will project this sphere onto a parabola in the xy-plane except (1,2,2) and (1,2,4). Of course, 2 + 4 = 6. Rob Johnson take out the trash before replying === Subject: Re: Closed-form expression for a combinatorial problem >I am looking for a closed-form for sum_{k=i}^n C_k^i x^k where C_k^i is k chooses i, x is between 0 and 1, i and n are given >integers. Using the identity C(-n,k) = (-1)^k C(n+k-1,k) we get oo --- k > C(k,n) x --- k=n oo --- k = > C(k,k-n) x --- k=n oo --- k-n k = > (-1) C(-n-1,k-n) x --- k=n oo --- k k+n = > (-1) C(-n-1,k) x --- k=0 oo n --- k = x > C(-n-1,k) (-x) --- k=0 x^n = ----------- [1] (1-x)^{n+1} Which converges for x in (-1,1). So, the sum in your question is n --- k x^i x^{n+1} > C(k,i) x = ----------- - ----------- --- (1-x)^{i+1} (1-x)^{n+2} k=i Which is true for all x. Rob Johnson take out the trash before replying === Subject: Re: Closed-form expression for a combinatorial problem >I am looking for a closed-form for >sum_{k=i}^n C_k^i x^k >where C_k^i is k chooses i, x is between 0 and 1, i and n are given >integers. Using the identity C(-n,k) = (-1)^k C(n+k-1,k) we get oo > --- k > > C(k,n) x > --- > k=n oo > --- k > = > C(k,k-n) x > --- > k=n oo > --- k-n k > = > (-1) C(-n-1,k-n) x > --- > k=n oo > --- k k+n > = > (-1) C(-n-1,k) x > --- > k=0 oo > n --- k > = x > C(-n-1,k) (-x) > --- > k=0 x^n > = ----------- [1] > (1-x)^{n+1} Which converges for x in (-1,1). So far, so good; but then I hurled: >So, the sum in your question is n > --- k x^i x^{n+1} > > C(k,i) x = ----------- - ----------- > --- (1-x)^{i+1} (1-x)^{n+2} > k=i Which is true for all x. This is not true. The coefficients of x^i beyond x^n are different in x^{n+1}/(1-x)^{n+2} than in your sum. Your sum is x^i d i 1 - x^{n-i} --- ( -- ) ----------- [2] i! dx 1 - x If x is in (-1,1) then x^{n-1} -> 0 as n -> oo. In that case, [2] becomes [1]. Rob Johnson take out the trash before replying === Subject: Re: Integer factorization, etc. posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > why did you subscribe to 'Soviet Life' and why did you write to > * the Soviet embassy? > * > * I need to clear this up. It's in the interest of national security. > * > * With the invocation of the sacred words national security, one of > * the most powerful mantras of the long-lived Cold War, Mrs. Bernard's > * seventy-nine-year-old husband burst out laughing. At any time, it > * would have been hard to imaging the connection between his wife and > * the fearsome world of espionage, the arms race and Check Point Charlie. > * > * But the wall had fallen, and Russia had a complete upheaval too. The FBI > * agent's linkage of his wife to national security seemed absurd. The > * agent, however, did not share George's amused astonishment. > * > * Don't mock me, the couple remembers Emmett warning them. > * > * She had subscribed to the magazine for its impressive photography, and > * had written to the Soviet embassy to thank them for sending an icebreaker > * to free some whales, as suggested by a television show I've reported the above spoofing of my post to Google. Obviously someone has been busy spoofing a variety of prior posters on this thread, and I thought it best that Google Groups look into the abuse. === Subject: Re: Integer factorization, etc. kinds : * of coding devices gradually became more explicit. The drug cartels : * are buying sophisticated communications equipment, he told Congress. : * Unless the encryption issue is RESOLVED soon, criminal conversations : * over the telephone and other communications devices will become : * indecipherable by law enforcement. This, as much as any issue, : * jeopardizes the public safety and national security of this country. Louis Freeh, banging the Drums of War. It's official: * http://epic.org/crypto/ban/fbi_dox/impact_text.gif * * SECRET FBI report * * NEED FOR A NATIONAL POLICY * * A national policy embodied in legislation is needed which insures * that cryptography use in the United States should be forced to be * crackable by law enforcement, so such communications can be monitored * with real-time decryption. * * All cryptography that cannot meet this standard should be prohibited. The U.S. asked the OECD to agree to internationally required Key Recovery. * What Is The OECD * * The Organization for Economic Co-operation and Development, based in * Paris, France, is a unique forum permitting governments of the * industrialized democracies to study and formulate the best policies * possible in all economic and social spheres. === Subject: Re: Integer factorization, etc. and would have provided for their expulsion. # # The Chairman of the Select Committee on Intelligence opposed the measure # as unnecessary and could lead to disclosing sensitive intelligence # sources. British wiretappers at the helm of the NSA's domestic spy-fest. **************************************************************************** ** **************************************************************************** ** **************************************************************************** ** And so it is up to all of you. To arm yourselves. With writing implements. COMPLAIN LIKE HELL! Write to all your Congressional representatives. Send them a copy of any/all of this manifesto with a cover letter stating the specific questions you demand be answered. Write to your local papers, radio stations, state supreme courts (make them aware of fingerprinting drivers is a violation of the 1974 Privacy Act). Write to all your state representatives. Take copies of this manifesto and go to your neighbors and ask they consider doing the same. Contact all your friends. : The New York Times, 2/10/87 : Is This America?, by Ant === Subject: Re: Integer factorization, etc. and unbreakable encryption, available world-wide. CISPES - Committee in Solidarity with the People of El Salvador Ultra-secret agencies: NSA - U.S. National Security Agency GCHQ - British Government Communications Headquarters CSE - Canada's Communications Security Establishment DSD - Australian Defense Signals Directorate GCSB - New Zealand's Government Communications Security Bureau **************************************************************************** ** Main() ---- Using mainly publicly available material, here is my documentation of: o Part 1: Massive Domestic Spying via NSA ECHELON This is highly detailed documentation of NSA spying. This spying is illegal, massive, and domestic. The documentation is comprehensive, especially since it is now brought together in this one section. o Part 2: On Monitoring and Being Monitored In this section, I describe the capabilities of ECHELON keyword monitoring. A detailed example --- how to use keywords to pick out conversations of interest --- is given. I also put forth a case of what it means to be monitored heavily by the government. o Part 3: 1984 Means a Constant State of War The politics of war, and the Orwellian tactics employed by by the U.S. Government to control its citizens. o Part 4: Why unlimited cryptography must be legislated NOW In additional to the reasons given in the previous sections, the 'debate' reasons constantly given by the government are reviewed and debunked. And our nation's experts say it will hurt security. The GAO says the same thing. o Part 5: There is no part five. o Part 6: Louis Freeh & The Creep === Subject: Re: Integer factorization, etc. to the managers of the * plant concerned. What are 'arousal filter' and 'homeostatic loops'? The scope of Cybernetics is, in a word, awesome. A cyberneticist can talk from atoms to cells to nervous systems, to management of a company, country, world, solar system. Whether an organism is mechanical, biological or social, it requires a feedback mechanism to survive. Your nervous system does some amazing things to fight off infections. It creates custom anti-bodies to attack foreign microbes. Custom living cells created through a system of feedback to spot that there was a problem, analysis of the problem, action on the problem. This is a life-sustaining feedback 'homeostatic' loop. [bracket comments are mine] When Stafford Beer says Cyberstride needed to filter 'homeostatic loops': * The Human Use of Human Beings - Cybernetics and Society * by Norbert Wiener, 1954, pre-ISBN * * The process [such as that employed by our nervous system] by which we * living beings resist the general stream of corruption and decay is * known as homeostasis. Stayin' alive, stayin' alive... So, statistical filtration for all homeostatic loops means one is checking on the health of the monitored system. The cybernetician uses the same language for feedback of weapons systems (picking out a submarine from the background noise of the ocean) as they do for describing human life, as they do for the political organization of a country. Like I said, an awesome scope. Norbert Wiener even came up with a physics-based description of how life is formed by information. Check it out. Hang in there too, it's worth it. * Platform for Change, by Stafford Beer, 1978, ISBN 0 471 06189 1 * * The term 'entropy' began life as a subtle measure of energy flow. * * When something hotter is systemically bound to something cooler, the * greater energy of the hotter stuff migrates---inexorably migrates--- * into === Subject: Re: Integer factorization, etc. actual or intended publication of such source code. */ ...followed by another email with a subset of the same source, > slightly modified, and the proprietary header stripped out. I hope it didn't flow past AT&T's ISP connections... ********** end excerpt from 'Corruption at Salomon Brothers' ********** This transfer of proprietary source code that USED to be owned by AT&T did not even qualify for action. Salomon legal stated Salomon has a lower obligation for third-party copyrights than they did for software they contracted for themselves, like Sybase. Salomon didn't have a UNIX source license, so obviously the employee had gotten it elsewhere. In the following statistic, it was the only non-Salomon source code. We went from zero monitoring of Internet email traffic to... > On 3/21/96 we had our first security incident report. By 3/26/96 we had an astonishing 38,000 lines of proprietary source code > outbound. We were mentally unprepared. Figuratively we were pulling our hair out > wondering when the madness would stop. It never did. As I said, the results of keyword monitoring were s === Subject: Re: Integer factorization, etc. society. The 'arousal filter' Stafford Beer and his cyberneticians set up was effectively keyword monitoring of traffic. When you use keywords to either select or exclude traffic, each step is a 'filter' step. If you make it past all the filters, a human then reviews the results to see if it calls for action. arousal filter Mr. Beer was trying to help the economy by massive real-time monitoring of factories and companies and banks, and thus help the people of Chile. * Brain of the Firm, Stafford Beer, 1986, ISBN 0 471 27687 1 * * Twenty-four hours a day, messages were flowing in non-stop. This instantly * posed an enormous problem in handling the inundation of information. * * Two of the senior cyberneticians organized a filtration system. The feedback was not simply machine throughput rates, but also---via the central computer---a system 'through which anyone could consult anyone else'. I used keyword monitoring to filter information from noise in Salomon's HUGE email traffic. What I did, of course, was small potatoes; what Stafford Beer did was a serious cybernetic attempt to control an entire nation's economy. In order for him to do that, he needed to set up a (cybernetic) monitoring infrastructure. The nation's banks, factories and industrial companies. It would have given Allende maximum control over the nations industrial infrastructure, real-time monitoring of everything. Everything had a computer monitoring it. * The Future of War - Power, Technology, and American World Dominance in * the 21st Century, by George & Meredith Friedman, 1996, ISBN 0-517-70403-X * * McNamara's revolution built on an idea that was central to operations * research and propounded by many nuclear strategists, that war was not * methodologically distinguishable from economics. The process whereby you * analyzed, managed, and controlled an economy was not essentially different * from the way you managed a war, except === Subject: Re: Integer factorization, etc. 4.7 murders per 100,000 people * * Amazing as it may seem that a leading law enforcement official might * try to buttress his cases through the selective use of statistics, that * was hardly the end of it. * * When the FBI director selected the years to illuminate his thesis for the * National Press Club, he compared a year when the nation's homicide rate * was at one of its *all-time lowest* points to that of a year when the rate * was near its *all-time high*. [extended discussion of homicides followed] * * Such selective use of statistics is dishonest. * * It is impossible to know what was going through Louis Freeh's mind as he * delivered his distorted, exaggerated and fundamentally flawed crime speech * to the National Press Club. * * We do know however, that for many decades, law enforcement officials * across the nation have advanced their careers and promoted their * political agendas by chanting the same Mantra of the Scary Numbers. Louis Freeh: The polls prove people are fed up with crime This book contains a DEVASTATING accounting of the manipulation of people's perception of crime rates. [not shown!] Fear, loathing, and somehow the public clamoring for a Police State. * Police chiefs, prosecutors, judges, FBI directors and the politicians who * supported their cause have long waved the bloody crime flag to rally the * public to their various causes. * * During the twenty-year period that presidents from Nixon to Clinton were * agitating the public a === Subject: Re: Integer factorization, etc. --- -- ----- * The New York Times * * December 7 1995. A&E Investigative Reports Seized by the Law draws * attention to a recent embellishment of the criminal law that permits * Federal agents and the state and local police to confiscate cash and * property on the suspicion that their owners are involved in drug * trafficking. * * Just suspicion. * * No arrest or indictment, much less conviction, is required. The Dark Ages in America. * And the fact that most of the proceeds stay with * the police may be a temptation to confiscation. Naw, that would never happen. ---- === === === === === > I think that it's necessary but not sufficient. >So what do you propose? > At this point I don't know. Until I saw your well-reasoned > a UDP against Google. I think you're right, though, about > cutting off your nose to spite your face, and that sent me > back to the drawing board. The thing is that a UDP does not have to be implemented to be effective. > The mere threat of a UDP with a deadline would be enough to generate > sufficient bad press that Google would be forced to act. It's happened in > the past with ISPs such as Bigpond in Australia. Why don't the morons apply the same filtering to the crap they propagate out > to usenet? Several reasons. thousands of files (and an equal number of additions to indexes), one per recipient. Secondly, they have a competing forum service, and no incentive to stop their servers spewing all over the thing they are competing against. Thirdly, you might be right about them being morons too. Phil -- -- Microsoft voice recognition live demonstration === > [ Is it me or during the last supernews merge, the text features (the Perhaps this is because the SuperNews admins have disappeared. === It's not very well propagated at 34.7% and it seems to be missing on > some popular servers: What I'd suggest doing is put a .sig line as an ad when you're > been newgrouped. If your news server isn't carrying it, ask your > system administrator to add it to the the active file. I think Adam can phrase it better, though. Well, it appears that in sci.math a minimal how-and-why-to- topic in that as anything else is. I have certainly considered groups sucks, and how to get more information about alleviating the problem. Phil -- -- Microsoft voice recognition live demonstration === > It's not very well propagated at 34.7% and it seems to be missing on > some popular servers: > What I'd suggest doing is put a .sig line as an ad when you're > been newgrouped. If your news server isn't carrying it, ask your > system administrator to add it to the the active file. > I think Adam can phrase it better, though. Well, it appears that in sci.math a minimal how-and-why-to- > topic in that as anything else is. I have certainly considered > groups sucks, and how to get more information about alleviating > the problem. That's great, but I was addressing the issue of getting the group propagated. B/ === Subject: Re: Fermat's Last Theorem >Er...a mathematical one, say...? Of course, you cannot understand >this, but that's what I had in mind, my boy. > In other words tangible and mathematical are synonymous? >Is it really necessary to cross-post such [OT] physics stuff to >c.a.p. ??? > Where issues of science and truth are concerned, personally I'm > inclined to solicit the widest possible distribution. I understand > others are more reluctant to expose their private languages and codes > to public criticism but then there is nothing to be gained from > reliance on supernatural mysticism in any event and I think you'll > find one of the things cap badly needs to explain is why doctrinaire > philosophers imagine there could be and that the field of artificial > intelligence can safely pretend otherwise. > I might expect the physics forums inhabitants to be grateful for [OT] >postings from behaviorists and librarians too. Hey bunkie, expose >yerself to the wider world. What's your point, Dan? You act as if you already know everything there is to be known about intelligence and the mechanization of artificial intelligence because you say the word feedback as if that were some magic keyword. I don't know anyone who agrees with you. The rest of the world has been doing feedback for a couple centuries at least and I see no evidence of emergent intelligence. What I see is you programming computers, calling results artificial intelligence, and walking the Rockies with your dogs, complaining anyone who disagrees with you is OT because you don't have a clue. I've exposed myself to your wider world for several years and see no indication that you're doing much of anything that wasn't being done by programmers in the seventies except for preaching simplistic academic doctrines you can't demonstrate have anything to do with intelligence. If you want to call the newsgroup comp.robotics you won't hear a peep out of me. But if you try to pretend you have some insight into the artificial mechanization of intelligence apart from naive slogans, you can expect to hear a lot more from me including a whole bunch of issues conventional ai wishes would just go away. ~v~~ === Subject: Re: Fermat's Last Theorem <19008729.1208600609878.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) The really odd thing is that Mehran Basti received his Ph.D. from Cambridge University in 1979 with a dissertation entitled Asymptotic Equivalence, Existence of Periodic Solutions and Topological Equivalence of Systems of Ordinary Differential Equations æOne wonders what went wrong. Psychosis. quasi Not necessarily. It's a bit rude of us to speculate on someone's state of mind where they can actually read it; but any number of accidents or afflictions could affect the intellect, from a car accident to frontal lobe epilepsy or of course a nervous breakdown, and perhaps the very single-mindedness that makes a great academic can be a weakness in bad circumstances or if taken to excess. I wonder if Mehran does have voluminous notes, just as he claims, but is paranoid about giving details here or on the web in case someone publishes a paper incorporating his ideas. I can see how it could happen - In practice there's no guarantee of priority except in an official journal or something like the arXiv. Even if one used one of those date-stamping services, in the end what counts is who everyone believes had an idea first, rather than what some lone voice claims on their own behalf. Also, perhaps there is a remote connection between the Riccati equation and FLT, via the Schwarzian derivative, and modular functions [ http://en.wikipedia.org/wiki/Riccati equation ] John Ramsden === Subject: Re: Fermat's Last Theorem >The really odd thing is that Mehran Basti received his Ph.D. from >Cambridge University in 1979 with a dissertation entitled >Asymptotic Equivalence, Existence of Periodic Solutions and >Topological Equivalence of Systems of Ordinary Differential Equations > æOne wonders what went wrong. > Psychosis. > quasi Not necessarily. It's a bit rude of us to speculate on someone's >state of mind where they can actually read it; Yes, I said it right to his face, not behind his back. >but any number of accidents or afflictions could affect the intellect, >from a car accident to frontal lobe epilepsy or of course a nervous >breakdown, Sure, it could very well be physical. Still, he's crazy. >and perhaps the very single-mindedness that makes a >great academic can be a weakness in bad circumstances or if >taken to excess. Absolutely -- many geniuses throughout history have gone off the deep end. >I wonder if Mehran does have voluminous notes, just as he claims, I believe he does. Perhaps 10,000 pages as he claimed earlier, or perhaps 2,000 pages as he claimed recently -- hey, what's 8,000 pages, give or take? But do I believe that those notes could ever be converted to a form which make sense to others? No way! I doubt that even _he_ could make sense out of most of them. >but is paranoid about giving details here or on the web in case >someone publishes a paper incorporating his ideas. His paranoia rings out loud and clear. He can be forgiven for that -- after all, ideas are easily stolen. >I can see how it could happen - In practice there's no guarantee >of priority except in an official journal or something like the arXiv. Or a self-published book -- the book he claims he will eventually write. >Even if one used one of those date-stamping services, in the >end what counts is who everyone believes had an idea first, >rather than what some lone voice claims on their own behalf. Which is why he has to write the book, and stop talking about it. >Also, perhaps there is a remote connection between the Riccati >equation and FLT, via the Schwarzian derivative, and modular >functions [ http://en.wikipedia.org/wiki/Riccati_equation ] I'm sure there could be. The _idea_ that a system of polynomial equations could be modeled by a system of differential equations, and solved using the methods of differential equations is a reasonable idea, but vague, and not earth-shakingly original. He talks about modeling polynomials as differential equations. Presumably that means he has discovered how to add, subtract, and multiply polynomials via their corresponding differential equations. But can he factor polynomials? And if he can, can he do it more efficiently than known methods? If so, he already has something of value. If not -- if he can't even decide irreducibility, it's highly unlikely that he can compute Galois groups (as he vaguely suggested), or that he could solve diophantine equations which are currently unsolved. The guy is a kook, no question about it. What does he actually want? For one thing he wants students -- students who will pay _money_ for the privilege of trying to untangle his mess of ideas. He envisions himself as the head of an unofficial school, with loyal students and proteges who will carry out the development and implementation (i.e. -- programming) of his ideas. But it's a scam. I'm not talking about the money -- he's not really after the money -- he only wants enough to live on. I'm talking about stealing people's time -- years perhaps. His credentials (PhD from Cambridge) are the bait, creating the illusion of credibility. If he just struggles on his own to self-publish, fine, I have no problem with that. But in fact, he wants to lure others to into the depths of his madness. To defend against that, his bluff needs to be called, and his lunacy exposed. quasi === Subject: Re: Fermat's Last Theorem > In one tour de force I read all your papers, > Basti...well, not really a tour de force since > all 4 papers are only 26 or so pages, and I found > not one single proof of any of your claims! You talk a lot about what your method with Riccti > equations, ODE's and stuff can achieve, how this is > gonna be much better than Galois methods and etc., > but you show no one single example of all this... If you expect someone to believe your claims and > then to invite you to give talks and stuff, you > better write down a paper and give a tangible proof > of what you claim, otherwise I think there's a very > very remote chance anyone will ever believe you based > only in your own claims. I looked at them as well, via the Math Forum's sci.math web pages, which now allow attachments to be included in posts archived there. My opinion is about the same. I've looked at a huge amount of mathematical literature over the past 30 years, so I think I have a reasonable feel for what is ligitimate and what is crankish. While there's going to be some grey area for me, especially since I know next to nothing about his subject matter, there are so many crank warning signs and so little (none, really) indications of real math that agreeing with you on this is a no-brainer. In fact, if I hadn't seen the math genealogy web page for him, I wouldn't have taken him for a college graduate (ESL status aside) simply on the basis of the level of writing. When I think back to the exceedingly precise and careful page-by-page editing and proofing my advisor and I did with my Dissertation, I can't help but wonder if this is one of those cases Dave L. Renfro === Subject: Re: Fermat's Last Theorem > Today I have received a form letter from chair of MIT > applied math, rejecting my application for a position > there. What courses have you taught? Is your teaching philosophy on the internet anywhere? Can you document any successful grant applications for your work? Are you familar with the use of a TI-83 calculator in the teaching of calculus? Dave L. Renfro === Subject: Re: Fermat's Last Theorem >Yup: psychosis, schizophrenia and paranoia and, so far, lack of any >mathematics to read, in spite of Lester Zick. But for this, I wonder >how come the MIT didn't want him... Obviously that's only because Lester knows whereof he speaks but you don't. ~v~~ === Subject: Re: Fermat's Last Theorem >By the way, by another performance for to reach FLT proof do you >mean an ACTUAL proof of FLT or what? > See, this is all very confusing. First you demand some kind of > tangible proof, tangible in your lexicon apparently being > synonymous with mathematical for incomprehensible reasons you're > unable to specify. Now you demand some kind of actual proof > according to which you no doubt also mean mathematical. So I suppose > we're left to conclude that tangible and actual mean > mathematical in some mystical neoplatonic, neopythagorean corner of > the universe you call home. > No wonder you find it a little difficult to satisfy your demands for > proof when you can't explain what those demands are. Doubtless you'd > claim to know it when you see it in which case everyone else should > probably qualify mathematics with Tonico's tangible, actual. . . In > other words just another inexplicable private language in which you > prefer to couch demands your unable to speficy. >******************************************************* I know all this is very confusing and hard to understand for you: >after all you are not a mathematician, as it was made clear by your >utter confussion in several threads where you displaid your ignorance >about set theory, Cantor Diagonal Proof and etc. Whereas you just displaid your ignorance of spelling. >Never mind, keep on learning and you shall get there...or not. Tonio Ps By the way, in your last line above, I bet you meant you're and >not your...right? I also probably meant specify instead of speficy whereas, clever devil that you are, you undoubtedly meant modern mathematiker instead of mathematician. You see, the difficulty here is it's reasonably easy to interpolate the intended meaning of misspellings careless editing allows to slip through. However when you use phrases like actually mathematical or really mathematical it's much more difficult to know exactly what you have in mind. Do you mean Peano mathematical, MIT mathematical, Stanford mathematical, Euclidean mathematical, Hilbert mathematical, Wikipedia mathematical or just what exactly? Obviously you have some abstract mathematical standard in mind, but it's really anyones guess simply because you decline to be more specific than to assert that anyone who disagrees with you isn't really a mathematician at all. Someone might try to satisfy one criterion only to have you come back and say no, no, that's not really mathematical at all. These are all really just mathematical doctrines and have no particular claim to being mathematics to the exclusion of other mathematical doctrines. So until you can demonstrate why one doctrine is really mathematical and others not, one can only assume you really have no critically exacting knowledge of what doctrines constitute mathematics. ~v~~ === Subject: Re: True Philosophers and Thought >A new entry for the list of modern oxymorons: >True philosopher > Nature abhors philosophers. > ~v~~ >Nature abhors Zickisms. > Ah. More fellatious nonsense >Who's the idiot who crossposted this crap to sci.logic? > See, here's the problem, lil Herbie. Doesn't he yap prettily? Do you mean the charming and witty fellatious remark, or do >you mean the pretentious dribble I snipped? He meant the former. He has no clue at to what you mean by the latter. >Never mind, the answer's no. > Of course, he yaps for the same reason little dogs yap at passing ice > cream trucks, but the reason isn't important to Zick, it's just how > pretty the yap is. He can yap all he wants. Please remove sci.logic from the newsgroups >list, as I have. We've got a full quota of self-important cranks >going on already. And, what, Herb, you aren't especially anxious for the competition? It might help if you could just explain what the problem is apart from screaming and hollering that it ain't true and you really don't wan't to hear it especially if it might be true. Rather reminisces one of doctrines concerning slander of the crown:bad if false, worse if true. I mean, even beyond supernal wittiness I'm a perfectly reasonable individual anxious to refine ideas of universal truth and science. So unless you're willing and able to advance some credible objection to the truth of my observations, I'm very much afraid you should hie thee to a nunnery where your faith can be tested instead of your arguments. ~v~~ === Subject: Re: True Philosophers and Thought >A new entry for the list of modern oxymorons: >True philosopher > Nature abhors philosophers. > ~v~~ >Nature abhors Zickisms. > Ah. More fellatious nonsense >Who's the idiot who crossposted this crap to sci.logic? > See, here's the problem, lil Herbie. I'm assured by all kinds of > mathematikers that mathematics and science generally rely essentiallly > on logic. So I'm naturally inclined to solicit the opinions of > academic logicians on such subjects as the truth of mathematical and > scientific propositions. > In fact I'm quite puzzled as to exactly why anyone would object. > Certainly if anything actually universally true were discovered > instead of merely some kind of private language code one would solicit > the widest possible distribution. So we are forced to conclude that > academic logicians have nothing to say on the subject of truth or > those more interested in its pursuit than in the mystical supernatural > you choose to call by similar names. > Nonetheless we do not object if you want to continue to post on > sci.logic as long as you remember that truth is the hallmark and > criterion of knowledge and not pretentious private languages. > ~v~~ Doesn't he yap prettily? >Of course, he yaps for the same reason little dogs yap at passing ice >cream trucks, but the reason isn't important to Zick, it's just how >pretty the yap is. Wit is wasted on the witless. ~v~~ === Subject: Re: True Philosophers and Thought <3qkh04huevfpdbnrikci6ghbc85dj09023@4ax.com> <480910C3.28CA316D@gmail.com> posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) >A new entry for the list of modern oxymorons: >True philosopher > Nature abhors philosophers. > ~v~~ Nature abhors Zickisms. Ah. More fellatious nonsense >Who's the idiot who crossposted this crap to sci.logic? > See, here's the problem, lil Herbie. I'm assured by all kinds of > mathematikers that mathematics and science generally rely essentiallly > on logic. So I'm naturally inclined to solicit the opinions of > academic logicians on such subjects as the truth of mathematical and > scientific propositions. > In fact I'm quite puzzled as to exactly why anyone would object. > Certainly if anything actually universally true were discovered > instead of merely some kind of private language code one would solicit > the widest possible distribution. So we are forced to conclude that > academic logicians have nothing to say on the subject of truth or > those more interested in its pursuit than in the mystical supernatural > you choose to call by similar names. > Nonetheless we do not object if you want to continue to post on > sci.logic as long as you remember that truth is the hallmark and > criterion of knowledge and not pretentious private languages. > ~v~~ Doesn't he yap prettily? >Of course, he yaps for the same reason little dogs yap at passing ice >cream trucks, but the reason isn't important to Zick, it's just how >pretty the yap is. Wit is wasted on the witless. ~v~~ Do you recognize yourself here, ZickWit? === Subject: Re: True Philosophers and Thought > According to the guys quoting so-called physicist philosophers on > the other threads, it's all just an illusion anyways, and even you, I > guess. And here, I thought it was the buddhists who thought that. As far as I can tell I can believe one of these three: Or all three together. >1. I am alone in the world but am also psychotic because I hear >voices. >2. I am not alone because I hear voices. >3. I am not alone but I am psychotic. > The voices I hear can have either source. One can substitute the other senses and come to the same choices. >Do you believe Buddhists dealth with the senses rather than the >desires of the senses? Do you believe western philosophy devoid >of thinking about the senses? ~v~~ === Subject: Re: True Philosophers and Thought >On Apr 15, 10:06 am, Douglas Eagleson A man would be always certain of the subject. æHe would alive make the > sentence relatable and so composition was to uniformly announce > topic. æA subject topic allowed the thinking. æAnother type as > composition was relation. æSubject considered would be a search for > the exact relation mentioned. > One reader has announced thought while the other uses all relation as > the possible subject. > So 2% can allow such act of thought. A consistency of composition was > the issue and my consistency would not fail a close scrutiny. > I am happy to announce a subject. æA relation, a single thought. > Either reader should be forwarned. > A. > As a student philosopher A means my name. æA person whose > composition skills are always relation. > All true philosophers are such in nature. æAnd to emulate them was my > goal. æA large relation. > I think therefore I am. > A certain foundation to the philosopher was this famous sentence. > Relationship as person, a mind, to the world was always its subject. > A mind acts within the body given substance examinable to the depths > of the DNA strand. æMinds examine. > So consider the complexity as a personal tribute. >A new entry for the list of modern oxymorons: >True philosopher > Nature abhors philosophers. > ~v~~ >Nature abhors Zickisms. > Ah. More fellatious nonsense from the Master of the Supernatural. > ~v~~ Supernatural? Nah. I hardly ever talk about the supernatural. Is this a joke? You never talk about anything else. Do you imagine, it isn't there if you don't use the the terms? In other words you speak in tongues. The whole purpose of science is to explain what your personal gods find themselves quite unable to explain. That's why they're supernatural to begin with. First there was Mati Meron who had some difficulty explaining the derivative of cross products correctly. Then Red Herring couldn't quite comprehend curves. Following which Dirk vdM had some difficulty defining clocks. Then Randy Poe not only couldn't figure out what definitions were but couldn't even explain the functional dependence of L=r x p on r with a straight face. And finally Bagel of the HMS Blivit had some difficulty grasping demonstrations of truth but nonetheless expressed willingness to make a few gigabucks off of anyone who could explain it to him. Followed by your own irretrievably lame attempts to pretend you actually know what you're talking about describing lines of longitude at the equator of spheres as parallel. Every now and again some pissant academic comes along pretending to accommodate everything in some private lexicon he assures us will cover everything worth knowing about everything worth knowing about. We've already had numerous lessons from modern mathematikers and behaviorists on the topic. We don't need more from you. You use terms like Zickisms and think without a clue as to exactly what you're talking about. But talk about them nonetheless you insist on doing. ~v~~ === Subject: Re: True Philosophers and Thought posting-account=bSICGQkAAADSbkxAJ5uMxFegr4rp0Qig Gecko/20071115 Firefox/2.0.0.10,gzip(gfe),gzip(gfe) > Then Randy Poe not only couldn't figure out what > definitions were Definitions are statements which associate an abbreviation with a longer word or phrase. For example: If I say A circle is defined as the set of points in a plane equidistant from a given point then everywhere I would use the phrase set of points in a plane equidistant from a given point I can substitute the letters circle without changing the meaning. Equivalently, everywhere I see the word circle I can substitute set of points in a plane equidistant from a given point. The definition is the sentence that establishes that I am making this association. > but couldn't even explain the functional dependence > of L=r x p on r with a straight face. I'm assuming you're talking about our discussion of straight line motion, where |r| = d/sin(theta), p = mv, and r x p = |r|*|p|*sin(theta) = d*mv So I guess we're still where we were. How does d*mv change with r? - Randy === Subject: Re: True Philosophers and Thought posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) On Apr 15, 10:06 am, Douglas Eagleson A man would be always certain of the subject. æHe would alive make the > sentence relatable and so composition was to uniformly announce > topic. æA subject topic allowed the thinking. æAnother type as > composition was relation. æSubject considered would be a search for > the exact relation mentioned. > One reader has announced thought while the other uses all relation as > the possible subject. > So 2% can allow such act of thought. A consistency of composition was > the issue and my consistency would not fail a close scrutiny. > I am happy to announce a subject. æA relation, a single thought. > Either reader should be forwarned. > A. > As a student philosopher A means my name. æA person whose > composition skills are always relation. > All true philosophers are such in nature. æAnd to emulate them was my > goal. æA large relation. > I think therefore I am. > A certain foundation to the philosopher was this famous sentence. > Relationship as person, a mind, to the world was always its subject. > A mind acts within the body given substance examinable to the depths > of the DNA strand. æMinds examine. > So consider the complexity as a personal tribute. A new entry for the list of modern oxymorons: >True philosopher Nature abhors philosophers. ~v~~ >Nature abhors Zickisms. > Ah. More fellatious nonsense from the Master of the Supernatural. > ~v~~ Supernatural? Nah. I hardly ever talk about the supernatural. Is this a joke? You never talk about anything else. Do you imagine, it > isn't there if you don't use the the terms? Well, Zick, religious faith is often characterized as believing something for which you have no evidence. Here, you believe that I talk about the supernatural, though you confess you have no evidence for it, and you say it is there nonetheless. It appears you have religious belief that I've been talking about the supernatural. > In other words you speak > in tongues. The whole purpose of science is to explain what your > personal gods find themselves quite unable to explain. That's why > they're supernatural to begin with. First there was Mati Meron who had some difficulty explaining the > derivative of cross products correctly. Then Red Herring couldn't > quite comprehend curves. Following which Dirk vdM had some difficulty > defining clocks. Then Randy Poe not only couldn't figure out what > definitions were but couldn't even explain the functional dependence > of L=r x p on r with a straight face. And finally Bagel of the HMS > Blivit had some difficulty grasping demonstrations of truth but > nonetheless expressed willingness to make a few gigabucks off of > anyone who could explain it to him. I'm sorry, but you seem now to be attributing statements of others to what I've been talking about. Do you also have a religious belief that what others say, I also say? > Followed by your own irretrievably > lame attempts to pretend you actually know what you're talking about > describing lines of longitude at the equator of spheres as parallel. Ah, finally we've arrived at something that I actually DID talk about, rather than an apparently religious belief in something that I did not talk about. And parallel lines or lines of longitude -- are these supernatural, Zick? Or is it your assumption that if you don't understand what's being said to you, that the subject must be about something supernatural? Every now and again some pissant academic comes along pretending to > accommodate everything in some private lexicon What's private about it, Zick. The definitions of these terms are all other media, for the taking by anyone interested with even a modicum of effort. You on the other hand, don't seem willing to take any effort other than what you can generate out of your own head -- and in doing so, you manage to generate the private lexicon you condemn. Please observe that published usually connotes publicly available. > he assures us will > cover everything worth knowing about everything worth knowing about. > We've already had numerous lessons from modern mathematikers and > behaviorists on the topic. We don't need more from you. You use terms > like Zickisms and think without a clue as to exactly what you're > talking about. But talk about them nonetheless you insist on doing. I'm sorry, you were babbling at some point about my talking about the supernatural, but you seem to have wandered off track. Where is the supernatural in any of this? ~v~~ === Subject: Re: More evidence proving Apollo Hoax > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms... > Find more at: > http://wms.selene.jaxa.jp/ > Oh. > When I read More evidence... I thought there would actually be some > evidence. > I want to see the flag > Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. > The Apollo programme was a total hoax. JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) Their 10 meter resolution of those crisp TC obtained images are more > than good enough to have shown us those NASA/Apollo landing sites. > With a good PhotoShop enlargement (plus image stacking where needed) > could make those 10m/pixel into nearly 1m/pixel. It's only going to get better, as time will eventually have the JAXA/ > Selene orbiting at merely 10 km, giving us a raw 1m/pixel look at > those supposed NASA/Apollo landing sites.. > . - Brad Guth And wont you look Very foolish === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms... > Find more at: >http://wms.selene.jaxa.jp/ > Oh. > When I read More evidence... I thought there would actually be some > evidence. > I want to see the flag > Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. > The Apollo programme was a total hoax. JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) Their 10 meter resolution of those crisp TC obtained images are more > than good enough to have shown us those NASA/Apollo landing sites. > With a good PhotoShop enlargement (plus image stacking where needed) > could make those 10m/pixel into nearly 1m/pixel. It's only going to get better, as time will eventually have the JAXA/ > Selene orbiting at merely 10 km, giving us a raw 1m/pixel look at > those supposed NASA/Apollo landing sites.. > . - Brad Guth And wont you look Very foolish Nearly nine years and counting, haven't so far, and of others having this similar deductive mindset as of the very get-go are in the same boat. But then unlike yourself and others of your mostly Semitic and Third Reich brown-nosed kind, I'll go along with whatever's the best available science, especially if it's made fully objective by other than just within the NASA/Apollo O-Ring cult. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=kxPkPAoAAACjJi8w0gL9bnyznPzdw9HW 2.0.50727),gzip(gfe),gzip(gfe) > ... > When I read More evidence... I thought there would > actually be some evidence. I want to see the flag With 40 years of bombardment by cosmic radiation and UV, it will > be two sticks and tatters. David A. Smith And the car will lock like a piece of stone === Subject: Re: More evidence proving Apollo Hoax > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms... > Find more at: > http://wms.selene.jaxa.jp/ > Oh. > When I read More evidence... I thought there would actually be some > evidence. > I want to see the flag > Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. > The Apollo programme was a total hoax. What unmanned craft? Must be the one in Saturn 5? === Subject: Re: More evidence proving Apollo Hoax > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms.selene . jaxa.jp/data/en/hdtv/000/hdtv_000_4_l.jpghttp://wms.selene.jaxa.jp/data/en/h d tv/000/hdtv_000_5_l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_6 _ l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_7_l.jpghttp://wms.s e lene.jaxa.jp/data/en/hdtv/000/hdtv_000_8_l.jpghttp://wms.selene.jaxa.jp/data / en/hdtv/000/hdtv_000_9_l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_ 0 00_10_l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_1/hdtv_001_1_ l .jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_2/hdtv_001_2_l.jpght t p://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_3/hdtv_001_3_l.jpghttp://wm s .selene.jaxa.jp/data/en/hdtv/001/hdtv_001_4/hdtv_001_4_l.jpghttp://wms.selen e .jaxa.jp/data/en/hdtv/001/hdtv_001_5/hdtv_001_5_l.jpghttp://wms.selene.jaxa. j p/data/en/hdtv/001/hdtv_001_6/hdtv_001_6_l.jpghttp://wms.selene.jaxa.jp/data / en/hdtv/002/hdtv_002_1/hdtv_002_1_l.jpghttp://wms.selene.jaxa. jp/data/en/hdtv/002/hdtv_002_2/hdtv_002_2_l.jpghttp://wms.selene.jaxa.jp/dat a/en/hdtv/002/hdtv_002_3/hdtv_002_3_l.jpghttp://wms.selene.jaxa.jp/data/en/h d tv/002/hdtv_002_4/hdtv_002_4_l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002 / hdtv_002_5/hdtv_002_5_l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_0 0 2_6/hdtv_002_6_l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_4/hd t v_005_4_l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_2/hdtv_005_ 2 _l.jpg > Find more at: > http://wms.selene.jaxa.jp/ Oh. When I read More evidence... I thought there would actually be some > evidence. > Same here! All I see are orbital photos === Subject: Re: More evidence proving Apollo Hoax > The astronauts were in low-earth orbit. That accounts for that signal. > In fact there was a massive blunder in one of the shoots where a fake > far-away earth could be seen in one window then the real close-earth > was briefly seen on another. Bart Sibrel found that one. Google it and you'll probably find it. Bart Sibrel found some blurry video of astronauts rehearsing for a telecast, then made up a story about what it showed. Sibrel is the guy that kept pestering astronauts. He'd ask them to swear on the bible, saying they could end the controversy by doing so. Some wanted nothing to do with him. Others clearly stated that they walked on the Moon, but declined to participate in his Bible-swearing stunt. Eugene Cernan and Alan Bean did swear on the Bible. If you were expecting Sibrel to be good to his word that doing so would end his controversy, you don't know Bart Sibrel. Particularly funny is watching what a worm Sibrel is when Alan Bean insists on telling the truth. Bean agrees that the tape of him swearing on the bible could be used as a video deposition, and will swear under penalty of perjury. Then Sibrel adds treason and Bean objects: treason has nothing to do with it. Bean is right: under penalty of treason would be false. He's entirely willing to swear in various ways Sibrel suggest, but only to the truth. Sibrel keeps demanding Bean swear under penalty of treason even though Bean makes clear he believes it would be false. -- --Bryan === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms... Find more at: http://wms.selene.jaxa.jp/ Oh. When I read More evidence... I thought there would actually be some > evidence. I want to see the flag Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. The Apollo programme was a total hoax. JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) Their 10 meter resolution of those crisp TC obtained images are more > than good enough to have shown us those NASA/Apollo landing sites. > With a good PhotoShop enlargement (plus image stacking where needed) > could make those 10m/pixel into nearly 1m/pixel. Do you actually believe you can get a factor of ten increase in > resolution from photoshop? I can accomplish 8X with reasonable results, a 5th grader should be able to accomplish 4X right off the bat. BTW, I'd said along with image stacking, although other than PhotoShop (perhaps PhotoZoom) can accomplish a little better job of enlarging to 10X without distorting one damn thing. A digital stack of 10 frames couldn't hurt. . - Brad Guth It's only going to get better, as time will eventually have the JAXA/ > Selene orbiting at merely 10 km, giving us a raw 1m/pixel look at > those supposed NASA/Apollo landing sites.. > . - Brad Guth China is planning on doing the same reduced orbital range, and thus offering more than sufficient raw resolution. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008032620 Firefox/3.0b5,gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpghttp://wms... Find more at: http://wms.selene.jaxa.jp/ Oh. When I read More evidence... I thought there would actually be some > evidence. I want to see the flag Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. The Apollo programme was a total hoax. JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) Their 10 meter resolution of those crisp TC obtained images are more > than good enough to have shown us those NASA/Apollo landing sites. > With a good PhotoShop enlargement (plus image stacking where needed) > could make those 10m/pixel into nearly 1m/pixel. Do you actually believe you can get a factor of ten increase in > resolution from photoshop? I can accomplish 8X with reasonable results, a 5th grader should be > able to accomplish 4X right off the bat. BTW, I'd said along with image stacking, although other than PhotoShop > (perhaps PhotoZoom) can accomplish a little better job of enlarging to > 10X without distorting one damn thing. æA digital stack of 10 frames > couldn't hurt. . - Brad Guth Explain to me how you obtain information that is not there with Photoshop. Image stacking doesn't remove the fact that the object in question is still smaller than the pixel size. It's only ægoing to get better, as time will eventually have the JAXA/ > Selene orbiting at merely 10 km, giving us a raw 1m/pixel look at > those supposed NASA/Apollo landing sites.. > . - Brad Guth China is planning on doing the same reduced orbital range, and thus > offering more than sufficient raw resolution. > . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms... Find more at: http://wms.selene.jaxa.jp/ Oh. When I read More evidence... I thought there would actually be some > evidence. I want to see the flag Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. The Apollo programme was a total hoax. JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) Their 10 meter resolution of those crisp TC obtained images are more > than good enough to have shown us those NASA/Apollo landing sites. > With a good PhotoShop enlargement (plus image stacking where needed) > could make those 10m/pixel into nearly 1m/pixel. Do you actually believe you can get a factor of ten increase in > resolution from photoshop? I can accomplish 8X with reasonable results, a 5th grader should be > able to accomplish 4X right off the bat. BTW, I'd said along with image stacking, although other than PhotoShop > (perhaps PhotoZoom) can accomplish a little better job of enlarging to > 10X without distorting one damn thing. A digital stack of 10 frames > couldn't hurt. . - Brad Guth Explain to me how you obtain information that is not there with > Photoshop. Image stacking doesn't remove the fact that the object in > question is still smaller than the pixel size. It's only going to get better, as time will eventually have the JAXA/ > Selene orbiting at merely 10 km, giving us a raw 1m/pixel look at > those supposed NASA/Apollo landing sites.. > . - Brad Guth China is planning on doing the same reduced orbital range, and thus > offering more than sufficient raw resolution. > . - Brad Guth So, no matters how reliable the raw pixels are, and of no matters how many images are stacked or having been properly resampled, you don't believe in anything that's enlarged unless it's of inert eye-candy. Are you also Muslim? Of course 100% of all cosmic eye-candy pictures that are published for public review are of those stacked, resampled and colorized to death, whereas oddly that's perfectly OK by your hocus-pocus standards. How interesting. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=Y2v6DQoAAACGpOrX04JGhSdsTevCdArN Gecko/2008032620 Firefox/3.0b5,gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 7 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 8 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 9 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 10 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 1/hdtv 001 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 2/hdtv 001 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 3/hdtv 001 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 4/hdtv 001 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 5/hdtv 001 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 6/hdtv 001 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 1/hdtv 002 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 2/hdtv 002 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 3/hdtv 002 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 4/hdtv 002 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 5/hdtv 002 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 6/hdtv 002 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 4/hdtv 005 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 2/hdtv 005 2 l.jpg Find more at: http://wms.selene.jaxa.jp/ Same old idiocy. 1. Who put the mirror lunar ranging equipment on the Moon? Little green men? 2. Who was transmitting TV broadcast signals from the Moon at the time of Apollo missions (as shown by recently declassified Soviet spy antennas records)? Little green men? -- === Subject: Re: More evidence proving Apollo Hoax posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > 1. Who put the mirror lunar ranging equipment on the Moon? Little > green men? The task could be achieved through unmanned missions not necessarily short men painted green. of Apollo missions (as shown by recently declassified Soviet spy > antennas records)? Little green men? What is the nonsense about the Soviet soy antenna records? Is that where you got these little green men from? How do you suppose these Apollo astronauts with 0.25g/cm^2 of shield is going to come up totally unharmed after being bombarded with 3E-14 solar mass per year of energy? Little green men reported from unclassified Soviet antenna spy whatever archive? http://en.wikipedia.org/wiki/Solar wind probability of causing some sorts of cancer in a few years. The lower- energy ones would manifest shorter term illness. It is not advisable to be bombarded with 3E-14 solar mass per year of energy at earthÍs orbit with just 0.25g/cm^2 of shielding from the command module. Stop watching more useless films. Do the math yourself, film critic. === Subject: Re: More evidence proving Apollo Hoax posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008032620 Firefox/3.0b5,gzip(gfe),gzip(gfe) 1. Who put the mirror lunar ranging equipment on the Moon? Little > green men? The task could be achieved through unmanned missions not necessarily > short men painted green. æ What unmanned missions ? 2. Who was transmitting TV broadcast signals from the Moon at the time > of Apollo missions (as shown by recently declassified Soviet spy > antennas records)? Little green men? What is the nonsense about the Soviet soy antenna records? æIs that > where you got these little green men from? How do you suppose these Apollo astronauts with 0.25g/cm^2 of shield > is going to come up totally unharmed after being bombarded with 3E-14 > solar mass per year of energy? æLittle green men reported from > unclassified Soviet antenna spy whatever archive? http://en.wikipedia.org/wiki/Solar wind probability of causing some sorts of cancer in a few years. æThe lower- > energy ones would manifest shorter term illness. æIt is not advisable > to be bombarded with 3E-14 solar mass per year of energy at earthÍs > orbit with just 0.25g/cm^2 of shielding from the command module. > Oh this again? You were proven wrong with the actual ACE/SOHO spacecraft data and here you are repeating the same again. Stop watching more useless films. æDo the math yourself, film critic. === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > 1. Who put the mirror lunar ranging equipment on the Moon? Little > green men? The task could be achieved through unmanned missions not necessarily > short men painted green. What unmanned missions ? 2. Who was transmitting TV broadcast signals from the Moon at the time > of Apollo missions (as shown by recently declassified Soviet spy > antennas records)? Little green men? What is the nonsense about the Soviet soy antenna records? Is that > where you got these little green men from? How do you suppose these Apollo astronauts with 0.25g/cm^2 of shield > is going to come up totally unharmed after being bombarded with 3E-14 > solar mass per year of energy? Little green men reported from > unclassified Soviet antenna spy whatever archive? http://en.wikipedia.org/wiki/Solar wind probability of causing some sorts of cancer in a few years. The lower- > energy ones would manifest shorter term illness. It is not advisable > to be bombarded with 3E-14 solar mass per year of energy at earthÍs > orbit with just 0.25g/cm^2 of shielding from the command module. > Oh this again? You were proven wrong with the actual ACE/SOHO > spacecraft data and here you are repeating the same again. > Stop watching more useless films. Do the math yourself, film critic. > 1... BTW, our naked moon is unavoidably reactive because it's made of such a hard density worth of matter, instead of a vapor/gas that's far less reactive, thus our physically dark and nasty moon is contributing it's secondary/recoil anticathode worth of gamma and hard-X-rays, like none other. Each and every one of those Apollo miisions to/from the moon were essentially a two-part series of their unmanned orbital missions that went onward from the moon's L1, into lunar orbiting and as best could deploying technology up until each of their hard/impact landings. At least that's pretty much the best we can manage to pull off as of today. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms... Find more at: http://wms.selene.jaxa.jp/ Same old idiocy. 1. Who put the mirror lunar ranging equipment on the Moon? Little > green men? > 2. Who was transmitting TV broadcast signals from the Moon at the time > of Apollo missions (as shown by recently declassified Soviet spy > antennas records)? Little green men? -- Same old duh. What has a easily robotic deployed retroreflector (or several retroreflective items) have to do with moon walking? . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax -- This message is brought to you by Androcles http://www.androcles01.pwp.blueyonder.co.uk/ > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. > Find more at: http://wms.selene.jaxa.jp/ | Same old idiocy. Can't you get him a job changing light bulbs, like you? === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > -- > This message is brought to you by Androcles > http://www.androcles01.pwp.blueyonder.co.uk/ Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. Find more at: http://wms.selene.jaxa.jp/ | Same old idiocy. Can't you get him a job changing light bulbs, like you? In other words, you've got nothing outside of your NASA/Apollo Old Testament Qur'an. As of A-11, A-14 and A-16, where's Venus? . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 7 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 8 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 9 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 10 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 1/hdtv 001 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 2/hdtv 001 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 3/hdtv 001 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 4/hdtv 001 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 5/hdtv 001 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 6/hdtv 001 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 1/hdtv 002 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 2/hdtv 002 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 3/hdtv 002 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 4/hdtv 002 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 5/hdtv 002 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 6/hdtv 002 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 4/hdtv 005 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 2/hdtv 005 2 l.jpg Find more at: http://wms.selene.jaxa.jp/ Is this another bogus topic? Besides all the JAXA images (plus the other 99.99% of them we're not even being shown) that so far do not support our NASA/Apollo ruse, seems as though you haven't taken hardly anything other into account, that which clearly proves we have not walked on our moon. BTW, why exactly are those Google/Usenet gold stars locked up? . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Odd that when I keep trying to give this topic those nifty gold stars (Google/Usenet), that somehow others are continually taking them away just as fast as I put them on. What the hell gives? . - Brad Guth > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_4_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_5_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_6_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_7_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_8_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_9_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_10_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_1/hdtv_001_1_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_2/hdtv_001_2_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_3/hdtv_001_3_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_4/hdtv_001_4_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_5/hdtv_001_5_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_6/hdtv_001_6_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_1/hdtv_002_1_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_2/hdtv_002_2_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_3/hdtv_002_3_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_4/hdtv_002_4_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_5/hdtv_002_5_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_6/hdtv_002_6_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_4/hdtv_005_4_l.jpg > http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_2/hdtv_005_2_l.jpg Find more at: http://wms.selene.jaxa.jp/ === Subject: Re: More evidence proving Apollo Hoax posting-account=ML9J7goAAAAS6N3k57S2qk4WxczSttuL 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) > They lost all moon rocks too. Liar. === Subject: Re: More evidence proving Apollo Hoax posting-account=ML9J7goAAAAS6N3k57S2qk4WxczSttuL 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpghttp://wms... Find more at: http://wms.selene.jaxa.jp/ Oh. When I read More evidence... I thought there would actually be some > evidence. I want to see the flag Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. The Apollo programme was a total hoax. JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) Their 10 meter resolution of those crisp TC obtained images are more > than good enough to have shown us those NASA/Apollo landing sites. > With a good PhotoShop enlargement (plus image stacking where needed) > could make those 10m/pixel into nearly 1m/pixel. Do you actually believe you can get a factor of ten increase in > resolution from photoshop? I can get anything from photoshop. === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpghttp://wms... Find more at: http://wms.selene.jaxa.jp/ Oh. When I read More evidence... I thought there would actually be some > evidence. I want to see the flag Didn't hear about these photos on the media did you? There is no flag, > there is no tracks, there are only retroflectors deployed via unmanned > craft. The Apollo programme was a total hoax. JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) Their 10 meter resolution of those crisp TC obtained images are more > than good enough to have shown us those NASA/Apollo landing sites. > With a good PhotoShop enlargement (plus image stacking where needed) > could make those 10m/pixel into nearly 1m/pixel. Do you actually believe you can get a factor of ten increase in > resolution from photoshop? I can get anything from photoshop. Try PhotoZoom. . - BG === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. > As for the kook stuff, there I have to laugh in your face. These > photos are entirely consistent with the Apollo record; they'd > debunk Apollo Hoax kooks were there any debunking left to be > done. Count the stars appearing in these authentic pictures. Looks > like NASA had it right; the kooks, not so much. Of course that > kook stuff was debunked long ago, but still it's nice to see > the real stuff. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_5_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_6_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_7_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_8_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_9_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_10_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_1/hdtv_001_1_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_2/hdtv_001_2_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_3/hdtv_001_3_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_4/hdtv_001_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_5/hdtv_001_5_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_6/hdtv_001_6_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_1/hdtv_002_1_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_2/hdtv_002_2_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_3/hdtv_002_3_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_4/hdtv_002_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_5/hdtv_002_5_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_6/hdtv_002_6_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_4/hdtv_005_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_2/hdtv_005_2_l.jpg Find more at: http://wms.selene.jaxa.jp/ Good stuff. Say, who's the most notable person on this project to > say that the Apollo missions were fake? Let me guess: everything > the notable scientists and engineers say refutes the Apollo-deniers, > but the kooks dream up a giant conspiracy to explain why all the > evidence is against them. -- > --Bryan Isn't denial and evidence exclusion a good thing, especially for those of the Semitic Third Reich (like yourself). . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_5_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_6_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_7_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_8_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_9_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_10_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_1/hdtv_001_1_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_2/hdtv_001_2_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_3/hdtv_001_3_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_4/hdtv_001_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_5/hdtv_001_5_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_6/hdtv_001_6_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_1/hdtv_002_1_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_2/hdtv_002_2_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_3/hdtv_002_3_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_4/hdtv_002_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_5/hdtv_002_5_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_6/hdtv_002_6_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_4/hdtv_005_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_2/hdtv_005_2_l.jpg Find more at: http://wms.selene.jaxa.jp/ We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - The astronauts were in low-earth orbit. That accounts for that signal. > In fact there was a massive blunder in one of the shoots where a fake > far-away earth could be seen in one window then the real close-earth > was briefly seen on another. Bart Sibrel found that one. Google it and you'll probably find it. I think as a brave crew they may have actually made it to/from the moon's L1, because that's technically doable via the Saturn V as having nearly a 30% inert GLOW to deal with, but then I could be wrong. I also believe mission A-13 was a manned effort at accomplishing a brief half+ orbit of our moon, at a somewhat safer orbital distance and just for that one brief radiation exposure from their having been so close to our reactive/anticathode moon. The vast majority of our NASA/Apollo science about our moon was otherwise obtained robotically from orbit, with only limited surface probes that survived their hard/impact landings. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=UM3jRwkAAADTHFmJ20qgwageu031CeWA 5.1),gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 5 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 6 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 7 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 8 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 9 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 10 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 1/hdtv 001 1 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 2/hdtv 001 2 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 3/hdtv 001 3 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 4/hdtv 001 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 5/hdtv 001 5 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 6/hdtv 001 6 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 1/hdtv 002 1 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 2/hdtv 002 2 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 3/hdtv 002 3 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 4/hdtv 002 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 5/hdtv 002 5 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 6/hdtv 002 6 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 4/hdtv 005 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 2/hdtv 005 2 l.jpg Find more at: http://wms.selene.jaxa.jp/ æ æWe intercepted the live broadcast from the Moon in 1969 when > æ æI was in the Military.- Hide quoted text - The astronauts were in low-earth orbit. That accounts for that signal. > In fact there was a massive blunder in one of the shoots where a fake > far-away earth could be seen in one window then the real close-earth > was briefly seen on another. Bart Sibrel found that one. Google it and you'll probably find it. I think as a brave crew they may have actually made it to/from the > moon's L1, because that's technically doable via the Saturn V And it's all down hill from there and in both directions. So what the hell are you talking about? === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_3_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_4_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_5_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_6_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_7_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_8_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_9_l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv_000_10_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_1/hdtv_001_1_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_2/hdtv_001_2_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_3/hdtv_001_3_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_4/hdtv_001_4_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_5/hdtv_001_5_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv_001_6/hdtv_001_6_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_1/hdtv_002_1_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_2/hdtv_002_2_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_3/hdtv_002_3_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_4/hdtv_002_4_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_5/hdtv_002_5_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv_002_6/hdtv_002_6_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_4/hdtv_005_4_l.jpg http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv_005_2/hdtv_005_2_l.jpg Find more at: http://wms.selene.jaxa.jp/ We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - The astronauts were in low-earth orbit. That accounts for that signal. > In fact there was a massive blunder in one of the shoots where a fake > far-away earth could be seen in one window then the real close-earth > was briefly seen on another. Bart Sibrel found that one. Google it and you'll probably find it. I think as a brave crew they may have actually made it to/from the > moon's L1, because that's technically doable via the Saturn V And it's all down hill from there and in both directions. So what the > hell are you talking about? What's down hill? Isn't accomplishing the NASA/Apollo thing of getting our brave folks to/from the moon's L1, and of accomplishing all of that remote science of our moon impressive enough? (it certainly is for me, and it's most certainly better than anything USSR/Russia has ever accomplished) . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > You are insane. Unlike yourself, at least our evidence is easily peer replicated > outside of your NASA/Apollo cult. Too bad you folks still don't have > anything to work with, other than whatever's scripted within your NASA/ > Apollo Qur'an. > . -BradGuth I wonder what other insane conspiracy theories you believe in. Do you > have ... unorthodox ... opinions about the war of 1812 as well? Here's a quick overview: By 1810,The House of Rothschild not only had a substantial stake in > the Bank of the United States, they were quietly gaining control of > the Bank of England. Although foreign owners were not, by law, allowed > a say in the day to day operations of the Bank of the United States, > there is little doubt that the American share holders and directors > were, if not affiliated, complicit in the aims and goals of the > Illuminati and their central bankers. In 1811 the charter for the First Bank of America was not renewed. As > a result, the House of Rothschild lost millions. This enraged Nathan > Rothschild so much that he, almost single handedly fomented the War of > 1812. Using his formidable power and influence, he coerced the British > Parliament to attempt to retake the Colonies. The first military > attempt failed. The second strategy was to divide and conquer. Any > serious historian will find that the Civil War was largely stirred up > by Rothschild's illuminati agents in the United States. http://www.redicecreations.com/specialreports/2005/08aug/redshield.html That's offering way too much truth and consequences for all of these Semitic brown-nosed minions of their Third Reich. Notice all the mainstream flak that your informative topic has drawn. It's as though one of our lose cannon shots made a direct hit upon some of their mostly Semitic private parts. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax > We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - > The astronauts were in low-earth orbit. That accounts for that signal. No it doesn't. 1) There were several ground stations recieving signals at the same time. 2) The ground stations would have noticed if the signal wasn't coming from the general direction of the moon. 3) They astronaughts couldn't have stayed on a line between the recieving station and the moon as there were multiple ground stations. At the very least one geostationary sat would have been required per ground station. === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) On Apr 21, 11:38 am, CWatters > We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - > The astronauts were in low-earth orbit. That accounts for that signal. No it doesn't. 1) There were several ground stations recieving signals at the same time. > 2) The ground stations would have noticed if the signal wasn't coming from > the general direction of the moon. > 3) They astronaughts couldn't have stayed on a line between the recieving > station and the moon as there were multiple ground stations. At the very least one geostationary sat would have been required per ground > station. Where is the moon's L1 ? (duh! general direction of the moon?) . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax > On Apr 21, 11:38 am, CWatters > We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - > The astronauts were in low-earth orbit. That accounts for that signal. > No it doesn't. > 1) There were several ground stations recieving signals at the same time. > 2) The ground stations would have noticed if the signal wasn't coming > from > the general direction of the moon. > 3) They astronaughts couldn't have stayed on a line between the recieving > station and the moon as there were multiple ground stations. > At the very least one geostationary sat would have been required per > ground > station. Where is the moon's L1 ? (duh! general direction of the moon?) > . - Brad Guth But the earth moon L1 isn't exactly low earth orbit now is it. === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) On Apr 22, 5:10 am, CWatters > On Apr 21, 11:38 am, CWatters > We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - > The astronauts were in low-earth orbit. That accounts for that signal. > No it doesn't. > 1) There were several ground stations recieving signals at the same time. > 2) The ground stations would have noticed if the signal wasn't coming > from > the general direction of the moon. > 3) They astronaughts couldn't have stayed on a line between the recieving > station and the moon as there were multiple ground stations. > At the very least one geostationary sat would have been required per > ground > station. Where is the moon's L1 ? (duh! general direction of the moon?) > . - Brad Guth But the earth moon L1 isn't exactly low earth orbit now is it. Is that a trick question? Making their mission turn-around within the moon's L1 still isn't quite the same thing as a controlled deorbit from 100+ km, safely down- range to a soft landing and of walking moonsuit butt naked on the physically dark and nasty moon, now is it. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) I knew it! It's a Jewish conspiracy!! === Subject: Re: More evidence proving Apollo Hoax <20080421115411.209$Bk@newsreader.com> posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) I knew it! It's a Jewish conspiracy!! So was WWII, the mutually perpetrated cold-war and lo and behold, now we're looking at WWIII just around the bloody fossil fuel corner. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax > JAXA/Selene doesn't exist as far as American mainstream media (mostly > Jewish owned media, and otherwise government moderated) I knew it! It's a Jewish conspiracy!! Them fellers got their hands in all kinda mischief.... -- http://fast.filespace.org/PaulRMays/Postulate.pdf -- Paul R. Mays I Believe in Nothing, I Know, I think I Know or I Do Not Know I Never Believe... For to Believe is a Religious Incantation === Subject: Re: More evidence proving Apollo Hoax posting-account=UM3jRwkAAADTHFmJ20qgwageu031CeWA 5.1),gzip(gfe),gzip(gfe) > On Apr 21, 2:20æpm, N:dlzc D:aol T:com (dlzc) ... > When I read More evidence... I thought there would > actually be some evidence. I want to see the flag With 40 years of bombardment by cosmic radiation and UV, it will > be two sticks and tatters. No flags, no tracks, no LEM, only fake photos and videos. The original video cannot be digitially enhanced as all the 700 boxes > of it were lost. They lost all moon rocks too. They can't get more because they lost the plans for that Saturn > rockets. > Did all this happen before or after you lost your mind? === Subject: Re: More evidence proving Apollo Hoax posting-account=UM3jRwkAAADTHFmJ20qgwageu031CeWA 5.1),gzip(gfe),gzip(gfe) > You are insane. Unlike yourself, at least our evidence is easily peer replicated > outside of your NASA/Apollo cult. æToo bad you folks still don't have > anything to work with, other than whatever's scripted within your NASA/ > Apollo Qur'an. > . - Brad Guth I wonder what other insane conspiracy theories you believe in. Do you > have ... unorthodox ... opinions about the war of 1812 as well? Here's a quick overview: By 1810,The House of Rothschild not only had a substantial stake in > the Bank of the United States, they were quietly gaining control of > the Bank of England. Although foreign owners were not, by law, allowed > a say in the day to day operations of the Bank of the United States, > there is little doubt that the American share holders and directors > were, if not affiliated, complicit in the aims and goals of the > Illuminati and their central bankers. In 1811 the charter for the First Bank of America was not renewed. As > a result, the House of Rothschild lost millions. This enraged Nathan > Rothschild so much that he, almost single handedly fomented the War of > 1812. Using his formidable power and influence, he coerced the British > Parliament to attempt to retake the Colonies. The first military > attempt failed. The second strategy was to divide and conquer. Any > serious historian will find that the Civil War was largely stirred up > by Rothschild's illuminati agents in the United States. > You left out the contributions of the martians, venusians, and the dwarves from middle earth. === Subject: Re: More evidence proving Apollo Hoax > You are insane. Unlike yourself, at least our evidence is easily peer replicated > outside of your NASA/Apollo cult. Too bad you folks still don't have > anything to work with, other than whatever's scripted within your NASA/ > Apollo Qur'an. > . - Brad Guth I wonder what other insane conspiracy theories you believe in. Do you > have ... unorthodox ... opinions about the war of 1812 as well? Here's a quick overview: By 1810,The House of Rothschild not only had a substantial stake in > the Bank of the United States, they were quietly gaining control of > the Bank of England. Although foreign owners were not, by law, allowed > a say in the day to day operations of the Bank of the United States, > there is little doubt that the American share holders and directors > were, if not affiliated, complicit in the aims and goals of the > Illuminati and their central bankers. In 1811 the charter for the First Bank of America was not renewed. As > a result, the House of Rothschild lost millions. This enraged Nathan > Rothschild so much that he, almost single handedly fomented the War of > 1812. Using his formidable power and influence, he coerced the British > Parliament to attempt to retake the Colonies. The first military > attempt failed. The second strategy was to divide and conquer. Any > serious historian will find that the Civil War was largely stirred up > by Rothschild's illuminati agents in the United States. > You left out the contributions of the martians, venusians, and the dwarves from middle earth. Love them little guys.. they come in so handy for yard work. -- http://fast.filespace.org/PaulRMays/Postulate.pdf -- Paul R. Mays I Believe in Nothing, I Know, I think I Know or I Do Not Know I Never Believe... For to Believe is a Religious Incantation === Subject: Re: More evidence proving Apollo Hoax posting-account=UlqQigoAAADUKXgHhhqS3Em_KfDZERQh 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 7 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 8 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 9 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 10 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 1/hdtv 001 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 2/hdtv 001 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 3/hdtv 001 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 4/hdtv 001 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 5/hdtv 001 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 6/hdtv 001 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 1/hdtv 002 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 2/hdtv 002 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 3/hdtv 002 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 4/hdtv 002 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 5/hdtv 002 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 6/hdtv 002 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 4/hdtv 005 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 2/hdtv 005 2 l.jpg Find more at: http://wms.selene.jaxa.jp/ So glad to hear from you again. I have enjoyed your laws of motion and especially your generalized mass formula: I am sure this ties in perfectly with this thread. Mike === Subject: Re: More evidence proving Apollo Hoax posting-account=HBtcCQoAAADVd8SErw3D-uqpIVTwauN3 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 7 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 8 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 9 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 10 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 1/hdtv 001 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 2/hdtv 001 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 3/hdtv 001 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 4/hdtv 001 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 5/hdtv 001 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 6/hdtv 001 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 1/hdtv 002 1 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 2/hdtv 002 2 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 3/hdtv 002 3 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 4/hdtv 002 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 5/hdtv 002 5 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 6/hdtv 002 6 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 4/hdtv 005 4 l.jpghttp://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 2/hdtv 005 2 l.jpg Find more at: http://wms.selene.jaxa.jp/ If you are absurde inough to belaive that it apollo being hoax, then fine but don't try to force your knowledgeing ideas on us! Franz === Subject: Re: More evidence proving Apollo Hoax > We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - The astronauts were in low-earth orbit. That accounts for that signal. No--The high gain antenna was tracking the moon for several hours. === Subject: Re: More evidence proving Apollo Hoax > We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - > The astronauts were in low-earth orbit. That accounts for that signal. > No--The high gain antenna was tracking the moon for several hours. No contradiction there. The astronauts were in low-earth orbit sending > live audio-stream and video-stream to base. > That would have added an additional 1.25-2.5 second delay that did not exist! === Subject: Re: More evidence proving Apollo Hoax > We intercepted the live broadcast from the Moon in 1969 when > I was in the Military.- Hide quoted text - > The astronauts were in low-earth orbit. That accounts for that signal. > No--The high gain antenna was tracking the moon for several hours. > No contradiction there. The astronauts were in low-earth orbit sending > live audio-stream and video-stream to base. That would have added an additional 1.25-2.5 second delay that did > not exist! Not to mention find a way of explaining why ground stations point in the wrong direction and not at the moon. === Subject: Re: More evidence proving Apollo Hoax On Apr 21, 2:20 pm, N:dlzc D:aol T:com (dlzc) When I read More evidence... I thought there would > actually be some evidence. I want to see the flag With 40 years of bombardment by cosmic radiation and UV, it will > be two sticks and tatters. No flags, no tracks, no LEM, only fake photos and videos. The original video cannot be digitially enhanced as all the 700 boxes of it were lost. No they didn't They lost all moon _rocks_ too. No they didn't They can't get more because they lost the plans for that Saturn rockets. No they didn't.. I have a pretty good set that they sent me during the NASA Student Study program in 1965. and at least 2 sets are at NASA in Titusville. Seen em myself in 95. Touched a moon rock. Designed and installed the Back up power system for the new data center in 95 and if they have a problem finding the plans they could always take a look at the 2 saturn 5's they have on display and in storage to get the details. > David A. Smith -- http://fast.filespace.org/PaulRMays/Postulate.pdf -- Paul R. Mays I Believe in Nothing, I Know, I think I Know or I Do Not Know I Never Believe... For to Believe is a Religious Incantation === Subject: Re: More evidence proving Apollo Hoax On Apr 21, 2:20 pm, N:dlzc D:aol T:com (dlzc) ... > When I read More evidence... I thought there would > actually be some evidence. I want to see the flag With 40 years of bombardment by cosmic radiation and UV, it will > be two sticks and tatters. No flags, no tracks, no LEM, only fake photos and videos. The original video cannot be digitially enhanced as all the 700 boxes > of it were lost. 700 boxes still not found. What monstrous stupidity to keep believing these lies of NASA. > No they didn't They lost all moon _rocks_ too. No they didn't Yes they did. This happened around the 80s. It was an excuse to not hand out real rocks for independent analysis. Only tiny dirt samples were consequently given for independent review. Von Braun at NASA went on an expedition to recover small samples of legitamite moon rock from a meteorite at Antarctica. But no moon _rock_ has ever been independently reviewed. > They can't get more because they lost the plans for that Saturn > rockets. No they didn't.. I have a pretty good set that they sent me during > the NASA Student Study program in 1965. and at least 2 sets > are at NASA in Titusville. Seen em myself in 95. Touched a moon rock. No you didn't. You touched a desert rock and were made to believe it was something more because you are easily misled. A spectral analysis would've revealed otherwise. damn, forgot mine at home. Oh I C... Ive been misled by bunches of folks that I have known, some I've read of, some be reputation and I of course was misled by them and you have the path to enlightenment.. Otay.. I'll pass > Designed and installed the Back up power system for the new data center > in 95 and if they have a problem finding the plans they could always take > a look at the 2 saturn 5's they have on display and in storage to get the > details. Manufacturing requires more than a play-do prototype. NASA admits they lost the blueprints for most of the Saturn engine, hull and various other important components. hint: that's why they cant go back and why their current programme to go back is stuck trying to solve problems they supposedly already solved. -- http://fast.filespace.org/PaulRMays/Postulate.pdf -- Paul R. Mays I Believe in Nothing, I Know, I think I Know or I Do Not Know I Never Believe... For to Believe is a Religious Incantation === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) On Apr 21, 2:20 pm, N:dlzc D:aol T:com (dlzc) ... > When I read More evidence... I thought there would > actually be some evidence. I want to see the flag With 40 years of bombardment by cosmic radiation and UV, it will > be two sticks and tatters. No flags, no tracks, no LEM, only fake photos and videos. The original video cannot be digitially enhanced as all the 700 boxes > of it were lost. 700 boxes still not found. What monstrous stupidity to keep believing > these lies of NASA. No they didn't They lost all moon rocks too. No they didn't Yes they did. This happened around the 80s. It was an excuse to not > hand out real rocks for independent analysis. Only tiny dirt samples > were consequently given for independent review. Von Braun at NASA went > on an expedition to recover small samples of legitamite moon rock from > a meteorite at Antarctica. But no moon rock has ever been independently reviewed. They can't get more because they lost the plans for that Saturn > rockets. No they didn't.. I have a pretty good set that they sent me during > the NASA Student Study program in 1965. and at least 2 sets > are at NASA in Titusville. Seen em myself in 95. Touched a moon rock. No you didn't. You touched a desert rock and were made to believe it > was something more because you are easily misled. A spectral analysis > would've revealed otherwise. damn, forgot mine at home. Oh I C... Ive been misled by bunches of folks > that I have known, some I've read of, some be reputation and I of course was > misled by them and you have the path to enlightenment.. Otay.. I'll pass Designed and installed the Back up power system for the new data center > in 95 and if they have a problem finding the plans they could always take > a look at the 2 saturn 5's they have on display and in storage to get the > details. Manufacturing requires more than a play-do prototype. NASA admits they lost the blueprints for most of the Saturn engine, > hull and various other important components. hint: that's why they cant go back and why their current programme > to go back is stuck trying to solve problems they supposedly already > solved. --http://fast.filespace.org/PaulRMays/Postulate.pdf -- > Paul R. Mays > I Believe in Nothing, I Know, I think I Know or I Do Not Know > I Never Believe... For to Believe is a Religious Incantation You're really pissing off those Semitic troops of our cloaked Third Reich. DARPA (our very own Third Reich collective of Semitic wizards) This agency brought forth the Saturn 5 rocket, surveillance satellites, the Internet, stealth technology, guided munitions, unmanned aerial vehicles, night vision and the body armor that's in use today, ñSo what's hot at DARPA right now? Bugs. The creepy, crawly flying kind. The Agency's Microsystems Technology Office is hard at work on HI-MEMS (Hybrid Insect Micro-Electro-Mechanical System), raising real insects filled with electronic circuitry, which could be guided using GPS technology to specific targets via electrical impulses sent to their muscles. These half-bug, half-chip creations - DARPA calls them insect cyborgs - would be ideal for surveillance missions, the agency says in a brief description on its website.î Are these fellow spooks, moles and Yids of our MI5/CIA~NASA and of their DARPA protected Third Reich, having a good enough cloak and dagger time yet? Are those Third Reich Semites and of their brown-nosed minions actually getting that pissed off and faith-based desperate? Is there perhaps some other faith-based group(s) of pretend-atheists or cults secretly in charge of Usenet? Best I can tell, thereÍs nothing of any pesky Islamic/Muslim sleeper cells at fault for these sorts of Usenet group stuffing or topic index stacking kinds of clownish mainstream damage control, just like all the rich and powerful that havenÍt been contributing anything negative as to their ongoing inflationary cost of energy, or even as to posting their superior opinions as to whatever negative consequences of WWIII. As far as theyÍre concerned, it is simply another win-win for the old Semite/Zionist Gipper, of which means they donÍt have to contribute on behalf sharing one constructive note or idea for making anything of energy, food, housing, medical care or education the least bit better off for the rest of us village idiots. . - Brad Guth === Subject: Re: More evidence proving Apollo Hoax posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008032620 Firefox/3.0b5,gzip(gfe),gzip(gfe) Compare the the below authentic pictures of the Lunar surface with the > fake ones from the Apollo hoax. http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 3 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 5 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 6 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 7 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 8 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 9 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/000/hdtv 000 10 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 1/hdtv 001 1 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 2/hdtv 001 2 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 3/hdtv 001 3 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 4/hdtv 001 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 5/hdtv 001 5 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/001/hdtv 001 6/hdtv 001 6 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 1/hdtv 002 1 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 2/hdtv 002 2 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 3/hdtv 002 3 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 4/hdtv 002 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 5/hdtv 002 5 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/002/hdtv 002 6/hdtv 002 6 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 4/hdtv 005 4 l.jpg >http://wms.selene.jaxa.jp/data/en/hdtv/005/hdtv 005 2/hdtv 005 2 l.jpg Find more at: http://wms.selene.jaxa.jp/ æ æWe intercepted the live broadcast from the Moon in 1969 when > æ æI was in the Military.- Hide quoted text - The astronauts were in low-earth orbit. That accounts for that signal. > In fact there was a massive blunder in one of the shoots where a fake > far-away earth could be seen in one window then the real close-earth > was briefly seen on another. Bart Sibrel found that one. Google it and you'll probably find it. Why even post? You will convince nobody and nobody - no matter what they say - will dissuade you from your delusion. === Subject: Re: More evidence proving Apollo Hoax -- This message is brought to you by Androcles http://www.androcles01.pwp.blueyonder.co.uk/ | Compare the the below authentic pictures of the Lunar surface with the | fake ones from the Apollo hoax. The Japanese pictures are a hoax; the spacecraft was damaged flying through the Van Allen belt and never got to the moon. It's all just a conspiracy to sell more Hondas, Toyotas, Mitsubishis, Yamahas, Sonys and Sanyos, you ing lunatic. === Subject: Moving Dimensions Theory's simplicity: The fourth dimension is expanding relative to the three spatial dimension: dx4/dt =ic posting-account=Y-0m4woAAACHSn5QuaMdzkFpwy_B_TeP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Moving Dimensions Theory by Dr. Ranger McCoy ABSTRACT Moving Dimensions Theory postulates that the fourth dimension is expanding relative to the three spatial dimensions, symbolized by the equation: dx4/dt =ic http://physicsmathforums.com MDT provides a physical model underlying both quantum mechanical and relativistic phenomenon. The simple postulate accounts for quantum mechanicsÍ action-at-a-distance and relativityÍs length contraction, as well as entanglement and the equivalence of mass and energy. MDT provides a simple physical model showing that diverse dualities.84wave/ principle. MDT provides a physical model underlying entropy and unifying timeÍs thermodynamic, classical, quantum, and radiative arrows. MDT provides a physical model accounting for the constant velocity of light, the fact that the maximum velocity through space is c, and the fact that c is independent of the velocity of the source, as MDT considers photons as matter surfing the fourth expanding dimension. Nonlocality is accounted for by an expanding fourth dimension that is inherently nonlocal, and MDT shows that this fundamental expansion is the origin of quantum mechanicÍs probability. MDT provides a physical model for time.84time is not the fourth dimension, but rather a phenomenon that emerges from a physical reality wherein the fourth dimension is expanding relative to the three spatial dimensions. The theory resolves the EPR paradox while also liberating us from the block universe implied by EinsteinÍs relativity. Relativity freezes the expansion of the fourth dimension, only ever considering instantaneous snapshots of the universe. Quantum Mechanics treats the fourth dimension as a dynamical element. Hence quantum mechanics is a science defined by flux.84by differential operators. I. MDT in Complete Agreement with Quantum Mechanics and Relativity Moving Dimensions Theory is in complete agreement with all experimental tests and phenomena associated with special and general relativity. MDT is in complete agreement with all physical phenomena as predicted by quantum mechanics and demonstrated in extensive experiments. The genius and novelty of MDT is that it presents a common physical model which shows that curious phenomena from both relativity and quantum mechanics derive from the same fundamental physical reality. Nowhere does String Theory (ST) nor Loop Quantum Gravity (LQG) account for quantum entanglement nor relativistic time dilation. MDT shows these derive from the same underlying physical reality. Nowhere does contraction. MDT shows these derive from the same underlying physical reality. Nowhere does ST nor LQG account for the constant speed of light, nor the independence of the speed of light on the velocity of the source, nor entropy, nor time's arrow. MDT shows these derive from the same underlying physical reality. Nowhere does String Theory nor Loop Quantum Gravity resolve the paradox of Godel's Block Universe which troubled Einstein. MDT resolves this paradox. String Theory and LQG lack definitive equations, whereas MDT presents a simple equation: It will be shown that relativity can be derived from this simple equation, as we return to EinsteinÍs original work. It will be noted that Einstein never stated that time is the fourth dimension, rather, he and MinkowskiÍs formulations imply that the fourth dimension, represented by x4 is equal to ict. Or x4 = ict. I. The Derivation of EinsteinÍs Relativity from Moving Dimensions Theory The fourth dimension is expanding relative to the three spatial dimensions. This simple postulate and reality underlies EinsteinÍs two postulates of relativity, and it can be expressed mathematically as: dx4/dt =ic This equation agrees with Einstein. Nowhere did Einstein ever say that time is the fourth dimension. Rather he and Minkowski stated Or x4 = ict. Many trained physicists have a knee-jerk reaction that the fourth dimension cannot be moving because ñdimensions cannot move.î But dimensions can and do move. First off, since the universe is expanding, space-time is also expanding, demonstrating that dimensions are moving and expanding. Secondly, general relativity demonstrates that massive objects warp space-time, meaning that as a massive object moves though space-time, it stretches space-time, showing again that space-time in one area can move, or deform, relative to space-time in another area. GR is a sound theory, backed up with multiple high- profile experiments, including the demonstration that starlight is bent by the sun and the verification that orbiting stars radiate energy in the form of gravity waves. Thus there exist neither philosophical nor physical barriers to the concept of moving dimensions, but for artificial ones within lazy minds. A curious sign of the times is that physicists will accept on blind faith the existence of ten, twenty, or thirty dimensions, dimensions that are curled up, or too small to measure, and yet they will reel in shock and horror at a perfectly obvious postulate.84the fourth dimension is expanding relative to the three spatial dimensions. They are to be forgiven.84it has been a long time since a simple postulate has been offered in the realm of physics, and the foreign nature of truthÍs simple beauty is seen as a violent affront to the String TheoristÍs convoluted sensibilities. Let us derive EinsteinÍs relativity and the Lorentz Transformations from MDTÍs simple formula: Let D be the constant -ica+x4(a) and re-label u with t. Then we have Dropping the arbitrary constant, we get: Or x4 = ict Armed with this simple and most remarkable result, we are ready to return to EinsteinÍs 1912 manuscript, and provide the motivation for a four-dimensional coordinate system where the fourth dimension is written as x4 = ict. Derivation of the Lorentz Transformation The principle of the constancy of the velocity of light demands the existence of a reference system á relative to which every light ray propagates in vacuum with velocity c. According to the relativity principle, all reference systemá? in uniform translation motion to á must possess the same property. Together with Laue, we call each such system ñjustified.î Now we ask: What kind of transformation equations must obtain between the space-time coordinates x, y, z, t (with respect to á) and x?,y?,c?,t? (with respect to á?) of the same point event so that the principle of the constancy of the velocity of light would hold with respect to both systems? We can further demand, without reducing their generality, that the transformation equations be homogeneous, because all that is needed for this is that the path described by the origin of á? with respect to á pass through the origin of á, and that the origin of time scales in á and á? be chosen in such a way that the clocks located at the origins of the systems á and á? both read zero at the moment when the two points coincide. Suppose that at this moment of the coincidence of the two origins a vacuum light signal is sent from O or O?, which, according to the principle of the constancy of the velocity of light, propagates in a spherical wave with respect to both systems then the spatial points that are just reached by the signal at times t and t? with respect to á and á?, respectively, will be determined by the equations and This means that the equations and must be equivalent. Thus, the transformation equations that we are seeking must be so constituted that the second equation turns into the first one if x?,y?,z?,t? are replaced by their expressions in terms of x,y,c,t. The transformation must therefore make the equation into an identity, where all that we know about the factor ?2 for the time being is that it must not vanish. But one can see that ?2 must be independent of x, y, z, t, for otherwise the right-hand side divided by ?2 could not be a homogeneous, complete function of second order in x,y,z,t after the substitution is carried out. For now we will examine the substitution for the case ?2 = 1 and we will show later that from a physical point of view this is the only case deserving of consideration. Instead of (15), we then have: If one introduces the variable u? = ict or u? = ict? in place of the time variables t, where i denotes the imaginary unit, one obtains, instead of (15a), the form Note that Einstein simply states ñIf one introduces the variable u? = ict or u? = ict? in place of the time variables t,î but he does not state why this works. MDT tells us why this works. It works because the fourth dimension is expanding relative to the three spatial dimensions. It works because x4 = ict and Einstein continues in his 1912 Manuscript: As is well known, this choice of time variables derives from Minkowski. Its great significance consists in the fact that by means of it, equation (15a), which governs the substitution that we are seeking, is brought into a form into which the spatial coordinates and the temporal coordinate enter in the same manner. Let the coefficients of the substitution that we are seeking be denoted as in the accompanying array; the second horizontal row, for example, shall signify that the equation: Obviously, those from among these coefficients that do not contain the index ñ4î or contain it twice are real, the rest being purely imaginary. x Y Z t x' ??? ??? ??? ??? y' ??? ??? ??? ??? z' ??? ??? ??? ??? t? ??? ??? ??? ??? Equation (15b) is satisfied identically when the following relations exist between the coefficients ?: This is a total of 4 + 4*3/2 = 10 conditions have to satisfy. Hence the substitution contains only 6 mutually independent determinations. This must also be so; because three determinations are needed to determine the orientation of á? with respect to á, and three more are needed for the determination of the magnitude and direction of its velocity. If one forms And replaces x?,y?,z?,u? by their expressions in terms of x, y, z, u then one obtains x as the result. The situation is analogous with the other vertical rows of the above array. Thus, the array also yields the inverse substitution, which expresses x etc. by means of x?,y?,z?,u?. Hence, the quantities ??must also satisfy those conditional equations that are analogous to equations (16) in that merely the vertical and the horizontal rows change their roles. As we already can see from equation 15b which determines them, the transformations we seek are exactly the same as those we have to apply to the spatial coordinates when passing from an orthogonal coordinate system to another one with the same origin, the only difference being that here one deals with a four-dimensional manifold rather than with a three-dimensional manifold as in the other case. This knowledge forms the basis of MinkowskiÍs four-dimensional treatment of the theory of relativity, which brought about a splendid simplification of the system of the theory of relativity. We shall go into this in greater detail in the next chapter, while in this chapter we will derive the most important results of the theory of relativity in the most elementary way, in order for its physical relationships to emerge more clearly. So it is that MDT underlies the Lorentz Transformation, MinkowskiÍs four-dimensional treatment of the theory of relativity, and all the implications of EinsteinÍs relativity. Photons Remain Do Not Move in The Fourth Expanding Dimensions Note that in the above, Einstein never says that time is the fourth dimension. Rather he states that x4 = u = ict. Let us write the following: Where s is the invariant interval. Then If we take the distance in space as: Then We know that a photon does not age. When a photon has traveled a distance ?r, then ?s = ?r, or And ?x4 = 0. In other words, the photon has not moved at all in the fourth dimension. Anything that travels the speed of light can never move in the fourth dimension, as ?s = ?r. An object can travel the velocity of light through space in the x direction, the y direction, or z direction; or some combination thereof, but the only way it can ever travel the velocity of light in the x4 dimension is too remain completely still in the three spatial dimensions. It is possible to remain at rest relative to the expanding time dimension, but it is difficult to measure this. An inertial frame is a frame that is defined by an object keeping its velocity components through space and time constant. An object which accelerates in the three spatial dimensions slows down in the expanding fourth dimension. On the Advancement of Physics by the Rugged Individual It is difficult to work as a physicist in this day and age without reflecting upon the massive amounts of groupthink and handwaving, backed by snark and intimidation, that have come to mark this era of subprime big-money physics. Physics has been furthered far more often by a rugged individual acknowledging the simple and obvious in a pursuit of the truth than book-keepers-in-training playing games in the abstruse in pursuit of tenure. The advancement of physics has ever depended far more on logic, reason, and Truth than government grants, tenure, group think, peer-reviewed journals, and aging bureaucracies. ñThat is the way things are because that is the way things are,î has lead to far more physics than the contemporary, ñthings can't be that way because the math dictates that we live in thirty-three dimensions and four are curled up, and that is what NSF is funding.î When nobody could measure nor detect the supposed ether, Einstein proclaimed, ñthere is no ether.î When experiments showed that light existed only in quantized packets, Einstein proclaimed that light only existed in quantized packets, and he won the Nobel Prize. When spectra from atoms showed discreet energies, Niels Bohr proclaimed that electrons orbits were quantized, and he received a Nobel Prize. When Maxwell's Equations had a recurring constant, Maxwell used c to denote it, and Einstein proclaimed that the speed of light must be constant for all observers-and so Special Relativity was born. When Einstein juxtaposed objects falling towards the earth getting closer together with the fact that two people starting at the equator, walking on originally parallel lines of longitude towards the North Pole, would come together because they were walking on a curve surface, Einstein proclaimed that the space-time around a massive object must also be curved. This along with Einstein's realization that the force of gravity would be rendered null in free-fall, lead to General Relativity. And so it is that in the above paragraph you have the roots of the greatest achievements of physics in the past 100+ years, dwarfing String Theory, Loop Quantum Gravity, and thousands of their variations, which deal in the abstruse, complicated, muddled, and mythological worlds which are safe from common sense physicsÍ simple rigor. Moving Dimensions Theory returns us to simpler times. It starts with the simple and keeps it simple. Light travels with a maximum velocity of c, because the fourth dimension is expanding at a rate relative to the three spatial dimensions at the velocity of c. A photon expands through space in a spherically symmetric manner. This is because the fourth dimension expands through the three spatial dimensions in a spherically symmetric manner. Energy and mass are equivalent, expressed by E=mc^2, because energy is nothing more than mass rotated into the expanding fourth dimension. The Einstein-Podolsky-Rosen effect (EPR) effect, which calls instantaneous action at a distance spooky, can be accounted for by the expanding dimension-as a point expands, it is yet a single locale in that dimension, and hence though same place in the time dimension, and hence connected. The null vector of the photon, which remains 0 no matter how far the photon travels in space-time, may be accounted for by the fact that the fourth dimension is moving, and thus the only way to stay still in the four dimensions is to move with along with the expanding dimension. In Lorentzian Transformations, there is no way for an object to be rotated into the time dimension without it moving-this can be explained by the fact seen as the result of the universe's existence upon a reality that has three stationary spatial dimensions and one expanding time dimension- when matter exists in the stationary dimensions, it is seen as mass, wave, or a photon, or energy. Depending how we choose to observer Photons are quantized bundles of energy that propagate at the velocity of c-this is because the fourth dimension is expanding relative to the three spatial dimensions in a quantized manner, in units of Planck's length at the rate of c. The Second Law of Thermodyamics, or the law of Entropy, states that the universe tends towards disorder. This is because the fourth dimension is expanding in a spherically symmetric from one another-thus a drop of food coloring in a pool will be carried outward and evenly distributed. In 1949 Godel published a paper showing that within the theory of relativity, time as we understand it, does not exist. Einstein recognized Godel's paper as ñan important contribution to the general theory of relativity,î and since then physicists have not been able to find any logical shortcomings in Godel's work, and nobody has been able to account for the existence of time. But the Theory of Moving Dimensions accounts for time as we know it by showing that it is an emergent property of the underlying dimension's intrinsic relative movement. Relativity becomes increasingly exact at long-length scales but fails at short ones because space-time itself is quantized, as the time dimension is expanding in units of the Planck length. The concept of general relativity's smooth geometry, at large scales, disappears on short-distance scales-this has been a problem to string theorists, but only because they were never bold enough to recognize that's the way it is because that's the way it is. Realizing this might have lead one of them to see that the fourth dimension is expanding at a rate of c relative to the three spatial dimensions. So it is seen that Moving Dimensions Theory offers a simple model upon which all known phenomena of Relativity and Quantum Mechanics may rest. And because the underlying architecture of the universe is quantized-because the fourth dimension expands at the rate of c in units of the Planck length relative to the three spatial dimensions, quantum mechanics works for the small, while general relativity works for the large. That is the way it is because that is the way it is- this was the realization that lead to the postulate of MDT: the fourth dimension is expanding relative to the three spatial dimensions. I. Time as an Emergent Phenomenon Nowhere does EinsteinÍs relativity actually state that time is the fourth dimension, and MDT agrees that time is not the fourth dimension. Rather, the fourth dimension in all of EinsteinÍs original manuscripts, as we shall soon see, is given by x4 = ict. Time, as defined by the ticking seconds on a clock, is not the fourth dimension, but rather it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions. Past, present, and future are but states contained in our mind.84past is what we remember.84order stored in our brains. The present is physical change that creates the order in our brain. The future is but in our imaginations.84changes we can potentially effect which will be recorded in the order of our memories. Time is not the fourth dimension, but it inherits properties of the fourth dimension; as time is an emergent property of the fourth dimension expanding relative to the three spatial dimensions. In relativity we often equate one second of time with 3x108 meters.84the distance traveled by a photon of light in one second. This is because photons are matter surfing the fourth expanding dimension, and the fourth dimension is expanding at the rate of c. The time on a watch or clock, whether linked to an oscillating circuit, quartz crystal, swinging pendulum, or unwinding copper spring, is based on changes in energy, which is based on the emission and propagation of photons. Photons surf the fourth expanding dimension, and thus time inherits properties of the fourth dimension, but time is not the fourth dimension. LetÍs travel on back to EinsteinÍs original 1912 manuscript on relativity, to where he does not say that time is the fourth dimension, but rather that the fourth coordinate u or x4 is defined by If, in three-dimensional geometry, a new orthogonal coordinate system with the same coordinate origin is introduced alongside the original system (x, y, z) (rotation of the coordinate system), then the laws of this coordinate transformation are possible from the following two stipulations: (1) The transformation equations are linear and homogeneous with respect to the coordinates (2) The distance of an arbitrary point from the coordinate origin is the same wityh respect to both systems For, according to (1), the transformation is determined by equations of the form Where the quantities ??are independent of x, y, z. According to (2), these equations must make the equation follow. With the help of these equations, by virtue of which only 3 of the constants ???can be chosen arbitrarily, one proves directly that the inverse substitution is given by the equations: ? Thus, both the original and the inverse substitution are completely governed by the table of coefficients: x Y Z x' ??? ??? ??? y' ??? ??? ??? z' ??? ??? ??? The coefficients are nothing other than the cosines of the angle between the original and new axes. The essential thing here is that the laws of the transformations in question are completely determined by the conditions in (1) and (2). If we compare this with the considerations leading to the general Lorentz transformation, then we see that the transformation equations holding between x, y, z, u = ict and xÍ, yÍ, zÍ, uÍ = ictÍ of two justified space-time reference systems satisfy the same conditions and are constructed in the same way as in the just considered three- dimensional case. The only difference is that we now have four coordinates instead of three. We can formulate this in the following way: All of the ñjustifiedî time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary. coordinates instead of three. We can formulate this in the following way: All of the ñjustifiedî time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary.î Nowhere does Einstein state that the fourth coordinate is time. He merely states, ñOne has to keep in mind that the fourth coordinate u It is imaginary because the expansion of the fourth dimension is orthogonal to the three spatial dimensions in every direction. II. Simple Proofs of MDT Proof I. The only way to stay stationary in the three spatial dimensions is to propagate at the velocity of c through the fourth dimension. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions. Stationary clocks undergo maximal aging. Proof II. The only way to stay stationary in the fourth dimension is to propagate at the velocity of c through the three spatial dimension. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions. Photons do not age. They stay at the exact same place in the fourth expanding dimension. These two simple proofs require only logic and reason.84two primary and traditional elements of science that big-money physics has done away with. http://www.fxstreet.com/futures/market-review/outside-the-box/2008-04-15.htm l reports, Modern financial theory as applied ranks with string theory in physics as one of the greatest intellectual frauds of our time. Whereas the vacuous pretensions of string theory have finally been exposed (we now know that the theory never generated a single falsifiable prediction), those of financial engineering are just beginning to be exposed both in the press and in lawsuits alike. What is remarkable to us is how this masquerade has continued for as long as it has both at a practical and at a theoretical level. II. Nonlocality and Relativity United by MDTÍs Physical Model RelativityÍs ageless photon implies that a photon stays stationary in the fourth dimension, while propagating at c in the three spatial dimensions. Quantum mechanicsÍ action-at-a-distance, entanglement, and nonlocality show that although separated in the three spatial dimensions, two photons originating from a common origin where they were interacting yet remain connected on a fundamental level. So it is that both Quantum Mechanics and relativity are built upon physical realities wherein no matter how far a photon travels in the three spatial dimensions, it yet remains in the same place in the fourth dimension. Ergo the fourth dimension is expanding, manifesting itself as an expanding 3D spherical surface, and every point on that sphere is yet at the exact same place in the fourth expanding dimension. Hence two initially-interacting photons separated by the width of the universe may yet influence one-another instantaneously, as they are yet in the same place in the fourth dimension, as relativityÍs math will quickly attest to. Nonlocality stems from the inherent nonlocality of the fourth dimension, which is nonlocal via its expansion. MDTÍs fundamental equation comes straight from EinsteinÍs manuscripts.84the only thing I have done is recognize that time is not the fourth dimension, as famous modern physicists have misleadingly supposed, but that time is a phenomenon that emerges because a fourth dimension is expanding relative to the three spatial dimensions. Consider the emission of a photon in free space. One second later, the photon has equal probability of being found anywhere upon a sphere with a radius of 186,000 miles, as the velocity of light, c, is 186,000 miles per second. If we covered the surface of said sphere with detectors, one, and only one, would click. And the photon, although having traveled 186,000 miles through space, will not have aged one iota, for relativity tells us that time stops at the velocity of light. The photon will have traveled 186,000 miles through the three spatial dimensions, and yet it will not have moved one iota in the fourth dimension. And there lies our first clue to moving dimensions theory. For how can a photon propagate 186,000 miles in the three spatial dimensions, and yet not budge an inch in the fourth dimension, unless that fourth dimension is moving, right along with it? Ergo, the fourth dimension is expanding relative to the three spatial dimensions. A photon, as we shall see time and again, is matter surfing the fourth expanding dimension. Consider two interacting photons that are directed to propagate in opposite directions, as in numerous definitive experiments conceived by Bell et al and conducted by Aspect et al. One second later, each photon's polarization is measured at detectors separated by 372,000 miles. According to the laws of quantum mechanics and numerous supporting experiments, the measurement at one detector instantaneously affects the measurement at the second detector. It is as if the photons are yet side-by-side for all intents and purposes. This ñspooky action-at-a-distance,î as Einstein called it, is not so spooky in the context of Moving Dimensions Theory, for MDT states that although separated by 372,000 miles, the photons are yet in the exact same place in the fourth dimension, as the fourth dimension is expanding relative to the three spatial dimensions. So it is that quantum phenomena on the photonic level, as well as relativistic phenomena on the photonic level, are both accounted for with simple elegance via MDT: the fourth dimension is expanding relative to the three spatial dimensions. The fourth dimension is inherently nonlocal. In the photoelectric effect, the photonÍs wave distribution immediately ñcollapsesî in the act of measurement. This is because although the expanding wavefront is distributed as spherically symmetric wavefront in 3D, it yet exists as the same point in the nonlocal fourth dimension. Now many people might state that a dimension cannot be nonlocal, but it so happens that the fourth expanding dimension is nonlocal, and they ought stop trying to tell dimensions what to do. Most trained physicists are content to shrug off nonlocality, as well as the unification of the hitherto unexplained nonlocality of quantum mechanics with relativity; and return to filling their grant proposals with buzzwords such as LQG and ST. For modern physics has an expensive myth to uphold and protect at all costs.84that physics derives from money and groupthink. This instantaneous collapse of the wave function in quantum mechanics invokes the notion of simultaneity in relativity. Both of these concepts.84instantaneous collapse of the wave function in QM, and the relativity of simultaneity in relativity, derive from the fact the fourth dimension is expanding relative to the three spatial dimensions. The PhotonÍs Null Vector The path described by a photon through space-time is the null vector. Is this not curious? Even when the photon has traversed the entire universe, the interval it has traversed is zero. This is because the photon is matter which exists purely in the fourth expanding dimension, and until it is measured, it remains fixed in the fourth expanding dimension, meaning that although it can traverse the entire universe, it yet remains in the exact same place in the fourth dimension. The only way to travel a zero total interval.84to remain at the origin in the four-dimensional space-time continuum.84is to move at the velocity of light through the three spatial dimensions. This is because the fourth cooridinate itself is moving. The Double Slit Experiment Figures will soon be added. The double slit experiment rests upon the nonlocal wave properties of all mass and energy; and the nonlocal wave properties of all mass and energy rest upon the nonlocality of the fourth expanding dimensions. MDT Underlying HuygenÍs Principle & FeynmanÍs Many Paths MDT underlies HuygenÍs Principl in all its forms. http://en.wikipedia.org/wiki/Huygens' principle The Huygens[CapitalEth]Fresnel principle (named for Dutch physicist Christiaan Huygens, and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation (both in the far field limit and in near field diffraction). It recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. This view of wave propagation helps better understand a variety of wave phenomena, such as diffraction. MDT states that the expansion of the fourth dimension appears as a spherically-symmetric wavefront through the three spatial dimensions. Via Huygen's Principle, MDT recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. And thus MDT provides a fundamental physical model underlying double-slit diffraction and all wave-related phenomenon. http://en.wikipedia.org/wiki/Huygens' principle: HuygenÍs principle follows formally from the fundamental postulate of quantum electrodynamics [CapitalEth] that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. It is then the result of interference (addition) of all path integrals that defines the amplitude and phase of the wavefunction of the object at this given point, and thus defines the probability of finding the object (say, a photon) at this point. Not only light quanta (photons), but electrons, neutrons, protons, atoms, molecules, and all other objects obey this simple principle. And so it is seen that MDT underlies Feynman's many-paths treatments and the fundamental postulate of quantum electrodynamics.84that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. All paths have a probability of being followed because of the fundamental nature of a fourth dimension that is expanding relative to the three spatial dimensions. The probability distribution of the photon expands at the rate of c, which is the rate of the expansion of the fourth dimension. After a photon is emitted, the spherical wavefront that defines its probability for being found at any point has a radius of 186,000 miles. This is the net result of billions and billions of quantum expansions of the fourth dimension, and during each expansion, the photon had an equal chance of being found anywhere on the surface of the net sphere, which is the sum total of billions upon billions of smaller spheres. These diagrams illustrate the basis of Huygen's Principle: http://www-laep.ced.berkeley.edu/~itr/literature/farsite/index.html MDT describes the fundamental motion of the universe. to the three spatial dimensions, captured in the simple equation d(x4)/dt=ic, the following emerges: Huygen's Principle The fundamental postulate of quantum electrodynamics [CapitalEth] that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. Time Entropy Entropy, as well as timeÍs classical arrow, may be explained via the proximity. The fourth dimension is expanding as a spherical wavefront probability of being caught in the fourth expanding dimension in proportion to their energy, and thus there is a probability that the proximity have a greater chance of moving further apart as opposed to closer together. Hence a drop of food coloring dropped in a swimming pool will dissipate, and never converge. Action at a Distance Double slit interference Relativity Length Contraction Time Dilation The equivalence of mass and energy: E=mc^2: Energy is but matter caught upon the fourth expanding dimension. Time's Radiative Arrow Time's Thermodynamic Arrow And finally, the goal of physics is ultimately to describe physical reality. We live in a universe whose physical reality is that the fourth dimension is expanding relative to the three spatial dimensions. HuygenÍs principle shows up in all realms of physics, reflecting MDTÍs deeper physical reality.84the fourth dimension is expanding relative to the three spatial dimensions. MDT & the Unity of The Dualities MDT unifies the dualities of mass and energy, space and time, and wave unification in the physical realm; and each unification represented a milestone in physics, two formerly disparate entities where united by a simpler and more beautiful model. MDTÍs simple postulate.84the fourth dimension is expanding relative to the three spatial dimensions.84 unifies all these three pivotal dualities with its simple equation: dx4/dt = ic Mass and Energy Duality: By following the implications of the duality of space and time in relativity, Einstein happened upon the duality and equivalence of mass and energy, or E=mc2. MDT sees energy as mass that exists in the fourth expanding dimension. The more energy a massive object gains, the more mass it has in the fourth expanding dimension. Only objects which exist entirely in the fourth expanding dimension can move at the velocity of light. Hence only photons move at the velocity of light. All motion automatically calculates the component of an object in the three spatial dimensions.84its rest mass.84and its component in the fourth expanding dimension.84its energy. Because the fourth dimension is moving relative to the three spatial dimensions at the rate of c, the more of an objectÍs total mass which exists in the fourth expanding dimensions, the more energy it has, and the faster it moves. wavefront because it surfs the fourth expanding dimension, which expands as a spherically symmetric wavefront. The fourth dimension may be seen as a pilot wave as decribed by de Broglie et al, which guides the probabilistic propagation of the particulate photon. The nonlocal and continually expanding as it distributes locality in the fourth dimension throughout the three spatial dimensions, and because is equal probability of finding the photon anywhere upon the wavefront defined by the fourth expanding dimension. Space-Time Duality: Space-time duality would be more properly described as the duality between the three spatial and the fourth expanding dimension. Time has oft been confused with the fourth dimension, but Einstein never stated that it is the fourth dimensions. Rather he and Minkowski stated x4 = ict, which directly leads to MDT, when one takes the derivative of both sides: Time inherits properties of the fourth expanding dimension; and certainly the fourth expanding dimension is a dimension, and thus is capable of having objects rotated into it and out of it. If we compare this with the considerations leading to the general Lorentz transformation, then we see that the transformation equations holding between x, y, z, u = ict and xÍ, yÍ, zÍ, uÍ = ictÍ of two justified space-time reference systems satisfy the same conditions and are constructed in the same way as in the just considered three- dimensional case. The only difference is that we now have four coordinates instead of three. We can formulate this in the following way: All of the ñjustifiedî time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary. coordinates instead of three. We can formulate this in the following way: All of the ñjustifiedî time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary.î Nowhere does Einstein state that the fourth coordinate is time. He merely states, ñOne has to keep in mind that the fourth coordinate u It is imaginary because the expansion of the fourth dimension is orthogonal to the three spatial dimensions in every direction. The only way to stay stationary in the three spatial dimensions is to travel at the velocity c through the fourth dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions. The only way to stay stationary in the fourth dimension is to travel at the velocity c through the three spatial dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions. A rotation (or boost) into the fourth dimension is always accompanied by an increased velocity in the three spatial dimensions. Ergo the fourth dimension is expanding relative to the three spatial dimensions. All moving objects appear shortened in the direction they are traveling. This is because in order to propagate in the three spatial dimensions, an object must be partially rotated into the fourth dimension. Picture a meter-stick at the end of a football field, parallel to the horizontal crossbar of the goalposts. If it rotates, it appears shorter and shorter to us, standing on the other end of the field. Now if it were passing by us close to the velocity of light, it would also appear foreshortened, as it is rotated in the fourth expanding dimension. This rotation occurs at a microscopic quantum level--each atom or quantum is rotated more into the fourth dimension, resulting in an overall foreshortening of the yardstick in the three spatial dimension. Velocity in the three spatial dimensions is always accompanied by foreshortening in the three spatial dimensions, as more of the object exists in the fourth expanding dimension. Rotate an object out of the three spatial dimensions and into the fourth expanding dimension, and it will gain velocity. TimeÍs Arrows Unified Moving Dimensions Theory accounts for and unifies all of timeÍs arrows. MDT provides a physical model underlying entropy and time itself. Time, as measured by the ticking seconds on a clock or the melting of snowman, is an emergent phenomena, which results because the fourth dimension is expanding relative to the three spatial dimensions, carrying energy in the form of matter rotated into the fourth expanding dimension. MDT's postulate.84the fourth dimension is expanding at the rate of c relative to the three spatial dimensions.84provides a physical model for the radiative arrow of time. As photons surf the fourth expanding dimension, the path of radiation is fundamentally denoted by expanding spherical wave-fronts. Entropy, as well as timeÍs classical arrow, may be explained via the proximity. The fourth dimension is expanding as a spherical wavefront probability of being caught in the fourth expanding dimension in proportion to their energy, and thus there is a probability that the proximity have a greater chance of moving further apart as opposed to closer together. Hence a drop of food coloring dropped in a swimming pool will dissipate, and never converge. MDT provides a physical model for the fact that there is a probability Energy is merely matter trapped in the fourth expanding dimension: hence E=mc2. When a photon propagates, it expands as a probability wave, appearing a spherically-symmetric wavefront propagating at c in the three spatial dimensions. When a photon collapses, it has equal probability of appearing at any point defined by the spherically symmetric wavefront. Wikipedia enumerates Time's arrows: http://en.wikipedia.org/wiki/Arrow of time The thermodynamic arrow of time is provided by the Second Law of Thermodynamics, which says that in an isolated system, entropy will only increase with time; it will not decrease with time. Entropy can be thought of as a measure of disorder; thus the Second Law implies that time is asymmetrical with respect to the amount of order in an isolated system: as time increases, a system will always become more disordered. This asymmetry can be used empirically to distinguish between future and past. Since the Second Law is statistical, it does not hold with strict universality: any system can fluctuate to a state of lower entropy (see the Poincar.8e recurrence theorem). However, the Second Law seems accurately to describe the overall trend in real systems toward higher entropy. This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the weak arrow of time. Time is an emergent phenomena, which results because the fourth dimension is expanding relative to the three spatial dimensions. is expanding as a spherical wavefront relative to the three spatial the fourth expanding dimension, and thus there is a probability that surfaces of the fourth dimension. Thus there is a probability the merely matter trapped in the fourth expanding dimension: hence E=mc^2. When a photon propagates, it expands as a probability wave, appearing a spherically-symmetric wavefront propagating at c in the three spatial dimensions. When a photon collapses, it has equal probability of appearing at any point defined by the spherically symmetric wavefront. http://en.wikipedia.org/wiki/Arrow of time [edit] The cosmological arrow of time See also: Entropy and Entropy (arrow of time) The cosmological arrow of time points in the direction of the universe's expansion. It may be linked to the thermodynamic arrow, with the universe heading towards a heat death (Big Chill) as the amount of usable energy becomes negligible. Alternatively, it may be an artifact of our place in the universe's evolution (see the Anthropic bias), with this arrow reversing as gravity pulls everything back into a Big Crunch. If this arrow of time is related to the other arrows of time, then the future is by definition the direction towards which the universe becomes bigger. Thus, the universe expands - rather than shrinks - by definition. The thermodynamic arrow of time and the Second law of thermodynamics are thought to be a consequence of the initial conditions in the early universe. Therefore they ultimately result from the cosmological set- up. Time is an emergent phenomena, which results because the fourth dimension is expanding relative to the three spatial dimensions. is expanding as a spherical wavefront relative to the three spatial the fourth expanding dimension, and thus there is a probability that surfaces of the fourth dimension. Thus there is a probability the merely matter trapped in the fourth expanding dimension: hence E=mc^2. When a photon propagates, it expands as a probability wave, appearing a spherically-symmetric wavefront propagating at c in the three spatial dimensions. When a photon collapses, it has equal probability of appearing at any point defined by the spherically symmetric wavefront. The radiative arrow of time http://en.wikipedia.org/wiki/Arrow of time Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations allow for solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments which have created convergent waves, so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it, making the latter contradictory to the Second Law of Thermodynamics in usual circumstances. Time is an emergent phenomena, which results because the fourth dimension is expanding relative to the three spatial dimensions. MDT accounts for the fundamental shape and direction of radiation--a spherically symmetric wavefront propagating and expanding at the rate dimension is expanding as a spherical wavefront relative to the three spatial dimensions. Energy is merely matter trapped in the fourth expanding dimension: hence E=mc^2. When a photon propagates, it expands as a probability wave, appearing a spherically-symmetric wavefront propagating at c in the three spatial dimensions. When a photon collapses, it has equal probability of appearing at any point defined by the spherically symmetric wavefront. Hence two photons which depart at a similar origin will most likely be found in different places, as each point on the spherically symmetric wavefront has an eqaul chance of where the photon may be found. Hence entropy and time's arrow. The causal arrow of time (from wikipedia http://en.wikipedia.org/wiki/Arrow of time) Causes are ordinarily thought to precede effects. The future can be controlled, but not the past. A problem with using causality as an arrow of time is that, as David Hume pointed out, the causal relation per se cannot be perceived; one only perceives sequences of events. Furthermore it is surprisingly difficult to provide a clear explanation of what the terms cause and effect really mean. It does seem evident that dropping the plate is the cause, the plate shattering is the effect. Physically speaking, this is another manifestation of the thermodynamic arrow of time, and is a consequence of the Second law of thermodynamics. Controlling the future, or causing something to happen, creates correlations between the doer and the effect, and these can only be created as we move forwards in time, not backwards. Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity and charge conjugation, but only very rarely. An example is the kaon decay [1]. According to the CPT Theorem, this means they should also be time irreversible, and so establish an arrow of time. Such processes should be responsible for matter creation in the early universe. This arrow is not linked to any other arrow by any proposed mechanism, and if it would have pointed to the opposite time direction, the only difference would have been that our universe would be made of anti-matter rather than from matter. More accurately, the definitions of matter and anti-matter would just be reversed. That the combination of parity and charge conjugation is broken so rarely means that this arrow only barely points in one direction, setting it apart from the other arrows whose direction is much more obvious. -- http://en.wikipedia.org/wiki/Arrow of time The quantum arrow of time According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schr.9adinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible. As the mechanism of wave function collapse is philosophically obscure, it is not completely clear how this arrow links to the others. While at the microscopic level, collapse seems to show no favor to increasing or decreasing entropy, some believe there is a bias which shows up on macroscopic scales as the thermodynamic arrow. According to the modern physical view of wave function collapse, the theory of quantum decoherence, the quantum arrow of time is a consequence of the thermodynamic arrow of time (also see Entropy (arrow of time)). -- http://en.wikipedia.org/wiki/Arrow of time The collapse of the wave function, or decoherence, corresponds to when the matter trapped in the expanding fourth dimension is brought to rest in the three spatial dimensions. A group of photons emitted at a single point all have equal probabilities of being found at any point defined by the spherically symmetric wavefront. The psychological/perceptual arrow of time Psychological time is, in part, the cataloguing of ever increasing items of memory from continuous changes in perception. In other words, things we remember make up the past, while the future consists of those events that cannot be remembered. The ancient method of comparing unique events to generalized repeating events such as the apparent movement of the sun, moon, and stars provided a convenient grid work to accomplish this. The consistent increase in memory volume creates one mental arrow of time. Another arises because one has the sense that one's perception is a continuous movement from the unknown (Future) to the known (Past). Anticipating the unknown forms the psychological future which always seems to be something one is moving towards, but, like a projection in a mirror, it makes what is actually already a part of memory, such as desires, dreams, and hopes, seem ahead of the observer. Time is not the fourth dimension, but it is an emergent property of a fourth dimension that is expanding relative to the three spatial dimensions. Thus time inherits properties of the fourth dimension, but there is no block time. The association of (behind = past) and (ahead = future) is itself culturally conditioned. For example, the Chinese and the Aymara people both associate (ahead = past) and (behind = future).[1]. In Chinese, for instance, the term the day after tomorrow literally means behind day while the day before yesterday is referred to as front day. The other side of the psychological passage of time is in the realm of volition and action. We plan and often execute actions intended to affect the course of events in the future. Hardly anyone tries to change past events. Indeed, in the Rubaiyat it is written (sic): Moves on: nor all thy Piety nor Wit Nor all thy Tears wash out a Word of it. - Omar Khayy.87m (Fitzgerald translation) The psychological arrow of time is thought to be reducible to the thermodynamic arrow: it has deep connections with Maxwell's demon and the physics of information; In fact, it is easy to understand its link to the Second Law of Thermodynamics if we view memory as correlation between brain cells (or computer bits) and the outer world. Since the Second Law of Thermodynamics is equivalent to the growth with time of such correlations, then it states that memory will be created as we move towards the future (rather than towards the past). -- http://en.wikipedia.org/wiki/Arrow of time MDT's postulate: The fourth dimension is expanding at the rate of c relative to the three spatial dimensions. Time is an emergent phenomena, which results because the fourth dimension is expanding relative to the three spatial dimensions. dimension is expanding as a spherical wavefront relative to the three caught in the fourth expanding dimension, and thus there is a the expanding surfaces of the fourth dimension. Thus there is a energy. Energy is merely matter trapped in the fourth expanding dimension: hence E=mc^2. When a photon propagates, it expands as a probability wave, appearing a spherically-symmetric wavefront propagating at c in the three spatial dimensions. When a photon collapses, it has equal probability of appearing at any point defined by the spherically symmetric wavefront. http://physicsmathforums.com A Physical Model for Entropy GodelÍs Block Universe Paradox Resolved! In 1949 Godel published a paper showing that within the theory of relativity, time as we understand it, does not exist. Einstein recognized Godel's paper as an important contribution to the general theory of relativity, and since then physicists have not been able to find any logical shortcomings in Godel's work, and nobody has been able to account for the existence of time. But the Theory of Moving Dimensions accounts for time as we know it by showing that it is an emergent property of the underlying dimension's intrinsic relative movement. sufficiently wide course, it is possible in these worlds to travel into any region of the past, present, and future, and back again, exactly as it is possible in other worlds to travel to distant parts of space. This state of affairs seems to imply an absurdity. For it enables one to travel into the near past of those places where he himself lived. There he would find a person who would be himself at some earlier period of life. Now he could do something to this person, which, by his memory, he knows has not happened to him. important contribution to the general theory of relativity, especially to the analysis of the concept of time. The problem here involved disturbed me already at the time of the building up of the general theory of relativity, without my having succeeded in clarifying it... The distinction earlier-later is abandoned for world-points which lie far apart in a cosmological sense, and those paradoxes, regarding the direction of the causal connection, arise, of which Mr. Godel has spoken. . . It will be interesting to weigh whether these are not to be excluded on physical grounds. -Michio Kaku The mistake Einstein made in his formulation was confusing time itself with the fourth dimension. Time is an emergent property that we witness because of the fourth dimension expanding relative to the three spatial dimensions, and because it thus inherits properties of a dimension, it is all too tempting for physicists to refer to time as a dimension. Time travel is impossible both in reality and Moving Dimensions theory, though I encourage prominent physicists to keep on writing books about time machines and bookstores to stock them in the science- fiction sections. Time arises from the interaction of the expanding fourth dimension with the three spatial dimensions, but many physicists mistakenly labeled the fourth dimension as the time dimension. A lot of confusion has arisen by from this mislabeling coupled with the physicists' tendency to over-extend metaphors. As soon as physicists mistakenly labeled the fourth dimension the time dimension, they were eager to see it as an entity analogous to the three spatial dimensions, where one can get from any point to any other point. Had they spent a moment thinking about it, they would have seen that space and time are very different entities. We can move up and down, back and forth, in space; but only ever forwards in time. Again, time is not the fourth dimension. The past is no longer a part of our physical reality, and the future is not yet a part of our physical reality. Unfortunately for Besso, block time does not exist but for within our minds. But fortunately for all of those who believe in free will, block time is but a figment of our imagination, and a misapplication of dimensionality to time; which is an emergent property of a fourth dimension expanding relative to the three spatial dimensions. Time is an emergent property deriving from the expansion of a single spatial dimension relative to the three other stationary spatial dimensions, and thus time, as we measure and contemplate it, inherits properties of a dimension. The fourth dimension expands in units of the Planck length at the rate of c, so in a sense the fourth dimension is only ever Planck's length deep to all macroscopic objects. Only a photon can exist in this dimension, orthogonal to the three dimensions, and at that point a photon is matter surfing the expanding dimension. Huygen's principle demonstrates that every point along a spherically symmetric wavefront is the source of a spherically symmetric wave, and so it is with a photon. This is because every point in space-time is the source of a spherically symmetric expansion of the fourth dimension relative to the three stationary dimensions. Time travel to any significant degree is impossible because the time dimension never reaches deeper than Planck's length. You could only go back in time by Planck's time, which wouldn't be very useful! Physicists enjoy viewing the time dimension on equal footing with the spatial dimensions. After all, they say it is just another a dimension that just happens to have a minus sign infront of it in the space-time metric. But they never seek to explain the minus sign, which implies the photonÍs null vector. Instead they rush straight ahead into all their ridiculous notions of time travel, stating that just as we can get from any point A to any point B in space, we can get from any point A to any point B in time. But time travel has never been accomplished, nor will it ever be. The notion of past, present, and future is more related to the change of energy than it is to the actual existence of a physical past, a physical present, and a physical future. Only the present ever exists, and the past is what is recorded in our minds-it exists nowhere else. But because inherits properties of the fourth expanding dimension, physicists were seduced into believing one could travel anywhere within it. But in reality we never get any further than Planck's length deep in time, and it is at that depth that photons surf through the universe, while electrons oscillate, and our bodies maintain their average position firmly in the three spatial dimensions as the time dimension expands relentlessly about us in units of Planck's length. For Godel, if there is time travel, there isn't time. The goal of the great logician was not to make room in physics for one's favorite episode of Star Trek, but rather to demonstrate that if one follows the logic of relativity further even than its father was willing to venture, the results will not just illuminate but eliminate the reality of time. -A World Without Time, Palle Yourgrau Unification of QM and Relativity Relativity becomes increasingly exact at long-length scales but fails at short ones because space-time itself is quantized, as the time dimension is expanding in units of the Planck length. The concept of general relativity's smooth geometry, at large scales, disappears on short-distance scales-this has been a problem to string theorists, but only because they were never bold enough to recognize that's the way it is because that's the way it is-GR does not break down at distances smaller than the Planck length because such distances do not exist with any degree of certainty. The fourth dimension is expanding relative to the three spatial dimensions in units of the Planck length, and thus distances smaller than the Planck length cannot be measured nor defined. problem in merging general relativity and quantum mechanics turns up when the central tenet of the former-that space and time constitute a smoothly curving geometrical structure-confronts the essential feature of the latter-that everything in the universe, including the fabric of space and time, undergoes quantum fluctuations that become increasingly turbulent when probed on smaller and smaller distance scales. On sub- Planck-scale distances, the quantum undulations are so violent that they destroy the notion of a smoothly curving geometrical space; this means that general relativity breaks down. But general relativity does not break down. It works perfectly well, holding the planets in their orbits, curving space and time about massive objects, bending light just so, in accordance with Einstein's equations. General relativity does not break down at sub-Planck-scale distances because such distances do not exist. The fourth dimension is expanding relative to the three spatial dimensions in units of the Planck length, and thus all physical measurements and physical definitions are larger than the Planck length. General relativity need have no fear of ever breaking down at distances smaller than the Planck length, because such distances do not exist in the physical world! Einstein's Annus Mirabilis As the contemplation of the photon lead to both quantum mechanics and relativity, let us also begin the presentation of Moving Dimensions Theory by contemplating the photon. Einstein's revolutionary 1905 papers included one devoted to the photoelectric effect-which considered the quantized nature of the photon-and a paper devoted to the electrodynamics of moving bodies-which considered electromagnetic radiation, relativity, and the wave properties of the photon as embodied by Maxwell's Equations. Another 1905 paper discussed statistical mechanics in the form of Brownian Motion, and Einstein's final three-page paper that year commented on the equivalence of mass and energy, as denoted with his famous equation, E=mc2. Moving Dimensions Theory underlies and unifies all of Einstein's 1905 papers with its simple postulate-the fourth dimension is expanding relative to the three spatial dimensions. Consider the emission of a photon in free space. One second later, the photon has equal probability of being found anywhere upon a sphere with a radius of 186,000 miles, as the velocity of light, c, is 186,000 miles per second. If we covered the surface of said sphere with detectors, one, and only one, would click. And the photon, although having traveled 186,000 miles through space, will not have aged one iota, for time stops at the speed of light. The photon will have traveled 186,000 miles through the three spatial dimensions, and yet it will not have moved one iota in the fourth dimension. And there lies our first clue to moving dimensions theory. For how can a photon propagate 186,000 in the three spatial dimensions, and yet not budge an inch in the fourth dimension, unless that fourth dimension is expanding, right along with it? Ergo, the fourth dimension is expanding relative to the three spatial dimensions. A photon, as we shall see time and again, is matter surfing the fourth expanding dimension. Consider two interacting photons that are directed to propagate in opposite directions, as in experiments conceived by Bell and conducted by Aspect et al. One second later, each photon's polarization is measured at detectors separated by 372,000 miles. According to the laws of quantum mechanics and numerous supporting experiments, the measurement at one detector instantaneously affects the measurement at the second detector. It is as if the photons are yet side-by-side for all intents and purposes. This spooky action-at-a-distance, as Einstein called it, is not so spooky in the context of Moving Dimensions Theory, for MDT states that although separated by 372,000 miles, the photons are yet in the exact same place in the fourth dimension, as the fourth dimension is expanding relative to the three spatial dimensions. So it is that quantum phenomena on the photonic level, as well as relativistic phenomena on the photonic level, are both accounted for with simple elegance via MDT: the fourth dimension is expanding relative to the three spatial dimensions. Another paper Einstein penned in 1905 was devoted to Brownian motion and statistical mechanics. Drop a thimbleful of food coloring in a pool. The laws of statistical mechanics dictate that there is a high probability that the coloring will spread throughout the entire pool, and never again reassemble in a localized region. That all systems tend towards random disorder is a fundamental law of physics and condition of physical reality, and this too can be accounted for by Moving Dimensions Theory. As the fundamental motion of the universe is the expansion of the fourth dimension relative to the three spatial dimensions, two photons originating from a common origin will harbor a vast probability of being found at great distances from one another one second later-distances far greater than the distance that separates them at their emission. This is because each one has an equal probability of being found anywhere upon the surface of a spherically-symmetric wave front of probability, corresponding to the wave front of the fourth expanding dimension. Recall our system of detectors placed everywhere upon the surface of a sphere with a radius of 186,000 miles-each photon has an equal chance of being found at any detector after one second after they were emitted at a common origin, and chances are that the detectors will be farther apart than the distance of zero that defines the separation between photon's common origin. Hence entropy. Entropy arises because the fourth dimension is undergoing thermal vibrations interact with photons, and all photons reside in the fourth expanding dimension, dragging all of entirety into random disorder. Yet another paper published by Einstein in his Miraculous Year (annus mirabilis), was devoted to the equivalence of mass and energy. Think about the fascinating physical reality implied by Einstein's most famous equation-E=mc2. A kilogram of gold or lead or feathers sitting on a desktop is the same thing as 9x10 16 joules of energy-an exorbitant amount of energy-enough to power, or to destroy, a major city. How is it that a stationary mass possesses such a great energy? It is because the mass, which is stationary in the three spatial dimensions, is yet propagating through the fourth dimension at the rate of c. This is because the fourth dimension is expanding relative to the three spatial dimensions. Matter surfing the fourth expanding dimension appears at photons. Furthermore, as noted earlier, the photons will propagate at the rate of c through the three spatial dimensions, and yet they will never age-they will stay in a fixed place in the fourth expanding dimension. The primary invariant is c- all matter and/or photons-be it propagating through space or time, or some combination thereof, always, always moves at the rate of c. To be stationary in the three spatial dimensions means to propagate at the rate of c through the fourth dimension. To be stationary in the fourth dimension means to propagate at the rate of c through the three spatial dimensions. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions. Most objects share motion between space and time, but the overall velocity of propagation through space-time is fixed at c- this primary invariance can never change, and this reality arises because of the deeper physical reality of Moving Dimensions Theory. And so it is that Moving Dimensions Theory underlies and unifies the papers Einstein Published during his Annus Mirabilis-his miraculous year. I highly recommend Harvard University Press's Einstein 1905: The Standard of Greatness by John S. Rigden, about which Publisher's The year 2005 will be the centenary of Einstein's annus mirabilis, when he published the five papers that marked him as one of the greatest scientists of all time. Washington University professor Rigden (Hydrogen: The Essential Element) sits readers down in front of his white board and explains what Einstein said in each of these papers, what was significant in them and how the scientific community reacted (not very well, in most cases-for a while). Einstein started off with a bang: in March he proposed that light was not a continuous his dissertation, on how to determine the size of molecules in a liquid (that may not sound very exciting, but this is one of motion, and then in June came the summit of his achievements that year: the paper proposing his principles of relativity and the consistency of the speed of light (commonly known as the Special Theory of Relativity). Finally, almost as an afterthought, in September came the three-page paper that unleashed his now-famous felicity, free of jargon and with everyday metaphors that Einstein himself would no doubt have appreciated. I encourage everyone to read Einstein's and Bohr's and Heisenberg's and Dirac's original papers, and contrast their majestic elegance, eloquence, reason, and logic to the snarky death threats and crackpot indexes manufactured by today's best and brightest, and the accompanying silence from their established elders-the founders of string theory's oppressive regime and hand-waving, reason-subjugating, PBS miniseries. The future book on Moving Dimensions Theory will look back to the giants of yesteryear with deep honor and reverence, so that tomorrow's physics might advance in the spirit of simple Truth and Beauty. Every effort will be maintained to demonstrate that true physics is marked by grace and simplicity, as opposed to obfuscation and bullying. Moving Dimensions Theory is an idea whose time has come, and ideas are bulletproof. MDT: The Best-Tested Theory of All Time MDT is the best-tested theory of all time. MDT predicts that an object's velocity through spacetime is always c. This is because the fourth dimension is expanding relative to the three spatial dimensions. MDT's postulate: The fourth dimension is expanding relative to the three spatial dimensions, in units of the planck length, at the rate of c. The above has been shown in experiment, after experiment, after experiment. MDT predicts that the only way to stay stationary in the three spatial dimensions is to move with a velocity of c relative to the fourth expanding dimension. This is because the fourth dimension is expanding relative to the three spatial dimensions. The above has been shown in experiment, after experiment, after experiment. MDT predicts that the only way to stay stationary in the fourth expanding dimension is to move with the velocity c relative to the three spatial dimensions. This is because the fourth dimension is expanding relative to the three spatial dimensions. The above has been shown in experiment, after experiment, after experiment. MDT predicts the equivalence of mass and energy. Matter, when rotated into the fourth expanding dimension is foreshortened, and it appears as photons. The above has been shown in experiment, after experiment, after experiment. MDT predicts the constant speed of light. The fourth dimension is expanding relative to the three spatial dimensions at the rate of c. Hence the speed of matter rotated into the the fourth dimension is c. No matter how fast the source is moving, the second the photon leaves thes ource, it is carried by the fourth expanding dimension, so its speed is always c, independent of the source. The above has been shown in experiment, after experiment, after experiment. dimension in the form of a photon, it appears as a spherically- symmetric wavefront. Hence Young's double-slit experiment and interference. When the wave--the matter being carried along by the fourth expanding dimension--is perturbed, it is collapsed, and brought into the the three stationary spatial dimensions. Hence the quantum nature of all energy. The above has been shown in experiment, after experiment, after experiment. MDT predicts entropy--the fundamental motion of the universe is the spherically-symmetric wavefront defiend by the fourth dimenion expanding relative to the three spatial dimensions--hence entropy. Two The above has been shown in experiment, after experiment, after experiment. Hence all radiation fundamentally appears as spherically-symmetric wavefronts propagating in the three stationary spatial dimensions. The above has been shown in experiment, after experiment, after experiment. MDT predicts the null vector for photons, as well as the - (minus) sign in the space-time metric. As the fourth dimension is expanding relative to the three spatial dimensions, the only way to have zero interval is to move with the origin--at the speed of light. The above has been shown in experiment, after experiment, after experiment. MDT unfreezes time. Time, as we consider it, is not the fourth dimension, but it is an emrgent property of a fourth dimension expanding relative to the three spatial dimensions. This confusion of time with the actual fourth dimension has lead to Godel's paradox and the block-universe, which although they have provided Paul Davies with a lucrative living for his fantasies and science fiction, are not real. Barbour gets close to this. The above has been shown in experiment, after experiment, after experiment. General Relativity freezes time.84the fourth dimensions is a tiny loop or sphere of locality at each given instant, but one second later, that loop or sphere has a radius of 186,000 miles. Moving dimensions theory predicts that as objects move, they will become shorter. This is because the fourth dimension is expanding relative to the three spatial dimensions, so as an object is rotated into the fourth dimension, it will appear shorter in the three spatial dimensions, and too, it will translate or gain velocity in the direction of its forshortening. The above has been shown in experiment, after experiment, after experiment, including the Michelson Morely experiment. Moving dimensions theory predicts that the measurement of the state of a photon can instaneously affect the state of a distant photon, when those two photons were initially interacting. This is because although they are now distant in space, they are yet at the same place in the expanding fourth dimension. The above has been shown in experiment, after experiment, after experiment. MDT does not predict wormholes, nor multiverses, nor stringy strings, nor M-theroy, which have never been supported by experiment, and thus it is to be utterly detested by the machine. MDT would underly all apsects of String Theory, and MDT does explain an interpretation of higher, numerous dimensions, if needed by Kaluza Klein et al. In fact, an instanaeous snapshot of the foruth expanding dimension would look something like this--every point is becoming a three- dimensional sphere in units of the planck radius: MDT predicts the gravitational red shift. A photon emitted in a region of streched spacetime will maintain its wavelength as it travels away from the mass, thus appearing red-shifted. MDT unifies the dualities--space and time, energy and mass, waves and dimension is expanding relative to the three spatial dimensions. Quantum mechanics, relativity, and entropy--interference, wave- contractions, the equivalence of mass and energy, and times arrow all derive from the physical model moving dimensions theory presents. The purpose of physics has ever been to unify and explain via deeper, fundamental, physical models, and that's what Moving Dimensions Theory provides. The fourth dimension is expanding relative to the three spatial dimensions. Moving Dimensions Theory accounts for the aetherless aether. This simple postulate offers a physical model underlying and unifiying: RELATIVITY: 1) length contraction 2) time dilation 3) the equivalence of mass and energy 4) the constant velocity of light 5) the independence of the speed of light from the velocity of the source QUANTUMN MECHANICS 1) action at a distance 3) interference phenomena 4) EPR paradox 1) Time's arrow 2) Entropy STRING THEORY'S MANY DIMENSIONS / KALUZA/KLEIN THEORY 1) a fourth expanding dimension can be interepreted as many dimensions, each time it expands THE UNITY OF THE DUALITIES 2) time/space duality 3) energy/mass duality 4) E/B duality GENERAL RELATIVITY 1) Gravitational redshift 2) Gravity waves 3) Gravitation attraction THE SPACE-TIME BACKGROUND 1) quantum foam 2) the smearing of space and time at small distances 3) Hawking's imaginary time PARADOXES 1) MDT explains away Godel's Block Universe 2) MDT unfreezes time 3) Resolves Zeno's Paradox ONE GETS ALL OF THIS FROM A SIMPLE POSTULATE: The fourth dimension is expanding relative to the three spatial dimensions in a spherically symmetric manner, in units of the Planck length, at the rate of c. http://physicsmathforums.com The Act of Measurement The act of measuring a photon, such as detecting it on a photographic plate, removes the photon from the fourth expanding dimension. Probability Our probabilistic universe derives from the fact that the fourth dimension is expanding relative to the three spatial dimensions. The expanding 3D spherical wavefront is how the expandion of x4 manifestist itself, and the surface of this 3D sphere represents a single point in the fourth dimension. Any photons emitted at the center of the sphere will find themselves on the surface of the expanding sphere, traveling at the velocity of c. All points on that sphere will represent a single point in the fourth dimension, and the photon has an equal chance of being found at any point on the surface of the sphere. The act of measurement takes the photon out of the expanding fourth dimension.84a realm of inherent nonlocality, and localizes it in the three spatial dimensions. Brian Green Gets Close Dark Energy Dark Matter Unifying Quantum Mechanics and Relativity The Purpose of Physics Predictions made by MDT Consider a four dimensional manifold wherein the fourth dimension is expanding relative to the three spatial dimensions: Such a universe would predict relativistic effects such as length contraction, time dilation, and the equivalence of mass and energy, all based on a physical model. A Dialogue With Roger Penrose A Dialogue With Lee Smolin A Dialogue with Stephen Hawking A Dialogue With Paul Davies Epic story is what religion is about, as epic story and mythology contain the roadmaps to our souls and spirits. So when science, which comes with no story, replaces religion, the rising generation loses the classical mythology that enriches their soul. It is not too often that one gets to present a new physical model underlying reality that explains diverse phenomena at the frontiers of all realms of physics. In doing so I have humbled myself before the giants.84Einstein, Newton, Bohr, Faraday, Fermi, and Dirac. And in humbling myself before the Greats, I have been deemed arrogant by many of my contemporaries who have razed the greats so as to exalt their postmodern politics and propaganda. String Theory, Loop Quantum Gravity, and Lisi Mania are all symptoms of big-money physics. One cannot serve two masters, and the central purpose of big-money physics is to foster and perpetuate the myth that millions upon millions of dollars are needed to advance physics. But the past thirty years have demonstrated the exact opposite, as physics has ground to a halt while snarky old men hype their egotistic fantasies to the popular media and play games with the lives of young scientists. Science has ever been the realm of the individual. Although they stand upon the shoulders of Giants, all advancements in physics are marked by a maverick individual following their private passions, leaving their distinctive mark on the field. The state and groupthinkers have ever been the perpetual enemy of these freethinkers; and as the state and groupthinkers win, raising record- setting sums in federal funding as a nation is forced into debt, science stalls and physics grinds to a halt. Rather than addressing the problem at its root, the groupthinkers are quick to come out with books titled ñThe End of Science.î The shortcoming is never with the hypesterÍs philosophy nor the tyrants whims and yearning for power, but it is always with Truth. Make no mistake.84a book called The End of Science is an attack on Truth; they want to tell all the young scientists to just go on home. Another troubling trend is that the snarky old men who failed to ever advance physics, or answer any questions of their own, are drawing up lists of ñleading questionsî to be answered. Well, every true physicist has always progressed by following their own curiosity.84not signing up to be dictated to by state-sanctified curiosity. Einstein did not seek out a graduate program headed by a master media manipulator, so that he could get his theories hyped on fox news; but rather, while working as a patent examiner and following his private curiosities, he revolutionized physics, penning five fabulous papers in 1905 which launched relativity and contributed to quantum mechanics and statistical mechanics. Wikipedia reports: In physics, Kaluza[CapitalEth]Klein theory (or KK theory, for short) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. The theory was first published in 1921 and was discovered by the mathematician Theodor Kaluza who extended general relativity to a five-dimensional spacetime. The resulting equations can be separated out into further sets of equations, one of which is equivalent to Einstein field equations, another set equivalent to Maxwell's equations for the electromagnetic field and the final part an extra scalar field now termed the radion. Kaluza-Klein theory posited that gravity and electromagnetism can be unified by adding a fifth dimension of compactified space, and MDT provides this compactified space. The novelty of MDT is that it proposes that this compactified space is not static, but that it is constantly appearing, as the fourth dimension expands. Thus MDT underlies all string theories. String Theory ignores EinsteinÍs insight that space and time can move, warp, and bend. MDT acknowledges that dimensions can move. Below is a figure depicting the compactified dimensions of Kaluza Klein .84not that it is very similar to the earlier figures depicting MDT in terms of a dimension that is expanding in a spherically-symmetric manner. http://jac leon.club.fr/gravitation/images/kaluza-klein.gif http://www.vcharkarn.com/uploads/17/17494.gif Wikipedia reports on Kaluza KleinÍs limitations: As an approach to the unification of the forces, it is straightforward to apply the Kaluza-Klein theory in an attempt to unify gravity with the strong and electroweak forces by using the symmetry group of the Standard Model, SU(3) .81~ SU(2) .81~ U(1). However, an attempt to convert this interesting geometrical construction into a bona-fide model of reality founders on a number of issues, including the fact that the fermions must be introduced in an artificial way (in nonsupersymmetric models). A less problematic approach to the unification of the forces is taken by modern string theory and M-theory. Nonetheless, KK remains an important touchstone in theoretical physics and is often embedded in more sophisticated theories. It is studied in its own right as an object of geometric interest in K-theory. Perhaps MDT, and the new, emergent picture of time, will provide a means for introducing fermions in a more natural manner. The exact nature and radius of the expanding fourth dimension could determine physical constants. Wikipedia reports: Even in the absence of a completely satisfying theoretical physics framework, the idea of exploring extra, compactified, dimensions is of considerable interest in the experimental physics and astrophysics communities. A variety of predictions, with real experimental consequences, can be made (in the case of large extra dimensions/ warped models). For example, on the simplest of principles, one might expect to have standing waves in the extra compactified dimension(s). If an extra dimension is of radius R, the energy of such a standing wave would be E = nhc / R with n an integer, h being Planck's constant and c the speed of light. This set of possible energy values is often called the Kaluza[CapitalEth]Klein tower. It is indeed interesting that M Theory and String Theory have 10 or 11 dimensions. MDT can account for these extra dimensions, starting with a three dimensional world. Wikipeida reports: http://en.wikipedia.org/wiki/Why 10 dimensions%3F#Number of dimensions Number of dimensions One intriguing feature of string theory is that it involves the prediction of extra dimensions. The number of dimensions is not fixed by any consistency criterion, but flat spacetime solutions do exist in the so-called critical dimension. Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions.84more precisely different values of the effective central charge, a count of degrees of freedom which reduces to dimensionality in weakly curved regimes.84are related by dynamical transitions.[15] Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions by hand, and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. Technically, this happens because a gauge anomaly exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. Furthermore, the absence of potential energy in the critical dimension explains why flat spacetime solutions are possible. This can be better understood by noting that a photon included in a an unbroken gauge symmetry) must be massless. The mass of the photon which is predicted by string theory depends on the energy of the string mode which represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions since for a larger number of dimensions, there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless.84and the theory consistent.84only for a particular number of dimensions.[16] When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation.[17] Starting from any dimension greater than four, it is necessary to consider how these are reduced to four dimensional space-time. Picture a fourth expanding dimension. It would appear as a sphere in three stationary dimensions. Now if each point on the sphere is always expanding, just as each point on a spherically-symmetric wavefront is always expanding as a spherically symmetric wavefront, six new, linearly independent compactified dimensions will be introduced, as there are six degrees of freedom, resulting in a total of ten dimensions. So it is that MDT easily accounts for the extra six dimensions, as the nature of the compactified, spherically-symmetric dimension is to be perpendicular to the point from which it emanated. That perpendicularity is implied by the i in MDTÍs fundamental equation: TimeÍs Arrows MDT at long last unifies timeÍs arrows and show that they all derive from the same underlying physical reality. In his book The Physical Basis of The Direction of Time, H. Dieter Zeh lists the six arrows of time: 1. Radiation 2. Thermodynamics 3. Evolution 4. Quantum Mechanical Measurement 5. Exponential Decay 6. Gravity For years we have been fed the opinion that physics is incomplete as if it were fact. Theoretical physicists have spent entire lifetimes in purely conjectured realms, in black holes and wormholes, where they have complained that quantum mechanics and general relativity cannot coexist. Seldom do they pause to consider that quantum mechanics and relativity coexist perfectly happily with one-another, as the moon is held in orbit, governed by EinsteinÍs General Relativity, and I am able to type this on a computer, whose workings are governed by quantum mechanics. I prefer to ask the question whether a unified theory would have any real physical menaing. The essence of any theory of quantum gravityis gravity, just like the photon which is a quantum of light. Such a discrete little packets called quanta, and a quantum of gravitational asking is whether there is any conceivable way in which we could detect the existence of individual gravitons. It is easy to detect individual photons, as Einstein showed, by observing the behavior of electorns kicked out of metal surfaces by light incident on metal. The difference between phtons and gravitons is that gravitationhal interactions are enormously weaker than elctromagentic interactions. If you try to detect individual gravitons by observing electrons kicked out of a metal surface by incident gravitational waves, you find that you have to wait longer than the age of the unviverse before you are likely to see a graviton. . . I propose as a hypothesis to be testd that it is impossible in principle to observe the existence of individual gravitons. I do not claim that this hypothesis is true, only that I can find no evidence against it. If it is true,m quantum gravity is physically meaningless. If individual gravitons cannot be observed in any conceivable experiment, then they have no physical reality and we might as well consider them sonexistent. They are like the ether, the classic solid medium which nineteenth-century physicists imagined filling space. Electric and magnetic fields were supposed to be tensions in thei either, and light was supposed to be a vibration of the ether. Einstein built his theory of relativity without the ether, and showed that the ether would be unobservable if it existed. He was happy to get rid of the ther, and I feel the same way about gravitons. Gravitatioonal waves exist and can be detected, but they are classical waves and not coolections of gravitons. If this hypothesis is true, then we have two separate worlds, the classical world of gravitation and the quantum world of atoms, described by separate theories. The two theories are mathematically different and cannot be applied simultaneously. But no inconsistency can arise from using both theories, because any differences between their predictions are physically undetectable. P.220-221 One of the fashionable past-times amongst physicists of our era are to dismiss the wisdom and insight of greats such as Einstein, Bohr, Feynman, and Dyson. Einstein showed that space and time themselves were dynamic in nature, capable of warping, stretching, and moving.84a fact born out by experiment after experiment after experiment.84and yet the String Theorists do not have a background-independent approach. They fix their space and time. Moving Dimensions Theory agrees with Einstein, and Bohr, and Dyson. Blaming String Theory on Einstein It is ironic that come conscienceless physicists blame String TheoryÍs indecipherable, and ultimately fruitless mathematics on Einstein. The argument usually goes like this.84Einstein trusted in math to create general relativity, succeeding in his faith that pure mathematics could lead us to deeper physical insights. Well, what theyÍre forgetting is that long before the math was brought in, general relativity was an idea born in physical reality.84in the ñhappiest thoughtî of EinsteinÍs life.84the fact that someone in freefall wouldnÍt feel their own weight. This lead to the equivalence of acceleration by an external force and the acceleration felt in the gravitational field, which lead to gravity being conceived as of the curvature of space-time. Objects in gravitational fields yet followed along straight lines through space-time, but the space- time was curved, resulting in accelerated motions. Einstein was first and foremost a physicist, like Bohr and Faraday. Bohr and FaradyÍs original notebooks contain far more expository words expressing their physical ideas than mathematical equations. Smolin talked about this in his book The Trouble With Physics, and when I posted it on WoitÍs blog, Woit quickly snarked me and removed the post. Woit yet worships at the altar of pure math, where Witten and Lisi shall prevail unto eternity, always promising that the next great physical insight shall magically emerge from staring at pretty geometric patterns all day long. Nothing in the history of actual physics suggests that this is how physics works. Feynman said, ñmath is to physics as masturbation is to sex.î And Einstein said Mathematics are well and good but nature keeps dragging us around by the nose. Unlike todayÍs snarky elite, Einstien was humble before physics. It is anomalous to replace the four-dimensional continuum by a five- dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself. [CapitalEth]Einstein to Paul Ehrenfest Moving Dimensions Theory & HuygensÍ Principle Wikipedia states, The answer is to be found in the Huygens-Freznel Principle: http://en.wikipedia.org/wiki/Huygens' principle The Huygens[CapitalEth]Fresnel principle (named for Dutch physicist Christiaan Huygens, and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation (both in the far field limit and in near field diffraction). It recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. This view of wave propagation helps better understand a variety of wave phenomena, such as diffraction. MDT states that the expansion of the fourth dimension appears as a spherically-symmetric wavefront through the three spatial dimensions. Via Huygen's Principle, MDT recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. And thus MDT explains double-slit diffraction. Huygens principle follows formally from the fundamental postulate of quantum electrodynamics [CapitalEth] that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. It is then the result of interference (addition) of all path integrals that defines the amplitude and phase of the wavefunction of the object at this given point, and thus defines the probability of finding the object (say, a photon) at this point. Not only light quanta (photons), but electrons, neutrons, protons, atoms, molecules, and all other objects obey this simple principle. And so it is seen that MDT underlies Feynman's many-paths treatments and the fundamental postulate of quantum electrodynamics [CapitalEth] that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. All paths have a probaility of being followed because of the fundamental nature of a fourth dimension that is expanding relative to the three spatial dimensions. The probability distribution of the photon expands at the rate of c. After a photon is emitted, the spherical wavefront that defines its probability for being found at any point has a radius of 186,000 miles. This is the net result of billions and billions of quantum expansions of the fourth dimension, and during each expansion, the photon had an equal chance of being found anywhere on the surface of the net sphere, which is the sum total of billions upon billions of smaller spheres. These diagrams illustrate the basis of Huygen's Principle: http://www-laep.ced.berkeley.edu/~i...site/index.html MDT describes the fundamental motion of the unvierse. to the three spatial dimensions, captured in the simple equation d(x4)/dt=ic, the following emerges: Huygen'sPrinciple The fundamental postulate of quantum electrodynamics [CapitalEth] that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. Time Entropy Action at a Distance Double slit interference Relativity Length Contraction Time Dilation The equivalence of mass and energy: E=mc^2: Energy is but matter caught upon the fourth expanding dimension. Time's Radiative Arrow Time's Thermodynamic Arrow And finally, the goal of physics is ultimately to describe physical reality. We live in a universe whose physical reality is that the fourth dimension is expanding relative to the three spatial dimensions. MDT & Brian GreeneÍs Elegant Universe In An Elegant Universe, Brian Greene almost characterizes the reality of Moving Dimensions Theory, but falls just short. ñEinstein found that precisely this idea.84the sharing of motion between different dimensions.84underlies all of the remarkable physics of special relativity, so long as we realize that not only can spatial dimensions share an objectÍs motion, but the time dimension can share this motion as well. In fact, in the majority of circumstances, most of an objectÍs motion is through time, not space. LetÍs see what this means.î Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49 Right here Brian almost grasps MDT. But time is not a dimension. Time is an emergent phenomena that arises because the fourth dimension is expanding relative to the three spatial dimensions at the rate of c. LetÍs rewrite BrianÍs paragraph as it should be written: ñEinstein found that precisely this idea.84the sharing of motion between different dimensions.84underlies all of the remarkable physics of special relativity, so long as we realize that not only can spatial dimensions share an objectÍs motion, but the time dimension can share this motion as well. In fact, in the majority of circumstances, most of an objectÍs motion is through the fourth dimension, not the three spatial dimensions. LetÍs see what this means.î Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49 Most objects are traveling far less than c through the three spatial dimensions. Thus most objects are traveling close to the rate of c through the fourth dimension. To be stationary in the three spatial dimensions implies a velocity of c through the fourth dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions. To be stationary in the fourth dimensions, as is a photon, implies a velocity of c through the three spatial dimensions. Ergo the fourth dimension is expanding relative to the three spatial dimensions. dx(4)/dt = ic Brian Greene continues: ñMotion through space is a concept we learn about early in life. Although we often donÍt think of things in such terms, we also learn that we, our friends, our belongings, and so forth all move through time, as well. When we look at a clock or a wristwatch, even while we idly sit and watch TV, the reading on the watch is constantly changing, constantly ñmoving forward in time.î We and everything around us are aging, inevitably passing from one moment of time to the next. In fact, the mathematician Hermann Minkowski, and ultimately Einstein as well, advocated thinking about time as another dimension of the universe.84the fourth dimension.84in some ways quite similar to the three spatial dimensions in which we find ourselves immersed.î Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49 What Greene misses is that the time measured on your watch.84the ticking seconds.84is not the fourth dimension, but it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions. The time measured on a clock or watch relies on the emission and propagation of photons, be it in the context of an unwinding clock spring or an oscillating quartz crystal, or even the beating of a heart. And photons are matter that surf the fourth expanding dimension. As time is so inextricably wed to the emission and propagation of photons, and as photons are matter caught in the fourth expanding dimension, our notion of ñtimeî inherits properties of the fourth expanding dimension. But the fact is that time emerges from a deeper physical reality.84a fourth dimension that is expanding relative to the three spatial dimensions. Brian Green continues on, heading off in the wrong direction that just misses the central postulate of MDT: ñAlthough it sounds abstract, the notion of time as a dimension is actually concretes.î But it is not. Can you move to where your watch reads three seconds back in time? Or can you move to where your watch reads an hour back in time? We can walk left or right. We can climb up or down. We can move forwards or backwards. But we canÍt move through time like we can through the three spatial dimensions. This is because time, as measured on our watch, is not the fourth dimension, but it is a construct we have devised which is based on the fundamental fact that the fourth dimension is expanding relative to the three spatial dimensions, governing the emission and propagation of photons. Brian Green continues on, ñWhen we want to meet someone, we tell them where ñin spaceî we will expect to see them.84for instance, the 9th floor of the building on the corner of 53rd Street and 7th avenue. There are three pieces of information here (9th floor, 53rd Street, 7th avenue) reflecting a particular location in the three spatial dimensions of the universe. Equally important, however, is our expectation of when we expect to meet them.84for instance, at 3 PM. This piece of information tells us where ñin timeî our meeting will take place. Events are therefore specified by four pieces of information: three in space and one in time. Such data, it is said, specifies the location of the event in space and in time, or in spacetime, for short. In this sense, time is another dimension.î But again, time is different from the three spatial dimensions. Time is inextricably wed to our sense of the past.84the order stored in our memory, long with our ability to imagine and dream of future events. The present is where we put our dreams into action. However, the time defined by past, present, and future is not a dimension akin to the three spatial dimensions, but rather it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions. MDT original paper: Derivation of the Lorentz Transofrmation The principle of the constancy of the velocity of light demands the existence of a reference system á relative to which every light ray propagates in vacuum with velocity c. According to the relativity principle, all reference systemá? in uniform translation motion to á must possess the same property. Together with Laue, we call each such system ñjustified.î Now we ask: What kind of transformation equations must obtain between the space-time coordinates x, y, z, t (with respect to á) and x?,y?,c?,t? (with respect to á?) of the same point event so that the principle of the constancy of the velocity of light would hold with respect to both systems? We can further demand, without reducing their generality, that the transformation equations be homogeneous, because all that is needed for this is that the path described by the origin of á? with respect to á pass through the origin of á, and that the origin of time scales in á and á? be chosen in such a way that the clocks located at the origins of the systems á and á? both read zero at the moment when the two points coincide. Suppose that at this moment of the coincidence of the two origins a vacuum light signal is sent from O or O?, which, according to the principle of the constancy of the velocity of light, propagates in a spherical wave with respect to both systems then the spatial points that are just reached by the signal at times t and t? with respect to á and á?, respectively, will be determined by the equations and This means that the equations and must be equivalent. Thus, the transformation equations that we are seeking must be so constituted that the second equation turns into the first one if x?,y?,z?,t? are replaced by their expressions in terms of x,y,c,t. The transformation must therefore make the equation into an identity, where all that we know about the factor ?2 for the time being is that it must not vanish. But one can see that ?2 must be independent of x, y, z, t, for otherwise the right-hand side divided by ?2 could not be a homogeneous, complete function of second order in x,y,z,t after the substitution is carried out. For now we will examine the substitution for the case ?2 = 1 and we will show later that from a physical point of view this is the only case deserving of consideration. Instead of (15), we then have: If one introduces the variable u? = ict or u? = ict? in place of the time variables t, where i denotes the imaginary unit, one obtains, instead of (15a), the form As is well known, this choice of time variables derives from Minkowski. Its great significance consists in the fact that by means of it, equation (15a), which governs the substitution that we are seeking, is brought into a form into which the spatial coordinates and the temporal coordinate enter in the same manner. MDT Original Paper: Godel's Block Universe Paradox Resolved In 1949 Godel published a paper showing that within the theory of relativity, time as we understand it, does not exist. Einstein recognized Godel's paper as an important contribution to the general theory of relativity, and since then physicists have not been able to find any logical shortcomings in Godel's work, and nobody has been able to account for the existence of time. But the Theory of Moving Dimensions accounts for time as we know it by showing that it is an emergent property of the underlying dimension's intrinsic relative movement. sufficiently wide course, it is possible in these worlds to travel into any region of the past, present, and future, and back again, exactly as it is possible in other worlds to travel to distant parts of space. This state of affairs seems to imply an absurdity. For it enables one to travel into the near past of those places where he himself lived. There he would find a person who would be himself at some earlier period of life. Now he could do something to this person, which, by his memory, he knows has not happened to him. important contribution to the general theory of relativity, especially to the analysis of the concept of time. The problem here involved disturbed me already at the time of the building up of the general theory of relativity, without my having succeeded in clarifying it... The distinction earlier-later is abandoned for world-points which lie far apart in a cosmological sense, and those paradoxes, regarding the direction of the causal connection, arise, of which Mr. Godel has spoken. . . It will be interesting to weigh whether these are not to be excluded on physical grounds. -Michio Kaku The mistake Einstein made in his formulation was confusing time itself with the fourth dimension. Time is an emergent property that we witness because of the fourth dimension expanding relative to the three spatial dimensions, and because it thus inherits properties of a dimension, it is all too tempting for physicists to refer to time as a dimension. Time travel is impossible both in reality and Moving Dimensions theory, though I encourage prominent physicists to keep on writing books about time machines and bookstores to stock them in the science-fiction sections. Time arises from the interaction of the expanding fourth dimension with the three spatial dimensions, but many physicists mistakenly labeled the fourth dimension as the time dimension. A lot of confusion has arisen by from this mislabeling coupled with the physicists' tendency to over-extend metaphors. As soon as physicists mistakenly labeled the fourth dimension the time dimension, they were eager to see it as an entity analogous to the three spatial dimensions, where one can get from any point to any other point. But time is an emergent property deriving from the expansion of a single spatial dimension relative to the three other stationary spatial dimensions. The fourth dimension expands in units of the Planck length at the rate of c, so in a sense the fourth dimension is only ever Planck's length deep to all macroscopic objects. Only a photon can exist in this dimension, orthogonal to the three dimensions, and at that point a photon is matter surfing the expanding dimension. Huygen's principle demonstrates that every point along a spherically symmetric wavefront is the source of a spherically symmetric wave, and so it is with a photon. This is because every point in space-time is the source of a spherically symmetric expansion of the fourth dimension relative to the three stationary dimensions. Time travel to any significant degree is impossible because the time dimension never reaches deeper than Planck's length. You could only go back in time by Planck's time, which wouldn't be very useful! Physicists enjoy viewing the time dimension on equal footing with the spatial dimensions. After all, they say it is just another a dimension that just happens to have a minus sign infront of it in the space-time metric. But they never seek to explain the minus sign. Instead they rush straight ahead into all their ridiculous notions of time travel, stating that just as we can get from any point A to any point B in space, we can get from any point A to any point B in time. But time travel has never been accomplished, nor will it ever be. Physicists were right in recognizing that time is a dimension, but they fell short in recognizing that it was different from the three spatial dimensions in that it is expanding at the rate of c relative to the three spatial dimensions. The notion of past, present, and future is more related to the change of energy than it is to the actual existence of a physical past, a physical present, and a physical future. Only the present ever exists, and the past is what is recorded in our minds-it exists nowhere else. But because time is a dimension, physicists were seduced into believing one could travel anywhere within it. But in reality we never get any further than Planck's length deep in time, and it is at that depth that photons surf through the universe, while electrons oscillate, and out bodies maintain their average position firmly in the three spatial dimensions as the time dimension expands relentlessly about us in units of Planck's length. For Godel, if there is time travel, there isn't time. The goal of the great logician was not to make room in physics for one's favorite episode of Star Trek, but rather to demonstrate that if one follows the logic of relativity further even than its father was willing to venture, the results will not just illuminate but eliminate the reality of time. -A World Without Time, Palle Yourgrau Unification of QM and Relativity Relativity becomes increasingly exact at long-length scales but fails at short ones because space-time itself is quantized, as the time dimension is expanding in units of the Planck length. The concept of general relativity's smooth geometry, at large scales, disappears on short-distance scales-this has been a problem to string theorists, but only because they were never bold enough to recognize that's the way it is because that's the way it is-GR does not break down at distances smaller than the Planck length because such distances do not exist with any degree of certainty. The fourth dimension is expanding relative to the three spatial dimensions in units of the Planck length, and thus distances smaller than the Planck length cannot be measured nor defined. in merging general relativity and quantum mechanics turns up when the central tenet of the former-that space and time constitute a smoothly curving geometrical structure-confronts the essential feature of the latter-that everything in the universe, including the fabric of space and time, undergoes quantum fluctuations that become increasingly turbulent when probed on smaller and smaller distance scales. On sub-Planck-scale distances, the quantum undulations are so violent that they destroy the notion of a smoothly curving geometrical space; this means that general relativity breaks down. But general relativity does not break down. It works perfectly well, holding the planets in their orbits, curving space and time about massive objects, bending light just so, in accordance with Einstein's equations. General relativity does not break down at sub-Planck-scale distances because such distances do not exist. The fourth dimension is expanding relative to the three spatial dimensions in units of the Planck length, and thus all physical measurements and physical definitions are larger than the Planck length. General relativity need have no fear of ever breaking down at distances smaller than the Planck length, because such distances do not exist in the physical world!! Any material entity gains more energy as its velocity increases, and relativity demonstrates that the entity also gains more mass. When energy is added to an entity, it may also appears as mass, as that energy has a finite chance of interacting with the spatial dimensions. All matter has a spatial component, or a probability of interacting with space, whereas a photon only interacts with that which is in the time dimension. In order to cause an entity to move, quanta of energy must be added to it, and the entity will thus gain a new probabilities for existing in the space and time dimensions, as its overall wavefunction, including its mass and energy, is rotated out of the spatial dimension and into the time dimension. This rotation into the time dimension will be proportional to the amount of energy that has been added. As only photons can exist purely in the spatial dimension, no entities but for photons can ever reach the speed of light, as all matter has a finite chance of existing purely in the spatial dimension. This property gives rise to the concept of mass, as to exist in the spatial dimension curves the fabric of space-time about the existence. An entity moves through space-time according to its probability of existing in space and time. The more energy a given entity has, the more likely it is to exist in the time dimension, or be moving along in the dimension which is expanding relative to the spatial dimensions. Hence its greater velocity, and also its augmented chance of interacting with matter over a fixed distance. This increased chance of interacting with matter over a given distance can be associated with a shorter deBroglie wavelength or a higher frequency. A more energetic photon has a higher frequency, as it is composed of more substance, and more momenergy must pass a given point at any given time. A less energetic photon carries less momenergy, and thus there is a smaller chance of it interacting with matter as it passes on by. A more energetic photon has a higher probability of interacting with matter as it passes it by, as its shorter wavelngth and higher frequency represent a greater, more persistant existence in space-time. A photon has no spatial dimensions, as it is matter rotated into the time dimension. Einstein's famous equation which expresses the equivalnce between matter and energy: E=mc^2 holds true because radiative energy, consisting of photons, is merely matter which has been rotaed tinto the expanding time dimension. In quantum mechanics energy is accounted for by the operator which represents the infinitesimal change with respect to time, while momentum is accounted for by an operator which represents the infinitesimal change with respect to space. Both momentum and energy are defined with the concept of change and probability. And too, inherent in all waves are the concepts of motion and probability. Einstein's postulates derive from the fact that in all inertial reference frames, the relative motions between the dimensions is fixed at a constant rate, because the relative motion between the dimensions is measured relative to the relative motion. Thus the laws of physics, and all physical concepts, which are all fundamentally based on the concept of motion or change with respect to time, are also fixed in all interial frames, and the speed of light is constant in all inertail frames. As physics concerns itself at all levels with changes relative to both space and time, it makes sense that all physics, time, motion, reality, life, and consciousness itself are founded upon a stage which is endowed with intrinsic motion. The underlying fabric of all reality, the dimensions themselves, are moving relative to one another. === Subject: Re: Moving Dimensions Theory's simplicity: The fourth dimension is expanding relative to the three spatial dimension: dx4/dt =ic posting-account=51499wkAAAAr0khaExEjlNiEzK2ubANQ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Posting the same stupid crap over and over under different names doesn't make it any less stupid, it just shows that you are a jackass as well as an idiot. Paul Cardinale === Subject: A Spiral Converging posting-account=dGiPYgkAAABSJ3xUlNLViQdT0h489hR6 AppleWebKit/523.10.3 (KHTML, like Gecko) Version/3.0.4 Safari/523.10,gzip(gfe),gzip(gfe) Imagine a spiral that, as theta -> +infinity, the radius approaches a finite positive value from below. In other words, the spiral approaches a circle. An example of such a spiral might be r = arctan(theta) + pi/2. I have tried to find any named examples of famous types of spirals that fit the conditions. But I have had no luck. Have such spirals been examined in any math literature? Leroy Quet === Subject: Re: A Spiral Converging posting-account=dGiPYgkAAABSJ3xUlNLViQdT0h489hR6 AppleWebKit/523.10.3 (KHTML, like Gecko) Version/3.0.4 Safari/523.10,gzip(gfe),gzip(gfe) > Imagine a spiral that, as theta -> +infinity, the radius approaches a > finite positive value from below. > In other words, the spiral approaches a circle. An example of such a spiral might be > r = arctan(theta) + pi/2. I have tried to find any named examples of famous types of spirals > that fit the conditions. But I have had no luck. > Have such spirals been examined in any math literature? Leroy Quet Of course, in my example I am talking about the PRINCIPLE value (-pi/2 <= arctan <= pi/2) of the arctangent. Leroy Quet === Subject: Sklansky logic posting-account=B_ql5woAAABEePt1fDMNH7lHfjEScu4Z .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) In Tournament Poker for Advanced Players, David Sklansky states, as an axiom, something every player must (according to him) understand: In tournament play, a chip lost is worth more than a chip gained. ON THE LINE! What do you all think? Mark === Subject: Re: Sklansky logic > In Tournament Poker for Advanced Players, > David Sklansky states, as an axiom, something > every player must (according to him) understand: > In tournament play, a chip lost is worth more > than a chip gained. ON THE LINE! What do you all think? > Mark Absolutely true. That is why it is usually incorrect to value bet the river, without a very strong hand. === Subject: Re: Sklansky logic posting-account=CBZzyQkAAADa8LlO-8hxEObjm8IdMLIc CLR 1.1.4322),gzip(gfe),gzip(gfe) > In Tournament Poker for Advanced Players, > David Sklansky states, as an axiom, something > every player must (according to him) understand: > In tournament play, a chip lost is worth more > than a chip gained. ON THE LINE! What do you all think? Mark Absolutely true. That is why it is usually incorrect to value bet the river, > without a very strong hand. Which is why tournament players leave a lot of profit on the table in cash games, where value-bets on the river are a decent part of your profit. Opponents call so often just to make sure you aren't bluffing them that it more than makes up for the times the river bet is incorrect. It is also true that Sklansky is right but... Most decent players overdo the whole risk-avoidance thing. -- Will in New Haven === Subject: Binary GCD over multiple integers posting-account=18YlVwoAAAAxTRVG0TG5IrbRKJSXzkDr Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Does anyone have a reference to an extended binary GCD algorithm that will operate on more than two variables, and that can calculate the Bezout coefficients? variables: http://en.wikipedia.org/wiki/Binary_GCD_algorithm === Subject: Game: Criss-Cross posting-account=dGiPYgkAAABSJ3xUlNLViQdT0h489hR6 AppleWebKit/523.10.3 (KHTML, like Gecko) Version/3.0.4 Safari/523.10,gzip(gfe),gzip(gfe) Here is another one of my games. It isn't as fun, probably, as some of the other games I have posted. But maybe someone will find it enjoyable anyway. Start with an n-by-n grid (n-by-n lines, (n-1)-by-(n-1) row/columns) on graph-paper. (n should be at least 5, maybe in the range of 10 or more.) There are two players who switch roles after each round, an offensive player and a defensive player. Say the grid is n lines wide((n-1) columns) and n lines high ((n-1) rows). The defensive player starts the round by writing the integers 1 through (2n) in any order to the left of the left-most vertical line (each integer lined up with a different horizontal line of the grid) and above the top-most horizontal line (each integer lined up with a different vertical line of the grid). Whether a particular integer is written either along the left side of the grid or along the top of the grid is up to the defensive player. Example: 6 lines -by- 6 lines: . 2 6 11 7 1 8 9 ------------- 4 | + + + + + 10| + + + + + 12| + + + + + 3 | + + + + + 5 | + + + + + (Note: In case ascii art doesn't look correct, the pluses are the intersections of the grid, and are supposed to each be directly below an integer of the top row of numbers and directly to the right of the left column of numbers.) The two players each take turns drawing a straight line-segment (with a straightedge) from the intersection of the grid last drawn-to by the opposing player to an intersection determined by the order of the move within the round. If the move is move m -- the defensive player moves on even-numbered moves, and the offensive player moves on odd-numbered moves -- then the player can move to any intersection in the same row/column lined up with the m along the grid's edges. In other words, if the value m is written along the top of the grid, then the player on the mth move can move to any one of the n intersections in the same COLUMN as the value m. And if the value m is written along the left side of the grid, then the player on the mth move can move to any one of the n intersections in the same ROW as the value m. Players cannot draw line-segments along already drawn line-segments. (ie Line-segments can only intersect at most at one point.) Line-segments cannot cross intersections that are already the endpoints of other line-segments. After 2n total moves (m moves for each player), the round is over. The offensive player gets a point for every time a line-segment (drawn by either player) crosses another segment. If k line-segments intersect at a common point, the offensive player gets k(k-1)/2 points for that intersection. This is the same as counting the number of line-segments intersected by a line-segment AS the line-segment is being drawn. (If your line segment is crossing an intersection with (k-1) line-segments already intersecting there, then add (k-1) to the offensive player's score. Or wait until after the game is over to enumerate the crossings, and give the offensive player k(k-1)/2 points for those k line-segments intersecting at a common point.) So, the defensive player moves so as to try to keep the lines from crossing. The offensive player moves to try to get as many crossings as possible. After a round is complete the players switch who is the offensive player and who is the defensive player. The highest score wins, after playing an even number of rounds, of course. What is a good strategy for this game? Leroy Quet === Subject: Re: Game: Criss-Cross posting-account=dGiPYgkAAABSJ3xUlNLViQdT0h489hR6 AppleWebKit/523.10.3 (KHTML, like Gecko) Version/3.0.4 Safari/523.10,gzip(gfe),gzip(gfe) >.... After 2n total moves (m moves for each player), the round is over. >... Should be: *n* moves for each player. Leroy Quet === Subject: solution manual posting-account=iTxlnwgAAAB64K2QSuuHzYG-REAFf5OD 1.1.4322; .NET CLR 3.0.04506.30; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) Hey, I want the solution for: Money, the financial system, and the economy. By Glenn Hubbard. Does it show the work, or only the answer? Can you e-mailme back as soon as possible.