mm-312 === Subject: : precession and space curvature Does precession angle (or its rate) of its inclined planetary orbit determine curvature of space? One would imagine from 3D euclidean space geometry of precessingelliptic trajectories thus: The plane of ellipse itself is rotatedthrough an axis which is passing through ellipse center but making anangle alpha to its major axis 2a and perpendicular to minor axis 2b.The resulting motion takes place on an ellipsoid,cylinder or one sheethyperboloid according as Sin[alpha] is less, equal to, or greater thanb/a. Could not the space curvature be termed elliptic,hyperbolic etc.? === Subject: : Re: precession and space curvature> Does precession angle (or its rate) of its inclined planetary orbit> determine curvature of space?Local curviture is determined by the local mass-energySee: http://hermes.physics.adelaide.edu.au/~dkoks/Faq/ === Subject: : Re: precession and space curvature>Does precession angle (or its rate) of its inclined planetary orbit>determine curvature of space?>One would imagine from 3D euclidean space geometry of precessing>elliptic trajectories thus: The plane of ellipse itself is rotated>through an axis which is passing through ellipse center but making an>angle alpha to its major axis 2a and perpendicular to minor axis 2b.>The resulting motion takes place on an ellipsoid,cylinder or one sheet>hyperboloid according as Sin[alpha] is less, equal to, or greater than>b/a. Could not the space curvature be termed elliptic,hyperbolic etc.?I know what you are saying, but spacetime actually is curved.It is very difficult to visualize.Try and imagine, a series of balloons, with vinegar and sodiumin them, which is causing them to expand.Now place these in a lubricating fluid so they don't have muchfriction. They will spin as they expand. They will even spin, towardseach other. Or away from each other.And I can see where you are heading with this, that if they arespinning in the opposite direction, how come they follow thesame trajectory on the same orbit? It has to do with intrinsicmass. Each atom has mass. The expansion is the determining factor, the spin is secondary and a much weaker effect. It is just thatthe lubrication is such that it is etherial like em wavesthere is very little resistance, so things can spin one wayor another and it does not affect things much.Until you reach very high speeds.If you look at how fast the earth is turning, and how fast we aremoving around the sun, and yet we do not lean one way or the otherbecause we have intrinsic mass and we are in contact with the earth.I read somewhere today, that if it weren't for gravity,we would need a steel cable 8,000 miles thick, to maintainour orbit around the sun. Gravity is in every nucleus.It is not magnetic, because magnetism is the flow ofelectrons, but is like magnetism, because it contributes to the flow of black body radiation which forms high and low presure areasand as the universe expands - accellerating and that is the key,it is the accelleration of the expansion of the universecreating intrinsic mass. And that mass acts like a gyroscope.But a gyroscope spins. try the same thing with a air bagin a car dash. It has inertia. Stand on one as it expands. You will feel that inertia. I wish there was a better analogy,sop that you could visualize the fact that this accelleration, causing the nucleus to have intrinsic mass, is the nulcear force.That is on that scale a very strong force.On the astronimical scale, it adds up so that planets are round etc.The spinning is always over stated in importance. People havea real difficult time understanding the expansion of the universeor how matter acts in a gravity well.Keep in mind that on the molecular level, the nucleus does notcontact another nucleus. The nulceus is very tiny.The electron contacts other electrons and that forms moleculescrystal lattices etc. with a covalent bond. co valent.(In common.)So space-time curvature is spherical, as it begins on the atomic level. The closer you are to a massive body, the moreit curves, that is to say the closer the topographical lineswould be together. If you plot dots on these topographical lines,you have a gravitational field.if you wanted to. But they wouldn't tell you anything that GR doesn't already tell you. === Subject: : Re: Probability question (sports competition)>Let's say that we have 5 discus throwers in a competition. Each>competitor's distance of their throw can be modeled as a Normal>Distribution with different means but the same variance (and SD). >Say,>Thrower A, mean throw distance 115, variance 100 (SD 10)>Thrower B, mean throw distance 111, variance 100 (SD 10)>Thrower C, mean throw distance 109, variance 100 (SD 10)>Thrower D, mean throw distance 106, variance 100 (SD 10)>Thrower E, mean throw distance 100, variance 100 (SD 10)>I want to calculate the chances of Thrower B winning a particular>competition (if they only throw once in this made-up competition).>(And, of course, the chances of the other Throwers winning>competitions.)>I see that it can be modeled by taking a single sample from each>distribution, and then seeing which one is the maximum. Knowing the>distributions of each, isn't there some sort of mathematical formula>that can give me the results? I can set it up with a Monte Carlo>method, but I am really looking for an exact way to solve this. Can>anyone help? >Terminology:>X~N( m,v ), X follows the normal distribution with mean m and variance>v.>F_N( x, m, v ), intergral from -inf to x of the density function of N(>m,v )>Method:>Let,>X_i = Distance thrown by thrower i>Y_i = 1 if thrower i wins, 0 otherwise>m_i = mean of thrower i>v_i = variance of thrower i>Assume X_i~N( m_i, v_i ).>(Can in most cases be assumed to be true asymptotically given the>samples are large.)>Let>X_i,j = X_i - X_j>=> X_i,j ~ N( m_i-m_j, v_i+v_j )>=> P( X_i,j > x ) = 1 - F_N( x, m_i-m_j, v_i+v_j ), where x belongs to>the set of real numbers.>P( Y_B=1 ) = P( X_B,A > 0 )P( X_B,C > 0 )P( X_B,D > 0 )P( X_B,E > 0 ).> Not at all: your X_(i,j) are not independent.True, my mistake.-Sunny === Subject: : Re: definition of prime in number theory and algebra> but there are, in many number fields, elements that> [are irreducible but not prime]. E.g., 2 in Z[sqrt(-5)].There are simpler examples of a non-prime irreducible. Let J < Q[x] be the ring of integer-valued polys: f(Z) < Z.In J the irred 2|x(x+1) but neither 2|x nor 2|x+1.Let T = R + x C[x] be the ring of polynomials in x with complex coefs and with real constant coef.In T, x is irred: x = fg => f or g of deg 0 so a unitand x|(ix)^2 but not x|ix, so x isn't prime.More generally let R < T be a ring extension with new unitu in TR. In R + x T[x]: x|(ux)(x/u) but neither factor.E.g. Z + x Q[x], u = 2/3; note this ring lies between twoUFDs Z[x], Q[x] but isn't a UFD since irred x isn't prime,or, explicitly: x x = ux x/u is a nonunique factorization.Rings of this form are a rich source of (counter-) examples,e.g. see [1] for a survey. Alternatively one may construct a generic counterexample along the lines of my prior post [2].-Bill Dubuque[1] Muhammad Zafrullah, Various Facets of Rings between D[X] and K[X]http://www.lohar.com/researchpdf/axbx.pdf[2] http://google.com/groups?threadm=y8zznru8v1d.fsf% 40nestle.ai.mit.edu === Subject: : Re: definition of prime in number theory and algebra> but there are, in many number fields, elements that [are> irreducible but not prime]. E.g., 2 in Z[sqrt(-5)].> There are simpler examples of a non-prime irreducible.> Let J < Q[x] be the ring of integer-valued polys: f(Z) < Z. In J> the irred 2|x(x+1) but neither 2|x nor 2|x+1.> Let T = R + x C[x] be the ring of polynomials in x with complex coefs> and with real constant coef.> In T, x is irred: x = fg => f or g of deg 0 so a unit> and x|(ix)^2 but not x|ix, so x isn't prime.> More generally let R < T be a ring extension with new unit u in> TR. In R + x T[x]: x|(ux)(x/u) but neither factor.> E.g. Z + x Q[x], u = 2/3; note this ring lies between two UFDs> Z[x], Q[x] but isn't a UFD since irred x isn't prime, or,> explicitly: x x = ux x/u is a nonunique factorization.> Rings of this form are a rich source of (counter-) examples, e.g. see> [1] for a survey. Alternatively one may construct a generic> counterexample along the lines of my prior post [2].> -Bill Dubuque> [1] Muhammad Zafrullah, Various Facets of Rings between D[X] and K[X]> http://www.lohar.com/researchpdf/axbx.pdf> [2]> http://google.com/groups?threadm=y8zznru8v1d.fsf% 40nestle.ai.mit.eduOK, great, but I am still curious --- at what point did the commutativealgebra authors (and some if not most algebraic number theory authors)decide to call irreducible what we all call prime in high school math, and to use the term prime for a different property? Does this go back to Hilbert or even Dedekind?This must be initially confusing for students in algebra courses, or is it?I know the two notions are equivalent in the ring of integers, but it takes a bit of work to prove the equivalence (the first proof is apparently due to Gauss, around 1800).C === Subject: : Re: definition of prime in number theory and algebra Adjunct Assistant Professor at the University of Montana.>OK, great, but I am still curious --- at what point did the commutative>algebra authors (and some if not most algebraic number theory authors)>decide to call irreducible what we all call prime in high school >math, and to use the term prime for a different property? Does this go >back to Hilbert or even Dedekind?Dedekind certainly already distinguishes between irreducible and theprime divisor property, but then, so does Kummer in his famous workon ideal prime divisors. I think it was fermenting already from thetime of Gauss, if not earlier.>This must be initially confusing for students in algebra courses, or is it?Since in most algebra courses, definitions are given explicitly, ithsould not be.>I know the two notions are equivalent in the ring of integers,In fact, in any Unique Factorization Domain.> but it >takes a bit of work to prove the equivalence (the first proof is >apparently due to Gauss, around 1800).That sounds like the proof of the Fundamental Theorem of Arithmetic,rather than an explicit proof that all irreducibles have the primedivisor property (the prime divisor property, by the way, is that if pdivides a*b then it divides a or it divides b, and that goes back toEuclid!). It is very easy to see that the prime divisor property impliesirreducibility; the difficulty is the other way around (since it isnot always true). -- ============Arturo Magidinmagidin@math.berkeley.edu === Subject: : Re: definition of prime in number theory and algebra|> but it |>takes a bit of work to prove the equivalence (the first proof is |>apparently due to Gauss, around 1800).||That sounds like the proof of the Fundamental Theorem of Arithmetic,|rather than an explicit proof that all irreducibles have the prime|divisor property (the prime divisor property, by the way, is that if p|divides a*b then it divides a or it divides b, and that goes back to|Euclid!). Section II. 14. If neither a nor b can be divided by a prime number p, the product ab cannot be divided by p.I don't see a definition of prime number given, but apparently he'susing the definition as irreducible.He claims Euclid had already proved this theorem in his Elements.The citation is to Book VII, No. 32, but that doesn't seem right. Thatproposition reads Any number either is prime or is measured by aprime number. I assume the citation has a typo, but I don't seewhere the actual proposition is.This is only a guess, but I would guess that when the concept ofideal divisor entered number theory (now often just called ideal),the irreducible definition lost ground relative to the prime definition.An element being prime is the same as the ideal generated bythe element being a prime ideal. The ideal generated by an irreducibleelement has no similarly nice property as far as I know.It doesn'tfactor into nontrivial principal ideals, but when the element is notactually prime, this seems to me more like a manifestation of thefact that the ideal factors happen not to be principal.I think in early grades, the irreducible definition probably would seemless mysterious and less complicated, though, so I'm guessing thatit will persist.Keith Ramsay === Subject: : New yahoo group, important works availableMuch of my important work has been explained in greater detail throughfiles available through the MSN group I had set up for AmateurMathematicans.In the past, some of you have complained about MSN, and therequirement of implementing the MSN passport in order to access thisbody of work.Now I have addressed such objections by creating a new group on Yahoo,which should be easier to access. The address for the new group ishttp://groups.yahoo.com/group/trollsareus/Nevermind the group name, this was chosen in mock irony during amoment of realization that the group names on Yahoo simply can not beas descriptive as those on MSN due to space limitations.I have been thinking about resuming chat discussion sessions, and willbase my decision in part on the interest this new group garners overthe upcoming weeks.James Harris === Subject: : Re: New yahoo group, important works available> Much of my important work has been explained in greater detail through> files available through the MSN group I had set up for Amateur> Mathematicans.Professional loud morons.Hey stooopid loud troll James Harris, put up or shut up,http://www.rsasecurity.com/rsalabs/challenges/factoring/ faq.htmlhttp://www.rsasecurity.com/rsalabs/challenges/ factoring/numbers.htmlhttp://www.crank.net/harris.html It's not every braying jackass that gets a whole page at crank.netIs a $10,000 prize no questions asked too small to justify yoursubmission of two little prime numbers? Uncle Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals)Quis custodiet ipsos custodes? The Net! === Subject: : Re: New yahoo group, important works available> Much of my important work has been explained in greater detail through> files available through the MSN group I had set up for Amateur> Mathematicans.> In the past, some of you have complained about MSN, and the> requirement of implementing the MSN passport in order to access this> body of work.> Now I have addressed such objections by creating a new group on Yahoo,> which should be easier to access. The address for the new group is> http://groups.yahoo.com/group/trollsareus/> Nevermind the group name, this was chosen in mock irony during a> moment of realization that the group names on Yahoo simply can not be> as descriptive as those on MSN due to space limitations.> I have been thinking about resuming chat discussion sessions, and will> base my decision in part on the interest this new group garners over> the upcoming weeks.So instead of signing up with MSN, possible readers must sign up with Yahoo? === Subject: : Re: how can i estimate the number of eigenvalues of an sparse matrix>I have to solve an eigenvalue problem of some large sparse matrix(symmetric>real and about 60000*60000 , 500 non-zero elements).> I haven't found a good computing package to solve it under linux .Now I get>the arpack++ from the netlib , it works not so well ,does anyone have any>good sugestion ?>the second problem is how can i estimate the number of eigenvalues of that>sparse matrix (not need to be the exact accurate),. I need this parameter to>pass to the arpack++ function which can help me solve the problem.Any n x n matrix has n eigenvalues, counted by algebraic multiplicity (which is the same as geometric multiplicity for a symmetric matrix).Your matrix has only 500 nonzeros, where n > 500. Therefore its rankis at most 500, and 0 is an eigenvalue of multiplicity at least n - 500. There are at most 501 distinct eigenvalues.You might get better results if you start by throwing away all those rows and columns that have no nonzero entries.Robert Israel israel@math.ubc.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: : Re: Countable Ordinals >In ZF, how is the set of all countable ordinals> constructed or shown to exist?>One can show in ZF that, for any ordinal a, there exists a>cardinal k > a. The following proof is verbatim from Kunen:>Assume a >= omega. Let W = {R in P(a x a): R well-orders a}.>Let S = {type(): R in W} (S exists by Replacement).>Then sup(S) is a cardinal > a.>Let X be a set and R be a well-ordering of X. The (order)>type of the well-ordered set (Kunen's notation for the>ordered pair of X and R) is the unique ordinal order-isomorphic>to . Since type is a well-defined operator which yields a>unique set fro a given argument, one may apply the axiom of>Replacement to form the set S above.type requires recursion on well ordered sets.How about that, my reference shows recursion only for ordinals.However the given proof apparently generalizes to well ordered sets.Let X0 be the R first of X, set f(X0) = 0Let X_n' be the R next after X_n, set f(X_n') = f(X_n) + 1Let X_n not be the R-first nor a R-next, set f(X_n) = /{ f(X_j) | X_j <_R X_n }To show f(X) is ordinal, show for all eta in f(X) eta subset f(X) by transfinite induction.if eta = 0, 0 subset f(X)if eta = xi+1 and xi subset f(X): eta / { eta } subset f(X)if limit ordinal eta = /{ xi | xi < eta }, and for all xi < eta, xi subset f(X), then directly eta subset f(X)Thus tau = type = f(X)Is there any easier ways of doing all this?** In particular would you assist showing the next part:To show tau and X equinumerous one needs f is injection.Actually something stronger should be provable f(seg_a ) = f(a), seg_a X = { x in X | x <_R a }and that f(X) is order isomorphic ie, f is order isomophism between tau and Finally if eta is ordinal equinumerous X show some well ordering R in P(XxX) with eta = type Let p:eta -> X be the bijection and make well ordering with xRy <-> p^-1(x) < p^-1(y)Thus eta order isomorphic .Also from above tau = type order isomorphic Thus ordinals eta, tau order isomorphic, giving eta = tau. >The point is that we must first show that there exists an ordinal >which is not countable before we can apply the axiom of specification >to get a set of all the countable ones.Indeed, we must find an upper bound for every set we want to have.'Specificiation'? Likely same as 'Seperation'. Ok.---- === Subject: : Re: Countable Ordinals>>In ZF, how is the set of all countable ordinals>> constructed or shown to exist?>>One can show in ZF that, for any ordinal a, there exists a>cardinal k > a. The following proof is verbatim from Kunen:>Assume a >= omega. Let W = {R in P(a x a): R well-orders a}.>Let S = {type(): R in W} (S exists by Replacement).>Then sup(S) is a cardinal > a.>Let X be a set and R be a well-ordering of X. The (order)>type of the well-ordered set (Kunen's notation for the>ordered pair of X and R) is the unique ordinal order-isomorphic>to . Since type is a well-defined operator which yields a>unique set fro a given argument, one may apply the axiom of>Replacement to form the set S above.>type requires recursion on well ordered sets.>How about that, my reference shows recursion only for ordinals.>However the given proof apparently generalizes to well ordered sets.Yes, transfinite recursion applies to general well-ordered sets, and this fact does not require AC. Nor does theCounting Theorem. Each well-ordered set is order-isomorphic to a unique ordinal number.>[WE provides a proof and asks for simplification]I strongly urge you to take a look at Halmos, Naive Set Theory, particularly chapters 17 through 20 thereof (his chapters are quite brief). He has clear and succinct proofs of all these facts. And as I have oft recommended, I think that this accessible little book is a gem that every mathematician really ought to read at least once. I think you, William, will enjoy it in particular.> [...]>Indeed, we must find an upper bound for every set we want to have.>'Specificiation'? Likely same as 'Seperation'. Ok.Yes, I think we determined in another thread that specification and separation are synonymous.Best regards,-- Stephen J. Herschkorn herschko@rutcor.rutgers.edu === Subject: : Re: Counterexample: A path- but not locally connected subset in =?iso-8859-1?Q?R=B2?=> I am searching for a subset of the Euclidean plane that is path> connected but not locally connected in *any* point. >Consider > {(1+ r e^{it})^2: 0 <= r < infinity, 0 < t < Pi, t rational} >in the complex plane.1 + 2r.e^it + r^2 e^(2it)1 + 2r.cos t + r^2.cos 2t + 2ri.sin t + r^2.i.sin 2tWhy isn't that space locally connected at 1 ?It doesn't work here.---- === Subject: : Re: Counterexample: A path- but not locally connected subset in =?iso-8859-1?Q?R=B2?=>> I am searching for a subset of the Euclidean plane that is path>> connected but not locally connected in *any* point.>Consider> {(1+ r e^{it})^2: 0 <= r < infinity, 0 < t < Pi, t rational}>in the complex plane.>1 + 2r.e^it + r^2 e^(2it)>1 + 2r.cos t + r^2.cos 2t + 2ri.sin t + r^2.i.sin 2t>Why isn't that space locally connected at 1 ?Because any neighbourhood of 1 contains pieces of curves (for t near Pi)in the lower half plane that only connect back to 1 by looping around 0.Robert Israel israel@math.ubc.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: : Re: I WILL GET MY MONEY> etc.....Its been a while since I laughed this hard.Van === Subject: : Re: Criterion of isomorphic finite groups> Given two finite groups, how can we determine whether they are> isomorphic or not without using the brute force method?I had this problem when developing my Mathematica programmeHoopalgebras.nb, available athttp://library.wolfram.com/infocenter/MathSource/4894. I needed to beable to identify any associative small (up to say 72 elements) Cayleytable. A generalised diagonal count went a long way, identifying manygroups, but a variety of table-invariant tests had to be added.Tests for the number of specific subgroups or factorgroups are oftenrequired. Routines are supplied to create Cayley tables, and id canthen give the location in the Gap atlas (I generated the Cayley tablesusing Gap). I still have not sorted out all the 64-element groups.Roger Beresford.'Go round-about said the Boyg' (Peer Gynt) === Subject: : Finding a beautiful proof for a propositionI was given the following prposition: Let D be a subset of R^n andsuppose every continuous function f:D-> R^m is bounded. Then, D iscompact.I gave the following proof, based on the contrapositive of theproposition:If D is not compact, then D is not bounded or not closed (Heine- BorelTheorem). If D is not bounded, then, for every x in D, define f(x) =||x||. Then, f is continuous and, for every M>0, we can find x in Dsuch that f(x) = ||x|| > M, which shows f is not bounded. So, in thiscase the contrapositive of the prposition holds.If D is not closed, then D has a limit point p that does not belong toD. Therefore, the function f given by f(x) = 1/||x-p|| is defined andcontinuous on the whole D. Since p is a limit point of D, then,keeping x in D, it's possible to make ||x-p||>0 as small as desired,which implies f(x) can be made > M for every M>0. Therefore, f is notbounded on D.We see the contrapositive of the proposition, and the therefore theproposition, are always true. This completes the proof.I think this is OK, but a guy who is considered really good at mathsaid my proof wasn't good enough because (1) It's based oncontradiction and not on direct arguments; (2) It uses Heine BorelTheorem and not the definition of compactness and (3) the mostimportant in his opinion, I invented particular functions not boundedon D it it's not compact.Actually, I think my proof uses contraposition and not contradiction.But anyway, what's wrong which such proofs? When, like in this case,you have the universal quantifier for every, it's almost alwaysreally easier to prove the contrapositive. It's true that in such caseyou have to produce a kind of counter example, invent something, but,again, what's the problem? When you prove those sequential criteriafor continuity and existence of limit at a point of a set, you usuallytake contrapositive arguments, even rigorous authors do that.And as for Heine Borel Theorem, well, I think the proble gets reallycomplicated if we think of open covers for D. But Heine Borel theoremholds in R^n, so is there any problem with susing it? I dont see why.Now, I have a question I couldn't answr and would like some help. Ifinstead of Euclidean spaces, f was a function between generic metricspaces, then does the proposition remain true? I thought of takingD=R1, R1 being R with the discreete topology, so that every functiondefined on R becomes continuous. Now, if we make R2=R, R with anymetric that makes it bounded (could be the discreete metric again),then every f:R1->R2 is continuous (actually, uniformly continuous) andbounded on R1, but R1 is not compact. So, the answer is no, theprposition doesnt hold for functions between general metric spaces.But this example really looks somewhat farfetched.Merry Xmas to everybody!Amanda === Subject: : Re: Finding a beautiful proof for a proposition>I was given the following prposition: Let D be a subset of R^n and>suppose every continuous function f:D-> R^m is bounded. Then, D is>compact.>I gave the following proof, based on the contrapositive of the>proposition:>If D is not compact, then D is not bounded or not closed (Heine- Borel>Theorem). If D is not bounded, then, for every x in D, define f(x) =>||x||. Then, f is continuous and, for every M>0, we can find x in D>such that f(x) = ||x|| > M, which shows f is not bounded. So, in this>case the contrapositive of the prposition holds.>If D is not closed, then D has a limit point p that does not belong to>D. Therefore, the function f given by f(x) = 1/||x-p|| is defined and>continuous on the whole D. Since p is a limit point of D, then,>keeping x in D, it's possible to make ||x-p||>0 as small as desired,>which implies f(x) can be made > M for every M>0. Therefore, f is not>bounded on D.>We see the contrapositive of the proposition, and the therefore the>proposition, are always true. This completes the proof.>I think this is OK, but a guy who is considered really good at math>said my proof wasn't good enough because (1) It's based on>contradiction and not on direct arguments;This is a mistake. The argument is NOT based on a contradiction. It isbased on the contrapositive, which is different. You gave a directproof of the contrapositive.> (2) It uses Heine Borel>Theorem and not the definition of compactnessIs the theorem true in general, or just for subsets of R^n with thestandard topology? If the latter, then using Heine-Borel is not reallyan obstacle: at some point you will have to use some property of R^nthat is not necessarily shared by arbitrary topological spaces, andtherefore, Heine-Borel is as good as any other.> and (3) the most>important in his opinion, I invented particular functions not bounded>on D it it's not compact.Why is this a problem?>Actually, I think my proof uses contraposition and not contradiction.Correct.>But anyway, what's wrong which such proofs? Nothing.>When, like in this case,>you have the universal quantifier for every, it's almost always>really easier to prove the contrapositive. It's true that in such case>you have to produce a kind of counter example, invent something, but,>again, what's the problem? I think his/her problem is that your proof is not the proof he/she hadin mind... [.snip.]-- ============Arturo Magidinmagidin@math.berkeley.edu === Subject: : Re: Finding a beautiful proof for a propositionContent-transfer-encoding: 8bit>I was given the following prposition: Let D be a subset of R^n and>suppose every continuous function f:D-> R^m is bounded. Then, D is>compact.>I gave the following proof, based on the contrapositive of the>proposition:>If D is not compact, then D is not bounded or not closed (Heine- Borel>Theorem). If D is not bounded, then, for every x in D, define f(x) =>||x||. Then, f is continuous and, for every M>0, we can find x in D>such that f(x) = ||x|| > M, which shows f is not bounded. So, in this>case the contrapositive of the prposition holds.>If D is not closed, then D has a limit point p that does not belong to>D. Therefore, the function f given by f(x) = 1/||x-p|| is defined and>continuous on the whole D. Since p is a limit point of D, then,>keeping x in D, it's possible to make ||x-p||>0 as small as desired,>which implies f(x) can be made > M for every M>0. Therefore, f is not>bounded on D.>We see the contrapositive of the proposition, and the therefore the>proposition, are always true. This completes the proof.>I think this is OK, but a guy who is considered really good at math>said my proof wasn't good enough because (1) It's based on>contradiction and not on direct arguments;> This is a mistake. The argument is NOT based on a contradiction. It is> based on the contrapositive, which is different. You gave a direct> proof of the contrapositive.But, logically, isn't it true that the equivalence of a statement toits contrapositive, and the method of proof by contradiction, are bothconsequences of the law of the excluded middle? impliction a ==> b means (~a) v b contrapos ~b ==> ~a means (~~b) v ~aBut to deduce that these are the same requires that ~~b = b, and isn'tthat equivalent to the law of the excluded middle (which I assume is bv (~b))?I don't see any difference between proof by contradiction and proof bycontrapositive, except stylistic.In general, I agree it's better to give direct arguments instead ofproofs by contradiction, on stylistic grounds. (Also on practicalgrounds, that you're more likely to satisfy those who reject the law ofthe excluded middle; but as the REST of your argument is unlikely tosatisfy them anyway, this isn't a very important reason.)--Ron Bruck === Subject: : Re: Finding a beautiful proof for a proposition>I was given the following prposition: Let D be a subset of R^n and>suppose every continuous function f:D-> R^m is bounded. Then, D is>compact.>I gave the following proof, based on the contrapositive of the>proposition:>If D is not compact, then D is not bounded or not closed (Heine- Borel>Theorem). If D is not bounded, then, for every x in D, define f(x) =>||x||. Then, f is continuous and, for every M>0, we can find x in D>such that f(x) = ||x|| > M, which shows f is not bounded. So, in this>case the contrapositive of the prposition holds.>If D is not closed, then D has a limit point p that does not belong to>D. Therefore, the function f given by f(x) = 1/||x-p|| is defined and>continuous on the whole D. Since p is a limit point of D, then,>keeping x in D, it's possible to make ||x-p||>0 as small as desired,>which implies f(x) can be made > M for every M>0. Therefore, f is not>bounded on D.>We see the contrapositive of the proposition, and the therefore the>proposition, are always true. This completes the proof.>I think this is OK, but a guy who is considered really good at math>said my proof wasn't good enough because (1) It's based on>contradiction and not on direct arguments;> This is a mistake. The argument is NOT based on a contradiction. It is> based on the contrapositive, which is different. You gave a direct> proof of the contrapositive.>But, logically, isn't it true that the equivalence of a statement to>its contrapositive, and the method of proof by contradiction, are both>consequences of the law of the excluded middle?> impliction a ==> b means (~a) v b> contrapos ~b ==> ~a means (~~b) v ~a>But to deduce that these are the same requires that ~~b = b, and isn't>that equivalent to the law of the excluded middle (which I assume is b>v (~b))?>I don't see any difference between proof by contradiction and proof by>contrapositive, except stylistic.Truth tables are not proofs. Hmm, maybe more what I meant to say isthis: a method of proof is not the same thing as a proof that thatmethod is valid. Anyway, there's a big difference between a proofby contradiction and a proof of the contrapositive:By definition (in some formal systems) a proof of A -> Bproceeds by assuming A and deducing B. A proof of the contrapositivebegins by assuming ~B and deducing ~A. In neither of these proofsdo we assume anything contradictory; 0 = 1 is never a consequenceof the current assumptions. On the other hand, a proof of A -> Bby contradiction begins by assuming A and ~B and deducingP and ~P for some P.There really is a difference. There's no point in the proof thatAmanda gave, that her colleague erroneously called a proofby contradiction, where it would have been correct to sayhence 0 = 1. While that _is_ a valid conclusion at somepoint in a proof by contradiction.It may well be that people with funny views about the_validity_ of proof by contradiction would have the sameviews about proving an implication by proving the contrapositive. That doesn't imply that the two are thesame thing.>In general, I agree it's better to give direct arguments instead of>proofs by contradiction, on stylistic grounds. (Also on practical>grounds, that you're more likely to satisfy those who reject the law of>the excluded middle; but as the REST of your argument is unlikely to>satisfy them anyway, this isn't a very important reason.)>--Ron Bruck************************David C. Ullrich === Subject: : Re: Finding a beautiful proof for a proposition Adjunct Assistant Professor at the University of Montana. [.snip.]> This is a mistake. The argument is NOT based on a contradiction. It is> based on the contrapositive, which is different. You gave a direct> proof of the contrapositive.>But, logically, isn't it true that the equivalence of a statement to>its contrapositive, and the method of proof by contradiction, are both>consequences of the law of the excluded middle?The equivalence, yes; and I guess, in this instance, you are alsoinvoking exlcuded middle.But the objection of the individual was not based on the problem withexcluded middle; it seemed to be with proofs by contradiction ingeneral. In a proof by contradiction, you have more hypothesis atyour disposal.> implication a ==> b means (~a) v b> contrapos ~b ==> ~a means (~~b) v ~a>But to deduce that these are the same requires that ~~b = b, and isn't>that equivalent to the law of the excluded middle (which I assume is b>v (~b))?>I don't see any difference between proof by contradiction and proof by>contrapositive, except stylistic.Well, depends on the statement, but that is also true for a proof bycontradiction. It is false that rejecting excluded middle impliesrejecting all proofs by contradiction, and likewise, there are proofsby contrapositive that may be done without invoking excluded middle(since (a->b) -> (~b -> ~a) is valid even without excluded middle).>In general, I agree it's better to give direct arguments instead of>proofs by contradiction, on stylistic grounds. (Also on practical>grounds, that you're more likely to satisfy those who reject the law of>the excluded middle; but as the REST of your argument is unlikely to>satisfy them anyway, this isn't a very important reason.)But it is also important not to confuse proof by contrapositive withproof by contradiction, and certainly not proof by contradictionwith using the excluded middle. The objection that was raised wassimply false: the proof was ->not<- a proof by contradiction. -- ============Arturo Magidinmagidin@math.berkeley.edu === Subject: : Re: Finding a beautiful proof for a proposition>I was given the following prposition: Let D be a subset of R^n and>suppose every continuous function f:D-> R^m is bounded. Then, D is>compact.>I gave the following proof, based on the contrapositive of the>proposition:>If D is not compact, then D is not bounded or not closed (Heine- Borel>Theorem). If D is not bounded, then, for every x in D, define f(x) =>||x||. Then, f is continuous and, for every M>0, we can find x in D>such that f(x) = ||x|| > M, which shows f is not bounded. So, in this>case the contrapositive of the prposition holds.>If D is not closed, then D has a limit point p that does not belong to>D. Therefore, the function f given by f(x) = 1/||x-p|| is defined and>continuous on the whole D. Since p is a limit point of D, then,>keeping x in D, it's possible to make ||x-p||>0 as small as desired,>which implies f(x) can be made > M for every M>0. Therefore, f is not>bounded on D.>We see the contrapositive of the proposition, and the therefore the>proposition, are always true. This completes the proof.>I think this is OK, but a guy who is considered really good at math>said my proof wasn't good enough because (1) It's based on>contradiction and not on direct arguments; (2) It uses Heine Borel>Theorem and not the definition of compactness and (3) the most>important in his opinion, I invented particular functions not bounded>on D it it's not compact.I think it's fine - none of these objections makes much sense to me.Well, (2) makes some sense, but see below and then ask himhow _he'd_ prove it using just the definition in terms of open covers.The other two objections don't make any sense to me (and I'malso considered really good at math, so there.)>Actually, I think my proof uses contraposition and not contradiction.That's correct.>But anyway, what's wrong which such proofs? There's nothing wrong with proving something by provingthe contrapositive. For that matter, there's nothing reallywrong with proofs by contradiction. There are two reasonspeople sometimes feel that you should avoid proofs bycontradiction if you can: (i) it's easy to give a wrong proof by contradiction, where the contradiction arises from some error (ii) if you give a direct proof that A implies B, by assumingA and then deducing B, the steps in the proof can givesome insight into what A really entails - you show A impliesB by showing A implies C and C implies B, and along theway you've shown two facts that might be interesting anduseful elsewhere, that A implies C and that C implies B.You don't get this sort of bonus from a proof by contradiction,since in the course of the proof you're assuming thingswhich it turns out never actually hold.But that's proof by _contradiction_, not proving thecontrapositive - (ii) doesn't apply to a proof of thecontrapositive, since it could well be that you learnthat not B implies C and that C implies not A.>When, like in this case,>you have the universal quantifier for every, it's almost always>really easier to prove the contrapositive. It's true that in such case>you have to produce a kind of counter example, invent something, but,>again, what's the problem? When you prove those sequential criteria>for continuity and existence of limit at a point of a set, you usually>take contrapositive arguments, even rigorous authors do that.>And as for Heine Borel Theorem, well, I think the proble gets really>complicated if we think of open covers for D. But Heine Borel theorem>holds in R^n, so is there any problem with susing it? I dont see why.Well, a proof that used only the definition of compactness withoutusing the Heine-Borel theorem would be better, because it wouldimply a stronger result.>Now, I have a question I couldn't answr and would like some help. If>instead of Euclidean spaces, f was a function between generic metric>spaces, then does the proposition remain true? I thought of taking>D=R1, R1 being R with the discreete topology, so that every function>defined on R becomes continuous. Now, if we make R2=R, R with any>metric that makes it bounded (could be the discreete metric again),>then every f:R1->R2 is continuous (actually, uniformly continuous) and>bounded on R1, but R1 is not compact. So, the answer is no, the>prposition doesnt hold for functions between general metric spaces.>But this example really looks somewhat farfetched.[Um, it's discrete. Discreet is also a word, meaning somethingelse; there's no such word as discreete.]The example shows that the proposition is false for a functionfrom one metric space to another. But that's not really theinteresting question, in my opinion, because it's too easy.The interesting question is this: If X is a metric space andevery continuous function from X to R (with the standardmetric!) is bounded, does it follow that X is compact?The answer's no if X is just a _topological_ space insteadof a metric space. (Which shows that the proof for subsetsof R^n can't use _just_ the definition in terms of opencovers, it _must_ use something else like Heine-Borelor at least the fact that you have a metric space, forexample the characterization of compactness in termsof sequential compactness.)I suspect that answer is yes if X is a metric space, althoughI don't see the proof after a minute's thought.>Merry Xmas to everybody!>Amanda************************David C. Ullrich === Subject: : Re: Finding a beautiful proof for a proposition <5e6juv4ktgrtu3jb074gb5b86klmt09uau@4ax.com>> The interesting question is this: If X is a metric space and> every continuous function from X to R (with the standard ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^> metric!) is bounded, does it follow that X is compact? ^^^^^^^^^^^^^^^^^^^That's the definition of pseudocompactness. Let me quote from sectionKenneth Kunen and Jerry E. Vaughan (editors), Handbook ofSet-Theoretic Topology (North-Holland, 1984), 347-422:A space X is pseudocompact if every continuous real valuedfunction on X has a bounded range. It is well known that a normalspace X is pseudocompact if and only if X is countably compact.[. . .]The next result is due independently to SCOTT [1979] and WATSON[1981].9.6. THEOREM. A Tychonoff, pseudocompact, metacompact space X iscompact.[. . .]The next result is due to BURKE and DAVIS [1982]. The proof can beextended to cover the sigma-para-Lindelof case.9.7. THEOREM. A Tychonoff pseudocompact para-Lindelof space X iscompact.[. . .]pseudocompact, meta-Lindelof space which is not compact.Burke gives the following references:D. K. Burke and S. W. Davis, Pseudocompact paralindelof spaces arecompact, Abstracts Amer. Math. Soc. 3 (1982), 213.B. M. Scott, Pseudocompact, metacompact spaces are compact, TopologyProc. 4 (1979), 577-587.W. S. Watson, Pseudocompact metacompact spaces are compact, Proc.Amer. Math. Soc. 81 (1981), 151-152. === Subject: : Re: Finding a beautiful proof for a proposition> The interesting question is this: If X is a metric space and> every continuous function from X to R (with the standard> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^> metric!) is bounded, does it follow that X is compact?> ^^^^^^^^^^^^^^^^^^^>That's the definition of pseudocompactness. Ah - I figured it must be the definition of compactnessfor a suitable value of prefix...>Let me quote from section>Kenneth Kunen and Jerry E. Vaughan (editors), Handbook of>Set-Theoretic Topology (North-Holland, 1984), 347-422:>A space X is pseudocompact if every continuous real valued>function on X has a bounded range. It is well known that a normal>space X is pseudocompact if and only if X is countably compact.>[. . .]>The next result is due independently to SCOTT [1979] and WATSON>[1981].>9.6. THEOREM. A Tychonoff, pseudocompact, metacompact space X is>compact.>[. . .]>The next result is due to BURKE and DAVIS [1982]. The proof can be>extended to cover the sigma-para-Lindelof case.>9.7. THEOREM. A Tychonoff pseudocompact para-Lindelof space X is>compact.>[. . .]>pseudocompact, meta-Lindelof space which is not compact.>Burke gives the following references:>D. K. Burke and S. W. Davis, Pseudocompact paralindelof spaces are>compact, Abstracts Amer. Math. Soc. 3 (1982), 213.>B. M. Scott, Pseudocompact, metacompact spaces are compact, Topology>Proc. 4 (1979), 577-587.>W. S. Watson, Pseudocompact metacompact spaces are compact, Proc.>Amer. Math. Soc. 81 (1981), 151-152.************************David C. Ullrich === Subject: : Re: Finding a beautiful proof for a proposition>I was given the following prposition: Let D be a subsetof R^n and>suppose every continuous function f:D-> R^m is bounded.Then, D is>compact.> [ . . . ]> I suspect that answer is yes if X is a metric space,although> I don't see the proof after a minute's thought.>Merry Xmas to everybody!>Amanda> ************************> David C. Ullrich****************************************************** Yes, it is true for a metric space. If a subset D of ametric space X is not compact, then it is not closed or itis not totally bounded. The former case can be treated aspreviously shown. If D is not totally bounded, then forsome e>0 there exists a sequence {x_n} of points in D suchthat d(x_n, x_m) > 2e for each m /= n. Let f_n(x) = n (1 - d(x, x_n)/e), if d(x, x_n) < e = 0, otherwise.Let f(x) = sum (f_n(x), n = 1, 2, . . .). Then f iscontinuous on D and unbounded.____________________________________________________ _____Eric J. Wingler (wingler@math.ysu.edu)Dept. of Mathematics and StatisticsYoungstown State UniversityOne University PlazaYoungstown, OH 44555-0001330-941-1817 === Subject: : Re: Finding a beautiful proof for a proposition>I was given the following prposition: Let D be a subset> of R^n and>suppose every continuous function f:D-> R^m is bounded.> Then, D is>compact.> [ . . . ]> I suspect that answer is yes if X is a metric space,> although> I don't see the proof after a minute's thought.>Merry Xmas to everybody!>Amanda> ************************> David C. Ullrich> ******************************************************> Yes, it is true for a metric space. If a subset D of a> metric space X is not compact, then it is not closed or it> is not totally bounded. There's a mistake here, right? If D is not compact, then D is nottotally bounded, like you said, and not COMPLETE. For example, if youconsider (0,1) with the Euclidean metric as a metric space itself,then it is totally bounded, is closed, but it is not complete. (1/n),n=2,3 is a Cauchy sequence in (0, 1) that does not converge at all.And actually, (0,1) is not compact. The collection of the openintervals {(1/n, 1-1/n), n=3, 4, 5...is} covers (0,1), but the unionof every finite subcollection is a proper subset of (0,1).Amanda The former case can be treated as> previously shown. If D is not totally bounded, then for> some e>0 there exists a sequence {x_n} of points in D such> that d(x_n, x_m) > 2e for each m /= n. Let> f_n(x) = n (1 - d(x, x_n)/e), if d(x, x_n) < e> = 0, otherwise.> Let f(x) = sum (f_n(x), n = 1, 2, . . .). Then f is> continuous on D and unbounded.> _________________________________________________________> Eric J. Wingler (wingler@math.ysu.edu)> Dept. of Mathematics and Statistics> Youngstown State University> One University Plaza> Youngstown, OH 44555-0001> 330-941-1817 === Subject: : Re: Finding a beautiful proof for a proposition> Yes, it is true for a metric space. If a subset D of a> metric space X is not compact, then it is not closed orit> is not totally bounded.> There's a mistake here, right? If D is not compact, then Dis not> totally bounded, like you said, and not COMPLETE.******************************************Yes, you are correct. I should have said that if D is notcompact, then D is not totally bounded or not complete. Myproof for the not totally bounded case still works, butnow I need to do the not complete case._________________________________________________________ Eric J. Wingler (wingler@math.ysu.edu)Dept. of Mathematics and StatisticsYoungstown State UniversityOne University PlazaYoungstown, OH 44555-0001330-941-1817 === Subject: : Re: Finding a beautiful proof for a proposition>I was given the following prposition: Let D be a subset>of R^n and>suppose every continuous function f:D-> R^m is bounded.>Then, D is>compact.> [ . . . ]> I suspect that answer is yes if X is a metric space,>although> I don't see the proof after a minute's thought.>Merry Xmas to everybody!>Amanda> ************************> David C. Ullrich>****************************************************** >Yes, it is true for a metric space. If a subset D of a>metric space X is not compact, then it is not closed or it>is not totally bounded. Yeah, I thought of that, but a more elementary proofseemed better.Also you didn't state the theorem quite correctly.(For example let X be the half-open interval[0,1) with the usual metric, and let D = X. ThenD is closed and totally bounded but it's notcompact.)What you meant is that if the metric space X isnot compact then it's not _complete_ or nottotally bounded. If X is not complete then youcan reason more or less as previously, butnot exactly, because you don't have a sequencethat converges to a point not in X, instead youjust have a Cauchy sequence that does notconverge. (If (x_n) is a Cauchy sequence thatdoes not converge then you could letg(x) = lim d(x, x_n), show the limit exists,show that g is continuous and strictly positive,and then f = 1/g will be an unbounded continuousfunction. But there are a few details to beworked out here...)>The former case can be treated as>previously shown. If D is not totally bounded, then for>some e>0 there exists a sequence {x_n} of points in D such>that d(x_n, x_m) > 2e for each m /= n. Let> f_n(x) = n (1 - d(x, x_n)/e), if d(x, x_n) < e> = 0, otherwise.>Let f(x) = sum (f_n(x), n = 1, 2, . . .). Then f is>continuous on D and unbounded.>___________________________________________________ ______>Eric J. Wingler (wingler@math.ysu.edu)>Dept. of Mathematics and Statistics>Youngstown State University>One University Plaza>Youngstown, OH 44555-0001>330-941-1817************************David C. Ullrich === Subject: : Re: Finding a beautiful proof for a proposition>[...]>The example shows that the proposition is false for a function>from one metric space to another. But that's not really the>interesting question, in my opinion, because it's too easy.>The interesting question is this: If X is a metric space and>every continuous function from X to R (with the standard>metric!) is bounded, does it follow that X is compact?>The answer's no if X is just a _topological_ space instead>of a metric space. (Which shows that the proof for subsets>of R^n can't use _just_ the definition in terms of open>covers, it _must_ use something else like Heine-Borel>or at least the fact that you have a metric space, for>example the characterization of compactness in terms>of sequential compactness.)>I suspect that answer is yes if X is a metric space, although>I don't see the proof after a minute's thought.Ah, here's a simple proof. Say X is a non-compact metricspace. As noted above, we need to use some fact that'sspecific to metric spaces; say (x_n) is a sequence withno convergent subsequence. Suppose as well thatx_n <> x_m when n <> m.Since the sequence has no convergent subsequence,in particular none of the points of the sequence isthe limit of a subsequence, so for every n thereexists r_n > 0 such that B(x_n, r_n) does not containany x_m except for x_n. We can also assume r_n -> 0(this is important in the details that I omit below).Now using the function d(x, x_n), you can constructa continuous function f_n >= 0 such that f_n(x_n) = nwhile f_n(x) = 0 for all x in the complement of B(x_n, r_n). Let f be the sum of the f_n.You need to show that the sum actually convergesand that it defines a continuous function - thisfollows from the fact that (x_n) has no convergentsubsequence and r_n -> 0. It's clear that f is unbounded.>Merry Xmas to everybody!>Amanda************************David C. Ullrich === Subject: : Re: Finding a beautiful proof for a proposition>> [...]> The example shows that the proposition is false for a function> from one metric space to another. But that's not really the> interesting question, in my opinion, because it's too easy.> The interesting question is this: If X is a metric space and> every continuous function from X to R (with the standard> metric!) is bounded, does it follow that X is compact?> The answer's no if X is just a _topological_ space instead> of a metric space. (Which shows that the proof for subsets> of R^n can't use _just_ the definition in terms of open> covers, it _must_ use something else like Heine-Borel> or at least the fact that you have a metric space, for> example the characterization of compactness in terms> of sequential compactness.)And in fact, the long line L ([0,1) * w_1, with topology oflexicographic order) is an famous counterexample; any countinuous functionfrom L to IR is not only bounded, but constant for x large enough. As L islocally compacr (and in fact any initial segment of L is isomorph to[0,+oo) ), it follows indeed that sequential properties are the key..> I suspect that answer is yes if X is a metric space, although> I don't see the proof after a minute's thought.> Ah, here's a simple proof. Say X is a non-compact metric> space. As noted above, we need to use some fact that's> specific to metric spaces; say (x_n) is a sequence with> no convergent subsequence. Suppose as well that> x_n <> x_m when n <> m.> Since the sequence has no convergent subsequence,> in particular none of the points of the sequence is> the limit of a subsequence, so for every n there> exists r_n > 0 such that B(x_n, r_n) does not contain> any x_m except for x_n. We can also assume r_n -> 0> (this is important in the details that I omit below).> Now using the function d(x, x_n), you can construct> a continuous function f_n >= 0 such that f_n(x_n) = n> while f_n(x) = 0 for all x in the complement of> B(x_n, r_n). Let f be the sum of the f_n.> You need to show that the sum actually converges> and that it defines a continuous function - this> follows from the fact that (x_n) has no convergent> subsequence and r_n -> 0. It's clear that f is unbounded.>> Merry Xmas to everybody!>> Amanda> ************************> David C. Ullrich === Subject: : Re: Finding a beautiful proof for a proposition> [...]>> The example shows that the proposition is false for a function>> from one metric space to another. But that's not really the>> interesting question, in my opinion, because it's too easy.>> The interesting question is this: If X is a metric space and>> every continuous function from X to R (with the standard>> metric!) is bounded, does it follow that X is compact?>> The answer's no if X is just a _topological_ space instead>> of a metric space. (Which shows that the proof for subsets>> of R^n can't use _just_ the definition in terms of open>> covers, it _must_ use something else like Heine-Borel>> or at least the fact that you have a metric space, for>> example the characterization of compactness in terms>> of sequential compactness.)>And in fact, the long line L ([0,1) * w_1, with topology of>lexicographic order) is an famous counterexample; any countinuous function>from L to IR is not only bounded, but constant for x large enough. As L is>locally compacr (and in fact any initial segment of L is isomorph to>[0,+oo) ), it follows indeed that sequential properties are the key..Actually the counterexample I had in mind was just w_1 itself.************************David C. Ullrich === Subject: : Re: Bilateral condensation points in R >> Interesting problem. An exercise from topology class or text? >No. Actually, I was trying to prove the following proposition a >fellow gave me: If uncountable S is a subset of R, then S contains >a subset T with the property that, for every distinct elements x and >y in T, there's a z in T between x and y. I noticed this proposition >is just a corollary of if S is uncountable, then every element of >B/S is a bilateral condensation point of B/S, B defined as >before. Anyway, there are different approachs to prove my fellow's >proposition.Seems you enjoy math.This problem is equivalent to showing for uncountable S,S is somewhere dense, that is not nowhere dense; int cl S /= nulsetA somewhere dense when A not nowhere dense iff some open nonnul U with cl U = cl U/A iff some open nonnul U with U subset cl A---- === Subject: : Finding a beautiful proof for a propositionHey, in my other post the function f was from R^n to R, not to R^m.But if it`s fron R^n to R^m, the same arguments can be slight modifiedto lead to the same conclusion.Amanda === Subject: : Re: Hexadecimal leads to insight.> Sure, math has little to do with actual numbersPardon? === Subject: : Re: Applications of Eigenvectors!?>5) If M represents a rotation matrix, the eigenvector represents the axis>of rotation. (Unless the rotation is through an angle of 0 there is just>one real eigenvalue.)> You might want to revise this one a bit.> Lee RudolphOops, quite right.--Dan Grubb === Subject: : Re: Applications of Eigenvectors!?>5) If M represents a rotation matrix, the eigenvector represents the axis>of rotation. (Unless the rotation is through an angle of 0 there is just>one real eigenvalue.)> You might want to revise this one a bit.> Lee Rudolph>Oops, quite right.And there, class, is a nice example of a participant in an argument^Wdiscussion gracefully doing a 180.Lee Rudolph === Subject: : Re: Applications of Eigenvectors!?>5) If M represents a rotation matrix, the eigenvector represents the axis>of rotation. (Unless the rotation is through an angle of 0 there is just>one real eigenvalue.)> You might want to revise this one a bit.> Lee Rudolph>Oops, quite right.> And there, class, is a nice example of a participant in an> argument^Wdiscussion gracefully doing a 180.eigenvalue -1Dirk Vdm === Subject: : Re: Interest in language> *Caveat*: this is what my good ol' Italian/Latin (and *vice versa*)> dictionary says, modulo my translation into English... ^^^^^^^^^^>videlicet doesn't have an original meaning, it has an *etymology*.>You cannot read meanings off of etymologies.Well, as I stressed above, this is more or less what my dictionary(the *de facto* standard one amongst italian students) says: actuallyit uses the term accezione that is not exactly meaning (should be:significato), but then I don't know how to translate it[1].However the point should be, as far as I can understand from the briefentry I (freely) quoted from, that videlicet had retained theoriginal meaning of the non-contracted form videre licet beforeacquiring the common transferred sense.>But in my experience in translating Medieval Latin--which is what I>usually read, not classical--videlicet is better read as that is.>Perhaps this is an artifact of the particular writers I read more.In any case I'll take your word both for your former claim quotedabove and for this one: there would be no point in discussing sincealthough I studied it in high school, I hardly remember any Latin atall, with the exception of a bunch of common phrases, just like, youknow, Alea iacta est, Hic sunt leones, Di tibi adsunto[2], etc.>Still, in my experience, videlicet normally introduces a sentence,>and scilicet normally introduces a noun phrase; so that I translate>the first as that is, and the second as namely.above, I had never even met scilicet (well, *I think* I never metit!).I've never really been proficient in Latin. But in any case it's apity I'm slowly losing what I knew... OTOH, due to some awkwardmechanism of my memory I can't forget the inscription of fibulapraenestina: Manios med vhe vhaked NumasioiJust think it's been something like 12 or 13 years since I read it(now, there may be some typos, but I don't think so)![1] And now that I check, my Italian to English dict suggests:acceptation, meaning.[2] I wouldn't regard this exactly as a common phrase, but can'tforget a disastrous translation of mine!Michele-- > Comments should say _why_ something is being done.Oh? My comments always say what _really_ should have happened. :)- Tore Aursand on comp.lang.perl.misc === Subject: : Re: Interest in language|[1] And now that I check, my Italian to English dict suggests:|acceptation, meaning.So far as I know, this is the very first time I've seen the wordacceptation, and I'm a native speaker of American English.I would guess, then, that it's not used very often here. AnEnglish dictionary I have ;-) defines it as the usual or generallyaccepted meaning, as of a word.Keith Ramsay === Subject: : Re: Interest in language permission for an emailed response. I don't have the slightest idea how to milk this cow, Tom said in utter confusion>Still, in my experience, videlicet normally introduces a sentence,>and scilicet normally introduces a noun phrase; so that I translate>the first as that is, and the second as namely.> above, I had never even met scilicet (well, *I think* I never met> it!).Scilicet is uncommon classically, according to Lewis&Short. It showsup as a scholarly abbreviation to, viz. sc.. :)Thomas === Subject: : Re: Apocalypse NOW!> Now in breakthrough in propulsion physics, I see 43 replies. But no> one is pointing out flaw in figure I have drawn on my webpage> The flaw is that you did not take account of the reaction> from the method you use to fix the angle ABC. Here is the> diagram that illustrates this:> http://www.dishman.me.uk/George/Abhi/abhi_rod.gif> Replacing the springs with magnets makes no difference since> the forces are still balanced.> http://www.geocities.com/actiondevice They are talking about law of> conservation of momentum, energy etc. No law is violated.> The law of conservaton of momentum is violated if you create> an unbalanced force since force is defined as rate of change> of momentum.> But if I> reply, they will drag me in theoretical discussion rather than actual> working of this device.> So stop posting and build the device, all we can do in a> newsgroup is dicuss things. Two biros and a bit of wire is> all you need.But I think I am not using all elastic potential energy stored in thisbended stick, bow. So I would like to use a sling, which is used tothrow stones by rotating it around us. I would like to tie both endsof this sling to both ends of bended stick, with center of this slingnear center point of this bended stick. And I will place this stone inthat sling near center point of bended stick. This stone is tied tosling by loose thread. Now when this bended stick straightens ups,this sling will also straighten up throwing the stone in forwarddirection. When the stone is thrown in space and moving in space withconstant velocity, it has momentum. As the sling and hence stick istied to this stone, due to momentum of this moving stone, the slingand stick will be pulled in direction of motion of stone. Yes,velocity of stone and hence momentum of stone will decrease, but itwill be transferred to velocity and hence momentum gained by sling andstick.What I am trying to say that action force generated by stored elasticpotential energy in this bended stick, bow is far greater thanreaction or inertial force exerted by stone. Hence this bended stick,bow will generate net action force to propel the stone. And once thestone is propelled with constant velocity, its momentum is used topull the sling, bow in direction of motion of stone.So we can generate unidirectional net action force using just a bowand arrow . No reaction mass is expelled or propellant is used.Now things are really getting better and better , at the same timeworse and worse for me.Happy X'mas to all Sci.* NG!-Abhi. === Subject: : Re: Apocalypse NOW!Message-Id: <1072286323.6758.0@lotis.uk.clara.net>> Now in breakthrough in propulsion physics, I see 43 replies. But no> one is pointing out flaw in figure I have drawn on my webpage> The flaw is that you did not take account of the reaction> from the method you use to fix the angle ABC. Here is the> diagram that illustrates this:> http://www.dishman.me.uk/George/Abhi/abhi_rod.gif> Replacing the springs with magnets makes no difference since> the forces are still balanced.> http://www.geocities.com/actiondevice They are talking about law of> conservation of momentum, energy etc. No law is violated.> The law of conservaton of momentum is violated if you create> an unbalanced force since force is defined as rate of change> of momentum.> But if I> reply, they will drag me in theoretical discussion rather than actual> working of this device.> So stop posting and build the device, all we can do in a> newsgroup is dicuss things. Two biros and a bit of wire is> all you need.> But I think I am not using all elastic potential energy stored in this> bended stick, bow.The arrow has a mass, let's call it 'm'. The bow has abigger mass, let's call it 'M'. The string acts like aspring between the masses that exerts a force F on thearrow and the same force on the bow: m-wwwwwww-M ->F F<-Let the arrow go and it moves one way while the bow movesthe other way. The momentum of the arrow is equal andopposite to that of the bow. If you use more energy, bothwill be larger but still equal and opposite.> So I would like to use a sling, which is used to> throw stones by rotating it around us. I would like to tie both ends> of this sling to both ends of bended stick, with center of this sling> near center point of this bended stick. And I will place this stone in> that sling near center point of bended stick. This stone is tied to> sling by loose thread. Now when this bended stick straightens ups,> this sling will also straighten up throwing the stone in forward> direction. When the stone is thrown in space and moving in space with> constant velocity, it has momentum. As the sling and hence stick is> tied to this stone, due to momentum of this moving stone, the sling> and stick will be pulled in direction of motion of stone. Yes,> velocity of stone and hence momentum of stone will decrease, but it> will be transferred to velocity and hence momentum gained by sling and> stick.and since they momenta are equal and opposite, the stone, slingand stick will all be motionless, just further apart.> What I am trying to say that action force generated by stored elastic> potential energy in this bended stick, bow is far greater than> reaction or inertial force exerted by stone.Newton's Law says they are equal. The acceleration is a=F/m andif it acts for time t, the larger mass will move more slowly sincev=a*t, but the momentum is p=m*v so the momentum is p=m*(F/m)*tor simply p=F*t. If the forces are equal but opposite, the momentumis equal but opposite.> Hence this bended stick,> bow will generate net action force to propel the stone. And once the> stone is propelled with constant velocity, its momentum is used to> pull the sling, bow in direction of motion of stone.It only works in cartoons, sorry.> Happy X'mas to all Sci.* NG!And to you Abhi, forget the device and have a good time.best regardsGeorge === Subject: : Re: Apocalypse NOW!>> Now in breakthrough in propulsion physics, I see 43 replies. Butno> one is pointing out flaw in figure I have drawn on my webpage[snip of umpteenth well-thought out and detailed reply - will Abhi listen orsimply rant on?]Hey Abhi,Until you build a working version, or can demonstrate some component of yourperpetual motion / antigravity machine, you'll be forever trapped in therealm of 'suffering in near silence', composing and recomposing interminablearguments about how this spring pushes this lever that detents this arm....If you successfully build and demonstrate the device then you'll deserve theaccolades. As one individual advised you, build it and suspend it from astring, if it rises and makes a 45 degree angle with the ceiling, you'vesucceded.If you fail to build the device, you not only will have the fool's reward,but will also spend a considerable period in Internet pergatory where you'lleternally apologize to unheeding killfiles with your ultimate reward beingan entry into some Usenet Kook FAQ for future generations. How ignoble anend!Now go caroling, put up your tree, drink some egg nog and hope that Santawill put a clue in your stocking.Merry Christmas to all, and to all a good night!> Hence this bended stick,> bow will generate net action force to propel the stone. And once the> stone is propelled with constant velocity, its momentum is used to> pull the sling, bow in direction of motion of stone.> It only works in cartoons, sorry.> Happy X'mas to all Sci.* NG!> And to you Abhi, forget the device and have a good time.> best regards === Subject: : Re: Apocalypse NOW!> But if I> reply, they will drag me in theoretical discussion rather than actual> working of this device.> So stop posting and build the device, all we can do in a> newsgroup is dicuss things. Two biros and a bit of wire is> all you need.It is X'mas eve in India. I think what I need to do now is to take a 10 cm long, 10 gramweighing elastic wooden stick. I will put this stick on ratherfrictionless tiles of my room. I would like to bend this stick usingthumb and middle finger of my right hand. I would like to make surethat elastic potential energy stored in this curved stick is maximum.Now I will tie a thread to a small stone weighing about 15 gram andother end of loose thread to center point of curved stick. I willplace this stone near center point of bended, curved stick making surethat when I release both ends of stick, center point of stick strikesto center of gravity of stone. Now I will release both ends of stickto allow center point of bended stick to strike to center of gravityof stone. Now I will see stone propelled on rather frictionless tilesof my room. If the propelled stone pulls the stick through tied threadin direction of motion of stone, then I have propelled the stick,thread and stone in only one direction without having to expelreaction mass or using propellant.If I see that, I would like to welcome entire mankind to age of bowand arrow..-Abhi. === Subject: : Re: Apocalypse NOW!Message-Id: <1072273030.25216.0@lotis.uk.clara.net>> But if I> reply, they will drag me in theoretical discussion rather than actual> working of this device.> So stop posting and build the device, all we can do in a> newsgroup is dicuss things. Two biros and a bit of wire is> all you need.> It is X'mas eve in India.> I think what I need to do now is to take a 10 cm long, 10 gram> weighing elastic wooden stick. I will put this stick on rather> frictionless tiles of my room. I would like to bend this stick using> thumb and middle finger of my right hand. I would like to make sure> that elastic potential energy stored in this curved stick is maximum.> Now I will tie a thread to a small stone weighing about 15 gram and> other end of loose thread to center point of curved stick. I will> place this stone near center point of bended, curved stick making sure> that when I release both ends of stick, center point of stick strikes> to center of gravity of stone. Now I will release both ends of stick> to allow center point of bended stick to strike to center of gravity> of stone. Now I will see stone propelled on rather frictionless tiles> of my room. If the propelled stone pulls the stick through tied thread> in direction of motion of stone, then I have propelled the stick,> thread and stone in only one direction without having to expel> reaction mass or using propellant.> If I see that, I would like to welcome entire mankind to age of bow> and arrow..Your tiles are not frictionless. Do it vertically and seeif you can get it to stick to the ceiling (without glue).Only then will you have succeeded in what you claimed.Merry ChristmasGeorge === Subject: : Re: 9/11 --- an encore in the works: Same thing. You cannot show evidence to no connection, only no : evidence to connection. Evidence to no connection is same category : as proving the negative.I'm afraid that you are mistaken. :> For example, if it could be:>demonstrated that the funding for the two operations came from completely:>different sources, or if the political literature found in the apartments:>of the perpetrators came from totally independent organizations, that would:>be fairly clear evidence pointing in the direction of there being no:>connection.: : No, this is just in the no evidence to connection category. I'm afraid that you are mistaken. I also am afraid that you are oneof those people for whom admitting a mistake is more difficult than it is for the average person. I am therefore going to drop the subjecteffective immediately, as there is no point whatsoever in continuingthe discussion.-----Richard Schultz schultr@mail.biu.ac.ilDepartment of Chemistry, Bar-Ilan University, Ramat-Gan, IsraelOpinions expressed are mine alone, and not those of Bar-Ilan University-----Contrariwise, continued Tweedledee, if it was so, it might be, andif it were so, it would be; but as it isn't, it ain't. That's logic. === Subject: : Re: 9/11 --- an encore in the works charset=Windows-1252> : Same thing. You cannot show evidence to no connection, only no > : evidence to connection. Evidence to no connection is same category > : as proving the negative.> I'm afraid that you are mistaken. > :> For example, if it could be> :>demonstrated that the funding for the two operations came from completely> :>different sources, or if the political literature found in the apartments> :>of the perpetrators came from totally independent organizations, that would> :>be fairly clear evidence pointing in the direction of there being no> :>connection.> : > : No, this is just in the no evidence to connection category. > I'm afraid that you are mistaken. I also am afraid that you are one> of those people for whom admitting a mistake is more difficult than > it is for the average person. I am therefore going to drop the subject> effective immediately, as there is no point whatsoever in continuing> the discussion.No!...No, no, no,.....keep on going. That's very interesting.Like Bob Kolker once said: 2 Jews and 3 opinionsHappy Hanukah, you guys,ahahahaha......ahahahahanson> -----> Richard Schultz schultr@mail.biu.ac.il> Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel> Opinions expressed are mine alone, and not those of Bar-Ilan University> -----> Contrariwise, continued Tweedledee, if it was so, it might be, and> if it were so, it would be; but as it isn't, it ain't. That's logic. === Subject: : Re: 9/11 --- an encore in the works> : Same thing. You cannot show evidence to no connection, only no > : evidence to connection. Evidence to no connection is same category > : as proving the negative.> I'm afraid that you are mistaken. > :> For example, if it could be> :>demonstrated that the funding for the two operations came from completely> :>different sources, or if the political literature found in the apartments> :>of the perpetrators came from totally independent organizations, that would> :>be fairly clear evidence pointing in the direction of there being no> :>connection.> : > : No, this is just in the no evidence to connection category. > I'm afraid that you are mistaken. I also am afraid that you are one> of those people for whom admitting a mistake is more difficult than > it is for the average person. I am therefore going to drop the subject> effective immediately, as there is no point whatsoever in continuing> the discussion.>No!...No, no, no,.....keep on going. That's very interesting.>Like Bob Kolker once said: 2 Jews and 3 opinions>Happy Hanukah, you guys,>ahahahaha......ahahahahansonAnd that is another good question. Why the underpinnings on thespook sites trying to lay blame on the Jews?Are you trying to say that an Isreali fighter jet entered Americanair space and hit the pentagone with a missle? You're nuts. It was an act of sedition. I heard someone say recentlythat some senior members of the military would have to be lined upin front of firing squad. And I can only say that it is about time.http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm-*- === Subject: : Re: 9/11 --- an encore in the works> Not only that but if you take the time to listen to his evidence,> not conjecture, you will see that 9/11 was an inside job.> -*->WTF are you babbling about? Nevermind. I don't want to know.That's correct, you can't handle the truth.It never occurred to you, that since the election fiasco in Florida,where the Jewish Democratic lobby, made the Bush Republicans livesa living hell, as they stole the election, and they just might wantto get some revenge and blow the crap out of NY to make them get into line, and at the same time, switch the countriesfocus from high tech, to military and oil and war. Because thatis where their investments are.But then you never actually look for such things as motive.You get all your thinking orders from TV.MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.http://www.rense.com/general46/911V.HTMI find it so astonishing, that most Americans are so easilymanipulated by the press.Have you ever read or listened to Noam Chomsky?You should. Then you might have a clue about what sort of people run yourcountry. And what sort of country you live in.It is one frickin evil empire my friend. The worst the earthhas ever seen.-*- === Subject: : Re: 9/11 --- an encore in the works> Not only that but if you take the time to listen to his evidence,> not conjecture, you will see that 9/11 was an inside job.> -*->WTF are you babbling about? Nevermind. I don't want to know.> That's correct, you can't handle the truth.> It never occurred to you, that since the election fiasco in Florida,> where the Jewish Democratic lobby, made the Bush Republicans lives> a living hell, as they stole the election, and they just might want> to get some revenge and blow the crap out of NY to make them> get into line, and at the same time, switch the countries> focus from high tech, to military and oil and war. Because that> is where their investments are.> But then you never actually look for such things as motive.> You get all your thinking orders from TV.> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.> http://www.rense.com/general46/911V.HTM> I find it so astonishing, that most Americans are so easily> manipulated by the press.> Have you ever read or listened to Noam Chomsky?> You should.> Then you might have a clue about what sort of people run your> country. And what sort of country you live in.> It is one frickin evil empire my friend. The worst the earth> has ever seen.> -*-I suggest you post your blurb in alt.kooks, where you might just findsomeone low enough IQ to give a about your dumbass conspiracy theories,and leave these groups to people who would like to remain on topic. === Subject: : Re: 9/11 --- an encore in the works>> Not only that but if you take the time to listen to his evidence,>> not conjecture, you will see that 9/11 was an inside job.>> -*->WTF are you babbling about? Nevermind. I don't want to know.> That's correct, you can't handle the truth.> It never occurred to you, that since the election fiasco in Florida,> where the Jewish Democratic lobby, made the Bush Republicans lives> a living hell, as they stole the election, and they just might want> to get some revenge and blow the crap out of NY to make them> get into line, and at the same time, switch the countries> focus from high tech, to military and oil and war. Because that> is where their investments are.> But then you never actually look for such things as motive.> You get all your thinking orders from TV.> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.> http://www.rense.com/general46/911V.HTM> I find it so astonishing, that most Americans are so easily> manipulated by the press.> Have you ever read or listened to Noam Chomsky?> You should.> Then you might have a clue about what sort of people run your> country. And what sort of country you live in.> It is one frickin evil empire my friend. The worst the earth> has ever seen.> -*->I suggest you post your blurb in alt.kooks, where you might just find>someone low enough IQ to give a about your dumbass conspiracy theories,>and leave these groups to people who would like to remain on topic.You sound afraid George. And disappointed. Yes disappointed that youcould be so misled, that your trust, everything that you grewup to believe in, has been turned to worthless crap. You've beenhad. You've been lied to, and cheated out of your country bybad people George.Don't blame me. Blame yourself. Cause you did f' all about it. === Subject: : Re: 9/11 --- an encore in the worksgeorge@george.net says...>> Not only that but if you take the time to listen to his evidence,>> not conjecture, you will see that 9/11 was an inside job.>> -*->>WTF are you babbling about? Nevermind. I don't want to know.>> That's correct, you can't handle the truth.> It never occurred to you, that since the election fiasco in Florida,> where the Jewish Democratic lobby, made the Bush Republicans lives> a living hell, as they stole the election, and they just might want> to get some revenge and blow the crap out of NY to make them> get into line, and at the same time, switch the countries> focus from high tech, to military and oil and war. Because that> is where their investments are.> But then you never actually look for such things as motive.> You get all your thinking orders from TV.> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.> http://www.rense.com/general46/911V.HTM> I find it so astonishing, that most Americans are so easily> manipulated by the press.> Have you ever read or listened to Noam Chomsky?> You should.> Then you might have a clue about what sort of people run your> country. And what sort of country you live in.> It is one frickin evil empire my friend. The worst the earth> has ever seen.> -*->I suggest you post your blurb in alt.kooks, where you might just find>someone low enough IQ to give a about your dumbass conspiracytheories,>and leave these groups to people who would like to remain on topic.> You sound afraid George. And disappointed. Yes disappointed that you> could be so misled, that your trust, everything that you grew> up to believe in, has been turned to worthless crap. You've been> had. You've been lied to, and cheated out of your country by> bad people George.> Don't blame me. Blame yourself. Cause you did f' all about it.Denial is the first symptom, dude. Delusions of grandeur, and inability tofocus on reality are other serious symptoms. I recommend an aluminum foildeflector beanie (AFDB) for you ( see link for instructions on proper use -http://zapatopi.net/afdb.html), or electro-shock therapy, and if that doeswork, a lobotomy. === Subject: : Re: 9/11 --- an encore in the works>Denial is the first symptom, dude. Delusions of grandeur, and inability to>focus on reality are other serious symptoms. I recommend an aluminum foil>deflector beanie (AFDB) for you ( see link for instructions on proper use ->http://zapatopi.net/afdb.html), or electro-shock therapy, and if that does>work, a lobotomy.You are really scared to death aren't you?http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm === Subject: : Re: 9/11 --- an encore in the works>Denial is the first symptom, dude. Delusions of grandeur, and inabilityto>focus on reality are other serious symptoms. I recommend an aluminumfoil>deflector beanie (AFDB) for you ( see link for instructions on properuse ->http://zapatopi.net/afdb.html), or electro-shock therapy, and if thatdoes>work, a lobotomy.> You are really scared to death aren't you?> http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htmOf what? You?Bhwhahahahahahahahaha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!! === Subject: : Re: 9/11 --- an encore in the works>Denial is the first symptom, dude. Delusions of grandeur, and inability>to>focus on reality are other serious symptoms. I recommend an aluminum>foil>deflector beanie (AFDB) for you ( see link for instructions on proper>use ->http://zapatopi.net/afdb.html), or electro-shock therapy, and if that>does>work, a lobotomy.> You are really scared to death aren't you?> http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm>Of what? You?No George, why would you be afraid of me?The question I am asking, is why are you acting like a scaredrabbit, trying to avoid the issue and posting diatribe?Is it your job to try and get people off the topic of what actually happened George?http://www.angelfire.com/indie/pearly/htmls/ bush-carlyle.html === Subject: : Re: 9/11 --- an encore in the works> Not only that but if you take the time to listen to his evidence,> not conjecture, you will see that 9/11 was an inside job.>> -*->>WTF are you babbling about? Nevermind. I don't want to know.>> That's correct, you can't handle the truth.>> It never occurred to you, that since the election fiasco in Florida,>> where the Jewish Democratic lobby, made the Bush Republicans lives>> a living hell, as they stole the election, and they just might want>> to get some revenge and blow the crap out of NY to make them>> get into line, and at the same time, switch the countries>> focus from high tech, to military and oil and war. Because that>> is where their investments are.>> But then you never actually look for such things as motive.>> You get all your thinking orders from TV.>> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.>> http://www.rense.com/general46/911V.HTM>> I find it so astonishing, that most Americans are so easily>> manipulated by the press.>> Have you ever read or listened to Noam Chomsky?>> You should.>> Then you might have a clue about what sort of people run your>> country. And what sort of country you live in.>> It is one frickin evil empire my friend. The worst the earth>> has ever seen.>> -*->I suggest you post your blurb in alt.kooks, where you might just find>someone low enough IQ to give a about your dumbass conspiracy theories,>and leave these groups to people who would like to remain on topic.>You sound afraid George. And disappointed. Yes disappointed that you>could be so misled, that your trust, everything that you grew>up to believe in, has been turned to worthless crap. You've been>had. You've been lied to, and cheated out of your country by>bad people George.>Don't blame me. Blame yourself. Cause you did f' all about it.http://physics911.org/net/modules/http://www.serendipity.li /wtc.html#what_actually_happened http://www.serendipity.li/wot/anti-war.htm http://serendipity.ptpi.net/wot/holmgren/11.htm http://911research.wtc7.net http://wtc7.net http://911research.wtc7.net/talks/wtc7 http://news.globalfreepress.com/ http://www.911-strike.com/ http://home.comcast.net/~skydrifter/exp.htm http://whatreallyhappened.com/blackmail.html http://www.cooperativeresearch.org/timeline/main/dayof911.html Read em and weep George. Yes weep for your countrymen who havedied at the hands of these people who you look up to and callyour government.The same people who have routinely killed millions of innocent people around the world for little more than sport.And weep because there is nothing you can do to stop them,because they have you caged like animals, and programmedlike sheep.-*- === Subject: : Re: 9/11 --- an encore in the worksgeorge@george.net says...> Not only that but if you take the time to listen to his evidence,> not conjecture, you will see that 9/11 was an inside job.>> -*->>WTF are you babbling about? Nevermind. I don't want to know.>> That's correct, you can't handle the truth.>> It never occurred to you, that since the election fiasco in Florida,>> where the Jewish Democratic lobby, made the Bush Republicans lives>> a living hell, as they stole the election, and they just might want>> to get some revenge and blow the crap out of NY to make them>> get into line, and at the same time, switch the countries>> focus from high tech, to military and oil and war. Because that>> is where their investments are.>> But then you never actually look for such things as motive.>> You get all your thinking orders from TV.>> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.>> http://www.rense.com/general46/911V.HTM>> I find it so astonishing, that most Americans are so easily>> manipulated by the press.>> Have you ever read or listened to Noam Chomsky?>> You should.>> Then you might have a clue about what sort of people run your>> country. And what sort of country you live in.>> It is one frickin evil empire my friend. The worst the earth>> has ever seen.>> -*->I suggest you post your blurb in alt.kooks, where you might just find>someone low enough IQ to give a about your dumbass conspiracytheories,>and leave these groups to people who would like to remain on topic.>You sound afraid George. And disappointed. Yes disappointed that you>could be so misled, that your trust, everything that you grew>up to believe in, has been turned to worthless crap. You've been>had. You've been lied to, and cheated out of your country by>bad people George.>Don't blame me. Blame yourself. Cause you did f' all about it.> http://physics911.org/net/modules/> http://www.serendipity.li/wtc.html#what_actually_happened> http://www.serendipity.li/wot/anti-war.htm> http://serendipity.ptpi.net/wot/holmgren/11.htm> http://911research.wtc7.net http://wtc7.net> http://911research.wtc7.net/talks/wtc7> http://news.globalfreepress.com/> http://www.911-strike.com/> http://home.comcast.net/~skydrifter/exp.htm> http://whatreallyhappened.com/blackmail.html> http://www.cooperativeresearch.org/timeline/main/dayof911. htmlDick, er, Rick, your scrotum must be shriveling at the thought that you'vebeen able to post so much delusional tripe. You are truly a masterde-bater!P.S. You've just got to love this statement:Prologue: The Future History of Planet Earth. Since at least the time ofthe biblical prophets and the Oracle of Delphi, the attempt to foretell thefuture has captivated the imagination of our species. Hal Lindsey's LateGreat Planet Earth and his many other books represent a modern attempt atfortune-telling, in a Christian Zionist moldBwhahahahahahahahahahaha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! === Subject: : Re: 9/11 --- an encore in the works>Prologue: The Future History of Planet Earth. Since at least the time of>the biblical prophets and the Oracle of Delphi, the attempt to foretell the>future has captivated the imagination of our species. Hal Lindsey's Late>Great Planet Earth and his many other books represent a modern attempt at>fortune-telling, in a Christian Zionist moldI know what you are trying to suggest. That one hour after the planes were remotely controlled into the Twin Towers,that somehow the mossad targetted the pentagon, knowing itwas them who did it.Isn't it more likely that is was the US airforce, which found outand targetted them directly?http://www.asile.org/citoyens/numero13/pentagone/ erreurs_en.htmBut until the first hangings and shootings on the firing the squadsoccur, the full account won't come out.You know, as they try to save themselves, they sell each other out. That is how it usually works.But do have a look at the above link, with satellite photosof the pentagone crash site, and from the ground photos, and be sure to see the photos immediately after the so called crash and see that the hole is tiny compared to a 757 and there are no wings or any other debris from any plane, whatsoever.Caught red handed.Acts of sedition are punishable by execution.Those responsible will be summarily executed.End of story.-*- === Subject: : Re: 9/11 --- an encore in the works>Dick, er, Rick, your scrotum must be shriveling at the thought that you've>been able to post so much delusional tripe. You are truly a master>de-bater!>P.S. You've just got to love this statement:http://www.asile.org/citoyens/numero13/pentagone/ erreurs_en.htmSee the penta-gone. See no plane wreckage. See the firing squad. === Subject: : Re: 9/11 --- an encore in the works>Dick, er, Rick, your scrotum must be shriveling at the thought thatyou've>been able to post so much delusional tripe. You are truly a master>de-bater!>P.S. You've just got to love this statement:> http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm> See the penta-gone. See no plane wreckage. See the firing squad.'Put your sweet lips a little closer to the bone' === Subject: : Re: 9/11 --- an encore in the works>Dick, er, Rick, your scrotum must be shriveling at the thought that> you've>been able to post so much delusional tripe. You are truly a master>de-bater!>>P.S. You've just got to love this statement:> http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm> See the penta-gone. See no plane wreckage. See the firing squad.http://search.netscape.com/ns/boomframe.jsp?query= surveillance+photo+of+9%2F11+pentagon+impact&page=1&offset=1& result_url=redir%3Fsrc%3Dwebsearch%26amp%3BrequestId% 3D1d7cf1c2fa225715%26amp%3BclickedItemRank%3D5%26amp% 3BuserQuery%3Dsurveillance%2Bphoto%2Bof%2B9%252F11%2Bpentagon% 2Bimpact%26amp%3BclickedItemURN%3Dhttp%253A%252F% 252Fwww.thepowerhour.com%252Fpostings-four%252Ffrench-911.htm% 26amp%3BinvocationType%3D-%26amp%3BfromPage%3DNSCPSuggestion& remove_url=http%3A%2F%2Fwww.thepowerhour.com%2Fpostings-four% 2Ffrench-911.htm>'Put your sweet lips a little closer to the bone' === Subject: : Re: 9/11 --- an encore in the works>Dick, er, Rick, your scrotum must be shriveling at the thought that> you've>been able to post so much delusional tripe. You are truly a master>de-bater!>>P.S. You've just got to love this statement:> http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm> See the penta-gone. See no plane wreckage. See the firing squad.> 'Put your sweet lips a little closer to the bone'Note how nicely that web site did notinclude the surveillance cam's shots of theplane as it actually struck the building anddisintegrated.... there are 4 frames thatshow it just before, just as it tilts and the noseenters, just as it fireballs, and after its gone...But that would have shot down the conspiracy soit was left out to allow idiots like Sobie to beduped..... === Subject: : Re: 9/11 --- an encore in the works>Dick, er, Rick, your scrotum must be shriveling at the thought that>you've>been able to post so much delusional tripe. You are truly a master>de-bater!>P.S. You've just got to love this statement:> http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm> See the penta-gone. See no plane wreckage. See the firing squad.>'Put your sweet lips a little closer to the bone'Just curious. Which one are you?http://www.angelfire.com/ok5/pearly/bush/bushladen_ crime.jpg-*- === Subject: : Re: 9/11 --- an encore in the works> Not only that but if you take the time to listen to his evidence,>> not conjecture, you will see that 9/11 was an inside job.>> -*->>WTF are you babbling about? Nevermind. I don't want to know.> That's correct, you can't handle the truth.>> It never occurred to you, that since the election fiasco in Florida,> where the Jewish Democratic lobby, made the Bush Republicans lives> a living hell, as they stole the election, and they just might want> to get some revenge and blow the crap out of NY to make them> get into line, and at the same time, switch the countries> focus from high tech, to military and oil and war. Because that> is where their investments are.>> But then you never actually look for such things as motive.>> You get all your thinking orders from TV.>> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.>> http://www.rense.com/general46/911V.HTM>> I find it so astonishing, that most Americans are so easily> manipulated by the press.>> Have you ever read or listened to Noam Chomsky?>> You should.>> Then you might have a clue about what sort of people run your> country. And what sort of country you live in.>> It is one frickin evil empire my friend. The worst the earth> has ever seen.>> -*->>I suggest you post your blurb in alt.kooks, where you might just find>>someone low enough IQ to give a about your dumbass conspiracy theories,>>and leave these groups to people who would like to remain on topic.>You sound afraid George. And disappointed. Yes disappointed that you>could be so misled, that your trust, everything that you grew>up to believe in, has been turned to worthless crap. You've been>had. You've been lied to, and cheated out of your country by>bad people George.>Don't blame me. Blame yourself. Cause you did f' all about it.>http://www.serendipity.li/wtc.html#what_actually_happened >http://www.serendipity.li/wot/anti-war.htm >http://serendipity.ptpi.net/wot/holmgren/11.htm >http://911research.wtc7.net http://wtc7.net >http://911research.wtc7.net/talks/wtc7 >http://news.globalfreepress.com/ >http://www.911-strike.com/ >http://home.comcast.net/~skydrifter/exp.htm >http://whatreallyhappened.com/blackmail.html >http://www.cooperativeresearch.org/timeline/main/dayof911. html >Read em and weep George. Yes weep for your countrymen who have>died at the hands of these people who you look up to and call>your government.>The same people who have routinely killed millions of innocent people >around the world for little more than sport.>And weep because there is nothing you can do to stop them,>because they have you caged like animals, and programmed>like sheep.>-*-Here you go George. Even a blind idiot or corrupt officialcan see they are doomed with this sort of expose.In the below link, scroll down and examine the pictures at thePentagon. Where the story line goes that a 757 crashed into the Pentagon, except there was no wreckage, and examine the superimposed757's on the crash site. Where in all liklihood, a missle from theshadow government's airforce, took out some Pentagon peoplewho knew too much, or who were about to go public about someof their heinous crimes against humanity, (probably because every timethey thought about them, they felt the urge to vomit.)http://www.serendipity.li/wtc.html#what_actually_ happenedAnd you have the unmitigated gall to bad mouth me you frickin cretin?You deserve to live in America. I hope they slam the frickindoor on you and turn it into a stalag. I hope there are gestapoon every frickin block. I hope they put a frickin chip in yourdumb useless f*cking head, and make you bark like a dogfor their amusement.-*- === Subject: : Re: 9/11 --- an encore in the works> Not only that but if you take the time to listen to his evidence,> not conjecture, you will see that 9/11 was an inside job.>> -*->>WTF are you babbling about? Nevermind. I don't want to know.>> That's correct, you can't handle the truth.>> It never occurred to you, that since the election fiasco in Florida,>> where the Jewish Democratic lobby, made the Bush Republicans lives>> a living hell, as they stole the election, and they just might want>> to get some revenge and blow the crap out of NY to make them>> get into line, and at the same time, switch the countries>> focus from high tech, to military and oil and war. Because that>> is where their investments are.>> But then you never actually look for such things as motive.>> You get all your thinking orders from TV.>> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.>> http://www.rense.com/general46/911V.HTM>> I find it so astonishing, that most Americans are so easily>> manipulated by the press.>> Have you ever read or listened to Noam Chomsky?>> You should.>> Then you might have a clue about what sort of people run your>> country. And what sort of country you live in.>> It is one frickin evil empire my friend. The worst the earth>> has ever seen.>> -*->I suggest you post your blurb in alt.kooks, where you might just find>someone low enough IQ to give a about your dumbass conspiracy theories,>and leave these groups to people who would like to remain on topic.>>You sound afraid George. And disappointed. Yes disappointed that you>>could be so misled, that your trust, everything that you grew>>up to believe in, has been turned to worthless crap. You've been>>had. You've been lied to, and cheated out of your country by>>bad people George.>>Don't blame me. Blame yourself. Cause you did f' all about it.>http://www.serendipity.li/wtc.html#what_actually_happened >http://www.serendipity.li/wot/anti-war.htm >http://serendipity.ptpi.net/wot/holmgren/11.htm >http://911research.wtc7.net http://wtc7.net >http://911research.wtc7.net/talks/wtc7 >http://news.globalfreepress.com/ >http://www.911-strike.com/ >http://home.comcast.net/~skydrifter/exp.htm >http://whatreallyhappened.com/blackmail.html >http://www.cooperativeresearch.org/timeline/main/dayof911. html >Read em and weep George. Yes weep for your countrymen who have>died at the hands of these people who you look up to and call>your government.>The same people who have routinely killed millions of innocent people >around the world for little more than sport.>And weep because there is nothing you can do to stop them,>because they have you caged like animals, and programmed>like sheep.>-*->Here you go George. Even a blind idiot or corrupt official...Can see from reading the headers, that you don't know who youare replying to. Yet you seem to want people to take you seriously.Perhaps you should learn how to use Usenet first, then post yourwisdom.Jim === Subject: : This just in... was Re: 9/11 --- an encore in the worksI wonder, is the Bushladen gang upset at the fact thatthe so called pentagon crash was proven to be an inside job,by an expose done in France?http://www.asile.org/citoyens/numero13/pentagone/ erreurs_en.htmYou know the Bush gang are very dangerous people. Perhaps Air France should be careful. They wouldn't hesitate to bomb them.After all, they bomb their own people!I wonder how the real story story is going to break?Suicide of top official, or simple execution mob style?You know what would be great for TV? If one branch ofthe military exposed the criminals responsible and arresteda few of them, and showed their evidence. Immediatelythe rest would try to flee or similar.I'll bet right at this moment some are desparately trying toget on the TV to be interviewed so they can sell each other outto try and save themselves.You think other countries don't have evidence of what went on?Of course they do. France is just one country.Russia knows. They locked one of them up after an assination attempton Putin. But then Putin is ex KGB. I say bring it all out into the open.Clear the air. Lets see some firing squad executions.Traitors are traitors and sedition is sedition, the law is quiteclear on that.I doubt that it was the good guys, who sent a missle into the Pentagonto stop the bad guys who were responsible for the Twin Towersdemolition. I would suspect that it was part of destroying the evidence.When will these criminals learn not to trust each other?Some are selling each other out right now. That's what I heard.British Intelligence knows about Major and his involvement for instance.And Senator Orrin Hatch is ready to snap.-*- === Subject: : Re: This just in... was Re: 9/11 --- an encore in the worksDid you even read the stuff on that website? If so, how could youpossibly claim that they proved it to be an inside job? For one theydidn't prove ANYTHING, they merely put forth a somewhat interesting theorythat a boeing was not responsible for the damage. Interesting because Ican't answer their questions (though I have some ideas), but I certainlythink its much more likely that they have completely missed the point thanthat our president has demolished one of our government buildings (everhear of occam's razor?).And there's absolutely no mention of proof of an inside job. This istypical of the anti-bush rhetoric that surrounds the whole situation.You people won't find any real support until you approach the situationwithlevel-headed, logical arguments based on fact that comes from looking atall sides of the issues at hand objectively, something that seems to beextremely elusive to political discussion in general these days.> I wonder, is the Bushladen gang upset at the fact that> the so called pentagon crash was proven to be an inside job,> by an expose done in France?> http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm> You know the Bush gang are very dangerous people. Perhaps Air France > should be careful. They wouldn't hesitate to bomb them.> After all, they bomb their own people!> I wonder how the real story story is going to break?> Suicide of top official, or simple execution mob style?> You know what would be great for TV? If one branch of> the military exposed the criminals responsible and arrested> a few of them, and showed their evidence. Immediately> the rest would try to flee or similar.> I'll bet right at this moment some are desparately trying to> get on the TV to be interviewed so they can sell each other out> to try and save themselves.> You think other countries don't have evidence of what went on?> Of course they do. France is just one country.> Russia knows. They locked one of them up after an assination attempt> on Putin. But then Putin is ex KGB. > I say bring it all out into the open.> Clear the air. Lets see some firing squad executions.> Traitors are traitors and sedition is sedition, the law is quite> clear on that.> I doubt that it was the good guys, who sent a missle into the Pentagon> to stop the bad guys who were responsible for the Twin Towers> demolition. I would suspect that it was part of destroying the evidence.> When will these criminals learn not to trust each other?> Some are selling each other out right now. That's what I heard.> British Intelligence knows about Major and his involvement for instance.> And Senator Orrin Hatch is ready to snap. === Subject: : Re: 9/11 --- an encore in the works> Can see from reading the headers, that you don't know who you> are replying to. Yet you seem to want people to take you seriously.> Perhaps you should learn how to use Usenet first, then post your> wisdom.> JimHe's a kook, no doubt about it. === Subject: : Re: 9/11 --- an encore in the works> Can see from reading the headers, that you don't know who you> are replying to. Yet you seem to want people to take you seriously.> Perhaps you should learn how to use Usenet first, then post your> wisdom.> Jim>He's a kook, no doubt about it.Pease try to stay on topic.http://www.serendipity.li/wot/bushladen_ network.gif === Subject: : Re: 9/11 --- an encore in the works>Can see from reading the headers, that you don't know who you>are replying to. Yet you seem to want people to take you seriously.>Perhaps you should learn how to use Usenet first, then post your>wisdom.Why is everyone like you trying to avoid the issue? http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htmIs this some sort of desparate attempt to avoid being caughtor something? Are you implicated in these acts of treason yourself Jim?Of course people take this seriously.And they wonder why _you do not.-*- === Subject: : Re: 9/11 --- an encore in the works>Can see from reading the headers, that you don't know who you>are replying to. Yet you seem to want people to take you seriously.>Perhaps you should learn how to use Usenet first, then post your>wisdom.> Why is everyone like you trying to avoid the issue?Insanity: Doing the same thing over and over again, and expectingdifferent results - Albert Einstein === Subject: : Re: 9/11 --- an encore in the works>Can see from reading the headers, that you don't know who you>are replying to. Yet you seem to want people to take you seriously.>Perhaps you should learn how to use Usenet first, then post your>wisdom.> Why is everyone like you trying to avoid the issue?>Insanity: Doing the same thing over and over again, and expecting>different results - Albert EinsteinWhat are you talking about George?The title of this thread is 9/11 --- an encore in the works.Try to stay on topic George.In order to determine if there is in fact an encore in the works,we must first examine what actually occurred.Take the pentagon crash as an example. We have seen that there wasno plane crash, and the evidence is there in the numerous photographstaken immediately after the explosion at the Pentagon.So then you asked, well who did it?Was it the Zionists?These people here apparently were involved...http://www.serendipity.li/wot/bushladen_ network.gifhttp://www.angelfire.com/indie/pearly/htmls/ bush-carlyle.htmlBut when the President himself is implicated, you can see howdifficult it might be to get him to cooperate and releasesuch information as who shorted the airline stock prior to 9/11-*- === Subject: : Re: 9/11 --- an encore in the works charset=iso-8859-1says......> Not only that but if you take the time to listen to his evidence,> not conjecture, you will see that 9/11 was an inside job.>> -*->>WTF are you babbling about? Nevermind. I don't want to know.>> That's correct, you can't handle the truth.>> It never occurred to you, that since the election fiasco in Florida,>> where the Jewish Democratic lobby, made the Bush Republicans lives>> a living hell, as they stole the election, and they just might want>> to get some revenge and blow the crap out of NY to make them>> get into line, and at the same time, switch the countries>> focus from high tech, to military and oil and war. Because that>> is where their investments are.>> But then you never actually look for such things as motive.>> You get all your thinking orders from TV.>> MIKE_RUPPERT Truth & Lies of 911.MP3 on any peer 2 peer network.>> http://www.rense.com/general46/911V.HTM>> I find it so astonishing, that most Americans are so easily>> manipulated by the press.>> Have you ever read or listened to Noam Chomsky?>> You should.>> Then you might have a clue about what sort of people run your>> country. And what sort of country you live in.>> It is one frickin evil empire my friend. The worst the earth>> has ever seen.>> -*->I suggest you post your blurb in alt.kooks, where you might just find>someone low enough IQ to give a about your dumbass conspiracytheories,>and leave these groups to people who would like to remain on topic.>>You sound afraid George. And disappointed. Yes disappointed that you>>could be so misled, that your trust, everything that you grew>>up to believe in, has been turned to worthless crap. You've been>>had. You've been lied to, and cheated out of your country by>>bad people George.>>Don't blame me. Blame yourself. Cause you did f' all about it.>http://www.serendipity.li/wtc.html#what_actually_ happened>http://www.serendipity.li/wot/anti-war.htm>http:// serendipity.ptpi.net/wot/holmgren/11.htm>http:// 911research.wtc7.net http://wtc7.net>http://911research.wtc7.net/talks/wtc7>http:// news.globalfreepress.com/>http://www.911-strike.com/>http:// home.comcast.net/~skydrifter/exp.htm>http:// whatreallyhappened.com/blackmail.html>http:// www.cooperativeresearch.org/timeline/main/dayof911.html>Read em and weep George. Yes weep for your countrymen who have>died at the hands of these people who you look up to and call>your government.>The same people who have routinely killed millions of innocent people>around the world for little more than sport.>And weep because there is nothing you can do to stop them,>because they have you caged like animals, and programmed>like sheep. -*->Here you go George. Even a blind idiot or corrupt official...> Can see from reading the headers, that you don't know who you> are replying to. Yet you seem to want people to take you seriously.> Perhaps you should learn how to use Usenet first, then post your> wisdom.> JimJim, don't be so hard on Ricky. He likes to talk to himself and hismethod of posting is to preserve his wisdom from/to & for himself.Besides, it's for sci.environment and they are all like that in there.Ahahahahaha......ahahahahanson === Subject: : Re: 9/11 --- an encore in the works>Jim, don't be so hard on Ricky. He likes to talk to himself and his>method of posting is to preserve his wisdom from/to & for himself.>Besides, it's for sci.environment and they are all like that in there.>Ahahahahaha......ahahahahansonhttp://www.asile.org/ citoyens/numero13/pentagone/erreurs_en.htm === Subject: : Re: 9/11 --- an encore in the worksRick Sobie scratched his ass and burbled in the spew> Here you go George. Even a blind idiot or corrupt official> can see they are doomed with this sort of expose.Bwhahahahahahahahahahahahahahahahahahahahahahhahahahahah ahahahaha!!!!!!!!!!!!!!!!!!!!!!!ROFLOLYes, I agree. You are a idiot.> In the below link, scroll down and examine the pictures at the> Pentagon. Where the story line goes that a 757 crashed into the> Pentagon, except there was no wreckage, and examine the superimposed> 757's on the crash site. Where in all liklihood, a missle from the> shadow government's airforce, took out some Pentagon people> who knew too much, or who were about to go public about some> of their heinous crimes against humanity, (probably because every time> they thought about them, they felt the urge to vomit.)> http://www.serendipity.li/wtc.html#what_actually_ happenedBwhahahahahahahahahahahahahahahaha!!!!!!!!!!!!!!!!!!!! !!!!!!Urban legends taken from the psycho ward. Take your meds, dude.> And you have the unmitigated gall to bad mouth me you frickin cretin?Oh, it gets even better. I even have the balls to call you a sad littlepsychopath with no hope whatsoever for recovery. My advice, use one ofthese - http://zapatopi.net/afdb.html - and if that doesn't ease thesymptons, then you should end your sad excuse for a life now, because thereis no hope whatsoever for you.> You deserve to live in America.Actually, I am very proud to live in the US, would never consider livinganywhere else. So you are safe in your Igloo, sucking on your polar beartit.>I hope they slam the frickin> door on you and turn it into a stalag. I hope there are gestapo> on every frickin block. I hope they put a frickin chip in your> dumb useless f*cking head, and make you bark like a dog> for their amusement.Bhwhahahahahahahahahahahaha!!!!!!!!!!!The word is , you Canadian dick smoker. === Subject: : Re: 9/11 --- an encore in the works>Rick Sobie scratched his ass and burbled in the spew> Here you go George. Even a blind idiot or corrupt official> can see they are doomed with this sort of expose.> Bwhahahahahahahahahahahahahahahahahahahahahahhahahahahahahahaha ha!!!!!!!!!!!>!!!!!!!!!!!!>ROFLOLWhat are you 16 years old? >Yes, I agree. You are a idiot.How did you get a job in Eschelon with an atitude like that?> In the below link, scroll down and examine the pictures at the> Pentagon. Where the story line goes that a 757 crashed into the> Pentagon, except there was no wreckage, and examine the superimposed> 757's on the crash site. Where in all liklihood, a missle from the> shadow government's airforce, took out some Pentagon people> who knew too much, or who were about to go public about some> of their heinous crimes against humanity, (probably because every time> they thought about them, they felt the urge to vomit.)> http://www.serendipity.li/wtc.html#what_actually_happened> Bwhahahahahahahahahahahahahahahaha!!!!!!!!!!!!!!!!!!!!!!!!!!> Urban legends taken from the psycho ward. Take your meds, dude.And here we see your limited ability to think critically. And yourusual answer to everything. You are in denial. Probably hypnotized,programmed. Like some sort of MKULTRA zombie.See the so called crash site at the penta-gone , see the lack of plane debris, see you in front of a firing squad sh*tting your pantsand crying like a little baby.http://www.asile.org/citoyens/numero13/pentagone/erreurs_ en.htm-*- === Subject: : Re: Perplexing Patterns of Square Numbers by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBNBm9T24969;>...>> and a scintillating Perplex-9 pattern>...>A few more Perplex-9's, reading across -> 27261 21046 18089 13875 25123 15542 10937 14568 12712> 10591 11986 15238 12723 25879 30764 14723 29904 12842> 16191 25256 16688 13577 21641 29316 21307 28884 12842> 15869 23486 10908 29313 17279 22894 10723 26394 12842> 23161 19906 25746 20696 18581 13654 31392 15204 12908> 18042 15722 23972 22737 13629 17782 26966 26242 21093> 21146 20431 27918 12028 22842 18822 19437 12762 24788> 29466 26426 29761 15412 20766 23194 11907 23926 25719> 30746 20596 23361 17818 13924 25616 22873 10596 25719> 20627 16841 23091 21479 26823 19868 11065 16983 30186> 11477 18073 12839 27718 15293 11822 23229 14908 31488>Eg, squared out the first one looks like:>743162121>442934116>327211921>192515625>631165129> 241553764>119617969>212226624>161594944>and the last one like>131721529>326633329>164839921>768287524>233875849> 139759684>539586441>222248464>991494144>-jiw 4 2 5 4 7 3 1 2 9 - 20627^2 2 8 3 6 1 9 2 8 1 - 16841^2 5 3 3 1 9 4 2 8 1 - 23091^2 4 6 1 3 4 7 4 4 1 - 21479^2 7 1 9 4 7 3 3 2 9 - 26823^2 3 9 4 7 3 7 4 2 4 - 19868^2 1 2 2 4 3 4 2 2 5 - 11065^2 2 8 8 4 2 2 2 8 9 - 16983^2 9 1 1 1 9 4 5 9 6 - 30186^2 All 9 squares in this pattern read alike across and downwards. There are around 24 thousand zero-free 10 digit squares. I invite Mr James and others to try and discover possible existence of similar Perplex-10 patterns out of these squares. Again, wishing you all A HAPPY NEW YEAR .- B.S.Rangaswamy. === Subject: : Re: A tricky sum? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBO2XvQ22251;I believe you'll need to use the identity log(a) + log(b) = log(ab) and the fact that with k_n = n(k_(n-1) + 1) and k_1 = k^(-1), e^k = prod(i=1..infinity) (1 + 1/k_n) (If this made no sense see http://mathworld.wolfram.com/e.html, equations (29) (30) ) Looks like you might be able utilize this for your sum, then the Riemann sum maybe materialize easier.This are just suggestions, so good luck!MM.> I'm trying to evaluate the following limit:>lim (n->oo) (sum (k=1..n) (log(1 - 1/k + (1/k)*cos(t*sqrt(k/n)))))>I happen to know it equals -2*(int (x=0..1) ((1 - cos(tx))/x) dx), but I>can't figure out how to manipulate the sum to give this result. There>should be a Riemann sum somewhere in that expression, but I can't seem to>find it. The log is ruining everything. If someone could point me in>the right direction, I'd appreciate it!>Roman Garnett === Subject: : Hartshorne p.118 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBODK6Q32166;HiI'm just wondering if anyone could clear up a definition for me:On p.118 of Hartshorne, where S is a graded ring, X=Proj S, it says that given any s in S_d, there is a naturally associated global section of (O_X)(d) over X. How do you actually define this global section over X?Jason === Subject: : Re: Hartshorne p.118|On p.118 of Hartshorne, where S is a graded ring, X=Proj S, it says that|given any s in S_d, there is a naturally associated global section of|(O_X)(d) over X. How do you actually define this global section over X?The definition on the previous page of O_X(d) indicates that it isthe sheaf associated to the graded module S(d) by the ~ constructiondefined on the page before. Here, he's treating S as a graded moduleover S. Looking back at the definition on p. 50 of the twisted moduleM(d) where M is a module, M(d) is the module whose elements of degreei are the elements of the i+d-th degree of M. So an s in S_d alsocounts as an element of degree 0 of S(d).Then looking at the ~ construction on p.116, it says that a sectionis something which can be locally written as a fraction of an elementin the module and an element of the graded ring, of the same degree.Well, in S(d), the element s has degree 0, so s/1 serves as such afraction globally. In the preface Hartshorne says his rings are allcommutative rings with 1, so 1 is an element of S. Since S_d*S_e isa subset of S_{d+e}, we know 1 must have degree 0, too.s/1 defines the function on Proj S which to each graded prime idealp associates the element s/1 in S_(p)!I wish I'd had me to help out when I was studying Hartshorne.Keith Ramsay === Subject: : Re: Euclids plane geometry> Euclid's plane geometry implied and provided for points, lines, and plane flat> surfaces extending in only two dimensions; all without thickness: It was Rene> Descartes who added the third dimension, or coordinate that povided for> thickness; extension in a third; perpendicular dimension, and which gave us> solid geometry.Dumb Donny Head hopelessly brainfarts again. Hey stooopid...David Hilbert in Grundlagen der Geometrie (1899) completed planegeometry using 21 axioms. Riemann OTOH and Bolyai/Lobachevsky OTOHblew Euclid's Fifth Postulate out of the water. Thurston showed thereare eight simply-connected geometric 3-manifolds with compactquotients,WP Thurston, Three-dimensional manifolds, Kleinian groups andhyperbolic geometry, Bull. Amer. Math. Soc. 6 357-381 (1982).GP Scott, The geometries of 3-manifolds, Bull. Lond. Math. Soc.15(5) 401-487 (1983)WP Thurston, Three-dimensional geometry and topology, Vol. 1.Princeton Mathematical Press, Princeton, NJ, 1997.One hopes you were more skilled at shoving objects up your ass thanyou are at pulling them out.-- Uncle Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals)Quis custodiet ipsos custodes? The Net! === Subject: : Re: Euclids plane geometryX-SessionID: 4JmGb-1208-Y4-3250@news.uchicago.eduX-Hash-Info: post-filter,v:1.4X-Hash: 5f70e7e2 e67b7a09 ab4e59cd a6a233b5 1e331f4b> Euclid's plane geometry implied and provided for points, lines, and plane flat> surfaces extending in only two dimensions; all without thickness: It was Rene> Descartes who added the third dimension, or coordinate that povided for> thickness; extension in a third; perpendicular dimension, and which gave us> solid geometry.>Dumb Donny Head hopelessly brainfarts again. Hey stooopid...>David Hilbert in Grundlagen der Geometrie (1899) completed plane>geometry using 21 axioms. Riemann OTOH and Bolyai/Lobachevsky OTOH>blew Euclid's Fifth Postulate out of the water.One wonders how long you'll keep repeating this nonsense.Mati Meron | When you argue with a fool,meron@cars.uchicago.edu | chances are he is doing just the same === Subject: : Re: Euclids plane geometry> Euclid's plane geometry implied and provided for points, lines, and plane flat> surfaces extending in only two dimensions; all without thickness: It was Rene> Descartes who added the third dimension, or coordinate that povided for> thickness; extension in a third; perpendicular dimension, and which gave us> solid geometry.See Euclid, Book XI: solid geometry. === Subject: : Re: Euclids plane geometry> Euclid's plane geometry implied and provided for points, lines, and plane flat> surfaces extending in only two dimensions; all without thickness: It was Rene> Descartes who added the third dimension, or coordinate that povided for> thickness; extension in a third; perpendicular dimension, and which gave us> solid geometry.>See Euclid, Book XI: solid geometry.whether it was just attributed to him.Of course, Don Shead himself has provided thickness on just about anymathematical topic imaginable. === Subject: : Re: Euclids plane geometry> Euclid's plane geometry implied and provided for points, lines, and plane flat> surfaces extending in only two dimensions; all without thickness: It was Rene> Descartes who added the third dimension, or coordinate that povided for> thickness; extension in a third; perpendicular dimension, and which gave us> solid geometry. Perhaps you should re-read Book XI and Book XIII of Euclid's Elements.Darren> ----- Posted via NewsOne.Net: Free (anonymous) Usenet News via the Web -----> http://newsone.net/ -- Free reading and anonymous posting to 60,000+ groups> NewsOne.Net prohibits users from posting spam. If this or other posts> made through NewsOne.Net violate posting guidelines, email abuse@newsone.net === Subject: : Re: SPECIAL RELATIVITY DISPROVED!> Reproduce the double maxima of the nova, or give a> simple explanation for it, using your wave model. My> explanation is a simple as it can be.> Employ your own fully fledged loyalty to wave theory,> and research it yourself. Nobody is stopping you.> There is no scientific terrorism. Just prejudice. We've> always had that.> Androcles>> [EL]> I visited your web-page and do not see any equations> or data tables.> Those curves mean nothing since you failed to include> any explanation.> Please help me to conclude that I did not waste my time.>> El, I think the time has come for you to use> your secret Lady Sanity weapon on Androcles.> I'm sure he will appreciate it.> Good luck ;-)>> Dirk Vdm> [EL]> Dirk, I have no secret weapons,> Indeed, it isn't much of a secret anymore.> Let's call it *silly* weapons, okay?> but I am beginning to understand the> motivations behind your Fumble's collection. :)> Bravo, you are a fast learner.> You have read the top two lines of the page, right?> Keywords: Ignorance and Arrogance.[EL]Is that the entry of your CV?Do not forget to include the rest of your fabulous qualities such as:Rude.Insolent.Fraud.Imaginative villain.And then you may add that you are ignorant and arrogant at the end ofthe list of course.The big Surprise IS:That you have been criticising a mainstream mathematical notation thatI COPIED from a college edition of Probability and Statistics byMurray R. Spiegel who is Ph. D. Professor and Chairman of Mathematicsat Rensselaer Polytechnic Institute of Connecticut. > I still do not like it from an ethical point of view but it is quite> understandable also.> Having the honour of being on your page I really have an appeal hoping> that you are intelligent enough to understand it.> On the *Real Axis* take the set of all integers as {N | N is an> integer}.> This is the set of whole numbers, usually called Z.> Z = { ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... }> In this context the phrase On the same *Real Axis*> is utterly irrelevant.> On the same *Real Axis* there is a set of squares {M | M = N^2}.> Bad notation.> Try this:> S = { M | there is an element N of Z such that M = N^2 }> = { 0, 1, 4, 9, 16, ... }> Again, the phrase On the same *Real Axis*> is utterly irrelevant.> Now we can construct a set {X | X = M^(1/2)}> Bad and ambiguous notation.> Either you mean the set of natural numbers (positive wholes)> N = { 0, 1, 2, 3, 4, ... }> which is the standard definition of the sqrt or the power 1/2,> or you are explicitly working in the field of *complex* numbers> (which you irrelevantly said you are not), and then you have> created the following set:> { {0}, {-1,1}, {-2,2}, {-3,3}, {-4,4} ... }> Each element X is a binary subset holding two elements where X = {-N,> +N}> As you can see, this is wrong in both cases.> Even if you were working in the field of complex> numbers (which you said you are not), it would be> wrong because there is one subset with 1 element.> We can also say that X = (-N) XOR (+N) for any single determined> solution.> Utterly wrong and silly notation.> You disagreed with me on this and added me to your fumbles as a fumble> fumbled by you. :)> Do you still insist to intimidate those whom you do not agree with by> adding them to your list?> Stick with biochemistry and stay away from elementary> mathematics as far as possible. It is not your cup of tea,> i.o.w. you suck at it.> sqrt( 9 ) = 3> -sqrt(9) = -3> sqrt(x^2) = x for all x > 0> sqrt(x^2) = -x for all x < 0> and there is nothing your Lady Sanity can do about it.> By the way, I love the way you got kicked out of> the soc.women group> http://groups.google.com/groups?&threadm=a0133f8d .0312190645.76c89e05@posting.google.com> when you were trying to pretend to be a *real* Lady> after having been exposed as another instance of EL.> That was a real beauty.> But I do agree that you don't have any *secret* weapons.> You are sweet. A bit clumsy perhaps, a bit transparant,> but charming :-)> Dirk Vdm === Subject: : Re: SPECIAL RELATIVITY DISPROVED!> [EL]> Is that the entry of your CV?> Do not forget to include the rest of your fabulous qualities such as:> Rude.> Insolent.> Fraud.> Imaginative villain.> And then you may add that you are ignorant and arrogant at the end of> the list of course.> The big Surprise IS:> That you have been criticising a mainstream mathematical notation that> I COPIED from a college edition of Probability and Statistics by> Murray R. Spiegel who is Ph. D. Professor and Chairman of Mathematics> at Rensselaer Polytechnic Institute of Connecticut.> So call him, and take it out with him, mother-er.> I am expecting you to disappear in shame if there was one drop of> blood remaining in your face.> You can pretend all you wish to be the all knowing and fool the fools> who subscribe to your fraudulence.> But this time you swallowed the bait and the line whole.> Goodbye Jerk.> :-)> ELNot a ghost of a chance of a red face, EL.Dinky van der Mumble is the original Troll and useless idiot that preys onunsuspecting intellectuals as they crudely try out their ideas on s.p.r,prior to committing to a paper. After all, it is better to have someone elsecheck your real errors before you get egg on your face.Dinky jeers and sneers at everything, publishing what he considers aserrors. I've even set him up with V = (c+v)/(1-cv/c^2) and he took the baithook line and sinker, highlighting the minus sign and publishing. This isbecause I caught his goof in his own equation, which he shrugged off as atypo.Anyone else reading will know, if they are reasonable intelligent, so I getto have my work published on Dinky's site so long as I include an obviouserror.That's quite nice, really. The only problem is, nobody remotely intelligentwill bother reading Dinky's site.Androcles === Subject: : Re: 1 = 0.999999(9)... hehIn sci.math, Chris Mantoulidis:> Did you know that? 1 = 0.9999999999999999999.....> Here's why:> let's say a = 0.999999999999999999....> so 10*a = 9.999999999999999999999....> and a = 0.999999999999999999999....> -------------------------------------- (subtraction)> 9*a = 9> a = 9 / 9> a = 1> Weird isn't it?> So if you ever see (for example) 10.9999999999999 in a problem, just> make it 11, it's the same thing... Check it out ( 10*b - b => 109.999999 - 10.9999999 <=> 9*b = 99 <=> b = 11 )> cmadAh, is it that time of month again, to debate the 0.999... = 1 problem? :-)Yes, 0.999... = 1 = 1.000... but some runs into some interestingissues along the way; for starters, what does 0.999... really mean?It can be modeled as a Cauchy sequence: 0, 0.9, 0.99, 0.999, 0.9999, ...;this sequence tends towards a limit, a real number (pretty much bydefinition) -- which turns out to be 1, since the intermediateterms are in fact equal to 1 - 10^(-n).Or one can model it using a variant of Dedekind cuts; letset A be the set of all things less than 0.999... (moreformally, all numbers less than 0, and all numbers 0 < x <1 with at least one digit less than 9), and let set B bethe set of all things greater than or equal to 0.999... .It turns out 1 is in set B, and is the lowest elementthereof.If one assumes a = 0.999... = 1 - d for some inconceivablysmall d, one computes a/10 + 0.9 = 0.999... = 1 - d/10,with the same identical decimal expansion, as one hasmerely shifted all the digits 1 right place. The onlyway this works at all is to stipulate d being exactly 0.Also, the usual warnings apply; miswriting e = 2.718281828...for instance suggests that e is a rational number, when itin fact is anything but (a more accurate representation ise = 2.7182818284590452...).Notations such as 0.999...9998000...0001 are possible, butnot infinite (0.999...9998000...0001 = (0.999...9)^2).In any event, one could state that 9*0.999... = 8.999..., whichmakes for minor problems. (9*0.99999 = 8.99991, for example.)The symbol '=' also comes in for some scrutiny, asboth sides of the equality 0.999... = 1.000... can beconsidered as limits.If one does all this Cauchily (yes, that's a horrid pun!):a_n = 0.999...9910*a_n = 9.999...9010*a_n - a_n = 8.999...91which gets us nowhere, unfortunately, although the limits still match.One other problem with the infinite subtraction10*0.999... - 0.999...if it's treated as a purely formal positional digit problem,is that there's no last digit so one doesn't know whetherone has to borrow and get 8.999... as the borrow carriesthrough the entire number, or not, and get 9.000... .Happy symbol manipulating. :-)-- #191, ewill3@earthlink.netIt's still legal to go .sigless. === Subject: : Re: 1 = 0.999999(9)... heh> Did you know that? 1 = 0.9999999999999999999.....> Here's why:> let's say a = 0.999999999999999999....> so 10*a = 9.999999999999999999999....> and a = 0.999999999999999999999....> -------------------------------------- (subtraction)> 9*a = 9> a = 9 / 9> a = 1> Weird isn't it?> So if you ever see (for example) 10.9999999999999 in a problem, just> make it 11, it's the same thing... Check it out ( 10*b - b => 109.999999 - 10.9999999 <=> 9*b = 99 <=> b = 11 )> cmadHi Chris,don't mean to be rude, but you do realise most participants on s.m are*mathematicians*, don't you? (Yes, even David knew, but he was either beingnice or sarcastic...)Why don't you post this at DrMath's, e.g. the elementary section?Steven === Subject: : Re: 1 = 0.999999(9)... heh> Did you know that? 1 = 0.9999999999999999999.....> Here's why:> let's say a = 0.999999999999999999....> so 10*a = 9.999999999999999999999....> and a = 0.999999999999999999999....> -------------------------------------- (subtraction)> 9*a = 9> a = 9 / 9> a = 1> Weird isn't it?> So if you ever see (for example) 10.9999999999999 in a problem, just> make it 11, it's the same thing... Check it out ( 10*b - b => 109.999999 - 10.9999999 <=> 9*b = 99 <=> b = 11 )> cmad>Hi Chris,>don't mean to be rude, but you do realise most participants on s.m are>*mathematicians*, don't you? (Yes, even David knew, but he was either being>nice or sarcastic...)Moi?>Why don't you post this at DrMath's, e.g. the elementary section?>Steven************************David C. Ullrich === Subject: : Re: . Adding spatial dimensions .Hello dlzc , Re: Assuming that relativistic mass ' heat ' is very much dependent on time Relativistic mass is effected by gravity , and it also generates it .Even a Cold atom has a lot of relativistic mass from all the waves inside it .I just use the words Energy or heat to visualize relativistic mass . === Subject: : Re: . Adding spatial dimensions .> Dimesnions = number of parameters. Programmer deal in arbitrarily largeThat may be true, I've never dealt with dimesnions, maybe I missed out on theprogrammer deal, but topologically any object from over 1 spatial dimension is not simple,and they (we) are not purely indexed points as if in a matrix dimension.Herc === Subject: : Re: Iranaian Advance in Bohmian Quantum Gravity> bcc> Unlike the bad intelligence on Iraqi WMD capability, it is IMHO agrave> error to under estimate the potential for technological surprise from> the very excellent Muslim theoretical physicists in Teheran who are> second to none.> Gaaash, Jack, why do have to piss off all the Jews here by saying> that second to none bit!? Everybody knows that Jews are the> smartest, the Chosen ones. Bob Kolker even calculated that Jews> are 5.5 times smarter then the Wogs, as he calls them.> They'll get on your ass for saying that, Jack!>> Their eqs 41 to 43> seem to be compatible with my equations> consistent with the idea that Bohm's quantum> potential is another way to write the zero point energy!> [EL]> Read the message carefully hanson.> Ph. D. Physics, Professor Jack Sarfatti says;> seem to be compatible with my equations> AND> very excellent Muslim theoretical physicists in Teheran who are> second to none> So the hidden message should be very clear.> *They* are second to none *But Jack* of course.> He is the reference to that can judge that they are second to none> under God of course.> Jack is TEN times smarter than any other Jew and this makes him 55> times smarter than any other Iranian.> However, I do agree with Jack that the situation is critically> intolerable and scientists should do something about it quickly> before names such as Ali and Fatima get written in physics books.> Jack is our hope now and he should sue them for publishing equations> that seem compatible with his equations. How dare they! :)> Can you imagine the disaster if Tehran succeeded in opening one of> those Zero Point Energy Boxes!> Bohm's quantum potential will be all over the place contaminating the> Iraqi petrol and America can not fuel its cars with it any more, not> with that Bohmian quantum potential leering at you from every car> exhaust screaming and ranting.> :)Give congratulations where congratulations are due.You've done it, EL.{:-))Franz === Subject: : Re: Breakthrough In Propulsion Physics.> Franz Heymann:>in>> at 04:34 PM, Franz Heymann >> said:>>The assumptions are only that the laws of physics are ther same> >>everywhre and always.>> No. The assumption required is stronger than that. See>> , where Gauge gave>> a correct formulation. If the laws of Physics included a>> position-dependent Lagrangian then you would not be able to apply>> N.9ather's Theorem to get conservation of momentum, even though the laws>> were the same at every point.>>You are right. I apologise for giving a pop statement of Noether'sTheorem.>>I am beginning to wonder if Gauge and Bilge are not both being somewhat>pigheaded about this issue, and that they are both actually right,within>the domains each appears to be concerned with. Gauge's statement sounds>like a statement applicable in the classical domain, whilst Bilge'swould be>applicable in the QFT domain.> His example is not relevant to anything other than the fact that a> tautology is a tautology. First I'll include his original response> so that we have _exactly_ what he said:> In message-id:,> Pmb stated:> You missed the point. heyman was refering to the laws of physics and> Noether's theorm. The relationship is as follows> When> Space is homogenous - total momentum of system is conserved> Space is isotropic - total angular momentum of system is conserved> Time is homogeneous - total energy of system is conserved> Which is ok, as far as it goes, in that this result may be _derived_> from noether's thorem, as I demonstrated by deriving those results.> However, he goes on to say:> To be precise - Let L be the Lagrangian of a system. Let P = &L/&q => generalized momentum conjugate to q. If L does not depend on q then> P = constant. If L does not depend on t then Energy = constant.> Which has nothing to do with what he said above. In fact, arguing that> homogeneity of time leads to conservation of energy in a non-relativistic> system is manifestly false, since homogeneity of time is what gives you> conservation of energy in a relativistic system because homogeneity of> time is what gives you lorentz boosts. It isn't possible for homogeneity> of time to mean different things. To obtain results which agree with> nature and which reflect classical mechanics, you must incorporate the> galilean boosts as an _additional_ symmetry.> So, not only is his statement _not_ a precise description of what> he claims it is, it doesn't even depend on the principles he claimed.> But, aside from that, he completely failed to even say anything about> the role of noether's theorem.> Noether's theorem enters at the point you take an _arbitrary_lagrangian,> and find the conserved current which leaves the lagrangian unchanged> under a symmetry operation. It has nothing to do with assuming the> lagrangian in manifestly invariant as it stands. If that were the> case, no one would care about noether's theorem because she would have> never had a reason to develop it.> To use noether's theorem, one may proceed as follows. Under a time> translation, the change in the lagrangian is given by:> L'[t] = L[t + dt] = L + (dL/dt)delta t> If dL/dt is identically zero, you have a trivial result that doesn't> involve anything more than hamilton's principle and noether's theorem> never comes up. It tells you nothing about the symmetry associated with> the time translation. To compute the conserved current associated with> that time translation, you must compute the change in L with respect to> the generalized coordinates (or fields, whatever the case might be):> . .> delta L = (dL/dq)delta q + (dL/dq)delta q> The second term may be rewritten as,> . . .> (dL/dq)delta q = (d/dt) [(dL/dq)delta q] - [(d/dt) dL/dq] delta q> so that Delta L becomes:> . .> delta L = { (dL/dq) - [(d/dt) dL/dq] }delta q + (d/dt)[(dL/dq)delta q]> The term in { } brackets, vanishes by virtue of the euler-lagrange> equations. That leaves,> .> delta L = (d/dt)[(dL/dq)delta q]> The change in q is given by delta q(t) = q(t') - q(t) = (dq/dt)delta t,> so that upon equating the two expressions for delta L, you have:> .> (d/dt)[(dL/dq) (dq/dt)] = (dL/dt)> Which gives the relation:> .> (d/dt)[(dL/dq)(dq/dt) - L] = 0> The term in [ ] brackets is the conserved current, which might be> more recognizable in the form:> .> H = pq - L> So that the conservation law is given by dH/dt. dL/dt = 0, obviouslydoesn't> do it, unless the first term is also identically zero.>The version of the theorem of which I have a detailed proof to hand,>involves a classical Lagrangian, and says>If the Euler-Lagrange equations of motion are invariant under acoordinate>transformation typified by>t,q --> t'(t) , q'(q,t), then there exists an integral of motion, i'e' a>conserved quantity> Right.>( Greiner & Muller, Quantum Mechanics, Subtitle Symmetries)>Note the absence of references to Lagrangian densities and conserved>currents.> >>I wish I also had a quantum mechanical version of the theorem here, but>alas, I don't> It works the same way. Under a U(1) displacement, the wavefunction> becomes,> Psi -> Psi' = exp(-iS)Psi> Operating on that with the dirac lagrangian, p/ - m, for example,> gives you,> _ _> L' = Psi(p/ -m)Psi + iPsigamma^uPsi d_u S> The difference in L and L' is made to vanish by the addition of a field> which transforms as the lagangian, so as to cancel the additional term.> That field is the covariant derivative, D_u = d_u - ieA_u, where d_u S> is identified with eA_u so that (igamma^u D_u - m) is the correct> form of the lagrangian.Since I don't wish to be embroiled in this argument any longer, I'll revertto lurking.Franz === Subject: : Re: Breakthrough In Propulsion Physics.> You are right. I apologise for giving a pop statement of Noether'sTheorem.> I am beginning to wonder if Gauge and Bilge are not both being somewhat> pigheaded about this issue,> Ummm ... I haven't been pigheaded at all. Although bilge most> certainly has.> First off consider what Noether's theorem actually states:> ******************************> Noether's theorem: For every continuous symmetry of the laws of> physics, there must exist a conservation law. For every conservation> law, there must exist a continuous symmetry.> ******************************> In fact all I've done is give an example of an application of> Noether's theorem. I.e. I gave well known examples. I.e. I stated that> *****************************> When> Space is homogenous - total momentum of system is conserved> Space is isotropic - total angular momentum of system is conserved> Time is homogeneous - total energy of system is conserved> *****************************> The proof of each is rather trivial and is widely known. bilge> obviously never learned this since he incorrectly claimed that this> has nothing to do with Noether's theorem and such a claim is> obvioulsly wrong. bilge then stated> Noether's theorem says that for every continuous symmetry of> the lagrangian, there corresponds a conserved current.> While this does follow from Noether's theorem (that for every> continuous symmetry of the lagrangian, there corresponds a conserved> current) - this is *not* a *definition* of Noether's theorem. It's> just an application of it as was mine. In fact I *clearly* stated that> (i.e. that his statement was correct in that Noether's theorem implies> that) in my post which followed (where I corrected bilge), i.e. I> posted the statement> ********************************> In discrete dynamics the Lagrangian is the normal Lagrangian and the> symetries lead to constants of motion i.e. conserved quantities. In> field dynamics the Lagrangian is the Lagrangian density and the> symetries of lead to conserved currents. Same thing - A conserved> current is still something which is conserved.> Noether's theorem states that each symetry, as expressed by the the> independance of the Lagrangian on a on a variable, then there is a> conserved quantity associated with it. I.e. Nother's theorem regards> relations between> symmetries and conserved quantities.> ********************************> The rest of my posts in this thread were corrections to bilge's bogus> claims which followed (his problem has always been that he can't admit> when he's made an error).> So tell me - How is what I said above a reflection of me being> pigheaded?In spite of my having said in a companion letter that I will bow out of thisargument, I will give you a goodbye statement.The very fact that your intellect is incapable of perceiving that thisrestatement of your pigheadedness is a pigheadedness in itself.You have found yourself in this position so often by now that I wouldsuggest that your mentality is such as to make you unsuitable for pursuing aconversation in this ng. Why don't you just take up knitting instead?I tried to throw oil on troubled waters but you refused to be rescued. Sobe it.I snip the rest as I have nothing to say to it.Franz === Subject: : Re: Breakthrough In Propulsion Physics.> His example is not relevant to anything other than the fact that a> tautology is a tautology.Its comments like this which are a true indicator of your ignorance.This claim is utter nonsense. But that's par for the course forbilge's posts!> In fact, arguing that> homogeneity of time leads to conservation of energy in a non-relativistic> system is manifestly false, ..More nonsense as usual. Aren't you embarassed enough bilge? Do youreally need to provide more proof that you don't have a clue aboutanything?Listen carefully for once in your life - If, for a monogenic system (i.e. systems in which the Euler-Lagrangeequations hold), L does not depend on time then it follows that energyis constant - Period! Finito! End of Story!!!In fact I proved that to you a very long time ago herehttp://www.geocities.com/physics_world/sr/relativistic_ energy.htmPlease learn the facts before you post such utter nonsense as thesebopgus claims that you keep making.These facts can be found in most texts in analytical mechanics. Iguess that's why you hate textbooks so much. You have never been ableto fully understand them so you flame people who show them to you thuspointing out your errors!The proof is trivial in fact. Its a simple application of Noether'stheorem, i.e. foe a symmetry of the Lagrangian there is a conservedquantity.Homogeneity of time - This is defined as follows: The Lagrangian of aclosed system does not explicitly depend on time.Proof is given herehttp://www.geocities.com/physics_world/sr/relativistic_ energy.htmThe energy function h is defined as h = q'_k &L/&q'_k - LFor monogenic systems the Euler-Lagrange equation d/dt(&L/&q'_k) =&L/&q_k holds true. This implies thatdh/dt = -&L/&tSince L does not depend on time then &L/&t = 0 --> dh/dt = 0 --> h =constant.h is the energy of the system.Similar arguements show that momentum is conserved. I.e. conservationof linear mechanical momentum follows from the homogeneity of space.The Lagrangian of a closed system does not depend on positionexplicitly. It can be shown that this leads to conservation of linearmechanical momentum.Same with angular momentum - I.e. conservation of angular momentumfollows from the isotropy of space. The Lagrangian of a closed systemdoes not depend on angluar orientation in space. It can be shown thatthis leads to conservation of angular momentum.However when the system is not closed it doesn't mean that thecorresponding quantities above are not conserved. One then has to lookat the Lagrangian for symmetries. E.g. an infinitely long straightuniform wire (which is rotationally symetric) lying on the z-axis willmean that the Lagrangian will not depend on z. Choose cylindricalcoordinates. Then the Lagrangian will also not depend on theta. Thusthere are two conserved quantities - p_z = mv_z and the z-component ofangular momentumPlease learn these very basic facts before you come back and claim tounderstand what you're talking about.[snipped more of bilge's bogus claims][bilge claims]> Noether's theorem enters at the point you take an _arbitrary_ lagrangian,>and find the conserved current which leaves the lagrangian unchanged>under a symmetry operation.A complete lie as always. Why do you keep trying to change thestatement of Noether's theorem? The theorem clearly states thatFor each symmetry of the Lagrangian, there is a conserved quantity.It makes no difference if the Lagrangian is arbitrary or not.Noether's theorm applies to symmetries whether the symmetry is ageneral symmetry for a closed system in nature of whether the symmetryis due to the nature of a particular physical system. I gave you thelink to the Havard notes on this. Was the section on Noether's theoremtoo difficult for you to understand?>Which gives the relation:> (d/dt)[(dL/dq)(dq/dt) - L] = 0Ummmm ... bilge old boy!!! I explained that to you a **very** longtime ago. I explained all this to you herehttp://www.geocities.com/physics_world/sr/relativistic_ energy.htm*********************************If the Lagrangian, L, is not an explicit function of time then itfollows that h = constant, i.e. h is an integral of motion.*********************************That very basic result of analytical mechanics is the reason that Isaidwhen time is homogeneous - total energy of system is conservedSheesh! I sure wish you'd decided to stop being so arrogant and startpaying attention************* The term in { } brackets, vanishes by virtue of the euler-lagrangeequations.*************You got it correct this time. But you screwed it up last time. Whenyou first claimed that homogeneity of time didn't imply conservationof energy you failed to take into account that the Euler-Lagrangeequationd/dt(&L/&q'_k) - &L/&q_k = 0doesn't hold for systems with friction. And you gave a system withfriction as an example. Actually it turned out to be an example ofyour ignorance again.The correct equation of motion in cases of friction thatd/dt(&M/&q'_k) - &M/&q_k = Q_kBut as I said - Symmetries imply conserved quanties. In the cases I'vegiven then these symmetries were reflected in cyclic variables. In thecase of time the Lagrangian is cyclic in time t. Thus &L/&t = 0impies energy is constant.Read a decent mechanics texts and start studying this carefully.Landua and Lifs is a good place to start but you've demonstratedthat you're having trouble with these things. But you can always askfor help on the newsgroups.Turn to Chapter II and you can learn from them everything I've taughtyou over the last week on symmetries and conserved quanties.Then try to grow up === Subject: : Re: Breakthrough In Propulsion Physics.> at 01:31 PM, Pmb said:>My grad mechanics prof loosely described> The key word their is loosely.Not really. Its a precise statement if you understand what he meant.When he refered to physics he was refering to the Lagrangian.I also made an error in that quote. It should have read***********************************If physics is the same here as they are over there (i.e. if Ican move my lab and the results of my experiments remain the same)thenlinear momentum is conserved. If physics is the same in thisdirection as they are in that direction (i.e. I can rotate my labandtheresults of my experiments remain the same) then angular momentum isconserved. If physics is the same today as they are tommorow(I.e. if I can run my experiment today and tommorow and get the sameresult)then energy is conserved.***********************************I.e. it should have said If physics.. not If the laws ofphysics...> The second problem> is that N.9ather's Theorem has nothing to do with the results of your> experiment being the same when you move the lab, only with the> symmetries of the Lagrangian.That's incorrect. But it is incorrect as it pertains to the correctquote above. Symmetries are reflected by the absense of a variable inthe Lagrangian. The absense of such variables reflect symmetries innature, i.e. in the environment.For example: Consider an infinitely long straight charged wire with nocurrent in it (in the frame under consideration) which is lying on thex-axis. The effect of the charge on the Lagrangian is to given theCoulomb potential, Phi, an r = sqrt[x^2 + y^2]-dependance and only anr-dependance only. Thus L = L(r). Notice that it does not depend on x!That is a symmetry in the Lagrangian. It follows that the conservedquantity here is the x-component of canonical mometum.Pmb === Subject: : Re: Breakthrough In Propulsion Physics.> Really? Can you tell me how in the first place you measured the speed of the> inertial frame?> The only way you could measure distance by a clock only, is by assuming both> an absolute reference frame at rest and a constant speed of light. Those two> are mutually exclusive. You loose.Irrespective of that, physics is overdue for a major change. So ifyou can define a different system than the amazingly absurd ones oftoday then I am willing to look at it (although I warn you, I am not abeaurocratically certified crankademic and may not be able to respondwith empirically proven fallacies if this is what you seek).JS === Subject: : Re: Breakthrough In Propulsion Physics.> Really? Can you tell me how in the first place you measured the speed ofthe> inertial frame?> The only way you could measure distance by a clock only, is by assumingboth> an absolute reference frame at rest and a constant speed of light. Thosetwo> are mutually exclusive. You loose.> Irrespective of that, physics is overdue for a major change. So if> you can define a different system than the amazingly absurd ones of> today then I am willing to look at it (although I warn you, I am not a> beaurocratically certified crankademic and may not be able to respond> with empirically proven fallacies if this is what you seek).> JSI got one....So the Mays Absurd Postulate forms from the mist....I will start with an assumptions and explain why...I have heard both side of the arguments on whetherthe Universe is a product of a Big Bang (BB from now on)and I have heard the arguments on it not being a productof a BB.. and IMHO the argument, data and explanationsin favor of the Universe being a product of the BB seemsthe most plausable for the observed Universe we live in.So I will not make that argument as others have a much betterknowledge base and I would let their views stand and I willtake the position that I assume the Universe was the productof a conversion of the yet to be defined energy Quantumthat I coin a Quantum Point.I also consider most all existing mathematical modelshold with my postulate but the interpretation may bein question in some models. I think that some of themore contrived constructs are complicated by the Factthat we do not know all of the rules that apply to theobserved Universe and some mathematical constructshave been required to use assumed values and contrivedelements in order to fit experimental data when All therules are not yet defined.The primary missing rules are concerning gravitationalvariance in the presence of objects with rest mass. Wecan define the Effects aspect with great accuracy but wehave yet to define the cause and using existing physicalrules, I submit, we never will because All existingphysical rules only apply to the effect aspect of matterin motion in relation to other matter in motion...This is just my neophyte attempt to give a postulatethat gives a rational for that cause while maintainingthat existing rules of effects remain intact and explainsmany aspects of the observed universe that have alludedscience for a very long time......In The Beginning....To understand the foundation for this postulate some havecalled a Quack Theory of Everything I must try todescribe the Singularity of the BB before anything thatfollows. And in doing so I will postulate on the causationmechanism for the yet to be defined elements of gravitationaland magnetic variance.We consider that the yet to be defined energy form that wasthe source of the BB was following Einsteinian conversionthen looking at the reverse condition may explain a bit better.If I have a finite amount of matter and I convert it into an energyform we observe the energy forms (kinetic, thermal, inertial,)and are controlled by relativistic force forms ( EM,G,WN&SN)If we consider the matter without relation to external matter andconvert the matter to energy without reference to external matter(as is the case of a BB singularity) you have a unified yet to bedefined energy form that seems to have a infinite energy densitybut was converted from a finite amount of matter.In the case of a hypothesized Singularity ( I have a postulate I've postedbefore on the view of the Singularity as a Quantum Point of finiteenergy potential in base state of ciaos but its generally given theplonk treatment from the outset) it cannot be defined by any existingrules at this point and the laws of physics break down causing themathematically created illusion of infinity. I submit that the mentalconstruct of infinity is illusion, illusion that occurs in a modelwhen the existing rules fail due to scale.This was the Quantum Point of the BB ( I consider QP [Quantum Point]as a better descriptor for my postulate for several reasons, it betterrelays the concept after time 0+ , better explains the relationships ofmatter in both micro and macro regions, better expresses base formof nature. )The QP (Chaos Point, Singularity) was a finite amount of unified energyof a yet to be defined nature. It would have been governed by onlytwo rule's that we can identify and that is probability and uncertainty.Without matter all other laws fail... No mathematical construct can beapplied using the rules we today know... Not that there are not rulesthat apply, only that existing rules cannot.So I propose that the QP had the probability of converting a finiteof a finite size or not. And that the converted matter due touncertainties of conversion may tend to be of any finite amountand in a finite ratio of matter to antimatter. This view of energyconversion is fully in holding with Einsteinian conversion theory.The only consideration is in considering the conversion inthe absence of related other matter external of the local event.So I posit that the QP existed ( may be a multitude of QP in amultitude of conversion conditions existing without dimensionalproperties that apply from our set of rules in this Universe)of antimatter was converted ( a tad bit more matter thanantimatter).At time 0+ the matter and antimatter annihilated each otherconverting the matter and antimatter into energy and since we now have the left over matter we can model the conversionusing rules that apply to matter in relation to other matter inmotion. This period of annihilation was the inflationary periodthat is well written of. The energy was imparted into the base today. This imparted energy maintains the expansion thatfollowed the inflation with the imparted kinetic applied andball of stuff (very small) that produces a EM wave of avariable frequency with variable rate of decay of thefrequency and amplitude of the wave. I think it isdetectable and experimentally verifiable but notwith the technology and rules we have in use today.I consider the string theories to be on the right trackbut have yet to consider the bias of considering aconcept while imbedded in the construct in question.Consider the wave nature of a String as theorized and then consider it a slice of a EM wave propagatingfrom a EM producing SPP. If a variation of theview is applied to the String theory we see that variation asanother String at angle to our first construct andhave a new dimension to contend with. So I contendthat string theory describes the radiating EM fieldsof the base SPP and equates out as a slice in thefield at a specific distance of the radiating SPP.The uncertain nature of the wave is due to the Mediumthe wave propagates through and other EM producingSPP's.The Medium that I consider is not the medium of Maxwell'sAether its a bit different and needs a bit of explanation.After time 0+ there was a finite amount of matter convertedfrom the QP but it was not a 100% conversion. Probabilitytells us it could have been a <.00000001% to a > 99.999999%conversion so we have a remainder of the QP that did notconvert its unified yet to be defined energy form into matteror anti-matter.I contend that the Quantum Point of the BB still exists as aQuantum State between all SPP's. Its properties are that itproduces a inverse tensor (elastic mode variable) betweenall SPP's. Each SPP produces a EM wave and those EM wavemix, heterodyne, cancel out producing a composite EM signaturefor each local grouping of SPP's. Due to the complexities anduncertainty of the mixings end composite it tends to be aprobabilistic state. Locally when two or more SPP's are broughtin proximity they increase in tensor value in relation tolocal other SPP's but dependent of the interplay of the EM wavessome will be attracted and some repelled and will tend to formstructure as harmonic nodes form in the EM interplays.The crux of the problem is the position of the observer inrelation to the observed. Since the reader, writer and allknown methods to observe exist as conglomerates of SPP'sit contains intrinsic bias. We observe by detecting or producingEM waves and sampling the wave at specific intervals of time.Since we are connected to the observed by the Quantum Stateour act of observing impacts the observed and the observedimpacts the design and method of observing.As An Example I propose this:A ----------------------B----C--O--D------E--------------------- --ZA= Furthest SPP in some directionB= Furthest SPP in some direction relative to local SPP'sC= Closest SPP in some direction relative to local ObserverO= ObserverD= Closest SPP in some direction relative to local ObserverE= Furthest SPP in some direction relative to local SPP'sZ= Furthest SPP in some other direction--------- = Quantum StateA ----------------------B----C--O--D------E--------------------- --Z<--If A moves the total value of QS varies art the rate ofmovement. This is detectable as a variation in the UGC(Universal Gravitational Constant, Cosmological Constant)buy implied kinetic energy. Locally the observer would notethe variance on a much lesser scale as it would be locallymediated by local SPP's. If this rate occurs on auniversal scale the observer would consider the value aconstant in that its variance would not be detectable withinthe life span of the solar system if we consider the expansionon a universal scale. This also predicts that the rate ofexpansion will increase as the universe expands.A ----------------------B----C--O--D------E--------------------- --Z <--Now we move D ... the value of the QS is increasedbetween the observe and the QS value is decreasedbetween D and E. the UGC remains intact but locallythe value between D,O and C also vary . This separationdistance between SPP's set the local value of all locallyconsidered SPP's and gives rise to the illusion of curvedspace. Since we have yet to define the nature of thisQuantum State (QS), or even all the rules that apply to it,we model it and the calculation leads to an illusion ofcurvature due to the missing construct.existence connected to every other we look for observationsand detect the EM waves of groupings of SPP's and due toour interconnection the EM wave may be observed andempirically for a short duration of time, a time that isshort enough to fall below our ability to measure. ThisAnd also give rise to the constructs of infinity.So my own view is that infinity is just illusionary....An illusion that occurs when the existing rules faildue to scale or missing rules of causation.I actually think QM is getting closest to the true natureof the issue it still not advanced to the point of unification and that's the issue when speaking of Quantum points( Ciaos Point [Williams] , singularity)...The whole of the universe is expanding at an ever increasing rate as it expands... and the best rational is that the mechanismthat displays as an effect gravity is the Quantum, yet to be defined, energy that is the remainder of the finite energy that producedby conversion all the matter in our universe. That Quantum State exist as a inverse tensor field (elastic mode variance)where as the field strength reduces with separation distance of boundof matter and anti- matter into heat and kinetic during the inflation( universal gravitational constant ) to reduce... this causes a lowerUGC on a universal scale and the universe increases its rate ofexpansion...Consider the old view of a Universal Balloon.. if you were atoutside edge or close to it because it has no edge like a balloon( think of it as a balloon with the skin on the inside... eachThe UGC is set by the overall separation of all matter so the baselineGravitational field is not constant but varies at a rate set by thetotal separation of all matter so on our scale it would appearas a constant due to it not varying in any degree that could bemeasured on our scale..... But locally if the matter is dense thelocal gravitational set is varied.. this causes the gravitational wellsof massive objects. The baseline gravitational field is an effect aspectI truly think there are no constants or infinities in the universe.We call a mathematical construct a constant because we cannotever note a change in it.. But if it changes on a universal scalewe would never be able to note it as a variable,,, and I submitthat the concept of infinity is but a illusion that occurs whenknown mathematical laws break down.As an example.. try this thought experiment.. you have a finiteamount of matter.. consider it the only matter in the universe..Einsteinian rules say It can be converted into energy and energycan be converted into matter.. If its the only matter and youconvert it into energy you cannot get kinetic form becausethere is no other matter to impart to.. you cannot get thermalbecause thermal conversion must occur to other matter also..What you would end up with would be unified energy withoutany matter for effect physical laws to apply. Now try asyou like, if you wish to calculate the energy quanta of thisconversion you end up with infinite energy.. because allphysical laws we know are only applicable to matter in motion...and break down if you try to know the energy quanta ...youend up with the illusion of infinite energy even thoughyou know that it was converted from a finite amount of matter..And I now postulate another kook concept....The value of c is variable and is set by separation distancebase value is set by total separation distance of alllife span of our solar system. But will vary locallyis the reason for the velocity of EM waves to reducewhile traversing a medium. This is why we experimentallyobserve c as source independent because in vacuum it's valueis set by the total separation distance of all SPP's on a Universalscale. But in a local dense grouping of SPP's wenote a reduced value for c as when an EM wavetraverses a non zero distance through a medium, whichis nothing more than a local dense grouping of SPP's .The theory of velocity being reduced by absorbs andretransmission was only conceived because of the biasthat c was constant and a mathematical rational had tobe formed that explained why the measured value of cwas reduced in a medium. If you apply the sameformula to the concept and consider that the valueend results as the absorbs and retransmission model....Using this postulate I make a few predictions1. The Rate of Expansion will increase as the Universe expands.2. The UGC or CC will vary at the rate of expansion. [UGC = Universal Gravitational Constant CC = Cosmological Constant3. The Value of C in a vacuum will vary at the rate of expansion. ( Medium)5. The Value of G will vary locally with separation distance of local matter. EM waves sampled in a short time frame by a method and design that is intrinsically biased.7. The concepts of infinity and paradox are illusions created when existing rules fail due to scale or incompleteness.8. Gravity is the effect of varying the separation distance of9. Magnetism is the effect of EM waves through natural selection forming a heterodyned interplay that is detectable as the attractive force.10. the WN and SN forces are effects aspects of short range EM interplays finding equilibrium as SPP's group.And have as an experiment to show the effect is the Brown effectof applied static field which Tesla considered in his 1937 staticmotion demonstration.Here's a working variation to demonstrate the effect of alteringthe local QS by applied static charge....http://ripkaboroski.com/device5b.jpgIn closing let me repeat... This is not a theory...I have not the Mathematical ability to providemodels that can be examined but I do thinkthe model can be created and verified. For themost part I see no point where I disagree with theexisting standard models and all existing mathremains intact for the most part. My Postulateexplains many of the issues that have plaguedphysics for ever while maintaining that for themost part all existing physical laws are correct andviable. My postulate also address's the Zero PointEnergy theories that float about and fills in theproblems that exist in that area. It follows StringTheory to a great deal but gives predictions andasserts that there is no need for more than 4 dimto define any point in the universe. The postulateexplains the Brown Effect which has yet to be definedto a point the definition in agreement with GR or SR.I look for anyone to debate my view in detailand destroy it by showing me where I deviatefrom the existing theory to a point my postulate fails.Feel free to ask any question on any aspect not understoodand I will gladly explain my concept of the details mentioned.I cannot prove my postulate so don't ask for proof but I canexplain the construct and how it fits the existing observationof the reality around us. There is many aspects I do notfully grasp so there of course will be holes in the postulateand that's why I'm here looking for intelligent peopleto point out the holes and poke new ones so I can betterexpress the postulate.-- Paul R. Mays---------------------------------------------------------- -------------------Some where within the Quantum StateHttp://Paul.Mays.Com/story.htmlhttp://paul.mays.com/ mayday.htmlhttp://paul.mays.com/rainy.htmlThe man who cannot occasionally imagine events and conditions of existence that are contrary to the causal principle as he knows it will never enrichhis science by the addition of a new idea. -Max Planck === Subject: : Re: Breakthrough In Propulsion Physics.> Multiply the time interval measured by your clock by the speed of your> inertial reference frame> What is this speed of your inertial frame lark?> FranzI'm not surprised you don't understand these elementary concepts.JS === Subject: : Re: Breakthrough In Propulsion Physics.> Multiply the time interval measured by your clock by the speed of your> inertial reference frame> What is this speed of your inertial frame lark?> Franz> I'm not surprised you don't understand these elementary concepts.And I am not surprised that you don't realise that the speed of *your*inertial frame is at rest by definition.Franz === Subject: : Pythagorean triplet related sequenceLet a_n be the smallest non-zero natural number m such that n^2 + m^2= k^2, (n, m, k) is a Pythagorean triplet, or otherwise 0. Thisdefines a sequence that begins like this:n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21a_n 0 0 4 3 12 8 24 6 12 24 60 5 84 0 8 12 144 24 180 15 20Conjecture: For all n > 2, iff a_n > a_(n+1) then n is prime.Here is a method for calculating a_n. Find all factorings (f1 * f2) ofn^2 such that (f1 + f2) is even and f1 =/= f2. Then pick the one thatminimizes:m^2 = (f1 + f2)^2 / 4 - n^2It's easy to see that for all prime n the only possible factoringapart from the trivial case f1 = f2 = n is:f1 = 1, f2 = n^2since we know that for prime n, n^2 is always odd so we are guaranteedto find a solution other than a_n = 0, all but one of the zeroes inthe sequence fall on even n. === Subject: : Re: Pythagorean triplet related sequence charset=iso-8859-1> Let a_n be the smallest non-zero natural number m such that n^2 + m^2> = k^2, (n, m, k) is a Pythagorean triplet, or otherwise 0. This> defines a sequence that begins like this:> n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21> a_n 0 0 4 3 12 8 24 6 12 24 60 5 84 0 8 12 144 24 180 15 20> Conjecture: For all n > 2, iff a_n > a_(n+1) then n is prime.If n is an odd prime, we indeed have a_n > a_(n+1).On the other hand, if n > 2, there is always some m > 0 such thatn^2 + m^2 = k^2 for some k > 0.Therefore we have a_n > 0 for all n > 2.In particular, you should have a_14 = 48 > 8 = a_15, whereas 14 is NOT prime.So I'm afraid your conjecture fails in this direction....Tad === Subject: : Re: Pythagorean triplet related sequence> Let a_n be the smallest non-zero natural number m such that n^2 + m^2> = k^2, (n, m, k) is a Pythagorean triplet, or otherwise 0. This> defines a sequence that begins like this:> n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21> a_n 0 0 4 3 12 8 24 6 12 24 60 5 84 0 8 12 144 24 180 15 20> Conjecture: For all n > 2, iff a_n > a_(n+1) then n is prime.>If n is an odd prime, we indeed have a_n > a_(n+1).>On the other hand, if n > 2, there is always some m > 0 such that>n^2 + m^2 = k^2 for some k > 0.>Therefore we have a_n > 0 for all n > 2.>In particular, you should have a_14 = 48 > 8 = a_15, whereas 14 is NOT prime.>So I'm afraid your conjecture fails in this direction....Let's use the following method for discovering Pythagorean triplets.Assume n^2 + m^2 = k^2. Then:n^2 = k^2 - m^2 = (k - m)(k + m) = f1 * f2Let (k - m) and (k + m) be the integer factors of n^2. This gives us apair of equations:k + m = f1k - m = f2Adding together we get:2k = f1 + f2 => k = (f1 + f2) / 2so if f1 + f2 is even we have found a Pythagorean triplet. If none ofthe integer factorings of n^2 produce triplets, let a_n = 0.This method only gives some of the Pythagorean triplets but it doesproduce the sequence in my post as well as always find one tripletprovided n is prime. Specifically, since none of the non-trivialfactorings of14^2 = 1 * 196 = 7 * 28 = 4 * 49produces an even number as the sum then we say that for the purposesof the sequence there are no Pythagorean triplets. This remedies thecase n=14, but now I'm interested whether there are other cases whereeven this does not help. === Subject: : A little holiday amusementHi Kids, No I am not advertising for Furniture, USA. Back in the darkages, a colleague of mine gave me a problem of the type we called awork problem in the USA in those days. It involved two workers,probably not unionized, with the names of A and B. They were calledupon to do many a task, and they had to cooperate perfectly or theproblem could not be modeled accurately. Anyway, this particular timethey were assigned to build a sidewalk. A could do it in 4 hoursworking alone, and B could do it in 2 hours working alone. How longwould it take both of them to do the job working together. Well, I thought and thought and drew a sidewalk. I was at leastfamiliar with them, so I drew a sidewalk like this:| | | | |Naturally they started at opposite sides, and so after 1 hour (noticehow clever I was in choosing a sidewalk with 4 equal compartments. Not drawn to scale).After 1 hour, the sidwalk looked like this.|xxxx|xxxx| |xxxx|My next impulse was to cut the remaining empty space into four equalspaces and observe that in 1/4 hour, the two boys (that was myassumption, and of course, not necessarily correct) would again finish3 of the open areas and leave the fourth. Clearly this could becontinued indefinitely, and I dimly glimpsed that there could beinfinite series lurking here, and that scared me away as I was not yetdoing algebra but languishing back in arithmetic.However I am all grown up now and can solve this problem along thoselines. clearly the answer is ... (drumroll) 1 + 1/4 + 1/16 + ... =1/(1 - 1/4) = 4/3.I have never before or since seen such a problem done in such a way,but I suppose all of them could be.So how did a child innocent of algebra solve this problem? Noticethat in one hour 3 squares of the sidewalk have been completed and 1square has not been so much as touched. (I say squares because thesidewalks where I lived had square segments, although they wereactually 2 squares in width, but I abstracted things to do the math.) Anyway, my observation was that the amount remaining was precisely 1/3of the amount completed and so would take 1/3 the time. This gives ananswer of 1 + 1/3 = 4/3, and it is easier to explain when you don'tknow about infinite series.This was my greatest intellectual accomplishment ever and willprobably remain so. Unfortunately it is not an original result, so Ican't publish it.Achava === Subject: : Re: Math-tools> Hi. My only formal education in math is one exam from engineering-school,so> I'm a little out of my territory here, but I'd like to ask for some advice> concerning the possible use of math/logic to back up the theory/attempted> proof below. It has a rather rudimentary form, but as far as I can judgeit> is precise enough to form an opinion about its truth-value, so to speak.So> any tips are welcome; about specific areas of math, set-theory, for> instance, or more detailed information. I won't mind opinions as to the> truth-value of the theory either, but I hope it will be constructive. It'sa> rather pittorescque little thing I know, but anyway...> ----------> An attempted proof that all is consciousness, and that all structures are> composed of basic consciousness-structures:> --------> - Existence is necessary: nothingness/emptiness cannot exist (an empty> space has no content - it consists of nothingness - thus the consept> 'empty> space' must also be empty, have no content).If you spend some time reading some basic set theory you will find what iswrong with this statement.(hint. consider treat your empty space as empty set).I wont comment the rest of your text since it is meaningles set of sentencesmade up to sound like something smart to tell to somebody at party crowdunder condition that he/she have not a single clue of logic/mathematics. === Subject: : Re: differentiability of monotonic functions[We are discussing the following function, defined for real x>=0]>f(0)=0>f(x+1)=(f(x)+1)/2>f(1/x)=1-f(x)> f has vertical steps for irrationals which ultimately have only small> partial quotients -- by this I mean points without a derivative; f is> in fact continuous. The set of these points has measure zero (subset> of measure zero set of numbers with bounded partial quotients), but it> is still uncountable. At most irrationals and all rationals, f has> derivative zero. What I'm curious about is whether there are points> where the derivative exists and is positive: it seems one ought to be> able to pick partial quotients so as to balance their growing sum S> against the growing denominators of the partial convergents Q so that> the derivative, the limit of Q^2/2^S, has any desired value. Is there> anything known about this?I think I have an answer, but the reasoning involves some hand-wawing.Suppose we have a sequence of closer and closer CF convergents to x, andthe corresponding values y of f(x). Let the convergents be P_n/Q_n, andlet S_n be the sum of partial quotients up to that point. f(x) inbinary consists (after the radix point) of alternating runs of 1s and 0s,the lengths of the runs being the successive partial quotients of the CF(Continued Fraction) expansion of x. For any small change dx there is afirst partial quotient that has a corresponding change, and a first bitoffset in y=f(x) where a run of 1s or 0s increases or decreases in length.The smallest possible dx involving the corresponding partial convergentP/Q is 1/Q^2; the corresponding dy is 1/2^S, for dy/dx = Q^2/2^S as Imentioned above. Now, if the sequence of values (Q_n)^2/2^(S_n) were toconverge to a non-zero limit L, the sequence log(Q^2/2^S) (leaving outsubscripts for readability) would converge to log(L), so for each epsilonthere must be an N such that |log(L)-2*log(Q_n)+(S_n)*log(2)| < epsilonfor all n > N. But as n changes, the quantity between bars changes bydiscrete amounts: multiples of log(2) and (if one looks at how partialconvergents grow) multiples of a quantity between log(1.3) and log(2).(The 1.3 is an approximation of (3+sqrt(5))/4 here.) So although it maydip below epsilon as often as one wants, it will not stay below epsilon,and hence the limit cannot exist.In other words, there are only three possibilities for the derivativeof f(x): it is zero, it grows without bound as x is approached (it isinfinite), or it does not exist at all (dy/dx keeps bouncing around).(The infinite case is what Stephen Fortescue described as the inversefunction having zero derivative. But it seems there is this third case,where neither f(x) nor f^-1(y) has a derivative at that point.)Michel.P.S. Is this function mentioned in any textbook? I did not find it in Counterexamples in Analysis, which seemed a good place to look up. === Subject: : Dark Energy, Strings, Loops and Islamic Sufismhttp://www.bayarea.com/mld/mercurynews/entertainment/ television/6336570.htmInteresting. Happy Holidays in Saint Petersburg. :-)http://www.techgnosis.com/In connection with an interesting message of MARK DUNN Re: AI AND TIME might express following ideas.The task of Demiourgos/Ialdabaoth, - Gnostic Maker of Universes, whose task is to make a sturdy enough prison for souls, which consist of higher-plane stuff of Supreme God's essence, - may be compared to task confine superhot hydrogen plasma in as stable way as possible; - so as to extract from it its inner energy (as Demiourgos sucks Divine Energy out of captive souls).Slightest imperfection in this design will lead to runaway instabilities which lead to fast collapse of this small prison Universe.Similarly, miscalculations of Universe-maker lead to collapse of made by Him/Her/It 'larger-scale Universes: Soul Prisons, as they are called in Gnostic tradition.Their instabilities are manifested in the form of creation by their rebel inhabitants of various kinds of Universal WMD capable to destroy their Cosmic Prison. (This idea was most clearly expressed in prison Universe try to burn their Cosmic Prison - like rebels during mutiny in Attica, NY state - in order to attract attention of Supreme Observer to their sad plight (like Attica inmates which tried to attract attention of public & press). Cf. also '42 SF strory by A. Bester A Push of a Finger - and/or Bros. Strugatskys' '70s SF novel Billion of years before World's End - where is also touched the problem of 'universal weapons'.Jack comments:http://map.gsfc.nasa.gov/When you look at computer simulations of large scale universe with the tangled web of filaments, walls, voids punctuated by clusters of galaxies it looks like biological cell structure. Since 96% of the universe is IMHO unbalanced w = -1 zero point energy density of ALL quantum fields, and since Nobel Prize Cambridge University physicist, Brian Josephson, and others have postulated a connection of consciousness to vacuumzero point energy, e.g.http://www.arxiv.org/html/physics/0312012ABSTRACTA model consistent with string theory is proposed for so-called paranormal phenomena such as extra-sensory perception (ESP). Our mathematical skills are assumed to derive from a special mental vacuum state, whose origin is explained on the basis of anthropic and biological arguments, taking into account the need for the informational processes associated with such a state to be of a life-supporting character. ESP is then explained in terms of shared thought bubbles generated by the participants out of the mental vacuum state. The paper concludes with a critique of arguments sometimes made claiming to rule out the possible existence of paranormal phenomena.http://www.tcm.phy.cam.ac.uk/~bdj10/Note that quantum computing theory is now mainstream and it recognizes that the quantum wave is an information BIT or qubit wave more akin to thoughts than matter. The Bohm quantum realism has the thought-like (Stapp) BIT (Wheeler) pilot wave of active or field configurations i.e. IT (Wheeler).The Bohm quantum potential is a way of describing vacuum thought-like BIT zero point energy and is important to understand 96% of the stuff of the Universe! The Muslim physicists in Teheran are way ahead of the Elegant Tailors weaving strings and spin foams into the fabric of space-time in this regard probably because of the Sufi Doctrine of Tauhid made known to me by Robert Dickson Crane 24 years ago. The Universe is not only more and more like a Great Thought said Sir James Jeans (at least 96%) it is like Stan Lem's Solarishttp://vislab.cs.wright.edu/~rbryll/ LemLinks.htmlUniverse. Recall also his Black Cloud, PK Dick's VALIS,John Lilly's Cosmic Coincidence Control, Olaf Stapledon's Star Maker, Robert Anton Wilson's Cosmic Trigger and Martin Gardner'sMagic and Paraphysics in Science, Good, Bad and Bogus.And do not miss Stephen Schwartz'sAll The King's Men are not seeing Humpty Dumpty as SHE really is. No dark matter detector (Omega ~ 0.3) will ever click with The Right Dark making The Voids, The Filaments, The Walls, The Clusters.Constraints Algebra and Equations of Motion in Bohmian Interpretation ofQuantum Gravityhttp://www.arxiv.org/abs/gr-qc/0311076Authors: Ali Shojai, Fatimah ShojaiComments: 9 journal pagesIt is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general coordinate transformations to the spatial and temporal diffeomorphisms. The quantum Einstein's equations are derived and it is shown that they are manifestly covariant under the above diffeomorphisms, as it would be.Quantum Effects and Cluster Formationhttp://www.arxiv.org/abs/astro-ph/0211272Authors: Ali Shojai, Fatimah ShojaiComments: 25 pages, 17 figuresJournal-ref: Spacetime and Substance 2 (2001) 134-139The causal interpretation of quantum mechanics is applied to the universe as a whole and the problem of cluster formation is studied in this framework. It is shown that the quantum effects be the source of the cluster formation.CI continued: === Subject: : Re: Shannon defeats Cantor = single infinity type > But can you find any ONE number in your list that matches the diagonal> number in EVERY position? If not, the diagonal number is not in the> list.>> Depends on what you mean by EVERY position.> I can find a number in my list that matches the diagonal number> for ANY finite number of positions.>> When I say every, I mean every one of the infinitely many positons> required to represent most reals.> I haven't read the entire thread, but it appeared it was about> Turing machines (TM) and whether they can be used to> prove Cantor's diagonal argument.> TMs can have an unbounded tape, but not an infinitely long tape.> A TM would prove that the diagonal number is on my list.> Since the input tape containing the diagonal number is not> infinite, the TM would always find a number in my list that> matched the input tape.An intrinsic method, this captures the notion of specification of numbers.The normal definition of a Turing Machine includes a specification ofthe starting conditions. A finite pattern on the tape is present, the read/writehead is positioned to the left of the pattern. After calculation and rewritingof the tape the head is positioned to the right of the result, so the TMhas to make a sweep of the data from left to right.> There is a number on my list that matches the diagonal number> at every finite position. Unless the diagonal number has positions> that are not finite, it must be on my list.It does demonstrate that within_a_computational_framework there isnow atleast no contradiction to the axiom of a complete list. <()> <^> ----------------------------->> When I say every, I mean every one of the infinitely many positons>> required to represent most reals.>> But any finite number of positions would only work if every real could>> be expressed exactly with only a finite number of (radix) positions.>the logic we use has to be pre Cantorian, there is no infinity, only constructs>of numbers, a quantification is either bounded under a fixed number or>it is not bounded, we would call that infinite but we don't require the term.>any finite number of positions>= *any* number of postions>= unlimited number of positions>In practicality unlimited is the same as infinite.> In practicality, both are the same as unimaginable or> absurd. In mathematics such shortcuts are not permissable.> Unlimited and infinite are defined terms - and defined> differently. I am not a mathematician, but I am a linguist. You are> not permitted to arbitrarily create synonyms in order to bypass the> requirements of mathematical proof.>What is wrong with this statment?>Any number up to an infinite number of digits is on the list. It is a hypothesis. No such list exists - neither is itpossible (for purely logistical reasons) to create any such list.>Or this?>Given a fixed ordering of all computable numbers, any number specified there after>will appear on the list to an infinite number of digits. Unproven assertion - and probably unprovable. That doesn'tmean it is necessarily false. It does mean, however, that if you evermanage to find a way to prove it there are apt to be fewer than 20people on the planet who understand it, and only three of them willgive a . My argument was not with your math. It was with your assertionthat unlimited and infinite are synonyms. They are not.>Herc>The number appears on the list to *any* number of terms.>The number appears on the list to 1 term.>The number appears on the list to 2 terms.>The number appears on the list to 3 terms.>..>(by induction the number appears on the list for all terms)>You cannot specify an irrational that doesn't appear on the list.