mm-3689 === Subject: Re: The Axiom of Regularity > Can you remind us exactly what you want to show? Yes I will repost (though you can always view the original at MathForum, e.g. http://mathforum.org/kb/message.jspa?messageID=4487738&tstart=60) The axiom of regularity states, basically, that every set has an element disjoint from that set. This implies that no set can be a member of itself, and no infinite descending sequence of sets can exist (thus ruling out cases such as a e b e a, because then a e b e a e b e a e ... is such an infinite descending sequence). Various sources say that the axiom of regularity is technically not required; indeed, Wikipedia states The axiom of regularity is arguably the least useful ingredient of Zermelo-Fraenkel set theory, since virtually all results in the branches of mathematics based on set theory hold even in the absence of regularity., and a similar statement was constructed in Godel's paper (in which he actually presented the axioms of NBG, my favourite set theory), but I can't remember it (my copy of the book is at home). However, consider Peano's 3rd axiom. This is a THEOREM in ZFC/NBG. It states: The map s(A) = A U {A} is injective when viewed as a function from N to N{0}. (P3) Using the axiom of regularity, the injectivity of AU{A} is easy to prove. For suppose for a contradiction that A U {A} = B U {B} A does not equal B Then B is not in {A}, so B e A (since B e B U {B}). Similarly, A e B. This is a contradiction by regularity above. So we must have A = B. However, without regularity this argument falls apart and I can't see how to repair it. In fact, presumably without regularity, the function s is not injective with any old set as its domain, but when you set its domain as N, where N = {0, s(0), s(s(0)), ...} then regularity is somehow provable from the other axioms in that context, or there is some other way of proving P3. But I can't see how to do this. Help! === Subject: Re: The Axiom of Regularity However, consider Peano's 3rd axiom. This is a THEOREM in ZFC/NBG. It states: >The map s(A) = A U {A} is injective when viewed as a function from N to N{0}. >Using the axiom of regularity, the injectivity of AU{A} is easy to prove. For >suppose for a contradiction that A U {A} = B U {B} and A does not equal B >Then B is not in {A}, so B e A (since B e B U {B}). Similarly, A e B. This is a >contradiction by regularity above. So we must have A = B. Your proof works fine without the axiom of regularity when you recall that the sets A,B are ordinals. Usually, the von Neumann ordinals are defined to be the class of those transitive, pure sets A that are well founded with respect to inclusion, that is, (A, e | A) is a well ordering. Thus A e B e A cannot happen when A is an ordinal. The natural numbers N are then defined to be the smallest set of von Neumann ordinals that contains 0 and is closed under successor. The axiom of infinity guarantees that they form a set rather than a proper class. Since every element of N is an ordinal, every element of N is a pure, transitive, set that is well-founded under inclusion. In particular, A e B e A cannot happen for any member of N. === Subject: Re: Elementary Number Theory (Modular Arithmetic) > This exercise is number 4.4.3 in Burton's Elementary > Number Theory text (6th edition): > Find all solutions of 3x - 7y = 11 (mod 13). > How should I solve this problem? I was thinking of > rewriting it as 3x = 11 + 7y (mod 13), but after that > I'm stuck. I'd look at it this way. This is an inhomogeneous linear equation. The general solution is the sum of a particular solution and the general solution of the homogeneous linear equation (as eg in the solution of differential equations). A particular solution is (x,y) = (6,1). The associated homogeneous equation is 3x = 7y mod 13. So the solution of the original equation is (6+u,1+v) where (u,v) is any solution of 3u = 7v mod 13. To solve the homogeneous equation, note that 2.7 = 1 mod 13. So it can be written as 6x = y mod 13. This has general solution (x,y) = (s, 6s + 13t). So the general solution to the original equation is (6 + s, 1 + 6s + 13t). Subject: Re: Elementary Number Theory (Modular Arithmetic) >> This exercise is number 4.4.3 in Burton's Elementary >> Number Theory text (6th edition): >> Find all solutions of 3x - 7y = 11 (mod 13). >> How should I solve this problem? I was thinking of >> rewriting it as 3x = 11 + 7y (mod 13), but after that >> I'm stuck. > I'd look at it this way. > This is an inhomogeneous linear equation. > The general solution is the sum of a particular solution > and the general solution of the homogeneous linear equation > (as eg in the solution of differential equations). > A particular solution is (x,y) = (6,1). > The associated homogeneous equation is 3x = 7y mod 13. > So the solution of the original equation is (6+u,1+v) > where (u,v) is any solution of 3u = 7v mod 13. > To solve the homogeneous equation, note that 2.7 = 1 mod 13. > So it can be written as 6x = y mod 13. > This has general solution (x,y) = (s, 6s + 13t). > So the general solution to the original equation is > (6 + s, 1 + 6s + 13t). That is overkill. The integers (mod 13) form a field. To find all points on a line over a field is trivial: a Y + b X = c, a != 0, <-> Y = (c-bX)/a Hence { (x, (c-bx)/a) : x in F } is precisely the set of all points on the line (all solutions). There's no need to simplify 1/a or proceed any further since the statement of the problem does not ask for such. One should not forget high-school geometry simply because one is working on a problem from a number theory textbook. This reminds me of a related problem from a recent post [1] >> Let x and y be positive integers such that 3x + 7y is divisible by 11. >> Which of the following must also be divisible by 11? >> (a) 4x + 6y (b) x + y + 5 (c) 9x + 4y (d) 4x - 9y (e) x + y - 1 > The mathematics has been pretty well explored in this thread, > so here's something of a historical note. > The Eotvos contests for Hungarian students in their last year of > high school began in 1894. The first problem on that first exam was > Prove that the expressions 2x + 3y and 9x + 5y are divisible by 17 > for the same set of integral values of x and y. Both sets comprise the (unique) line between the two points (0,0),(3,-2) over the field Z/17. Yet another example of the power of uniqueness theorems for proving equalities. See my prior posts for more examples: === Subject: Re: Elementary Number Theory (Modular Arithmetic) days. My association with the Department is that of an alumnus. >>This exercise is number 4.4.3 in Burton's Elementary >>Number Theory text (6th edition): >>Find all solutions of 3x - 7y = 11 (mod 13). >>How should I solve this problem? I was thinking of >>rewriting it as 3x = 11 + 7y (mod 13), but after that >>I'm stuck. Easier than what I proposed earlier: If (x,y)=(a,b) is any solution, then so is (a+13n,b+13m) for any integers n and m. Thus it is enough to find all solutions with 0<= x,y <13. Finding the multiplicative inverse of 3 modulo 13, call it b, you get x = (11+7y)b ( mod 13) which means that each value of y gives you one and only one value of x (modulo 13). These 13 solutions will yield all solutions after adding arbitrary multiples of 13 to either x or y. -- === Subject: Re: Elementary Number Theory (Modular Arithmetic) >>This exercise is number 4.4.3 in Burton's >>Elementary Number Theory text (6th edition): >>Find all solutions of 3x - 7y = 11 (mod 13). >>How should I solve this problem? I was thinking of >>rewriting it as 3x = 11 + 7y (mod 13), but after >>that I'm stuck. > Easier than what I proposed earlier: > If (x,y)=(a,b) is any solution, then so is > (a+13n,b+13m) for any integers n and m. > Thus it is enough to find all solutions with > 0<= x,y <13. Yeah, this way seems easier. > Finding the multiplicative inverse of 3 modulo 13, > call it b, you get > x = (11+7y)b ( mod 13) > which means that each value of y gives you one and > only one value of x (modulo 13). These 13 solutions > will yield all solutions after adding arbitrary > multiples of 13 to either x or y. Sounds like a plan to me. I get b = 3^(-1) = 9 (mod 13) which implies x = 63y + 99 = 11y + 8 (mod 13). The solutions (x, y) modulo 13 came out to be (0, 4), (1, 10), (2, 3), (3, 9), (4, 2), (5, 8), (6, 1), (7, 7), (8, 0), (9, 6), (10, 12), (11, 5), (12, 11). The text provides a parametric solution for these as x = 11 + t (mod 13) ...and... y = 5 + 6t (mod 13). I can't see how this is derived. I can't help but notice that this is some sort of bijection of the residue class modulo 13 onto itself. I can imagine that the explanation for this kind of automorphism is beyond me at the moment; I should focus on getting the parametric representation. Kyle Czarnecki === Subject: Re: Elementary Number Theory (Modular Arithmetic) days. My association with the Department is that of an alumnus. >This exercise is number 4.4.3 in Burton's >Elementary Number Theory text (6th edition): >>Find all solutions of 3x - 7y = 11 (mod 13). >Sounds like a plan to me. I get b = 3^(-1) = 9 (mod 13) >which implies >x = 63y + 99 = 11y + 8 (mod 13). >The solutions (x, y) modulo 13 came out to be >(0, 4), (1, 10), (2, 3), (3, 9), (4, 2), (5, 8), (6, 1), >(7, 7), (8, 0), (9, 6), (10, 12), (11, 5), (12, 11). >The text provides a parametric solution for these as >x = 11 + t (mod 13) ...and... y = 5 + 6t (mod 13). So they only want the solutions modulo 13, not ALL integer solutions. You should have said so to begin with. >I can't see how this is derived. They did it the other way, which is a bit simpler. Solving for y gives 7y = 3x - 11 = 3x + 2 (mod 13) The multiplicative inverse of 7 modulo 13 is 2, so 14y = 6x + 4 (mod 13) y = 6x + 4 (mod 13). Pick an arbitrary value of x to get a solution. For example, x = 11. Then y = 6(11) + 4 = 70 = 5 (mod 13) So one solution is x = 11, y = 5. If instead of x=5 you have x=5+t, then 6(5+t) + 4 = 6(5)+4 + 6*t = 5 + 6*t (mod 13) Why did they pick x=11, y = 5? They solved 3x - 7y = -2 as a linear diophantine equation, which gives x=11, y = 5. >I can't help but notice that this is some sort of >bijection of the residue class modulo 13 onto itself. This is because the coefficients of x and y are both invertible modulo 13; it amounts to a function that defines x and y implicitly in terms of each other (modulo 13). So what you have is a function from Z/13Z to itself, relating x and y. You can get a similar parametrization from the list you have: >(0, 4), (1, 10), (2, 3), (3, 9), (4, 2), (5, 8), (6, 1), >(7, 7), (8, 0), (9, 6), (10, 12), (11, 5), (12, 11). Pick your favorite solution, say x=0, y = 4. You have the explicit formula x = 11y + 8 (mod 13). So if y = 4 + t, then x = 11(4+t)+8 = 11(4) + 8 + 11(t) = 11t so a parametrization of the solutions is x = 11t , y = 4 +t (mod 13). -- === Subject: Re: Elementary Number Theory (Modular Arithmetic) > <26902851.1141263307759.JavaMail.jakarta@nitrogen.mathforum.org>, > Narcoleptic Insomniac >This exercise is number 4.4.3 in Burton's >Elementary Number Theory text (6th edition): >>Find all solutions of 3x - 7y = 11 (mod 13). >Sounds like a plan to me. I get b = 3^(-1) >= 9 (mod 13) which implies >x = 63y + 99 = 11y + 8 (mod 13). >The solutions (x, y) modulo 13 came out to be >(0, 4), (1, 10), (2, 3), (3, 9), (4, 2), (5, 8), >(6, 1), (7, 7), (8, 0), (9, 6), (10, 12), (11, 5), >(12, 11). >The text provides a parametric solution for these as >x = 11 + t (mod 13) ...and... y = 5 + 6t (mod 13). > So they only want the solutions modulo 13, not ALL > integer solutions. You should have said so to begin > with. The original exercise was stated exactly as: Find all solutions to the linear congruence 3x - 7y = 11 (mod 13) I just left out the linear congruence part since it was somewhat obvious. >I can't see how this is derived. > They did it the other way, which is a bit simpler. > Solving for y gives > 7y = 3x - 11 = 3x + 2 (mod 13) > The multiplicative inverse of 7 modulo 13 is 2, so > 14y = 6x + 4 (mod 13) > y = 6x + 4 (mod 13). > Pick an arbitrary value of x to get a solution. For > example, x = 11. Then > y = 6(11) + 4 = 70 = 5 (mod 13) > So one solution is x = 11, y = 5. > If instead of x=5 you have x=5+t, then > 6(5+t) + 4 = 6(5)+4 + 6*t = 5 + 6*t (mod 13) Sweet, this is the part that I couldn't see. > Why did they pick x=11, y = 5? They solved 3x - 7y = > -2 as a linear diophantine equation, which gives x=11, > y = 5. >I can't help but notice that this is some sort of >bijection of the residue class modulo 13 onto >itself. > This is because the coefficients of x and y are both > invertible modulo 13; it amounts to a function that > defines x and y implicitly in terms of each other > (modulo 13). So what you have is a function from Z/13Z > to itself, relating x and y. > You can get a similar parametrization from the list > you have: >(0, 4), (1, 10), (2, 3), (3, 9), (4, 2), (5, 8), >(6, 1), (7, 7), (8, 0), (9, 6), (10, 12), (11, 5), >(12, 11). > Pick your favorite solution, say x=0, y = 4. You have > the explicit formula x = 11y + 8 (mod 13). > So if y = 4 + t, then > x = 11(4+t)+8 = 11(4) + 8 + 11(t) = 11t > so a parametrization of the solutions is > x = 11t , y = 4 +t (mod 13). Kyle Czarnecki === Subject: V1agra 20 P1lls 100 mg $99.95 boundary=------------ms000202030707040100080600 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k220F8329776 for ; Wed, 1 Mar 2006 19:15:09 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: simple equation Find function f such that f(a-1)+f(a+1)=2a^2 Is that possible? === Subject: Re: simple equation > Find function f such that > f(a-1)+f(a+1)=2a^2 > Is that possible? Possibly f(x) = x^2 - 1 + g(x) where g is any function satisfying (for every x) g(x + 2) = - g(x), for example g(x) = 0 or g(x) = sin((pi)x/2). Ken Pledger. === Subject: Re: simple equation Yaroslav Bulatov nous a r.8ecemment amicalement signifi.8e : > Find function f such that > f(a-1)+f(a+1)=2a^2 > Is that possible? The general solution is f(x) = x^2 - 1 + g(x/4) - g((x+2)/4) where g(x) is any periodic function with period 1. For example : g(x) = c ==> f(x)=x^2 - 1 g(x) = c*sin(2pi*x) ==> f(x)=x^2 - 1 + 2c*sin(pi*x/2) g(x) = x - int(x) ==> f(x)=x^2 - int((x+2)/4) - int(x/4) - 3/2 g(x) = 2int(x) - 2x ==> f(x)=x^2 + 2int(x/4) - 2int((x+2)/4) ... -- Patrick === Subject: Re: simple equation <44069859$0$29182$8fcfb975@news.wanadoo.fr> Interesting, how did you derive this? === Subject: Re: simple equation reply-type=response Patrick Coilland nous a r.8ecemment amicalement signifi.8e : > Yaroslav Bulatov nous a r.8ecemment amicalement signifi.8e : >> Find function f such that >> f(a-1)+f(a+1)=2a^2 >> Is that possible? > The general solution is f(x) = x^2 - 1 + g(x/4) - g((x+2)/4) where > g(x) is any periodic function with period 1. > For example : > g(x) = c ==> f(x)=x^2 - 1 > g(x) = c*sin(2pi*x) ==> f(x)=x^2 - 1 + 2c*sin(pi*x/2) > g(x) = x - int(x) ==> f(x)=x^2 - int((x+2)/4) - int(x/4) - 3/2 > g(x) = 2int(x) - 2x ==> f(x)=x^2 + 2int(x/4) - 2int((x+2)/4) > ... g(x) = cos(2pi*x)/2 ==> f(x) = x^2 - 2sin^2(pi*x/4) === Subject: Re: simple equation > Find function f such that > f(a-1)+f(a+1)=2a^2 > Is that possible? More generally: f(a) = a^2 - 1 + (-1)^((a - 1) / 2)*k for any constant k, of which f(a) = a^2 - 1 is a special case (k = 0). What happens if a is not an even integer? Does it still work I wonder? === Subject: Re: simple equation > Find function f such that > f(a-1)+f(a+1)=2a^2 > Is that possible? Let f(0) be your favorite number. Let f(1) be your second favorite number. Define f(2), f(3), etc., in turn, to make the equation hold. Ditto for f(-1), f(-2), etc. Or did you want f to be defined for all real a, not just integers? Then define f any way you like on the interval [0, 2) and let the equation define f for you everywhere else. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: simple equation Find function f such that > f(a-1)+f(a+1)=2a^2 > Is that possible? > Let f(0) be your favorite number. > Let f(1) be your second favorite number. In this case, possibly something like a even: f(a) = a^2 - 1 + (-1) ^ ((a - 1) / 2) * (f(0) + 1) * i a odd: f(a) = a^2 - 1 + (-1) ^ ((a - 1) / 2) * f(1) === Subject: Re: simple equation f(a) = a^2 - 1 + (-1) ^ ((a - 1) / 2) * (f(0) + 1) * i I think I mean f(a) = a^2 - 1 + (-1) ^ (a / 2) * (f(0) + 1) or something....! === Subject: Re: simple equation > Find function f such that > f(a-1)+f(a+1)=2a^2 > Is that possible? How's about f(x) = x ^ 2 - 1 ?? === Subject: Re: simple equation > Find function f such that > f(a-1)+f(a+1)=2a^2 > Is that possible? f(a) = a^2 - 1 === Subject: Re: Near-isometries of the plane > Suppose f : R^2 --> R^2 has the property that > dist( P, Q ) = 1 implies dist( f(P), f(Q) ) = 1 > Is f an injection? > dave Yes, f is actually an isometry. This is valid in R^n for n>1 (it is easy to see that it is false for n=1). It is proved in Intelligencer 10(4)(1988) by S. Kolodziej. Valeriu === Subject: Re: Near-isometries of the plane > Dave Rusin asked: >> Suppose f : R^2 --> R^2 has the property that >> dist( P, Q ) = 1 implies dist( f(P), f(Q) ) = 1 >> Is f an injection? > Yes, f is actually an isometry. This is valid in R^n for n>1 > (it is easy to see that it is false for n=1). Well, easy is correct, ... but only *after* you know, why ;-) It took me about 15 minutes to find out. And I am even quite happy with my finding ;-) spoiler follows ... spoiler spoiler spoiler ... Caution: end of spoiler Let f: R --> R be defined by f(2z+x) = 0 and f(2z+1+x) = 1 for 0 <= x < 1 and integer numbers z. Rainer Rosenthal r.rosenthal@web.de === Subject: Re: Near-isometries of the plane >> Suppose f : R^2 --> R^2 has the property that >> dist( P, Q ) = 1 implies dist( f(P), f(Q) ) = 1 >> Is f an injection? >> dave >Yes, f is actually an isometry. This is valid in R^n for n>1 (it is easy to see that it is false for n=1). >It is proved in Intelligencer 10(4)(1988) by S. Kolodziej. assigned! (I intended the students to prove that f is an isometry, as you note, but in order to get the proof rolling I intended the students to show f also preserves distances when dist(P,Q) = sqrt(3), by consideration of some equilateral triangles. That first step falters unless there is an easy way to show that f(P) <> f(Q) in that case.) Once one knows that f carries the hexagonal lattice isometrically, and can barely increase any distances (by the triangle inequality applied to polygonal paths of integer lengths) it is not hard to show f is an isometry, and it is clear the proof generalizes to R^n. dave === Subject: Re: Near-isometries of the plane <13217929.1141259578413.JavaMail.jakarta@nitrogen.mathforum.org> as you note, but in order to get the proof rolling I intended the students > to show f also preserves distances when dist(P,Q) = sqrt(3), by > consideration of some equilateral triangles. That first step falters > unless there is an easy way to show that f(P) <> f(Q) in that case.) Let PQR be a triangle with d(P,Q) = d(P,R) = sqrt(3), d(Q,R) = 1. Then d(f(Q),f(R)) = 1, while d(f(P),f(R)) is sqrt(3) or 0. This is impossible if f(P) = f(Q). === Subject: Re: Near-isometries of the plane >> >> Suppose f : R^2 --> R^2 has the property that >> >> dist( P, Q ) = 1 implies dist( f(P), f(Q) ) = 1 >> >> Is f an injection? >> >> dave >Yes, f is actually an isometry. This is valid in R^n for n>1 (it is easy to >see that it is false for n=1). >It is proved in Intelligencer 10(4)(1988) by S. Kolodziej. > assigned! (I intended the students to prove that f is an isometry, > as you note, but in order to get the proof rolling I intended the students > to show f also preserves distances when dist(P,Q) = sqrt(3), by > consideration of some equilateral triangles. That first step falters > unless there is an easy way to show that f(P) <> f(Q) in that case.) > Once one knows that f carries the hexagonal lattice isometrically, > and can barely increase any distances (by the triangle inequality > applied to polygonal paths of integer lengths) it is not hard to > show f is an isometry, and it is clear the proof generalizes to R^n. Oh, lovely--what course is this for? And where do you get students you could expect to solve it? (I might have a couple--but I wouldn't expect a significant fraction of a CLASS to do this.) I was vaguely familiar with the result, although I didn't have the reference at my fingertips. I think it's been a topic on sci.math before. --Ron Bruck === Subject: Bayesian Analysis Hello everyone, I read a book in Bayesian Analysis and it says that: Let Y_i=X_i+A where i=1,2,3,4...... X_i is IID normal random variable N(a,b^2) where a is mean and b^2 is variance. A is a independent random variable with finite mean. Then E(A| Y_1, Y_2, ..., Y_n) -> A almost sure when n tends to infinity. However, the book does not give any proof to show that. Could someone explain this statement or point me some reference? === Subject: Re: The math of CRC functions > you might be more interested in using a collision-resistant > (cryptographic) hash function, these might help, or at least give > you good references: > http://en.wikipedia.org/wiki/Hash_function > http://en.wikipedia.org/wiki/Cryptographic_hash_function That brings me to another question I had--while cryptographic hash functions are carefully designed not only to reduce the probability of collisions but also to have other characteristics such as producing hashes that give no information about the input and maximizing the difficulty of finding a particular text that produces a given hash. So given that I don't care about the latter requirements on cryptogrophic hashes, is there any way to trade off those requirements for execution speed--i.e. to get an algorithm that minimizes collisions but doesn't have all the characteristics necessary of a good cryptographic hash but can be comptued more quickly thas, say, MD5 or SHA1. -Peter -- Peter Seibel * peter@gigamonkeys.com Gigamonkeys Consulting * http://www.gigamonkeys.com/ Practical Common Lisp * http://www.gigamonkeys.com/book/ === Subject: Re: GOOG's equilibrium price is $154 > draccarlawpet announces: >> I ran quite a few regression models on 23 different internet stocks, >> all competing in the same sector and industry. According to 2 of my >> models (R^2=0.99, K=2 and 3 variables), the conservative price estimate >> for GOOG is around $154. My 2-variable model uses Book Value and >> Income, and the equation is: >> Market Cap (Book Value, Earnings) = >> 3.10909494(BV)+11.50074578(Earn's)+110044234.5 > Now's your big chance...... > Why don't you short the stock($365)??? > First he has to turn the herd. :) Well, actually, the herd does show some signs of having been turned... > I like this science math thing.. give > the guy a shot I don't know exactly what he's doing here, but didn't Barron's come up with exactly the same target price a couple weeks ago without all the R^2=0.99 mumbo-jumbo, just the same basic idea of comparing Google(TM) with its peers and doing a little growth slow-down extrapolations? --- William Ernest Reid Post count: 236 === Subject: Re: GOOG's equilibrium price is $154 >> draccarlawpet announces: > I ran quite a few regression models on 23 different internet stocks, > all competing in the same sector and industry. According to 2 of my > models (R^2=0.99, K=2 and 3 variables), the conservative price > estimate > for GOOG is around $154. My 2-variable model uses Book Value and > Income, and the equation is: >> Market Cap (Book Value, Earnings) = > 3.10909494(BV)+11.50074578(Earn's)+110044234.5 >> Now's your big chance...... >> Why don't you short the stock($365)??? >> First he has to turn the herd. :) > Well, actually, the herd does show some signs of having been turned... >> I like this science math thing.. give >> the guy a shot come up with exactly the same target price a couple weeks ago > without all the R^2=0.99 mumbo-jumbo, just the same basic > idea of comparing Google(TM) with its peers and doing a little > growth slow-down extrapolations? > --- > William Ernest Reid > Post count: 236 Could be.. Barron's does this 'mumbo-jumbo' comparisons al the time. GOOG seems a prime candidate for major hypothafication (sp?). But not to take away from this poster if he actually dit it himself as well. :) === Subject: Re: GOOG's equilibrium price is $154 <4405e723$0$96008$742ec2ed@news.sonic.net> <44073f03$0$95980$742ec2ed@news.sonic.net> I actually ran a few models, and the value of GOOG based on it's *past* and *present* situation (and not discounting the future earnings) is between $120-$210. I ran about 5 different models using 1, 2, and/or 3 variables. The R^2 were all consistently over 0.86. I'd be happy to show you my methods and the data. === Subject: Re: GOOG's equilibrium price is $154 Thread-Topic: GOOG's equilibrium price is $154 Thread-Index: AcY+Rtk+F6Sueqo6EdqQXgANk0DKpA== draccarlawpet says: > I actually ran a few models, and the value of GOOG based on it's *past* > and *present* situation (and not discounting the future earnings) is > between $120-$210. I ran about 5 different models using 1, 2, and/or 3 > variables. The R^2 were all consistently over 0.86. > I'd be happy to show you my methods and the data. Investors, traders, speculators don't really care much about methods and the data.......They care about BOTTOM LINE.....Bottom line in the real world is how much profit do these fancy calculations produce.....GOOG was $365 when you announced GOOG's equilibrium price is $154........Do you really believe that statement is something you're going to proudly put on a resume in the future??? === Subject: Re: GOOG's equilibrium price is $154 <4405e723$0$96008$742ec2ed@news.sonic.net> <44073f03$0$95980$742ec2ed@news.sonic.net> I agree Goog is worth somewhere around $150 a share. But with this market, all they hype, and the frankly unknown territory Goog occupies, I don't think it is a very good short candidate. Too volatile. Goog is one of these fad stocks......Avoid, or buy a few shares for entertainment if you must. === Subject: Medicines before Valentine Day !!! boundary=------------ms010701010502070601040203 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k2218L304180 for ; Wed, 1 Mar 2006 20:08:21 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: Re: Medicines before Valentine Day !!! Medicines AND a time machine! This deal can't be beat! --- A. C. Fenderson === Subject: Re: dirac distribution >Hi there, just a quick query. >I know the derivative of the dirac distribution (at 0 is the spike) >is minus derivative of the test function evaluated at 0, (-phi ' (0)) No. The derivative of the Dirac distributions *maps* phi to -phi'(0), i.e. the derivative of Dirac distribution is a function whose domain is the space of test functions, and the value that it takes at the test function phi is -phi'(0). ----- === Subject: Re: dirac distribution >I know the derivative of the dirac distribution (at 0 is the spike) >is minus derivative of the test function evaluated at 0, (-phi ' (0)) No. The derivative of the Dirac distributions *maps* phi to -phi'(0), i.e. the derivative of Dirac distribution is a function whose domain is the space of test functions, and the value that it takes at the test function phi is -phi'(0). if anyone can help with my question on The fact that this fourier transform be induced by a ordinary function? i know the fourier transform is it. i just want to know how to find if it it is induced by an ordinary function === Subject: Re: dirac distribution > if anyone can help with my question on > The fact that this fourier transform be induced by a ordinary function? > i know the fourier transform is it. i just want to know how to find if > it it is induced by an ordinary function Why do you think it is not an ordinary function> === Subject: Re: dirac distribution if anyone can help with my question on > The fact that this fourier transform be induced by a ordinary function? > i know the fourier transform is it. i just want to know how to find if > it it is induced by an ordinary function Why do you think it is not an ordinary function> My question (if not clear) is the fourier transform equal to the distribution by an ordinary function g(t)=it enough? === Subject: Re: dirac distribution > if anyone can help with my question on > The fact that this fourier transform be induced by a ordinary function? > i know the fourier transform is it. i just want to know how to find if > it it is induced by an ordinary function > Why do you think it is not an ordinary function > My question (if not clear) > is the fourier transform equal to the distribution by an ordinary > function > g(t)=it enough? We've established F(D(delta))(f) = int_R (it)f(t)dt for all test functions f. In the parlance of distribution theory, the distribution F(D(delta)) is the function it. That ends the matter as far as I can see. If you have something else in mind, please state it exactly. === Subject: Normal distribution Let X be Normal (0,1). Let P(Z=1)=P(Z=-1)=1/2 for some random variable Z and let X and Z be independent. Then let Y= X * Z. I'm confused if in this setting Y is also distributed normal? Can anyone help me with this? === Subject: Re: Normal distribution > Let X be Normal (0,1). > Let P(Z=1)=P(Z=-1)=1/2 for some random variable Z and let X and Z be > independent. > Then let Y= X * Z. > I'm confused if in this setting Y is also distributed normal? > Can anyone help me with this? Try to evaluate P{Y <= y} for both y > 0 and y < 0. R.G. Vickson === Subject: Re: Normal distribution That's what I'm confused on. If y>0 then P(Y <= y ) = P(x <= y/z) = cdf of X evaluated at (y/z). Do I integrate from - infinity to (y/z) [ 1/sqrt(2pi) exp(-t^2/2)] dt ?? and do I plug in the 1/2 for Z? === Subject: Re: Normal distribution > That's what I'm confused on. > If y>0 then P(Y <= y ) = P(x <= y/z) = cdf of X evaluated at (y/z). > Do I integrate from - infinity to (y/z) [ 1/sqrt(2pi) exp(-t^2/2)] dt > ?? > and do I plug in the 1/2 for Z? P{Y <=y} = P{Y <=y | Z = 1} P{Z = 1} + P{Y <= y | Z = -1} P{Z = -1}. What can you say about P{Y <= y | Z = 1}? What about P{Y <= y | Z = -1}? Remember: X and Z are independent. RGV === Subject: Iteratively reweighted least squares I'm looking for a result that is apparently well-known but that I cannot find a source of. Let's say I'm able to minimize the nonlinear least-squares problem min || f(x) || in the 2-norm, where f is a vector-valued function and x is a vector. Apparently, there exists an iteratively reweighted least-squares scheme by which I can make weights that make the weighted 2-norm solution to min || f(x) || equal to the infinity-norm solution to min || f(x) || (or maybe it's the 1-norm). I think the answer is to make the diagonal elements to the weight matrix equal to the reciprocals of the residuals. Has anybody heard of this result? === Subject: Re: Iteratively reweighted least squares >I'm looking for a result that is apparently well-known but that I >cannot find a source of. Let's say I'm able to minimize the nonlinear >least-squares problem min || f(x) || in the 2-norm, where f is a >vector-valued function and x is a vector. Apparently, there exists an >iteratively reweighted least-squares scheme by which I can make weights >that make the weighted 2-norm solution to min || f(x) || equal to the >infinity-norm solution to min || f(x) || (or maybe it's the 1-norm). I >think the answer is to make the diagonal elements to the weight matrix >equal to the reciprocals of the residuals. Has anybody heard of this >result? >SF you surely mean Lawson's algorithm, see for example Cline, A.K.: Rate of convergence of Lawson's algorithm Math. of Comp. 26, pages 167-176, (1972) hth peter === Subject: Re: Iteratively reweighted least squares What is your goal? To cope with outliers? If yes, you can look up robust statisitcs. I used to have a book with such a name but I do not rember the author. Evgenii === Subject: EXTRATERRESTRIALS, You Want? EXTRATERRESTRIALS, You Get! -- THE BILLY MEIER CASE -- Space -- UFOs -- Universe. < < > http://www.billymeier.com < > http://www.billymeier.com/photos.htm < > http://www.theyfly.com < < Ed Conrad > http://www.edconrad.com < Man as Old as Coal Proof of Life After Death === Subject: Re: Cantorian pseudomathematics > As far as I know (according to your definition) 1/x is not > computable for arbitrary precision reals, so I would think it is not a > function in your book. > It is not a function defined on all of R. When the uncertainty of a > given finite precision real is comparable in size to the real number > itself, then we cannot compute its reciprocal. Again using some pretty undefined words. What is the uncertainty of a given finite precision real? If I show the rational (or real) 3.14, what is the uncertainty of it? > And when you say it is, when you restrict the > range to all reals not equal to 0, I counter with 1/(x^2 - 2). That > one is *not* computable for arbitrary precision reals, so at least that > one is not a function in your book. Am I right? > Again, it's not a function on all of R. It's not defined for 'x' when > the uncertainty in 'x' is comparable to the value of x - sqrt(2) no single value that can be assigned to sqrt(2), only finite precision numbers with some uncertainty. So what is the value? > I admit I really don't get your point. My point is that I still do not get your definition, because it is based on further undefined terms: > With a little imagination, you could probably figure it out yourself. > One way to think about the reals in constructive mathematics is to > first consider finite precision reals (rationals with uncertainty), and > then consider the limit as the uncertainty goes to zero. It makes > sense to apply functions to these finite precision reals (in fact, > applied mathematicians, scientists and engineers always use finite > precision reals in practice), and if the result of applying a function > to the finite precision reals converges as the uncertainty goes to > zero, then we can say that the function is computable for arbitrary > precision reals. So my question remains: where is the function 1/(x^2 - 2) defined, and where is it not defined? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: vec calc question Find the area of the portion of the upper hemisphere of the sphere with center (0, 0, 0) and radius R that obeys x^2 + y^2 - Ry <= 0 I know the surface area formula, but I guess I am having a hardtime visualizing the portion I am integrating over. What exactly is x^2 + y^2 - === Subject: Re: vec calc question > Find the area of the portion of the upper hemisphere of the sphere with > center (0, 0, 0) and radius R that obeys x^2 + y^2 - Ry <= 0 > I know the surface area formula, but I guess I am having a hardtime > visualizing the portion I am integrating over. What exactly is x^2 + I'm not sure, but I think you can write x^2 + y^2 - Ry <= 0 as x^2 + (y - R/2)^2 <= R^2/4. Does this help? Dave === Subject: Re: A question... In sci.archaeology message . . . : > According to Brokeback Mountain cockfighting started with > mounted cowboys, didn't it? :-) You haven't studied the Spartans have you. === Subject: Re: A question... >>According to Brokeback Mountain cockfighting started with >>mounted cowboys, didn't it? :-) >> >You haven't studied the Spartans have you. No, I'm more of a Trojan man myself... :-) Pat === Subject: Re: A question... > In sci.archaeology message > Pat Flannery > . . . : >> According to Brokeback Mountain >> cockfighting started with >> mounted cowboys, didn't it? :-) > You haven't studied the Spartans have you. Nor Lonesome Cowboys. === Subject: Re: JSH: So now you know as I found out ... > Ok here is where I provide a counterexample and you ignore it. > > Let w1(x) = 7/(x^2 +1), w2(x) = (x^2 +1), A'(x) = (x^2+1)A(x)/7, > B'(x) = B(x)/(x^2+1) > > Then (A(x) + 7) = w1(x)(A'(x) + (x^2+1)) > and (B(x) + 1) = w2(x)(B'(x) + 1/(x^2+1)) > > So 7C(x) = w1(x)( A(x)/w1(x) + 7/w1(x)) * w2(x)(B(x)/w2(x) + 1/w2(x)) > > and we see that there is more than one way for the 7 to > be multiplied through. > ... > No. You need functions that go to 0 when x=0 because that's how you > know what the constant terms are, and the result holds because the > constant terms are independent of the value of x. > > James, which of the functions A(x), A'(x), B(x) and B'(x) is not 0 > when x = 0 in Williams example above? > w1(x) and w2(x) > ALL functions must go to 0 at x=0. > Quit playing stupid. It's not that complicated. Ok, I am playing stupid. Why must w1(x) and w2(x) go to 0? If we consider the constant terms, they are still 7 and 1. So what is the problem? However, let me simplify it. Define C(x) = (x^2 + 3x + 2)/2, A(x) = x and B(x) = x. We have: 2C(x) = (A(x) + 2)(B(x) + 1). By your application of the distributive property we should have that A(x) is divisible by 2. This shows that the integers are incomplete. What is the essential difference with your example? Note that C(x) is well-defined on the integers. You are still back at your old error. The distributive property does *not* imply that (x^2 + 3x + 2)/2 = x^2/2 + 3x/2 + 2/2. That is a valid conclusion if and only if all three values on the right-hand side do exist in the realm you are looking at. As they do not exist in the integers, the conclusion is invalid in the integers. You are doing the same with division by 7. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: So now you know as I found out > Ok here is where I provide a counterexample and you ignore it. > > Let w1(x) = 7/(x^2 +1), w2(x) = (x^2 +1), A'(x) = (x^2+1)A(x)/7, > > B'(x) = B(x)/(x^2+1) > > Then (A(x) + 7) = w1(x)(A'(x) + (x^2+1)) > > and (B(x) + 1) = w2(x)(B'(x) + 1/(x^2+1)) > > So 7C(x) = w1(x)( A(x)/w1(x) + 7/w1(x)) * w2(x)(B(x)/w2(x) + 1/w2(x)) > > and we see that there is more than one way for the 7 to > > be multiplied through. > ... > > No. You need functions that go to 0 when x=0 because that's how you > > know what the constant terms are, and the result holds because the > > constant terms are independent of the value of x. > > James, which of the functions A(x), A'(x), B(x) and B'(x) is not 0 > when x = 0 in Williams example above? > > w1(x) and w2(x) > > ALL functions must go to 0 at x=0. > > Quit playing stupid. It's not that complicated. > Ok, I am playing stupid. Why must w1(x) and w2(x) go to 0? > If we consider the constant terms, they are still 7 and 1. So what > is the problem? The problem is that the functions can obscure what's happening, while they can't change the distributive property. So with something like 7(x+1) = (a_1(x) + 7)(a_2(x) + 7) there's an intuitive sense that there's no way that 7 turns into 7(7), and that intuitive sense can be considered rigorously. The point of using functions that go to 0 at x=0 is that the distributive property does not care about the value of the functions, so you can use that value to clear them out, revealing what is happening. It's not complicated. a(f(x) + b) = a f(x) + ab so if you set f(x) equal to 0, you see what happens. James Harris === Subject: Re: JSH: So now you know as I found out 7(x+1) = (a_1(x) + 7)(a_2(x) + 7) > there's an intuitive sense that there's no way that 7 turns into 7(7), > and that intuitive sense can be considered rigorously. > The point of using functions that go to 0 at x=0 is that the > distributive property does not care about the value of the functions, > so you can use that value to clear them out, revealing what is > happening. > It's not complicated. > a(f(x) + b) = a f(x) + ab > so if you set f(x) equal to 0, you see what happens. James: Do you think that If f(x)*g(x) = r(x)*s(x) for all x, and f(0) = r(0), g(0) = s(0), then we have to conclude f(x) = r(x), g(x) = s(x)? We don't. It doesn't follow. - Randy === Subject: Re: JSH: So now you know as I found out ... > > Ok here is where I provide a counterexample and you ignore it. > > > Let w1(x) = 7/(x^2 +1), w2(x) = (x^2 +1), A'(x) = (x^2+1)A(x)/7, > > B'(x) = B(x)/(x^2+1) > > > Then (A(x) + 7) = w1(x)(A'(x) + (x^2+1)) > > and (B(x) + 1) = w2(x)(B'(x) + 1/(x^2+1)) > > > So 7C(x) = w1(x)( A(x)/w1(x) + 7/w1(x)) * w2(x)(B(x)/w2(x) + 1/w2(x)) > > > and we see that there is more than one way for the 7 to > > be multiplied through. > ... > > No. You need functions that go to 0 when x=0 because that's how you > > know what the constant terms are, and the result holds because the > > constant terms are independent of the value of x. > > James, which of the functions A(x), A'(x), B(x) and B'(x) is not 0 > when x = 0 in Williams example above? > > w1(x) and w2(x) > > ALL functions must go to 0 at x=0. > > Quit playing stupid. It's not that complicated. > Ok, I am playing stupid. Why must w1(x) and w2(x) go to 0? > If we consider the constant terms, they are still 7 and 1. So what > is the problem? > The problem is that the functions can obscure what's happening, while > they can't change the distributive property. > So with something like > 7(x+1) = (a_1(x) + 7)(a_2(x) + 7) > there's an intuitive sense that there's no way that 7 turns into 7(7), > and that intuitive sense can be considered rigorously. > The point of using functions that go to 0 at x=0 is that the > distributive property does not care about the value of the functions, > so you can use that value to clear them out, revealing what is > happening. revealing what is happening *at 0*. Everyone agrees that when x=0 just one thing happens. It is when x is not 0 that there is disagreement. James: when x is not 0 the same thing happens as when x is 0 Everyone else: when x is not 0 different things can happen -William Hughes === Subject: Re: geometric Brownian Motion and log normal? How? That's actually my question! > Hi all, > I need help: > Let Y(t) = exp(X(t)), where X(t) follows a normal distribution N(mu * > t, sigma^2 * t), > Do you mean that X(t) is a Brownian motion with drift? (Just knowing > the distribution of X(t) is NOT enough.) > How can I write Y(t) in the form of: > dY(t) = a * Y(t) * dt + b * Y(t) * dB(t), > where B(t) is the standard Brown Motion? > Use Ito's formula. > R.G. Vickson > > Disclaimer: this is NOT a homework problem! === Subject: Re: geometric Brownian Motion and log normal? > How? That's actually my question! Google Ito's Formula to find out. Or, look in your textbook. Or, ask the TA. Or, ask your professor. R.G. Vickson > Hi all, > I need help: > Let Y(t) = exp(X(t)), where X(t) follows a normal distribution N(mu * > t, sigma^2 * t), > Do you mean that X(t) is a Brownian motion with drift? (Just knowing > the distribution of X(t) is NOT enough.) > How can I write Y(t) in the form of: > dY(t) = a * Y(t) * dt + b * Y(t) * dB(t), > where B(t) is the standard Brown Motion? > Use Ito's formula. > R.G. Vickson > > Disclaimer: this is NOT a homework problem! === Is your model point of view invariant? Pls. explain why symmetry is the key to physics. What's your thought about symmetry? PL > Hello All, > Please respect that Moving Dimensions Theory is just a theory. > I look forward to feedback and insights regarding its logic. > Moving Dimensions Theory > http://physicsmathforums.com > Questions Addressed by MDT: > Why is the speed of light constant in all frames? > Why are light and energy quantized? > Why are there non-local effects in quantum mechanics? > Why does time stop at the speed of light? > How come a photon does not age? > Why are inertial mass and gravitational mass the same thing? > Why do moving bodies exhibit length contraction? > Why are mass and energy equivalent? > Why does time's arrow point in the direction it points in? Why > entropy? > Why do photons appear as spherically-symmetric wavefronts traveling > with the velocity c? > Why is there a minus sign in the following metric? > x^2+y^2+z^2-c^2t^2=s^2 > What deeper reality underlies Einstein's postulates of relativity? > What deeper reality underlies Newton's laws? > What underlies the laws of Inertia? > Why does general relativity fail at short distances? Why does quantum > mechanics dominate at short distances? > Why have so many great minds, Einestin, Godel, Wheeler, Hawking, and > Penrose called for a new conception of time? > If at first the idea is not absurd, then there is no hope for it. > --Albert Einstein > If I have seen further it is by standing on the shoulders of giants. > --Isaac Newton > Max Planck, the father of quantum theory, felt that the pioneer > scientist must have a vivid intuitive imagination, for new ideas are > not generated by deduction, but by artistically creative imagination. > An important scientific innovation rarely makes its way by gradually > winning over and converting its opponents: What does happen is that the > opponents gradually die out. > --Max Planck > Moving Dimensions Theory (MDT) > Today I am writing regarding Moving Dimensions Theory-a deeper model > for explaining diverse phenomena in both quantum mechanics and > relativity. > The General Postulate of Moving Dimensions Theory: > The fourth dimension is expanding relative to the three spatial > dimensions. > The Specific Postulate of Moving Dimensions Theory: > The fourth dimension is expanding relative to the three spatial > dimensions at the rate of c in quantized units of the Planck length. > Relativistic, classical, and quantum mechanical phenomena, as well as > time itself, are emergent properties of this fundamental principle. > Newton's laws, the principle of Inertia, Einstein's postulates, and > model. > A FEW YEARS BACK > A few years back, while surfing a towering wave on the Outer Banks of > North Carolina, a beautiful thought occurred to me. Suppose the wave I > was riding represented a coordinate in a dimension. Then although I was > approaching shore, I was not moving in this dimension. > The dimension itself was moving with me-I was surfing the dimension. > In a flash I saw that that is why photons never age-they are moving > along with the fourth dimension, and thus stationary relative to it. In > another flash I saw that that is why a photon's space-time interval > is represented by a null vector, or a 0, no matter how far it travels. > Indeed Einstein stated that an object's velocity through space-time > was always c-even stationary objects are traveling at the velocity c > through time! How could this be, were it not for a fourth expanding > dimension, which matter could surf as photons, giving rise to our > notion of time? And so it is that Moving Dimensions Theory was born as > the wave crested and crashed about me, thundering on down, as I fought > to remain surfing amidst the foam, facing the setting sun silhouetting > the Hatteras light. > And the waves kept on crashing that night. The nonlocal EPR > paradox/effect could be explained by the underlying nonlocality of an > expanding fourth dimension. The equivalence of mass and energy, the > light-it could all be understood via a single principle of Moving > Dimensions Theory: the fourth dimension is expanding relative to the > three spatial dimensions. MDT reached back thousands of years to > resolve Zeno's paradox, then voyaged forth to ease Godel's, > Einstein's, Hawking's, and Penrose's concerns with the > paradoxical nature of a block universe, and arrived in the present, > quelling the oft exaggerated conflicts between relativity and quantum > mechanics, and pointing the way to the future by accounting for > time's arrow and entropy herself. At long last GR and QM could be > married in theory as harmoniously as they are in nature with Moving > Dimensions Theory's simple postulate: > The General Postulate of Moving Dimensions Theory: > The fourth dimension is expanding relative to the three spatial > dimensions. > The Specific Postulate of Moving Dimensions Theory: > The fourth dimension is expanding relative to the three spatial > dimensions at the rate of c in quantized units of the Planck length. > Classical physics, quantum mechanics, and relativity descend from this > simple postulate. Light, and thus all energy, is quantized as the > dimension which transports it expands in a quantized manner. Light > travels at a constant velocity in all frames because velocity is > measured relative to time which is measured relative to the light that > is transported by the fourth expanding dimension. Thus both fundamental > constants h and c emerge from the fundamental nature of the expansion > of the fourth dimension relative to the three spatial dimensions. And > thus MDT provides a simple, unifying postulate accounting for the > classical, relativistic, and quantum mechanical properties of this > universe. > And it's always been simple postulates, as opposed to abstruse > mathematics and mythologies, that have furthered physics. > Moving Dimensions Theory Can Unify GR & QM: > By offering an underlying reality from where both branches of physics > emerge-an underlying reality of a fourth dimension expanding relative > to three spatial dimensions, MDT unifies relativity and quantum > mechanics not with indecipherable mathematical mythologies, but with a > simple postulate. MDT explains quantum mechanical effects such as > and energy, as well as the two postulates of relativity: the speed of > light is constant in all inertial frames and the laws of physics are > the same for all inertial observers. MDT also explains relativistic > effects such as time dilation and length contraction. The beauty of > Moving Dimensions Theory is that it explains properties of quantum > mechanics and relativity in the deeper context of a unified framework, > opening a door to a deeper physical reality-the fourth dimension is > expanding relative to the three spatial dimensions. > The Purpose of Physics > The purpose of physics has ever been to unify diverse physical > phenomena with simple postulates, laws, and formulas reflecting the > deeper physical reality. MDT unifies relativity and quantum mechanics > by positing that they are both emergent properties of moving > dimensions. MDT's simple postulate-the fourth dimension is > expanding relative to the three spatial dimensions-offers the first > satisfactory explanation of the Einstein Podolsky Rosen (EPR) effect > and the nonlocal behavior inherent to the math and physical reality of > quantum mechanics. Time itself is viewed not as the fourth dimension, > but as an emergent phenomena arising from the expansion of the fourth > dimension relative to the three spatial dimensions. This logic > alleviates a confusion of time with an actual fourth dimension where > one can travel back and forth at will, thus addressing Godel's, > Einstein's, Hawking's, Barbour's, and Penrose's concerns about > frozen time, and accounting for time's relentless arrow, the second > law of thermodynamics, and entropy. > This is but a brief treatment of a much larger project. > The General Postulate of Moving Dimensions Theory: > The fourth dimension is expanding relative to the three spatial > dimensions. > The Specific Postulate of Moving Dimensions Theory: > The fourth dimension is expanding relative to the three spatial > dimensions at the rate of c in quantized units of the Planck length. > and relativity, including the following: > The Constant Velocity of Light: > Light travels with constant velocity of c, because the fourth dimension > is expanding relative to the three spatial dimensions at the rate of c. > Light, or energy, is matter rotated completely into the expanding > fourth dimension, orthogonal to the three spatial dimensions. No matter > how fast a spaceship is traveling, when it turns its lights on, the > light can only propagate as fast as the expanding fourth dimension can > carry it. > The Constant Velocity of Light in All Inertial Frames: > The velocity of light is always measured relative to the velocity of > time, and the velocity of time is always measured relative to the > velocity of light. This tautology assures us that the velocity of light > will always be the same for all observers in all inertial frames, as > the velocity of light is being measured relative to the velocity of > light in that frame. However, as demonstrated by experiments, time and > light travel slower close to gravitational masses, when measured from > distant frames. > What is Time? > Time is an emergent property of the underlying reality that a fourth > dimension is expanding relative to the three spatial dimensions. All > our measurements of time are based on the emission and propagation of > photons, and all photons propagate by surfing the expanding fourth > dimension. So it is that time inherits properties of the fourth > dimension, but time is not the fourth dimension. > Too many physicists have extended dimensional properties to the notion > of time, rather than realizing that time is an emergent property tied > closely to a fourth expanding dimension. Because our notions of time > are linked to change, and because all change is linked to the emission > and propagation of photons, and because all photons propagate in the > expanding fourth dimension, time has naturally been confused with the > fourth dimension. Because the fourth dimension is expanding in > quantized units, macroscopic objects never make it any deeper into the > fourth dimension than a quantum unit. > Einstein On the Electrodynamics of Moving Bodies > of this sort, together with the unsuccessful attempts to discover any > motion of the earth relatively to the 'light medium,' suggest that > the phenomena of electrodynamics as well as of mechanics possess no > properties corresponding to the idea of absolute rest. There is no > frame of absolute rest, because the fourth dimension is expanding at a > constant rate equally in all directions. No relative motion of the > earth was ever discovered relative to the 'light medium,' because > the light medium is the fourth dimension which is expanding equally in > all directions. All of our notions of velocity are measured with > respect to time, and all our notions of time are wed inherently to the > propagation of energy, which is only propagating because it surfs the > crest of the expanding fourth dimension. > Einstein continues, They suggest that, as already has been shown to > the first order of small quantities, the same laws of electrodynamics > and optics will be valid for all frames of reference for which the > equations of mechanics hold good. We will raise this conjecture (the > purport of which will hereafter be called the Principle of > Relativity) to the status of a postulate, and also introduce another > postulate, which is only apparently irreconcilable with the former, > namely, that light is always propagated in empty space with a definite > velocity c which is independent of the state of motion of the emitting > body. These two postulates suffice for the attainment of a simple and > consistent theory of the electrodynamics of moving bodies based on > Maxwell's theory for stationary bodies. The introduction of a > luminiferous ether will prove to be superfluous inasmuch as the > view here to be developed will not require an 'absolutely stationary > space' provide with special properties, nor assign a velocity-vector > to a point of the empty space in which electromagnetic processes take > place. Again, there is no ether in the classical sense, but there is > a fourth dimension that is expanding relative to the three spatial > dimensions at the constant rate of c in units of the Planck length. > Time Dilation > As one approaches the velocity of light, one catches up with the > fundamental expansion of the fourth dimension, and there is a smaller > chance for a photon being emitted without being reabsorbed in any > process. The expanding fourth dimension is what carries photons away, > allowing the electro-chemical transitions that underlie all clocks, be > they mechanical, biological, or electronic. Thus time slows for the > moving clock, as all time, be it an unwinding clock spring, > oscillations in a quartz crystal, or a beating heart, rely on the > emission of photons. All photons propagate by surfing the crest of the > expanding fourth dimension, and as any object catches up with the > expanding dimension, as it is rotated more into the expanding fourth > dimension, there is less of a chance that a photon can be emitted to > foster the physical change that constitutes aging, and time slows. > Surfing the Fourth Dimension: > A Photon as a Spherically Expanding Wavefront: > A photon expands through space in a spherically symmetric manner > because the fourth dimension is expanding through the three spatial > dimensions in a spherically symmetric manner. A photon surfs the > crest of the expanding fourth dimension. > Time is not a Dimension: > In certain cases Einstein and other physicists extended the metaphor of > dimensions too far to time. For time is not a dimension. Time is > consciousness of change, replete with past, present, and future, and > cause and effect. The past and future exist only in our minds, one the > record of events, and the second a creation of what could be, based on > our powers of inductive reasoning, inspiration, and dreams. There is > one present for the universe, and although it might be measured > differently, there is one absolute present. At every point throughout > the universe the fourth dimension is expanding relative to the three > spatial dimensions. Every tiny point of the fourth dimension is > becoming a tiny sphere with a radius of the Planck length, and every > tiny point on that tiny sphere is becoming a tiny sphere in its own > right. A photon surfs the edge of this expansion, riding the crest, > appearing as a spherically-symmetric wavefront, expanding throughout > the three spatial dimensions. > Lorentz Contraction: > Relativistic length contraction (Lorentzian Contraction) is always > accompanied by an increase in velocity, as the probability that each > quantum of the object resides in the time dimension is increased. > Relativistic length contraction can be accounted for by the fact that > as an object gains velocity its probabilistic wave function, is rotated > more into the time dimension, and thus it appears shorter from the > persepective of the three spatial dimensions. At the speed of light the > object would have to be a photon, so as to be completely orthogonal to > is in the spatial dimnsion means that there is a probability that the > time dimension will expand without carrying it along, in essence > leaving it behind for that moment it exists in the spatial dimension. > QFT: > The Equivalence of Mass and Energy: > Energy and mass are equivalent, expressed by E=mc^2, because the only > difference between mass and energy is the degree to which the matter > exists in the fourth dimension that is expanding at the rate of c > relative to the three spatial dimensions. When matter is rotated into > the expanding dimension, it is carried along at the velocity c relative > to the three spatial dimensions, and appears as photons. Thus all rest > mass has the potential to liberate immense amounts of energy by > existing in the expanding fourth dimension, surfing the expanding > dimension as photons. > a reality that has three stationary spatial dimensions and one > expanding dimension. Freely traveling photons are the extreme case of > matter that exists completely in the expanding fourth dimension, > orthogonal to the three spatial dimensions. When a freely traveling > photon interacts with a measurement device in the stationary > dimensions-when it blackens a grain in a photographic plate-it > locality as its wave function collapses. When matter exists in the > expanding fourth dimension, it is seen as wave, or a photon, or energy. > Depending how and when we choose to observe matter determines whether > bundles of energy that propagate at the velocity of c-this is because > photons represent matter rotated into the fourth dimension which is > expanding relative to the three spatial dimensions in a quantized > manner, in units of Planck's length at the rate of c. > Philosophical and Physical Barriers to Moving Dimensions > Many trained physicists have a knee-jerk reaction that the time > dimension cannot be moving because dimensions cannot move. First > off, since the universe is expanding, space-time is also expanding, > demonstrating that dimensions are moving and expanding. Secondly, > general relativity demonstrates that massive objects warp space-time, > meaning that as a massive object moves though space-time, it stretches > space-time, showing again that space-time in one area can move, or > deform, relative to space-time in another area. GR is a sound theory, > backed up with multiple high-profile experiments, including the > demonstration that starlight is bent by the sun and the verification > that orbiting stars radiate energy in the form of gravity waves. Thus > there exist neither philosophical nor physical barriers to the concept > of moving dimensions, but for artificial ones within lazy minds. > A curious sign of the times is that physicists will accept on blind > faith the existence of ten, twenty, or thirty dimensions, dimensions > that are curled up, or too small to measure, and yet they will reel in > shock and horror at a perfectly obvious postulate-the fourth > dimension is expanding relative to the three spatial dimensions. > They are to be forgiven-it has been a long time since a simple > postulate has been offered in the realm of physics, and the foreign > nature of truth's simple beauty is seen as a violent affront to the > String Theorist's convoluted sensibilities. > The Mysterious Minus Sign in The Metric > Consider the metric for a space-time interval: > x^2+y^2+z^2-c^2t^2=s^2 > Consider the metric for a photon, which travels at the speed of light. > x^2+y^2+z^2-c^2t^2=0 > Supposing that it is traveling along the x direction, we can write: > x^2-c^2t^2=0 > x^2=c^2t^2 > x=ct > Now let us ask a question, as we must certainly be free to ask > questions if we are to further physics. For a photon, how is the x > coordinate changing relative to the time coordinate? Would not the > answer just be the slope of the line in x=ct? > dx/dt=c > And so it is that for the photon-for all photons-the x coordinate > is changing at the rate of c relative to the t coordinate. > But no matter how far the photon travels in space, it will have moved > the same distance in space-time-0-not at all-the null vector. > This is because the time coordinate itself is moving, or more correctly > I should state that this is because the fourth dimension which carries > photons at the rate of c relative to the three spatial dimensions is > expanding at the rate of c relative to the three spatial dimensions, > and the propagation of photons/energy gives rise to our notions of > time. Remember that all time is based on the transportation of energy, > or the propagation of photons, so that our notion of time and clocks is > inherently wed to the fact that photons propagate at the rate of c > relative to the three spatial dimensions, which is inherently wed to > the fact that a fourth dimension is expanding relative to the three > spatial dimensions. Thus it makes sense that time does not pass for the > photon, and too, it makes sense that the distance a photon travels > through space-time is defined as the null vector. > Rather than just accepting the minus sign in front of the c^2t^2 as > being there because it just is there, MDT aims to look at the > deeper reality which gives rise to the minus sign. A physicist's job > is not to accept things on blind faith, nor only ask questions that are > allowed to be asked, but a physicist's job is to wonder freely-to > roam and range upon the frontiers of logic and reason. And that wonder, > which seems all but forgotten in the bureaucratization of modern > physics, with its billions of dollars for elegant fabrications woven > from string theories which yet leave the Emperor naked, leads to the > deeper beauty. Imagination is more important than knowledge, was > how Einstein put it. > The Collapse of the Wave Function: > The collapse of the wave function is also known as an irreversible > process, or a measurement, akin to a photon blackening a grain in > photographic film, or a photon being measured in front of one slit or > the other in a double-slit experiment, whereupon the interference > pattern disappears because the slit is ascertained, the wave has > collapsed, and the matter exhibits particulate behavior. Before it was > measured, the photon expanded through space as a spherically-symmetric > wave front, as it was matter surfing the expanding fourth dimension, > which is expanding through space in a spherically-symmetric manner. > Until the photon interacts with matter, or a measurement device in the > lab, the photon has equal probability of existing anywhere upon the > crest of the spherically symmetric wavefront, and thus it appears to > travel all paths-a physical reality Feynman took advantage of his > many paths formulation of quantum mechanics. > As Huygen's principle states that each point on an expanding > spherical wavefront is itself an expanding spherical wavefront, the > photon also has a probability of appearing earlier along on its > journey, or somewhere upon a smaller sphere centered upon its point of > origination. But over time the probabilities average out such that the > photon surfs along with the crest of the expanding fourth dimension, > and it appears to travel at the constant rate of c. > The collapse of the wave function is what happens when matter changes > its rotation relative to the time dimension. All measurements entail a > transfer of energy, and all measurements thus entail photons leaving > the expanding fourth dimension and being trapped in matter that is > stationary in an inertial lab frame. Perhaps this is why photons exert > no gravity while propagating freely, but do add gravitational mass > after their wave functions have collapsed, when they are trapped by > electrons within lab measurement apparatuses or photographic film. > The EPR Effect & Nonlocality of Quantum Mechanics: > The Einstein-Podolsky-Rosen effect (EPR) effect, which calls > instantaneous action at a distance spooky, can be accounted for > by the intrinsic nonlocality of an expanding fourth dimension. As a > point expands into a tiny sphere in the fourth dimension, it is yet a > single locale in that dimension, and hence though two initially > yet exist in the same place in the time dimension, and hence be > connected before they're measured-before the wave function > collapses. Quantum Mechanics exhibits nonlocal properties because the > fourth dimension exhibits nonlocal properties, as it is expanding > relative to the three spatial dimensions. > Please see the dialogue with Penrose later on. > The Photon's Null Vector > The null vector of the photon, which remains 0 no matter how far or > fast the photon travels in space-time, may be accounted for by the fact > that the fourth dimension is moving, and thus the only way to stay > still in the four dimensions with an effective null movement, is to > move along with, or surf the expanding fourth dimension. > The Ageless Photon > A photon does not age. No time passes for a photon. This is because > although a photon travels with the velocity c, it stays at the exact > same place in the fourth dimension as it surfs the expanding fourth > dimension. How else, other than with a moving fourth dimension, can we > explain that the only way to stay stationary in the fourth dimension is > to move at the velocity of c relative to the three spatial dimensions? > And how else, but with a moving fourth dimension, can we explain that > any object stationary in the three spatial dimensions is moving with a > velocity of c relative to the fourth dimension? > Time is an Emergent Phenomena of Moving Dimensions-It is Not a > Dimension > Einstein's, Penrose's (and many leading physicist's) mistaken view > of the future being out there in a block universe arises because > physicists misleadingly label time the fourth dimension, thus > implying that just as we can move anywhere in the three spatial > dimensions, such as up and down and back again, so too can we move > anywhere in the time dimension, to the past, the future, and back > again, implying that both the past and future must exist, as sure as > New York and Los Angeles. > But time is not so much the fourth dimension as it is an emergent > phenomena that arises because a fourth dimension is expanding at the > rate of c relative to the three spatial dimensions in a spherically > symmetric manner in units of the Planck length. > Einstein was Right: > Einstein proclaimed that all objects travel through space-time at c. > Even though we perceive a ruler along the x axis to be stationary, it > is yet traveling through space-time at the fixed speed of c, implying > that it is moving through time at the rate of c. Rotate it towards the > y axis, and its projection upon the x axis shortens, yet it still > appears to be stationary, and it is still traveling through space-time > at the rate of c, meaning that it is still traveling at the rate of c > through time, as it is stationary in space. Rotate it into the time > dimension instead of into the y dimension, and its projection along the > x axis still shortens (Lorentz contraction), but now it begins to move > through the three spatial dimensions, while maintaining the fixed speed > of c through space-time. Again, we see it propagate faster through the > three spatial dimensions as it is rotated into the fourth time > dimension (via a boost) because the fourth dimension is moving relative > to the three spatial dimensions. > Simply put, it is not possible to rotate an object into the fourth > time dimension without that object's velocity through the three > stationary dimensions changing. Thus the time dimension itself must be > expanding relative to the three spatial dimensions. Another way of > looking at this is asking, Why must something always gain a greater > velocity through space when it is rotated into the fourth time > dimension? If someone can conduct a Lorentz transformation on a > ruler, and rotate it into the fourth dimension without its velocity > augmenting through the three spatial dimensions, I would very much like > to hear about it. > Brian Greene's Treatment-The Time Dimension is Moving Relative to > the Spatial Dimension > As Brian Greene points out in the Appendix to Chapter 2 of The Elegant > Universe, we note that from the space-time position 4-vector > x=(ct,x1,x2,x3), we can create the velocity 4-vector u=dx/d(tau), where > tau is the proper time defined by > d(tau)^2=dt^2-c^-2(dx1^2+dx2^2+dx3^2). Then the speed through > space-time is the magnitude of the 4-vector u, > ((c^2dt^2-dx^2)/(dt^2-c^-2dx^2))^(1/2), which is identically the speed > of light c. Now, we can rearrange the equation > c^2(dt/d(tau))^2-(dx/d(tau))^2=c^2 to be > c^2(d(tau)/dt))^2+(dx/d(tau))^2=c^2. This shows that an increase of an > object's speed through space, (dx/d(tau))^2)^(1/2)= dx/d(tau) must be > accompanied by a decrease in d(tau)/dt which is the object's speed > through time, which also may be considered the rate at which time > elapses on its own clock d(tau) or the proper time, as compared with > that on our stationary clock dt. > Here again we see that even a stationary object has the velocity of c > through space-time. How can a stationary object have such a high > velocity? This is because the fourth dimension is expanding relative to > the three spatial dimensions at all points. So a stationary object will > see photons being carried away upon the crests of the expanding > dimension, at the rate of c, and this will be interpreted that that > object is aging, or moving through time at the rate of c, although in > reality the object itself never goes much deeper than the Planck length > into the expanding fourth dimension. Again, time is not the fourth > dimension, but it is an emergent property of an expanding fourth > dimension. > The Movement of All Objects That Exist More in Time: > In Lorentzian Transformations, there is no way for an object to be > rotated into the time dimension without it moving-this can be > explained by the fact that the time dimension is expanding. > The Debate Over the Block Universe: MDT To the Rescue: > Again we see quantum mechanics and relativity at odds over the debate > of the block universe implied by relativity, which seems to imply a > definitive, real future, which seemingly contradicts quantum > mechanic's inherent randomness and free will. MDT resolves this > paradox by viewing time not as the fourth dimension, but as a phenomena > that emerges because the fourth dimension is expanding relative to the > three spatial dimensions. Because all time is measured via the > propagation of photons, and because all photons propagate as matter > carried along by the expanding fourth dimension, time has oft been > ascribed properties of a fourth dimension similar to the three spatial > dimensions, resulting in paradoxical, misleading interpretations of the > universe. Suffice it to say MDT sees time not as a dimension, but as an > emergent property of a fourth dimension expanding relative to three > spatial dimensions. > In their paper concerning the paradoxes outlined above, The Debate > over the Block Universe, Isham, C.J. and J.C. Polkinghorne write: > http://www.meta-library.net/ctns-vo/isham-body.html > Proponents of the block universe appeal to special and general > relativity to support a timeless view in which all spacetime events > have equal ontological status. The finite speed of light, the light > cone structure, and the downfall of universal simultaneity and with it > the physical status of flowing time in special relativity result > in a heightened tendency to ontologize spacetime. The additional > arbitrariness in the choice of time coordinates in general relativity > makes flowing time physically meaningless. Thus no fundamental meaning > can be ascribed to the present as the moving barrier with the > kind of unique and universal significance needed to unequivocally > distinguish past from future. Instead the flowing present > is a mental construct, and four-dimensional spacetime is an > eternally existing structure. God may know the temporality of > events as experienced subjectively by creatures, but God cannot act > temporally, since flowing time has no fundamental meaning in nature. > Theologians must accept the Boethian and even gnostic implications of > the block universe. > http://www.meta-library.net/ctns-vo/isham-body.html > Isham and Polkinghorne continue: Opponents of the block universe > begin by distinguishing between kinematics and dynamics. Special > relativity imposes only kinematic constraints on the structure of > spacetime. The dynamics of quantum physics and chaos theory encourages > a view of nature as open and temporal, thus allowing for both human and > divine agency. The problem of the lack of universal simultaneity is > lessened since simultaneity is an a posteriori construct. > Philosophically disposed to critical realism, opponents are wary of the > incipient reductionism of the block view. They resist the Boethian > implications of relativity, and argue instead that divine omnipresence > must be redefined in terms of a special frame of reference, perhaps one > provided by the cosmic background radiation. God's knowledge of > spacetime events in terms of this frame of reference will be > constrained by both the world's causal sequence and the distinction > between past and future. Similarly God's actions will be consistent > with relativity theory. > http://www.meta-library.net/ctns-vo/isham-body.html > In MDT, both quantum mechanics and relativity are in perfect harmony, > but the time in relativity is not a dimension on equal footing with the > three spatial dimensions. Rather, time is an emergent parameter arising > from matter (photons) being carried along with a fourth dimension that > is expanding at a constant rate relative to the three spatial > dimensions. > Time's Arrow / 2nd Law of Thermodyamics / Entropy > Entropy states that the universe tends towards disorder. This is > because the fourth dimension is expanding in a spherically symmetric > away from one another-thus a drop of food coloring in a pool is > carried outward and evenly distributed as time evolves. Because the > fourth dimension is expanding as a spherically symmetric wavefront > through the three spatial dimensions, photons, as well as all matter > that interacts with photons, exhibits a probability to move in a > spherically symmetric manner. Thus, if we have a clump of atoms in the > middle of a room, a probability exists for the atoms to spread apart in > a spherically symmetrical manner, being carried along by the expanding > time dimension. > Traveling Backwards in Time: > The fourth dimension is expanding relative to the three spatial > dimensions. The expansion appears as a spherically-symmetric wave-front > propagating throughout the three spatial dimensions. This is the prime > mover-the fundamental source of all time, energy, and motion. When > matter exists completely in the fourth dimension, it appears as a > photon, expanding in a spherical wave-front relative to the three > spatial dimensions. Now Huygen's Principle shows that each point upon > the crest of a spherically symmetric wavefront is itself a spherically > symmetric wavefront. That means that there is a finite probability that > a photon's spherical wavefront will collapse into a smaller region, > in which case it might be measured to be somewhere where it was. Such a > photon may be said to be traveling back in time, and such a photon will > have traveled less than the speed of light. > On the quantum scale, where the fourth dimension is expanding in units > of the Planck length, there is a higher chance of light being measured > to move slower or faster than the speed of light-there is a higher > chance of a photon traveling backwards, or its expanding wave front > getting a little smaller as opposed to bigger, but over large distances > the speed of light is determined to be c. > to go back in time. All this means is that their wave functions are > surfing a region of the fourth-dimension which is contracting as > opposed to expanding-there is a small probability of this happening, > due to Huygen's principle, as elaborated on above. > But time travel on a macroscopic scale is prohibited, as the past and > future do not exist. We do not live in a block universe, wherein time > is a dimension, but rather time is an emergent phenomena, accounted for > with MDT's postulate: the fourth dimension is expanding relative to > the three spatial dimensions. > Godel's Block Universe Paradox Resolved > In 1949 Godel published a paper showing that within the theory of > relativity, time as we understand it, does not exist. Einstein > recognized Godel's paper as an important contribution to the > general theory of relativity, and since then physicists have not > been able to find any logical shortcomings in Godel's work, and > nobody has been able to account for the existence of time. But the > Theory of Moving Dimensions accounts for time as we know it by showing > that it is an emergent property of the underlying dimension's > intrinsic relative movement. > sufficiently wide course, it is possible in these worlds to travel into > any region of the past, present, and future, and back again, exactly as > it is possible in other worlds to travel to distant parts of space. > This state of affairs seems to imply an absurdity. For it enables one > to travel into the near past of those places where he himself lived. > There he would find a person who would be himself at some earlier > period of life. Now he could do something to this person, which, by his > memory, he knows has not happened to him. > important contribution to the general theory of relativity, especially > to the analysis of the concept of time. The problem here involved > disturbed me already at the time of the building up of the general > theory of relativity, without my having succeeded in clarifying it... > The distinction earlier-later is abandoned for world-points which > lie far apart in a cosmological sense, and those paradoxes, regarding > the direction of the causal connection, arise, of which Mr. Godel has > spoken. . . It will be interesting to weigh whether these are not to be > excluded on physical grounds. -Michio Kaku > The mistake Einstein made in his formulation was confusing time itself > with the fourth dimension. Time is an emergent property that we witness > because of the fourth dimension expanding relative to the three spatial > dimensions, and because it thus inherits properties of a dimension, it > is all too tempting for physicists to refer to time as a dimension. > Time travel is impossible both in reality and Moving Dimensions theory, > though I encourage prominent physicists to keep on writing books about > time machines and bookstores to stock them in the science-fiction > sections. > Time arises from the interaction of the expanding fourth dimension with > the three spatial dimensions, but many physicists mistakenly labeled > the fourth dimension as the time dimension. > A lot of confusion has arisen by from this mislabeling coupled with the > physicists' tendency to over-extend metaphors. As soon as physicists > mistakenly labeled the fourth dimension the time dimension, they were > eager to see it as an entity analogous to the three spatial dimensions, > where one can get from any point to any other point. > But time is an emergent property deriving from the expansion of a > single spatial dimension relative to the three other stationary spatial > dimensions. The fourth dimension expands in units of the Planck length > at the rate of c, so in a sense the fourth dimension is only ever > Planck's length deep to all macroscopic objects. Only a photon can > exist in this dimension, orthogonal to the three dimensions, and at > that point a photon is matter surfing the expanding dimension. > Huygen's principle demonstrates that every point along a spherically > symmetric wavefront is the source of a spherically symmetric wave, and > so it is with a photon. This is because every point in space-time is > the source of a spherically symmetric expansion of the fourth dimension > relative to the three stationary dimensions. > Time travel to any significant degree is impossible because the time > dimension never reaches deeper than Planck's length. You could only > go back in time by Planck's time, which wouldn't be very useful! > Physicists enjoy viewing the time dimension on equal footing with the > spatial dimensions. After all, they say it is just another a > dimension that just happens to have a minus sign infront of it in > the space-time metric. But they never seek to explain the minus sign. > Instead they rush straight ahead into all their ridiculous notions of > time travel, stating that just as we can get from any point A to any > point B in space, we can get from any point A to any point B in time. > But time travel has never been accomplished, nor will it ever be. > Physicists were right in recognizing that time is a dimension, but they > fell short in recognizing that it was different from the three spatial > dimensions in that it is expanding at the rate of c relative to the > three spatial dimensions. > The notion of past, present, and future is more related to the change > of energy than it is to the actual existence of a physical past, a > physical present, and a physical future. Only the present ever exists, > and the past is what is recorded in our minds-it exists nowhere else. > But because time is a dimension, physicists were seduced into believing > one could travel anywhere within it. But in reality we never get any > further than Planck's length deep in time, and it is at that depth > that photons surf through the universe, while electrons oscillate, and > out bodies maintain their average position firmly in the three spatial > dimensions as the time dimension expands relentlessly about us in units > of Planck's length. > For Godel, if there is time travel, there isn't time. The goal of > the great logician was not to make room in physics for one's favorite > episode of Star Trek, but rather to demonstrate that if one follows the > logic of relativity further even than its father was willing to > venture, the results will not just illuminate but eliminate the reality > of time. -A World Without Time, Palle Yourgrau > Unification of QM and Relativity > Relativity becomes increasingly exact at long-length scales but fails > at short ones because space-time itself is quantized, as the time > dimension is expanding in units of the Planck length. The concept of > general relativity's smooth geometry, at large scales, disappears on > short-distance scales-this has been a problem to string theorists, > but only because they were never bold enough to recognize that's the > way it is because that's the way it is-GR does not break down at > distances smaller than the Planck length because such distances do not > exist with any degree of certainty. The fourth dimension is expanding > relative to the three spatial dimensions in units of the Planck length, > and thus distances smaller than the Planck length cannot be measured > nor defined. > in merging general relativity and quantum mechanics turns up when the > central tenet of the former-that space and time constitute a smoothly > curving geometrical structure-confronts the essential feature of the > latter-that everything in the universe, including the fabric of space > and time, undergoes quantum fluctuations that become increasingly > turbulent when probed on smaller and smaller distance scales. On > sub-Planck-scale distances, the quantum undulations are so violent that > they destroy the notion of a smoothly curving geometrical space; this > means that general relativity breaks down. > But general relativity does not break down. It works perfectly well, > holding the planets in their orbits, curving space and time about > massive objects, bending light just so, in accordance with Einstein's > equations. > General relativity does not break down at sub-Planck-scale distances > because such distances do not exist. The fourth dimension is expanding > relative to the three spatial dimensions in units of the Planck length, > and thus all physical measurements and physical definitions are larger > than the Planck length. General relativity need have no fear of ever > breaking down at distances smaller than the Planck length, because such > distances do not exist in the physical world!! > Moving Dimensions & String Theory > The jury is still out on String Theory, as is the theory itself. Before > it can be tested, it first must step forward with something to test. > String theory must first step forward with simple postulates and > laws-until that day, it will remain a hoax to the degree it is > funded. > Whereas String Theory retreats into realms beyond physical reality, > beyond experimental tests, beyond postulates, laws, and predictions, > Moving Dimensions Theory stays simply wedded to a single > postulate-the fourth dimension is expanding relative to the three > spatial dimensions. Where String Theory retreats into a mathematical > realm where postulates, laws, words, and physical intuition are blinded > so that politics and strategic faith might reign supreme, MDT seeks a > return to those simpler days of physics, where physics was reduced to > first principles. > Perhaps String Theory could find a new home as a subset of MDT, wherein > the vibrating strings are vibrating/surfing upon wavefronts of the a > fourth dimension that's expanding relative to the three spatial > dimensions. > Zeno's Paradox > If you travel from point A to point B, you must travel half of the > distance to point B before traveling the complete distance. Now from > that point you must again travel half the remaining distance. If you > continue to do so (travel half the remaining distance) you will never > reach point B. > Extended to its logical conclusion, this reasoning implies that you > could never move in the first place. > But things move. > Motion is a fundamental part of the universe. And that is because it is > embedded within the four dimensions, which consist of three stationary > dimensions and one that is expanding with a velocity of c in a > spherically symmetric manner, in units of Planck's length, relative > to the three stationary dimensions. > Because the time dimension is expanding at a uniform rate equally in > different than where it currently is as time moves on. For every > Hawking's Block Universe: Wrong > imaginary time. Imaginary time may sound like science fiction, and it > has been brought into Doctor Who [an English Star Trek]. But never the > less, it is a genuine scientific concept. One can picture it in the > following way. One can think of ordinary, real, time as a horizontal > line. On the left, one has the past, and on the right, the future. But > there's another kind of time in the vertical direction. This is called > imaginary time, because it is not the kind of time we normally > experience. But in a sense, it is just as real, as what we call real > time. > Hawking's logic succumbs to a common physical misinterpretation of > time. In stating, One can think of ordinary, real, time as a > horizontal line. On the left, one has the past, and on the right, the > future, Hawking is confusing our notion of time that is an emergent > phenomena arising from a fourth dimension expanding relative to three > spatial dimensions with the fallacious view of time as a dimension, on > equal footing with space. Hawking's and Penrose's mistaken view of > the future being out there arises because of physicists > misleadingly labeling time the fourth dimension, thus implying > that just as we can move anywhere in the three spatial dimensions, such > as up and down and back again, so too can we move anywhere in the time > dimension, to the past, the future, and back again, implying that both > the past and future must exist, as sure as New York and Los Angeles. > Time is an emergent phenomena of a fourth dimension expanding relative > to the three spatial dimensions-thus time sometimes appears to have > dimensional properties. A Lorentz transformation can rotate an object > into the time dimension, and we can appear to travel through the > time dimension, but in both cases the time dimension is our > interpretation of physical events in a universe with a fourth dimension > that is expanding relative to the three spatial dimensions. > All time is measured relative to the propagation of photons, and > because all photons propagates via surfing the fourth dimension that is > expanding relative to the three spatial dimensions, time has oft been > ascribed properties of a fourth dimension. > Peter Lynds' View of Time: Closer to MDT's Reality > In Peter Lynds' abstract to Time and classical and quantum > mechanics: Indeterminacy vs. discontinuity, Lynds states, It is > postulated there is not a precise static instant in time underlying a > dynamical physical process at which the relative position of a body in > relative motion or a specific physical magnitude would theoretically be > precisely determined. It is concluded it is exactly because of this > that time (relative interval as indicated by a clock) and the > continuity of a physical process is possible, with there being a > necessary trade off of all precisely determined physical values at a > time, for their continuity through time. This explanation is also shown > to be the correct solution to the motion and infinity paradoxes, > excluding the Stadium, originally conceived by the ancient Greek > mathematician Zeno of Elea. Quantum Cosmology, Imaginary Time and > Chronons are also then discussed, with the latter two appearing to be > superseded on a theoretical basis. (Lynds, Peter, Foundations of > This is because time is an emergent phenomena, arising because the > fourth dimension is expanding at a rate of c relative to the three > stationary spatial dimensions in unitis of the Planck length. There is > no precise time underlying a physical process because all measurements > of time are limited by Heisenberg's uncertainty principle, as the > expansion of the fourth dimension, by which time is defined, is > occurring in quantized units of the Planck length. > Lynds sees that there is no precise time underlying a physical process > because he argues that to have a defined position with respect to time > would mean that a moving object would have to be frozen. However, this > never happens, because all motion takes place upon a backround where > time is not a dimension nor a parameter, but a device that we have used > as a tool to measure distance, interval, and motion as best we know > how. That this has led to paradoxes is no wonder, but the paradoxes are > resolved with viewing time not as a fourth dimension, but as an > emergent phenomena that rises because a fourth dimension is expanding > relative to the three spatial dimensions in units of the Planck length, > and that it is this fourth dimension that carries photons by which all > measurements of time are made. Thus time is fundamentally quantum > mechanical in behavior, inheriting a probabilistic and quantized > nature, and when quantum mechanics manifests itself throughout the > macroscopic world, it is often deemed paradoxical. > MDT & Heisenberg's Uncertainty Principle: > Because the fourth dimension is expanding in quantized units, and > because all measurements require energy which only ever propagates in > quantized units as all energy is the result of photons surfing the > expanding fourth dimension, there is an inherent limitation to the > detail of measurement, arising from the nature of the quantized > expansion of the fourth dimension relative to the three spatial > dimensions. > Newton's Laws, Inertia & The Conservation Laws: > The Law of Inertia: All objects conserve their relative rotation in > space-time. An accelerated objected is rotated more into the expanding > fourth dimension, resulting in an increased probability it will move > relative to the three spatial dimensions. This is accomplished by > adding photons to the object, thereby increasing its mass along with > the net object's (object+photons) probability of existing in the > expanding third dimension. A decelerated electron emits photons, > lowering its probability of being in the fourth expanding dimension, as > its velocity relative to the three spatial dimensions slows. > Probability/Rotation are Conserved: > Every entity has a probability of existing in both space and time. The > greater a probability an entity has of existing in time, the more > energy it will be observed to have from a stationary observer. Energy > is added to an object by the way of photons, and thus all additions of > energy to any object increase the objects mass. > added to it, it circles the accelerator faster and faster and gains > more and more mass. The more photons that are added to it, the higher > the probability it exists in the time dimension. It is rotated into the > time dimension, and its time slows down as its effective length > contracts. > The probability of being in the space and time dimensions is a > conserved quantity, manifesting itself as the conservation of momentum > and energy. If no energy is added or subtracted, its momentum and > energy remain constant-its rotation in space-time remains constant. > As an object is given energy, the added photons give the net object a > higher probability of being in the time dimension, and thus it > propagates faster through the three spatial dimensions, as it > surfs upon crests of the expanding dimension through space-time. > Explanations of Dark Matter & Dark Energy > The Unification of Relativity & QM > Relativity is what generally emerges at great distances and high > speeds, and quantum mechanics generally emerges at tiny distances for > tiny objects. The quantized expansion of > THE QM, GR & MDT: A DIALOGUE WITH PENROSE ET. AL > Roger Penrose longs for Moving Dimensions Theory. Where he falls short > in the following discussion is where he states, the future is out > there. The future is not out there. But where Penrose steers close > is in acknowledging, I think we need a new way to look at time, not > either Quantum Mechanics or Relativity. MD Theory offers this new > way. > Time is an emergent phenomena. Time happens because a fourth dimension > is expanding relative to the three spatial dimensions. > Moving Dimensions Theory offers a new way of looking at time underlying > both QM and SR a phenoma that emerges from the MD Theory: THE FOURTH > DIMENSION IS EXPANDING AT A RATE OF C RELATIVE TO THE THREE SPATIAL > DIMENSIONS IN QUANTIZED UNITS OF THE PLANCK LENGTH, GIVING RISE TO TIME > AND ALL QUANTUM MECHANICAL AND RELATIVISTIC PHENOMENA. > http://physicsmathforums.com > Penrose's mistaken view of the future being out there arises > because of physicists misleadingly labeling time the fourth > dimension, thus implying that just as we can move anywhere in the three > spatial dimensions, such as up and down and back again, so too can we > move anywhere in the time dimension, to the past, the future, and back > again, implying that both the past and future must exist, as sure as > New York and Los Angeles. > But time is not so much the fourth dimension as it is an emergent > phenomena that arises because a fourth dimension is expanding at the > rate of c relative to the three spatial dimensions in a spherically > symmetric manner in units of the Planck length. > Dr. E has added to the following dialogue with Roger Penrose, showing > how Moving Dimensions Theory can unify the concept of time in SR and > QM-in fact all phenomena in SR and QM might be accounted for by > Moving Dimensions Theory. The original dialogue may be found here: > http://members.fortunecity.com/templarser/flowtime.html > Roger Penrose : I think there's always something paradoxical about > the way we seem to perceive time to pass and the way physics describes > time. > Dr. E: Moving Dimensions Theory alleviates this paradox by viewing time > as an emergent phenomena-something that arises because the fourth > dimension is expanding relative to the three stationary spatial > dimensions. > Roger Penrose : Space-time is certainly different stuff from space > because its 4 dimensional instead of 3-D (RP larfs!) which is a big > diff. Time really has to be brought into the picture; this one thing > which is space/time. > Physicist : Just imagine what this might be like: 3-D space implies a > volume, and you can move any where in that volume. Once you add time as > a 4th dimension, another axis, then this block of space/time would > contain within it past, present and future, all at once. Time is > frozen, all times exist together; so just as you can say over here, > over there in 3-D space, you can talk about over then, in 4-D > space/time. > Roger Penrose : It's a way of looking at things if you like which > physically we seem to be forced into. I say physically from the point > of view of what the theory of rel. tells us. And Relativity is > remarkably well tested, I mean, 14 places of decimal, it's just > incredible. So we know that this theory does describe the universe to > an extraordinarily precise degree, so we have to take it seriously. And > that theory tells us that we have to regard space and time as one > thing, it's all out there, it's one thing. In the same sense that > space is out there, time is out there. > Dr. E: No-the past and future are not out there. There is indeed a > fourth dimension, and that dimension is expanding relative to the three > spatial dimensions at the rate of c in units of the Planck length. We > perceive time-the past and the future-as events and dreams in our > memories and minds, based on the interaction of the fourth expanding > dimension with the three stationary dimensions. > Narrator : Like the Medieval God's-view of time, Einstein's physics > says that the future is already out there. The moments of our lives are > just waiting for us to step into them. > Roger Penrose : But there's no more problem about the future being out > there than saying that space is out there. You say, Mars is out > there, but why is that more comprehensible than saying next week is > out there? It's just as far away in a certain sense. > Physicist : If you take this block of 4-D space/time literally, it > means you have to abandon free will. It means not only is the future > pre-ordained, but its already there, its already happened. There's no > point in making any decisions, whatever you do has already happened. If > I choose to drop this stone into a pond, I think of it being my own > free choice, but of course in 4-D space/time I had no choice in > dropping the stone ; the splash is already there in the future and so > we lose all free will. If time travel was possible, you can imagine > people coming back from the future to visit us; its no good us saying, > you cant exist - you haven't happened yet.They've come from a time > which they consider to be their 'now' and for them we're in their path. > Roger Penrose : So this means that in a sense, the present past and > future are out there, and that also gives us a very deterministic view > of the world. We have no control of what happens in the future because > its all laid out. I think the trouble that people have with this idea > is that you think the future is under your control, to some degree, and > so this means that if the future's laid out then in a sense its not > under your control. > Physicist : Personally I'm very uncomfortable about the block universe > idea. Now this may be just a gut feeling or just irrational, but can't > accept the future's already 'out there'. I don't accept that I don't > have any free will. > Roger Penrose : I think there is a positive side to this picture of > space and time being laid out there as 4 dimensions, because it tells > you that all times are there once and it can affect the way one thinks > about people who have died. I mean, I remember thinking in this kind of > way when my mother died. In some sense she was still there because her > existence is still out there in space/time although in our time she is > not alive. A colleague of mine had a son who died in tragic > circumstances and I presented this idea to him and it helped his > understanding also. This was before I heard that Einstein had a > there, and that somehow this was reassuring. I certainly think this way > often, that space/time is laid out and that things in the past and > things in the future are out there still. > Narrator : But almost at the same time that Relativity was gaining > universal acceptance a radically different picture of the universe was > emerging. > Physicist : The way out if you don't want to accept the block universe > idea is quantum mechanics. Now, Quantum Mechanics is the second great > discovery of the 20th century physics and that states that the future > isn't predetermined and preordained. > Narrator : Quantum Mechanics was born out of a series of experiments > whose results even today have no satisfactory explanation. Relativity > works at the large scale where it provides exact predictions as to what > will happen next. But when physicists started looking down at the > atomic and sub-atomic level, the familiar laws failed. At this level, > there were no certainties, only probabilities. How can the future of > the universe be already out there if the future of a single molecule is > so utterly unpredictable? > Dr. E: The future of the universe is not already out there. Both > quantum mechanics and relativity derive from the same underlying > physical reality of a fourth dimension expanding relative to three > spatial dimensions at the rate of c in units of the Planck length. The > any matter at a point in the expanding dimension, which would appear as > photons expanding in a spherically symmetric manner at the rate of c. > The constant speed of light also comes from the physical reality of the > fourth dimension expanding relative to the three stationary spatial > dimensions. No matter how fast the emitter is traveling, the expanding > dimension yet carries the photon at the rate of c. > Physicist : Before we look to see what the atom is doing, not only is > there a gap in our knowledge, the atom itself has not decided what to > do. It had an infinite number of choices to make, it will be doing all > those choices all at once, and its only when we look to see what is > happening do we force it to make a choice. In Quantum Mechanics the > future is not determined, and so Quantum Mechanics in a sense rescues > us and rescues free will. > Roger Penrose : In a sense you don't have the future laid out in > Quantum Mechanics So Quantum Mechanics. is basically different in the > way we look at it. You do have this indeterminacy about the future and > a necessary feature of this is its incompatibility with Special > Relativity. So we have these 2 great theories, both of which are > extremely accurate, tell us something about how the world operates, > something very insightful and profound and accurate, but they're > incompatible with each other. So there's no doubt there's something > missing here. How important it is to how we 'feel' the passage of time > is I think very important. > Dr. E: But QM and SR perfectly compatible theories. In SR there is no > certain future-that is a byproduct of mistakenly looking at time as a > fourth dimension on equal footing with the three spatial dimensions. > The passage of time happens because of matter interacting with a > dimension that is expanding relative to the three spatial dimensions. > And all quantum mechanical and relativistic effects may be traced back > to Moving Dimensions Theory. > Narrator: The tragedy of modern physics is that it explains so much of > the objective universe but at the cost of what we subjectively feel; > about our conscious free will and our feeling that time does flow. > Faun Flynn: I very much think there's a flow to time. If you consider > what music would be like if there was no flow to time. You couldn't > have music if you didn't have memory, or if you didn't have an > expectation generated by that memory. You'd have an isolated note in > the 'now'. Music unfolds in time in such a way that we have a memory of > what we've heard, and this memory conditions to what we expect. This of > course is something that everybody is familiar with, because if you > hear ( 7 note scale played on piano) you have a very strong expectation > that the next note will be (plays final octave note of scale) . Music > is a distillation or a side-effect of that mental faculty we employ to > perceive time, and things changing in time. > Roger Penrose : The question of the passage of time is something the > scientists have rather set aside, and taking the view that its not > really physics, it's a subjective issue; and subjective questions are > not part of science. Now when you start talking about phenomena like > one's own perception of the passage of time, then that is a subjective > thing. And that's almost a taboo subject for science because it's > subjective. The physical world at least according to Relativity, is out > there, and there is no flow of time, it's just there; whereas our > feeling (we have this feeling of the passage of time) are intimately > connected to our perceptions. > Dr. E: Indeed scientists too often choose their battles selfishly, > thereby solving problems by saying that they do not need to be solved, > while simultaneously concentrating on obscure theories, spending > millions on building empty temples for the herd. The physical future is > not out there according to relativity. The passage of time is the > result of the propagation of energy. The aging of cells, the > oscillations of a quartz crystal, the unwinding of a clock spring, the > swing of a pendulum-all of these have to do with the exchange of > photons and thus the propagation of energy. And energy propagates at > the constant rate of c throughout the universe because the fourth > dimension, which carries matter that we perceive as photons, is > expanding at the rate of c relative to the three spatial dimensions, in > units of the Planck length. > Physicist : We have this subjective feeling, that time goes by, but > physicists would argue this is just an illusion. > Roger Penrose : Yes I think physicists would agree that the feeling of > time passing is simply an illusion, something that is not real. It has > something to do with our perceptions. > Dr. E: The passage of time is real. Time's arrow, or entropy, or the > second law of thermodynamics are all explained by Moving Dimensions > Theory. Because a fourth dimension is expanding at the rate of c in a > close to each other will wander apart. > Narrator : Illusion or not, our perceptions emerge somewhere between > the cosmic scale of Relativity where the flow of time is frozen and the > quantum scale, where flow descends to uncertainty. Our world is on a > scale governed by a mixture of chance and necessity. > Roger Penrose : My view is that there is some large scale quantum > activity going on in the brain. Physics does not say that Quantum > Mechanics takes place in small areas, but also take place over larger > areas. I think this has to do with the consciousness. I think we need a > new way to look at time, not either Quantum Mechanics or Relativity. > Dr. E: Moving Dimensions offers this new way of looking at time. Time > is not the fourth dimension, but it is a phenomena that arises because > a fourth spatial dimension is expanding relative to the three > stationary spatial dimensions. > Narrator : If Quantum Mechanics is taking place in the brain then the > same randomness of outcome and unpredictability might explain our > ability to make sometime random choices. Opening up the future to the > possibility of change would provide the first step of restoring to > physics the flow of time it currently denies. > Physicist : I don't think time flows, I feel that time flows, but I > feel we can only understand this if we have a better understanding of > how consciousness works. I think human consciousness probably has the > secrets as to how and why we think of time as going by. > Roger Penrose : I don't think we have the tools, I don't think we have > the physical picture to accommodate these things yet. We're not very > close to it. > Dr. E: Moving Dimensions Theory has just brought us closer. > The original dialogue may be found here: > http://members.fortunecity.com/templarser/flowtime.html > Wheeler's Quantum Foam: > central principle of general relativity, is destroyed by the violent > fluctuations of the quantum world on short distance scales. On > ultramicroscopic scales, the central feature of quantum mechanics-the > uncertainty principle-is in direct conflict with the central feature > of general relativity-the smooth geometrical model of space (and of > spacetime)... The equations of general relativity cannot handle the > roiling frenzy of quantum foam. Nor do they have to. > MDT happily unifies relativity and quantum mechanics with a simple > postulate. The fourth dimension is expanding relative to the three > spatial dimensions. > And because the fourth dimension is expanding in units of the Planck > length, quantum mechanical behavior manifests itself in all phenomena > that touch upon the notion of tiny distances. However, over large > distances, the expansion of the fourth dimension seems smooth and > continuous. Thus space and time appear smooth and continuous over large > distances. > Likewise, although light has a probability of traveling slower or > faster than c, due to the quantum mechanical nature of the expansion of > the dimension that carries it through space, over large distances time > is observed to travel at a the constant rate of c. > Relativity and quantum mechanics have always existed peaceably in > nature, and now, via Moving Dimensions Theory, relativity and quantum > mechanics exist peaceably in theory too. > String Theory's Admitted Shortcomings FROM ITS TEXTBOOKS!!!: > The great irony of string theory, however, is that the theory itself is > not unified. To someone learning the theory for the first time, it is > often a frustrating collection of folklore, rules of thumb, and > intuition. (IN OTHER WORDS IT IS NOT PHYSICS!!!) At times, there seems > to be no rhyme or reason for many of the conventions of the model. For > a theory that makes the claim of providing a unifying framework for all > physical laws, it is the supreme irony that the theory itself appears > so disunited!! > Introduction to Superstrings and M-Theory, page 5. -Michio Kaku > Supersymmetry is one of the most elegant of all symmetries, uniting > bosons and fermions into a single multiplet: > Fermions ¤.88 Bosons > By uniting fields of differing statistics, supersymmetry and > supergroups have also opened up an entirely new area of mathematics... > However, the irony is that there is not a single shred of experimental > evidence in its favor. For example, physicists have tried to fit the > electron or neutrino into supersymmetric multiplets, but the scalar > partners of these leptons have never been seen. In fact, none of the > Should New Ideas be Allowed in Contemporary Physics? > All of physic's greatest hits are contained in simple postulates, > laws, and equations that have stood the test of time and provided a > lever by which we could disturb the universe. For this reason, I am > advocating a return to physics that is expressed in simple postulates, > laws, and equations that can be discussed and tested by experiment. > Postmodern theories such as string theory are dangerous to physics and > physicists alike. Like Narcissus, who fell in the water while staring > at his own reflection, it seems many String Theorists have fallen into > a world of reflection, where they're not looking at physical reality, > but only themselves. Hundreds of millions of dollars have been poured > into String Theory, and yet not one postulate, nor law, nor proof, nor > success. > But the purpose of this paper is not to criticize string theory, but to > light the way to a new day with a simple postulate: the fourth > dimension is expanding relative to the three spatial dimensions. > After Einstein published his two postulates of special relativity and > his foundational paper on quantum mechanics, it was yet many years, and > tens of thousands of man hours, before a nobler physics bore itself > out-the realm of physics that is now known as relativity, that has > stood the tests of time and continues to inspire young physicists. And > so it is that today, Quantum Mechanics and Relativity, which came out > of either side of Einstein's mind, are yet the towering beacons that > inspire young physicists. When one wants to see further, one climbs on > top of the shoulders of giants-Newton, Bohr, Einstein, Dirac, > Shrodinger, and Wheeler. And it was from such a vantage point that I > saw Moving Dimensions Theory. > Contemporary physics, like much of academia, is cluttered with > political factions, charlatans, hypesters, and fund-raisers. Such a > system is self-reinforcing, and as time goes on, truth means less and > less, as politics, hype, and blind-faith land the postdocs, government > grants, and tenure. > Young physicists are bullied by pomo-hipster the truth does not > exist String Theorists who tell questioning young physicists that > they cannot question. When the young physicists continue to question > undeterred, the tenured string theorist waves her hands and makes it > personal, projecting their infinite shortcomings, telling the young > physicists that simply cannot comprehend the beauty of the ten, eleven, > twenty-two, or thirty dimensions. > But there are changes afoot, and prominent physicists-Nobel Prize > winners and true leaders-are stepping forth to criticize string > theory: > If Einstein were alive today, he would be horrified at this state of > affairs. He would upbraid the profession for allowing this mess to > develop and fly into a blind rage over the transformation of his > beautiful creations into ideologies and the resulting proliferation of > logical inconsistencies. Einstein was an artist and a scholar but above > all he was a revolutionary. His approach to physics might be summarized > as hypothesizing minimally. Never arguing with experiment, demanding > total logical consistency, and mistrusting unsubstantiated beliefs. The > unsubstantial belief of his day was ether, or more precisely the na.95ve > version of ether that preceded relativity. The unsubstantiated belief > of our day is relativity itself. It would be perfectly in character for > him to reexamine the facts, toss them over in his mind, and conclude > that his beloved principle of relativity was not fundamental at all but > emergent-a collective property of the matter constituting space-time > that becomes increasingly exact at long length scales but fails at > short ones. This is a different idea from his original one but > something fully compatible with it logically, and even more exciting > and potentially important. It would mean that the fabric of space-time > was not simply the stage on which life played out but an organizational > phenomenon, and that there might be something beyond. -A Different > Winner of the Nobel Prize in physics for his work on the fractional > quantum Hall effect. > Despite its having become embedded in the discipline, the idea of > absolute symmetry makes no sense. Symmetries are cause by things, not > he cause of things. If relativity is always true, then there has to be > an underlying reason. Attempts to evade this problem inevitably result > in contradictions. Thus if we try to write down relativistic equations > describing the spectroscopy of a vacuum, we discover that the equations > are mathematical nonsense unless either relativity or guage invariance, > an equally important symmetry, is postulated to fail at extremely short > distances. No workable fix to this problem has ever been discovered. > String theory, originally invented for this purpose, has not succeeded. > In addition to its legendary appetite for higher dimensions, it also > has problems at short length scales, albeit more subtle ones, and has > never been shown to evolve into the standard model at long length > scales, as required for compatibility with experiment. -A > Laughlin, Winner of the Nobel Prize in physics for his work on the > fractional quantum Hall effect > Thus the innocent observation that the vacuum of space is empty is > not innocent at all, but is instead compelling evidence that light and > gravity are linked and probably both collective in nature. Real light, > like real quantum-mechanical sound, differs from its idealized > Newtonian counterpart in containing energy even when it is stone cold. > According to the principle of relativity, this energy should have > generated mass, and this, in turn, should have generated gravity. We > have no idea why it does not, so we deal with the problem the way the > government might, namely by simply declaring empty space not to > gravitate. In chutzpah, this ranks with the famous case of the Indiana > state legislature passing a law declaring Pi to have the value three. > It also demonstrates the severity of the problem, for one does not > resort to such desperate measures when there are reasonable > alternatives. The desire to explain away the gravity paradox > microscopically is also the motivation for the invention of > supersymmetry, a mathematical construction that assigns a special > superpartner ever discovered in nature, the hope for a reductionist > explanation for the emptiness of space might be rekindled, but this has > not happened, at least not yet. > [String Theory] has no practical utility, however, other than to > sustain the myth of the ultimate theory. There is no experimental > evidence for the existence of strings in nature, nor does the special > mathematics of string theory enable known experimental behavior to be > calculated or predicted more easily. Moreover, the complex > spectroscopic properties of space accessible with today's mighty > accelerators are accountable in only as low-energy > phenomenology-a pejorative term for transcendent emergent > properties of matter impossible to calculate from first principles. > String theory is, in fact, a textbook case of Deceitful Turkey, a > beautiful set of ideas that will always remain just barely out of > reach. Far from a wonderful technological hope for a greater tomorrow, > it is instead the tragic consequence of an obsolete belief system-in > which emergence plays no role and dark law does not exist. > Robert B. Laughlin, Winner of the Nobel Prize in physics for his work > on the fractional quantum Hall effect. > The master antitheory of the age is the idea that there is no > fundamental thing left to discover, so that the world we inhabit is > simply a swarm of detail that belongs to no one and thus can be > legitimately handled by business tactics-resource management, > competitive advertising, survival of the fittest, and so forth. A > corollary is that there is no absolute truth, but only products, like > shirts or hamburgers, that one throws away when their usefulness is > exhausted. Antitheories are dangerous ideologies not only because they > impede inquiry but because they lull one into ignoring threats that > one's opponents can exploit to their advantage. > Robert B. Laughlin, Winner of the Nobel Prize in physics for his work > on the fractional quantum Hall effect. > Acceleration occurs when an object is rotated in space-time, and the > conservation of momentum and energy were based on the conservation of > something more fundamental-the conservation of dimension. > Conservation Laws: Newton's Laws & The Law of Inertia > The conservation of energy and the conservation of momentum can be > has a probability of existing in ace or time. A photon has close to a > 100% probability of existing in time and close to a 0% chance of > existing in space. Mass has close to a 100% chance of existing in > space, and close to 0% chance of existing in time. When one adds > photons to massive objects, one gives them energy, the net photon-mass > object has a greater chance of existing in time than did the massive > object on its own. > | / > | / > | / > | / > | / > | | | | |/ | > B A C > Because massive objects curve space-time, the probability of being in > space and time are altered by gravitational fields. > Consider point A in the figure above, close to a massive object. The > rate at which the fourth dimension expands is always proportional to > the space metric at the exact point from where the expansion > originates. So the time metric at point B is shorter than the time > metric at point A which is shorter than the time metric at point C. The > fourth dimension, expanding from point A, will arrive at point B before > it arrives at point C. > Acceleration occurs when an object is rotated in space-time, and the > conservation of momentum and energy were based on the conservation of > something more fundamental-the conservation of dimension. > Because space is stretched towards the massive object, and all objects > try to preserve their relative rotation with respect to space and time, > the object has a greater chance of being in the time dimension where > the space is stretched. Hence the acceleration expected due to the laws > of relativity. > [img]file:///C:%5CDOCUME%7E1%5Ce%5CLOCALS%7E1%5CTemp%5Cmsohtml1 > %5C01%5Cclip image002.jpg[/img] > And so too is it seen that in the Schroedinger equation that the change > of probability with respect to time results in an acceleration in > space. > Questions Addressed by MDT: > Why is the speed of light constant in all frames? > Why are light and energy quantized? > Why are there non-local effects in quantum mechanics? > Why does time stop at the speed of light? > How come a photon does not age? > Why are inertial mass and gravitational mass the same thing? > Why do moving bodies exhibit length contraction? > Why are mass and energy equivalent? > Why does time's arrow point in the direction it points in? > Why do photons appear as spherically-symmetric wavefronts traveling at > a velocity c? > Why is there a minus sign in the following metric? > x^2+y^2+z^2-c^2t^2=s^2 > What deeper reality underlies Einstein's postulates of relativity? > What deeper reality underlies Newton's laws? > How MDT Is Aiding Fellow Physicists > The conclusions from Bell's theorem are philosophically startling; > either one must totally abandon the realistic philosophy of most > working scientists or dramatically revise our concept of space-time. > -Abner Shimony and John Clauser > Moving Dimensions Theory provides this new concept of space-time. > http://physicsmathforums.com > The underlying expanding fourth dimension gives rise to non-local > phenomena. > For me, then, this is the real problem with quantum theory: the > apparently essential conflict between any sharp formulation and > fundamental relativity. It may be that a real synthesis of quantum and > relativity theories requires not just technical developments but > radical conceptual renewal. --John Bell > Moving Dimensions Theory provides this radical conceptual renewal. > http://physicsmathforums.com > Entanglement is not one but rather the characteristic trait of quantum > mechanics. --Erwin Schrodinger > The discovery of the quantum of action shows us not only the natural > limitation of classical physics, but, by throwing a new light upon the > old philsophical problem of the objective existence of phenomena > indepedently of our observations, confronts us with a situation > hitherto unknown in natural science. --Niels Bohr > I think we need a new way to look at time, not either Quantum > Mechanics or Relativity. -Roger Penrose > Should we be prepared to see some day a new structure for the > foundations of physics that does away with time? . . . Yes, because > 'time' is in trouble. -John Wheeler > Time is clothed in a different garment for each role it plays in our > thinking. -John Wheeler > The word time came not from heaven but form the mouth of man. > -John Wheeler > My ideas about time all developed from the realization that if > nothing were to change we could not say that times passes. Change is > primary, time, if it exists at all, is something we deduce from it. > My Italian collaborator Bruno Bertotti and I found that the deep > structure of Einstein's general theory of relativity does correspond to > this truth. It is telling us that time does not exist as an independent > thing and that change is indeed primary. However, this is in the > framework of so-called classical physics, the form of physics that > developed before quantum mechanics was discovered. When the idea that > time has no independent existence is combined with the basic facts of > quantum mechanics in the simplest possible way, the implications are > startling. > The quantum universe is static. Only timeless Nows exist. The quantum > rules give them different probabilities. We experience the most > probable Nows as individual instants of time. The appearance of motion > and a flow of time are both illusions created by very special structure > of the instants that we experience. -Julian Barbour, > http://www.platonia.com/ideas.html > The mystery of time's arrow is the oldest problem in science > concerning the nature of time, predating even the theory of > relativity. -Paul Davies, About Time > Moving Dimensions Theory & On The Advancement Of Physics > Physics has been furthered far more often by a rugged individual > acknowledging the simple and obvious in a pursuit of the truth than > book-keepers-in-training playing games in the abstruse in pursuit of > tenure. The advancement of physics has ever depended far more on logic, > reason, and Truth than government grants, tenure, group think, > peer-reviewed journals, and aging bureaucracies. That is the way > things are because that is the way things are, has lead to far more > physics than the contemporary, things can't be that way because > the math dictates that we live in thirty-three dimensions and four are > curled up, and that is what NSF is funding. > When experiments showed that light existed only in quantized packets, > Einstein proclaimed that light only existed in quantized packets, and > he won the Nobel Prize. When spectra from atoms showed discreet > energies, Niels Bohr proclaimed that electrons orbits were quantized, > and he received a Nobel Prize. When Maxwell's Equations had a > recurring constant, Maxwell used c to denote it, and Einstein > proclaimed that the speed of light must be constant for all > observers-and so Special Relativity was born. When Einstein > juxtaposed objects falling towards the earth getting closer together > with the fact that two people starting at the equator, walking on > originally parallel lines of longitude towards the North Pole, would > come together because they were walking on a curve surface, Einstein > proclaimed that the space-time around a massive object must also be > curved. This along with Einstein's realization that the force of > gravity would be rendered null in free-fall, lead to General > Relativity. > And so it is that in the above paragraph you have the roots of the > greatest achievements of physics in the past 100+ years, dwarfing > String Theory, Loop Quantum Gravity, and thousands of their variatons, > which deal in the abstruse, complicated, muddled, and mythological > worlds which are safe from physics simple rigor. > Moving Dimensions Theory returns us to simpler times. It starts with > the simple and keeps it simple. Light travels with a maximum velocity > of c, because the fourth dimension is expanding at a rate relative to > the three spatial dimensions at the velocity of c. A photon expands > through space in a spherically symmetric manner. This is because the > fourth dimension expands through the three spatial dimensions in a > spherically symmetric manner. Energy and mass are equivalent, expressed > by E=mc^2, because energy is nothing more than mass rotated into the > expanding fourth dimension. The Einstein-Podolsky-Rosen effect (EPR) > effect, which calls instantaneous action at a distance spooky, > can be accounted for by the expanding dimension-as a point expands, > it is yet a single locale in that dimension, and hence though separated > the time dimension, and hence connected. The null vector of the photon, > which remains 0 no matter how far the photon travels in space-time, may > be accounted for by the fact that the fourth dimension is moving, and > thus the only way to stay still in the four dimensions is to move with > along with the expanding dimension. In Lorentzian Transformations, > there is no way for an object to be rotated into the time dimension > without it moving-this can be explained by the fact that the time > result of the universe's existence upon a reality that has three > stationary spatial dimensions and one expanding time dimension-when > matter exists in the stationary dimensions, it is seen as mass, or a > or a photon, or energy. Depending how we choose to observer matter > are quantized bundles of energy that propagate at the velocity of > c-this is because the fourth dimension is expanding relative to the > three spatial dimensions in a quantized manner, in units of Planck's > length at the rate of c. The Second Law of Thermodyamics, or the law of > Entropy, states that the universe tends towards disorder. This is > because the fourth dimension is expanding in a spherically symmetric > from one another-thus a drop of food coloring in a pool will be > carried outward and evenly distributed. In 1949 Godel published a paper > showing that within the theory of relativity, time as we understand it, > does not exist. Einstein recognized Godel's paper as an important > contribution to the general theory of relativity, and since then > physicists have not been able to find any logical shortcomings in > Godel's work, and nobody has been able to account for the existence > of time. But the Theory of Moving Dimensions accounts for time as we > know it by showing that it is an emergent property of the underlying > dimension's intrinsic relative movement. Relativity becomes > increasingly exact at long-length scales but fails at short ones > because space-time itself is quantized, as the time dimension is > expanding in units of the Planck length. The concept of general > relativity's smooth geometry, at large scales, disappears on > short-distance scales-this has been a problem to string theorists, > but only because they were never bold enough to recognize that's the > way it is because that's the way it is. Realizing this might have > lead one of them to see that the fourth dimension is expanding at a > rate of c relative to the three spatial dimensions. > So it is seen that Moving Dimensions Theory offers a simple model upon > which all known phenomena of Relativity and Quantum Mechanics may rest. > And because the underlying architecture of the universe is > quantized-because the fourth dimension expands at the rate of c in > units of the Planck length relative to the three spatial dimensions, > quantum mechanics works for the small, while general relativity works > for the large. That is the way it is because that is the way it > is-this was the realization that lead to the postulate of MDT: the > fourth dimension is expanding relative to the three spatial dimensions. > http://physicsmathforums.com === Hello All, Please respect that Moving Dimensions Theory is just a theory. I look forward to feedback and insights regarding its logic. No you don't. You are a spamming crank with delusions of competence. Rest of junk snipped. Bill === Also kind of funny that in the forums link he posted himself, there are a few people giving him critique but of course he has no answers to their questions. He couldn't even be bothered to refine his ideas before presenting them to the public, which is just bad practice in any given sense. === http://physicsmathforums.com/showthread.php?t=56 Tied Up & Strung Out: Hollywood String Theory Movie!!! Looking For Extras!!! FOR IMMEDIATE RELEASE: ALL TIED UP & STRUNG ALONG, a movie about String Theorists and their expansive theories which extend human ignorance, pomposity, and frailty into higher dimensions, is set to start filming this fall. Jessica Alba, John Cleese, Eugene Levie, Jackie Chan, and David Duchovney of which is still cheaper than String Theory itself, and will likely displace less physicists from the academy. As contemporary physics is about money, hype, mythology, and chicks, Ed Witten explained from his offices at the Princeton Institute for Advanced Study, The next logical step was Hollywood, although I thought Burt Reynolds should play me instead of Eugene Levy. http://physicsmathforums.com/showthread.php?t=56 Brian Greene, the famous String Theorist who will be played by David the truth is out there Duchovney, explained the plot: String theory's muddled, contorted theories that lack postulates, laws, and experimentally-verified equations have Einstein spinning so fast in his grave that it creates a black hole. In order to save the world, we String Theorists have to stop reformulating String Theory faster than the speed of light. We are called upon to stop violating the conservation of energy by mining higher dimensions to publish more BS than can accounted for with the Big Bang alone, and I win the Nobel prize for showing that M-Theory is in fact the dark matter it has been searching for. Greene continues: At first my character is reluctant to stop theorizing and start postulating, but when my love interest Jessica Alba is sucked into the black hole, I search my soul and find Paul Davies there, played by John Cleese. I ask him what he's doing in my soul, and he explains that the answer is contained in the mind of God, which only he is privy too, but for a small fee, some tax and tuition dollars, a couple grants here and there, and an all-expense-paid book tour with stops in Zu and Honolulu, he can let me in on it. And he shows me God in all her greater glory, as he points out that we can make more money in Hollywood than writing coffee-table books that recycle Einstein, Bohr, Dirac, Feynman, and Wheeler. I am quickly converted, and I agree to turn my back on String Theory's hoax and save Jessica Alba. But it's not that easy, as standing in Greene's way is Michio king of pop-theory-hipster-irony-the-theory-of-everything-or-anything-made- you-read-this Kaku, played by Jackie Chan. Kaku beats the crap out of Greene for alomst blowing the ironic pretense his salary, benefits, and all-expense paid trips depend on. WE MUST HOLD BACK THE YOUNG SCIENTISTS WITH OUR NON-THEORIES!! WE MUST FILL THE ACADEMY WITH THE POMO DARK MATTER THAT IS STRING THEORY TO KEEP OUR UNIVERSE FROM FLYING MONEY MACHINE FROM STOPPING!! Kaku argues as he delivers a flying back-kick, There can be ony ONE! I WILL be String Theory's GODFATHER as referenced on my web page!! I have better hair! But Greene fights back as he signs his seventeenth book deal to make the hand-waving incoherence of String Theory accessible to the South Park generation, senior citizens, and starving chirldren around the world. Kaku! Kaku! (pronounced Ka-Kaw! Ka-Kaw! like Owen Wilson did in Bottle Rocket), Greene shouts. It is theoretically impossible to build a coffee tables strong enough to support any more coffee-table physics books!!! Time travel is also theoretically impossible, but there's a helluva lot more money for us in flushing physics down a wormhole. Nobody knows what the #&#%&$ M stands for in M theory ya hand-waving, TV-hogging crank!!! Get it?? Ha Ha Ha! We're laughing at the public! We're the insider pomo hipsters! Get with the gangsta-wanksta-pranksta CRANKSTER bling-bling program!! How does it all end? Does physics go bankrupt funding theories that have expanded our ignorance from four dimensions into ten, twenty, and thirty dimensions? Do tax payers revolt? Do young physicists overthrow the hand-waving, contortionist bullies and revive physics with a classical renaissance favoring logic, reason, and Truth over meaningless mathematical abstractions? Does Moving Dimensions Theory (MDT) prevail with its simple postulate? We'll all just have to wait! But in the meantime, how do you think it will play out? Will theories with postulates ever be allowed in physics again? Or will the well-funded, tenured pomo String Theory / M-Theory (Maffia-Theory) Priests send their armies of desperate, snarky postdocs and starving graduate students forth to displace and destroy all common sense, logic, reason, and physics in the academy? It must be so--for the greater good of physics, the individual physicist, and thus physics, must be sacrificed. MDT's postulate: THE FOURTH DIMENSION IS EXPANDING AT A RATE OF C RELATIVE TO THE THREE SPATIAL DIMENSIONS IN QUANTIZED UNITS OF THE PLANCK LENGTH, GIVING RISE TO TIME AND ALL CLASSICAL, QUANTUM MECHANICAL, AND RELATIVISTIC PHENOMENA. http://physicsmathforums.com/showthread.php?t=56 === speaking of handwaving, misterroger'shood, can you do any calculations with this moving dimensional stuff. or does the matter of nomenclature have yet to be worked-out? > But Greene fights back as he signs his seventeenth book deal to make > the hand-waving incoherence of String Theory accessible to the South > Park generation, senior citizens, and starving chirldren around the > world. Kaku! Kaku! (pronounced Ka-Kaw! Ka-Kaw! like Owen Wilson did in > Bottle Rocket), Greene shouts. It is theoretically impossible to > build a coffee tables strong enough to support any more coffee-table > physics books!!! > Time travel is also theoretically impossible, but there's a helluva > lot more money for us in flushing physics down a wormhole. Nobody knows > what the #&#%&$ M stands for in M theory ya hand-waving, TV-hogging > crank!!! Get it?? Ha Ha Ha! We're laughing at the public! We're the > insider pomo hipsters! Get with the gangsta-wanksta-pranksta CRANKSTER > bling-bling program!! > http://physicsmathforums.com/showthread.php?t=56 --Welcome ot the Googolplex; you can login any time, like, you, but.... http://tarpley.net/bush23.htm http://www.benfranklinbooks.com/ http://members.tripod.com/~american_almanac http://www.wlym.com/pdf/iclc/howthenation.pdf http://www.rand.org/publications/randreview/issues/rr.12.00/ http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html === Subject: Least-square fitting I am having trouble figuring out the correct way to solve the following problem. For problem 6.7 in Data reduction and error analysis by Bevington, it states, A student measures the temperature (T) of water in an insulated flask at times (t) separated by 1 minute and obtains the following values: ( time (s), Temp. (c) ) = ( 0 , 98.51 ) , ( 1 , 98.50 ) , ( 2 , 98.50 ) , ( 3 , 98.49 ) , ( 4 , 98.52 ) , ( 5 , 98.49) , ( 6 , 98.52 ) , ( 7 , 98.45 ) , ( 8 , 98.47 ) a) Calculate the mean temperature and its standard error. b) To test whether or not the water is cooling, plot a graph of the temperature versus the time and make a least-squares fit of a straight line to the data. Is there a statistically significant slope to the graph? When I am doing the linear (y = bx+c ) least-squares fit what should I use as the uncertainty for temperature? Should we just use the sample variance S2 =1 / (N-1) * Sum[Xi-Mean, {Xi, 0, N}]^2? The chapter this problem is in is only covers weighted least square fits. The solution in the back of the book has provided me with no help as to the correct way to do. === Subject: Re: Least-square fitting > I am having trouble figuring out the correct way to solve the > following problem. For problem 6.7 in Data reduction and error > analysis by Bevington, it states, A student measures the > temperature (T) of water in an insulated flask at times (t) separated > by 1 minute and obtains the following values: > ( time (s), Temp. (c) ) = ( 0 , 98.51 ) , ( 1 , 98.50 ) , ( 2 , 98.50 > ) , ( 3 , 98.49 ) , ( 4 , 98.52 ) , ( 5 , 98.49) , ( 6 , 98.52 ) , ( > 7 , 98.45 ) , ( 8 , 98.47 ) > a) Calculate the mean temperature and its standard error. > b) To test whether or not the water is cooling, plot a graph of the > temperature versus the time and make a least-squares fit of a straight > line to the data. Is there a statistically significant slope to the > graph? > When I am doing the linear (y = bx+c ) least-squares fit what should I > use as the uncertainty for temperature? Don't use anything; just use the _measured_ temperatures. The MODEL is that termperature Y_i at the i'th time x_i is given by Y_i = beta * x_i + gamma + e_i, where e_i is a measurement error (assumed to have mean zero and common variance sigma^2 for any i). The true intercept and slope, gamma and beta, are unkown, as is the variance sigma^2 of the errors. These all get estimated by fitting the least-square line: c estimates gamma, b estimates beta, and the usual statistical formulas from regression theory will estimate sigma^2. (All this assumes that time, x, is measured accurately; if there are also sizable random errors in x, some of the interpretations must be changed.) > Should we just use the sample > variance S2 =1 / (N-1) * Sum[Xi-Mean, {Xi, 0, N}]^2? No, absolutely not! Think about it: if there is a large slope, the Y-values (i.e., the temperatures) will differ a lot from one point to the next, but they would do so even if there were no random errors at all! In fact, testing significance of the fitted slope is tantamount to testing whether the total squared error S = sum{(Y_i - mean)^2} is due primarily to randomness, or whether the slope must also be accounted for. R.G. Vickson Adjunct Professor, University of Waterloo > The chapter this > problem is in is only covers weighted least square fits. The solution > in the back of the book has provided me with no help as to the correct > way to do. === Subject: Re: Least-square fitting >>I am having trouble figuring out the correct way to solve the >>following problem. For problem 6.7 in Data reduction and error >>analysis by Bevington, it states, A student measures the >>temperature (T) of water in an insulated flask at times (t) separated >>by 1 minute and obtains the following values: >>( time (s), Temp. (c) ) = ( 0 , 98.51 ) , ( 1 , 98.50 ) , ( 2 , 98.50 >>) , ( 3 , 98.49 ) , ( 4 , 98.52 ) , ( 5 , 98.49) , ( 6 , 98.52 ) , ( >>7 , 98.45 ) , ( 8 , 98.47 ) >>a) Calculate the mean temperature and its standard error. >>b) To test whether or not the water is cooling, plot a graph of the >>temperature versus the time and make a least-squares fit of a straight >>line to the data. Is there a statistically significant slope to the >>graph? >>When I am doing the linear (y = bx+c ) least-squares fit what should I >>use as the uncertainty for temperature? > Don't use anything; just use the _measured_ temperatures. The MODEL is > that termperature Y_i at the i'th time x_i is given by Y_i = beta * x_i > + gamma + e_i, where e_i is a measurement error (assumed to have mean > zero and common variance sigma^2 for any i). The true intercept and > slope, gamma and beta, are unkown, as is the variance sigma^2 of the > errors. These all get estimated by fitting the least-square line: c > estimates gamma, b estimates beta, and the usual statistical formulas > from regression theory will estimate sigma^2. (All this assumes that > time, x, is measured accurately; if there are also sizable random > errors in x, some of the interpretations must be changed.) Ah! Ok, I see what you're saying. >>Should we just use the sample >>variance S2 =1 / (N-1) * Sum[Xi-Mean, {Xi, 0, N}]^2? > No, absolutely not! Think about it: if there is a large slope, the > Y-values (i.e., the temperatures) will differ a lot from one point to > the next, but they would do so even if there were no random errors at > all! In fact, testing significance of the fitted slope is tantamount to > testing whether the total squared error S = sum{(Y_i - mean)^2} is due > primarily to randomness, or whether the slope must also be accounted > for. Ok, I am little lost here, does this mean that the correct way to find the standard deviations of the individual measurement is via S^2 =1 / (N-2) * Sum[Yi-bXi-c, {Xi, 0, N}]^2? Then you use this uncertainty to find the uncertainty in the values b and c? > R.G. Vickson > Adjunct Professor, University of Waterloo >>The chapter this >>problem is in is only covers weighted least square fits. The solution >>in the back of the book has provided me with no help as to the correct >>way to do. === Subject: Re: Least-square fitting >I am having trouble figuring out the correct way to solve the >>following problem. For problem 6.7 in Data reduction and error >>analysis by Bevington, it states, A student measures the >>temperature (T) of water in an insulated flask at times (t) separated >>by 1 minute and obtains the following values: >>( time (s), Temp. (c) ) = ( 0 , 98.51 ) , ( 1 , 98.50 ) , ( 2 , 98.50 >>) , ( 3 , 98.49 ) , ( 4 , 98.52 ) , ( 5 , 98.49) , ( 6 , 98.52 ) , ( >>7 , 98.45 ) , ( 8 , 98.47 ) >>a) Calculate the mean temperature and its standard error. >>b) To test whether or not the water is cooling, plot a graph of the >>temperature versus the time and make a least-squares fit of a straight >>line to the data. Is there a statistically significant slope to the >>graph? >>When I am doing the linear (y = bx+c ) least-squares fit what should I >>use as the uncertainty for temperature? > Don't use anything; just use the _measured_ temperatures. The MODEL is > that termperature Y_i at the i'th time x_i is given by Y_i = beta * x_i > + gamma + e_i, where e_i is a measurement error (assumed to have mean > zero and common variance sigma^2 for any i). The true intercept and > slope, gamma and beta, are unkown, as is the variance sigma^2 of the > errors. These all get estimated by fitting the least-square line: c > estimates gamma, b estimates beta, and the usual statistical formulas > from regression theory will estimate sigma^2. (All this assumes that > time, x, is measured accurately; if there are also sizable random > errors in x, some of the interpretations must be changed.) > Ah! Ok, I see what you're saying. >>Should we just use the sample >>variance S2 =1 / (N-1) * Sum[Xi-Mean, {Xi, 0, N}]^2? > No, absolutely not! Think about it: if there is a large slope, the > Y-values (i.e., the temperatures) will differ a lot from one point to > the next, but they would do so even if there were no random errors at > all! In fact, testing significance of the fitted slope is tantamount to > testing whether the total squared error S = sum{(Y_i - mean)^2} is due > primarily to randomness, or whether the slope must also be accounted > for. > Ok, I am little lost here, does this mean that the correct way to find > the standard deviations of the individual measurement is via S^2 =1 / > (N-2) * Sum[Yi-bXi-c, {Xi, 0, N}]^2? I have absolutely no idea what your notation means. I do understand the notation SS (sum of squares) = sum {(y_i - c - b x_i)^2 : i = 1,...,n}. Anyway, if the individual errors are identically distributed (so,in particular, they all have the same variance sigma^2), the quantity SS/(n-2) is an unbiased estimator of sigma^2. (I guess this is the same as your S^2 above, in which case the answer to your question is YES.) In addition, if the errors are normally distributed, the random variable SS has a chi-squared distribution with n-2 degrees of freedom. > Then you use this uncertainty to > find the uncertainty in the values b and c? Basically, yes. However, the formulas are a bit complicated to present in a newsgroup setting, and are much better gotten from a book. Even an introductory statistics book should suffice. (You mentioned a book, but not its title or content, so I don't know if it is a statistics book, or a civil engineering book, or what.) Alternatively, you might try to Google on Linear Regression, and I would bet you will turn up many web pages giving the details. RGV > R.G. Vickson > Adjunct Professor, University of Waterloo >>The chapter this >>problem is in is only covers weighted least square fits. The solution >>in the back of the book has provided me with no help as to the correct >>way to do. > === Subject: SAT question If a triangle has sides ABC which one of the folowing is true. A.) C= A+B B.) C= A-B C.) C+2 = A+B+3 D.) C+3 = A+B+2 E.) C= 2A+B I tried using heros formula and exhausted all my avenues can someone help me please? === Subject: Re: SAT question If a triangle has sides ABC which one of the folowing is true. A.) C= A+B B.) C= A-B C.) C+2 = A+B+3 D.) C+3 = A+B+2 E.) C= 2A+B The problem, as stated is nonsense. (1) When one says 'sides ABC' one is applying LABELS to the sides. This is not the same as saying that the LENGTHS are A, B, C. Indeed, the problem does not even state the DOMAIN for the variables A,B,C. for example, A,B.C might be VECTORS (A triangle certainly can be formed from 3 vectors, making both A.) and B.) true) however, we will assume LENGTHS of A,B,C (2) the problem does not distinguish, 'for all' A,B,C vs 'for some' A,B,C, Both A.) and B.) are permissible. One gets a DEGENERATE triangle (with area 0), but a degenerate triangle is still a triangle. The problem, if correctly posed should state specifically: 'non-degenerate triangle'. Some might argue this point. It is somewhat a matter of definition. Note that A.) and B.) are EQUIVALENT statements. It asserts that the length of one side equals the sum of the other two. C.) and E.) are clearly not permissible. D.) clearly is. for SOME A,B,C. but not for ALL A,B,C. (take an equilateral triangle with A=B=C = 2, for example. However, A=B=C=1 does work) The problem, as stated, is meaningless gibberish. There is also a difference between 'is true' and 'can be true'. I would take 'is true' to mean FOR ALL A,B,C, whereas 'can be true' would mean 'FOR SOME A,B,C'. In the first interpretation there is no correct answer. === Subject: Re: SAT question > If a triangle has sides ABC which one of the folowing is true. > A.) C= A+B > B.) C= A-B > C.) C+2 = A+B+3 > D.) C+3 = A+B+2 > E.) C= 2A+B > I tried using heros formula and exhausted all my avenues can someone > help me please? Hint on the SAT: No one is expected to know Hero's formula. I believe you have mistated the problem. It should have been something like If a triangle has sides A, B, and C, which of the following can occur? The only thing you need to know to answer this is that in a triangle, the length of any side is less than the sum of the lengths of the other two sides. === Subject: Re: SAT question >> If a triangle has sides ABC which one of the folowing is true. >> A.) C= A+B >> B.) C= A-B >> C.) C+2 = A+B+3 >> D.) C+3 = A+B+2 >> E.) C= 2A+B Could be A, as a default case (zero area) Ditto for B C is C=A+B+1 cant be true, cant draw a triangle D is C=A+B-1 Could be true, sketch it out. E cant be true either. Why cant you sketch these out in 2 seconds ??? This is NOT a SAT question too simple. === Subject: Re: SAT question so what could possibly be the answer then? === Subject: Re: SAT question : so what could possibly be the answer then? The way it usually works is that you ask for help and then once help has been given, in the form of a hint, you go off and actually do some work yourself rather than coming back and asking us why we didn't do every last step for you. Justin === Subject: Re: SAT question duhhh, the answer is B === Subject: Re: SAT question > duhhh, the answer is B Whoops. Well, community college can be a wonderful experience. === Subject: Re: SAT question If a triangle has sides ABC which one of the folowing is true. > A.) C= A+B > B.) C= A-B > C.) C+2 = A+B+3 > D.) C+3 = A+B+2 > E.) C= 2A+B > I tried using heros formula and exhausted all my avenues can someone > help me please? Hero's formula should work, but it's probably more than you need... In any triangle, the longest side has to be SHORTER than the other two sides put together. You've got to be able to get back from the ends of the longest side, using the other two sides, with some slack left over,,, So, fore example, if E were true, you'd be at the ends of C, 2A+B apart, with only A and B to get you back. The triangle won't close. The same logic can be applied to the other options... If you use Hero's formula on an impossible triangle, you get a zero or imaginary area if the sides fail the test above... === Subject: Re: order statistics for distribution-free confidence intervals for population percentiles This is fantastic!!! Roy === Subject: trigonometry question I have also tried solving this to no avail even by using the double angle formula. The equation is 4/pi = 2sinx-sin2x to solve for x. I used sin2x= 2sinxcosx Can someone help please ? === Subject: Re: trigonometry question > I have also tried solving this to no avail even by using the double > angle formula. > The equation is 4/pi = 2sinx-sin2x to solve for x. > I used > sin2x= 2sinxcosx > Can someone help please ? Sure you really want to do this? The equation becomes 2 sin x (1 - cos x) = 4/pi. Put u = sin x, then cos x = plus-or-minus sqrt(1-u^2). You get two equations, u(1 - sqrt(1-u^2)) = 2/pi, u(1 + sqrt(1-u^2)) = 2/pi, which are solved by dividing both sides by u, subtracting 1, squaring, getting 1-u^2 = (2/(pi u) - 1)^2 in either case. Multiplying by u^2 you get u^2 - u^4 = (2/pi - u)^2 = 4/pi^2 - 4 u/pi + u^2 so u^4 - (4/pi) u + (4/pi^2) = 0. This quartic equation has two real roots, u = 0.32732582523678125628009495430567833253989034438263703408146..., u = 0.94520584025868828426162950484955860705201356102757787437762... (It's possible, but pointless, to write them out precisely using the quartic formula.) You have to be careful here with sign of the cosine: for sin x = 0.9452058... you get cos x = 0.3273... (which looks like the other root BUT ISN'T), whereas for sin x = 0.3273258252... you get cos x = -0.9449115. The two solutions for x therefore lie in the first quadrant, x = 1.2382245216054871564858230188077793365313518155959698591910... (in radians), whereas the other solution lies in the second quadrant (sin > 0, cos < 0), x = 2.8081205503453334222695893228932279210592693663724279790365647.. (in radians). An ugly problem. What was the point? --Ron Bruck === Subject: Re: trigonometry question >> I have also tried solving this to no avail even by using the double >> angle formula. >> The equation is 4/pi = 2sinx-sin2x to solve for x. >> I used >> sin2x= 2sinxcosx >> Can someone help please ? >Sure you really want to do this? >The equation becomes 2 sin x (1 - cos x) = 4/pi. Put u = sin x, then >cos x = plus-or-minus sqrt(1-u^2). You get two equations, > u(1 - sqrt(1-u^2)) = 2/pi, > u(1 + sqrt(1-u^2)) = 2/pi, >which are solved by dividing both sides by u, subtracting 1, squaring, >getting > 1-u^2 = (2/(pi u) - 1)^2 >in either case. Multiplying by u^2 you get > u^2 - u^4 = (2/pi - u)^2 = 4/pi^2 - 4 u/pi + u^2 >so u^4 - (4/pi) u + (4/pi^2) = 0. >This quartic equation has two real roots, > u = 0.32732582523678125628009495430567833253989034438263703408146..., > u = 0.94520584025868828426162950484955860705201356102757787437762... >(It's possible, but pointless, to write them out precisely using the >quartic formula.) You have to be careful here with sign of the cosine: >for > sin x = 0.9452058... you get cos x = 0.3273... >(which looks like the other root BUT ISN'T), whereas for > sin x = 0.3273258252... you get cos x = -0.9449115. >The two solutions for x therefore lie in the first quadrant, > x = 1.2382245216054871564858230188077793365313518155959698591910... >(in radians), whereas the other solution lies in the second quadrant >(sin > 0, cos < 0), > x = 2.8081205503453334222695893228932279210592693663724279790365647.. >(in radians). >An ugly problem. What was the point? The problem is a little nicer using u = tan(x/2) where sin(x) = 2u/(1+u^2) and 1-cos(x) = 2u^2/(1+u^2) so that the equation becomes 8u^3/(1+u^2)^2 = 4/pi or 4 3 2 u - 2 pi u + 2 u + 1 = 0 whose real solutions are .71256966539 and 5.94182121448 and the corresponding values of x are 1.23822452161 and 2.80812055034. The nice thing about using u = tan(x/2) is that knowing u means you know x mod 2 pi. We don't have to worry about quadrants. Rob Johnson take out the trash before replying === Subject: Re: trigonometry question <010320062123248560%bruck@math.usc.edu> <20060302.022605@whim.org >> I have also tried solving this to no avail even by using the double >> angle formula. >> The equation is 4/pi = 2sinx-sin2x to solve for x. >> I used >> sin2x= 2sinxcosx >> Can someone help please ? >> snip > whose real solutions are .71256966539 and 5.94182121448 and the > corresponding values of x are 1.23822452161 and 2.80812055034. > The nice thing about using u = tan(x/2) is that knowing u means you > know x mod 2 pi. We don't have to worry about quadrants. > Rob Johnson problem that required this. === Subject: Kids getting smarter younger? Hi All; Article in the local Kind of interesting. Don === Subject: Indices of Maximal Subgroups of Finite Groups If a finite group is supersolvable, then all of its maximal subgroups have prime index. The converse is also true. The analogous statement for solvable groups is that all maximal subgroups have index equal to a power of a prime. The converse of this is false for the simple group GL(3,2) = PSL(2,7), since all of its maximal subgroups have index 8 or 7. Are there any other counterexamples among the nonabelian finite simple groups? How difficult is it to classify all finite groups where every maximal subgroup has prime power index based on a complete knowledge of the set of these counterexamples? ---- David The email address included in this posting has been defunct for > 1 year. The currently working version of that email address may be obtained from it by moving the r at the beginning to the end of the part before the @ and inserting alum. immediately after the @. === Subject: Re: Indices of Maximal Subgroups of Finite Groups >If a finite group is supersolvable, then all of its maximal subgroups >have prime index. The converse is also true. >The analogous statement for solvable groups is that all maximal >subgroups have index equal to a power of a prime. >The converse of this is false for the simple group GL(3,2) = PSL(2,7), >since all of its maximal subgroups have index 8 or 7. >Are there any other counterexamples among the nonabelian finite simple >groups? How difficult is it to classify all finite groups where every >maximal subgroup has prime power index based on a complete knowledge of >the set of these counterexamples? My guess is that there are no other counterexamples, and that it would be routine, using known properites of maximal subgroups of finite simple groups to verify this - but I am not volunteering to do it for you! The sporadic groups you can check individually, using the ATLAS. For the alternating groups, a stabilizer of a 2-point set has index n(n-1)/2, which cannot be a prime power. For classical groups there is a book by Kleidman and Liebeck giving a vast amount of detail of maximal subgroups. For example, for PSL(n,q) for n>3, a stabilizer of a subsapce of dimension 2 would not have prime power index. For PSL(2,q), except for very small q which you can examine individually, use dihedral subgroup of order (q-1) or (q+1), etc. I know less myself about the exceptional groups of Lie type, but again there is some literature on their maximal sugbroups. Derek Holt. === Subject: Men Health boundary=------------ms070107050509030508060201 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k225NO300643 for ; Thu, 2 Mar 2006 00:23:24 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: Re: M's on a Lazy Susan > For a vector V = (V_1, V_2, ..., V_N), V_i - integer > define derivative DV = (V_2 - V_1, V_3 - V_2, ..., V_1 - V_N). > Hypothesis: > if (D^k)(1, 0, 0, ..., 0, 0) = (0, 0, 0, ..., 0, 0) mod M for some k > then N = p^s, M = p^t where s, t - integers, p - prime. > Can anyone prove/disprove the hypothesis (which I believe is true)? Yes, excluding the trivial case N = 1, D = 0, M = anything. Your hypothesis implies that D^k = 0 as an endomorphism of (Z_M)^N, where Z_M = Z/(MZ) is the ring of integers mod M. Of course (D+I)^N - I = 0, and that is the minimal polynomial of D. Thus, for any polynomial P in Z_M[t], P(D) = 0 if and only if P is a multiple of (t+1)^N - 1. So the question is, when is t^k a multiple of (t+1)^N - 1 in Z_M[t]? Let p be a prime that divides M. If t^k is a multiple of (t+1)^N-1 in Z_M[t], then it certainly must be in Z_p[t] as well, and it is easy to see that this is true if and only if the binomial coefficients (N choose j) == 0 mod p for j from 1 to N-1. Now by a theorem of Lucas, if N_0, ..., N_d are the base-p digits of N and j_0,...,j_d the base-p digits of j (padding with initial 0's if necessary) (N choose j) == product_{i=0}^d (N_i choose j_i) mod p. The only way for these to all be 0 is for N to be a power of p (in particular if N_i > 0, (N choose (N - p^i)) <> 0 mod p). So N must be a power of p, and this is the only prime dividing M, i.e. M is also a power of p. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: M's on a Lazy Susan > For a vector V = (V_1, V_2, ..., V_N), V_i - > integer > define derivative DV = (V_2 - V_1, V_3 - V_2, ..., > V_1 - V_N). > Hypothesis: > if (D^k)(1, 0, 0, ..., 0, 0) = (0, 0, 0, ..., 0, 0) > mod M for some k > then N = p^s, M = p^t where s, t - integers, p - > prime. > Can anyone prove/disprove the hypothesis (which I > believe is true)? > Yes, excluding the trivial case N = 1, D = 0, M = > anything. .... .... > Robert Israel > israel@math.ubc.ca > Department of Mathematics > http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, > BC, Canada I think another proof may be obtained (as byproduct) by solving the coins on a lazy susan puzzle (citation from the forum): You and the devil are playing a game. There are N coins evenly spaced around a lazy susan (rotating disk), and the numbers 1 through N written on the table around the lazy susan. Thus, each coin has a number, and by rotating the lazy susan, you can cyclically permute the numbers of the coins. You would like all the coins to be heads up. You get to call out a subset of the set {1, ..., N}, indicating to the devil which coins you would like him/her to flip. But the devil is not so nice, s/he gets to rotate the lazy susan before flipping the coins. So if you call out {1, 2, 4}, coins {2, 3, 5} might get flipped instead. To make the game more interesting, you never get to see the coins (but you know how many there are)! If the coins are ever all heads, the devil announces that you've won and you get a (cash) prize. For what values of N can you win? The coins (M = 2) replaced with some devices having M sides, the question is: for what pairs (N, M) can you win? (I don't know whether such puzzle has been discussed here.) === Subject: PIONEER ANOMALY & SHIPOV'S TORSION FIELD THEORY Begin forwarded message: === Subject: Pioneer Anomaly http://arxiv.org/abs/gr-qc/0602089 http://arxiv.org/abs/gr-qc/0602089 This is a good paper from Norway. It shows that simple SSS 1915 GR geodesic motion cannot explain the back to back 2 NASA Pioneer anomalies. However it does not eliminate the Shipov torsion theory needed for my dark matter halo model! A geodesic in the larger connection field with torsion allows inhomogeneous dark matter and will look like a non-geodesic relative to Einstein's 1915 connection without Shipov torsion. So this is a promising development! === Subject: Re: PIONEER ANOMALY & SHIPOV'S TORSION FIELD THEORY I think we should try to get a reasoned reply. I can't see how the paper can be right. If you have an effect linear in r, no matter how tiny that effect is within the solarr system as soon as you get to cosmological distances it becomes the dominant term. In fact anything other than an inverse square would lead to the Universe being dominated by such energy. Even 1/r (Integral = Ln(r)) will dominate the Universe. Please do simple calculations and check the answer is reasonable. === Subject: Re: PIONEER ANOMALY & SHIPOV'S TORSION FIELD THEORY >I think we should try to get a reasoned reply. I can't see how the > paper can be right. If you have an effect linear in r, no matter how > tiny that effect is within the solarr system as soon as you get to > cosmological distances it becomes the dominant term. > In fact anything other than an inverse square would lead to the > Universe being dominated by such energy. Even 1/r (Integral = Ln(r)) > will dominate the Universe. > Please do simple calculations and check the answer is reasonable. We doubt that JS will even read these responses to his latest claim, let alone respond to them. To JS, Usenet is just a source of free advertising for his nonexistent super-genius. -- Crank Watch International === Subject: Re: PIONEER ANOMALY & SHIPOV'S TORSION FIELD THEORY Here's a picture of Jack in action: http://www.wga.hu/art/m/michelan/3sistina/1genesis/8plants/08_3ce8a.jpg === Subject: Re: PIONEER ANOMALY & SHIPOV'S TORSION FIELD THEORY > Here's a picture of Jack in action: > http://www.wga.hu/art/m/michelan/3sistina/1genesis/8plants/08_3ce8a.jpg Keep the filth off these groups. === Subject: induced homomorphism on homology groups just a quick question to clear some confusion. for a continuous map f : X --> Y we can an induced map on the free abelian groups spanned by singular n-chains for each n, f_# : C_n (X) --> C_n (Y), where we simply compose an n-chain with f. In fact we can show this is a chain map on the graded groups (with boundary operator) i.e. we get a bunch of commuting squares. So this is supposed to imply that there is an induced homomorphism f_* : H_n (X) --> H_n (Y). Now is this map simply defined by f_* ( [s] ) = [ f o s ], where s is an n-chain in X and [s] is the equivalence class of s? The main thing confusing me is the wording of the following in my book... it is stated in such a way that makes me feel like I am missing a small result that leads to his conclusion. (loosely): if phi : C --> C' is a chain map between graded abelian groups (of degree -1), then phi (Z_*(C)) subset Z_*(C') and phi (B_*(C)) subset B_* (C'). Therefore phi induces a homomorphism on homology groups phi_* : H_* (C) --> H_* (C'). (I am using the usually Z_* and B_* to denote the graded abelian groups given by the kernels and images of the boundary operator) so how does that subset condition imply induced homomorphism? if that wasn't satisfied there wouldn't be an induced homomorphism? === Subject: Re: induced homomorphism on homology groups > just a quick question to clear some confusion. > for a continuous map f : X --> Y we can an induced map on the free > abelian groups spanned by singular n-chains for each n, f_# : C_n (X) > --> C_n (Y), where we simply compose an n-chain with f. > In fact we can show this is a chain map on the graded groups (with > boundary operator) i.e. we get a bunch of commuting squares. > So this is supposed to imply that there is an induced homomorphism f_* > : H_n (X) --> H_n (Y). > Now is this map simply defined by f_* ( [s] ) = [ f o s ], where s is > an n-chain in X and [s] is the equivalence class of s? Yes, that is how the induced homomorphism on singular chains is defined. > The main thing confusing me is the wording of the following in my > book... it is stated in such a way that makes me feel like I am missing > a small result that leads to his conclusion. > (loosely): if phi : C --> C' is a chain map between graded abelian > groups (of degree -1), then phi (Z_*(C)) subset Z_*(C') and phi > (B_*(C)) subset B_* (C'). Therefore phi induces a homomorphism on > homology groups phi_* : H_* (C) --> H_* (C'). (I am using the usually > Z_* and B_* to denote the graded abelian groups given by the kernels > and images of the boundary operator) > so how does that subset condition imply induced homomorphism? if that > wasn't satisfied there wouldn't be an induced homomorphism? Two observations: 1. If z were in Z(C), then if f_*(z) were not in Z(C'), it wouldn't have a homology class. Homology classes exist only for cycles, not for all chains. 2. Suppose b in B(C) were mapped to f_*(b) not in B(C'). Then, if z were in Z(C), z and z + b would be mapped to f_*(z) and f_*(z) + f_*(b), respectively. However, since (by assumption) f_*(b) is not in B(C'), its coset in Z(C')/B(C') is not B(C'), but f_*(b) + B(C'). Thus, the homology class of f_*(z) would not be equal to the homology class of f_*(z + b). However, in H(C), [z] = [z + b], and we see that in H(C'), [f_*(z)] is not equal to [f_*(z+b)]. As a result, the induced homomorphism would not be well-defined on homology. No problem. Dale. === Subject: Re: Standard Deviation of PSIA Thou shalt sniff schoolgirls' panties from vending machines. > I think that one was made illegal a couple of years back. However, > you can of course still buy telephone-book-thick hantai manga > from vending machines and no one thinks you're unusual if you read it > openly on the subways. > Me, I think John ought to look into tamakeri. Take his fevered > mind off his usual obsessions. I think he secretly reads yaoi. They're for my sister. Wouldn't be surprised surprised to learn he had a thing for Japanese boys. (Long before I was on alt.native, this guy AtoHakeem was obsessed with homosexuals, and they eventually got him to reveal that he once whored himself out to a man. He denied it, since he just masturbated in front of the guy for $20. But it's still prostitution.) > Thou shalt cut off thy daughter's clitoris. > I'm not sure, given his attitude towards women, that John thinks > that's such a bad thing. Probably. === Subject: Re: Standard Deviation of PSIA > Thou shalt sniff schoolgirls' panties from vending machines. > I think that one was made illegal a couple of years back. However, > you can of course still buy telephone-book-thick hantai manga > from vending machines and no one thinks you're unusual if you read it > openly on the subways. > Me, I think John ought to look into tamakeri. Take his fevered > mind off his usual obsessions. > I think he secretly reads yaoi. They're for my sister. Yeah, what IS the deal with that, anyhow? I mean, most women I know tend to like gay guys, but yaoi seems to be a few steps beyone that. typically Japanese, I suppose. Me, I see John as more a Banana Fish kind of guy. -- cary === Subject: Re: Standard Deviation of PSIA <4lasv1hv2gmt5hps890taobe6nfvlt59eu@4ax.com> Funny. Why would you think that educators, even QUALIFIED educators, even QUALIFIED CHRISTIAN EDUCATORS, would have more valid statistics than a valid scientific survey of the students themselves? Note that the Ministry of Education is a GOVERNMENT agency which controls the statistics, with an axe to grind, and can do all kinds of massaging before the public ever sees them. However, this would be nowhere CLOSE to believing something that came out of your mouth, could it? I'd bet on the objective PISA study any day, over any government agency, no matter where in the world it is. John Knight http://blackexile.com === Subject: Re: Standard Deviation of PSIA > Funny. > > Why would you think that educators, even QUALIFIED > educators, even QUALIFIED CHRISTIAN EDUCATORS, would have > more valid statistics than a valid scientific survey of the > students themselves? > > Note that the Ministry of Education is a GOVERNMENT agency > which controls the statistics, with an axe to grind, and > can do all kinds of massaging before the public ever sees > them. > Aaaahhh. The sekrit plot to suppress the g0d-honest truth > that Koreans are good Christian Israelites too(?) at last > emerges. Indeed. The thirteenth tribe, the fabled lost Tribe of Kim. -- cary === Subject: Re: Properties of Numbers > I'm not a mathematics student, however I have keen interest in numbers > and their properties. With all I know about numbers, I tend to believe > that For any property of numbers expressed generically( eg:- prime, > perfect number etc - ie., without specific reference to any of the > integers ), there would be either 1 or infinite number of numbers that > would have this property. ie., it cannot be 2, 3 or any other finite > number of numbers. > Is there any example that can disprove this assertion? > Numbers which are equal to themselves squared (3) Oops. I was thinking cubed and typed squared. --- Christopher Heckman > Perfect squares which can be written as n*n*n + n*n + n + 1, for some > integer n (3) > A triangular number which is the product of two consecutive triangular > numbers (2) > this week.) > --- Christopher Heckman === Subject: Re: 4CT > [...] > Then at least 18 vertices will have the same color. The > task of removing each of the 18 vertices in turn and reassigning the > remaining 17 seems impossible. But this is necessary if G is minimal. [...] > Things really aren't that bad ... There is a 5-coloring of G which uses > some color only once. Proof: Delete a vertex v, color the smaller graph > with 4 colors, then color v with a fifth color. > Even if it were possible to delete a vertex v, color the smaller > graph with 4 colors, then color v with a fifth color; it is not self > evident that (G-v) cannot be maximized to require 5 colors. Deleting > vertex v leaves graph (G-v) at least two edges short of maximality. > Okay; delete v, add edges to G-v to get a graph H which is maximally > planar. Then H can be 4-colored (since G is a mce). The same coloring > is valid for G-v, so G-v only needs 4 colors. > IT IS ALWAYS POSSIBLE TO FORCE GRAPH H TO BE 5-C BY THE CORRECT > PLACEMENT OF THE ADDED EDGES! > H plus some edges can be 4-colored, but not necessarily with the same > coloring as H. > That H plus some edges can be 4-colored is an untenable assumption! > What if the added edge connected two vertices in H that were the same > color? > You've ruined one coloring, but some other coloring will work. H does > not necessarily have have only one 4-coloring. > Thereoretically, every possible 4-coloring of H can be ruined' by the > placement of the maximizing edges. If the degree of v = 5, then there > are two maximizing edges. > There will always be two connectable vertices that have the same color! > It should > be noted that both of the ME's can be placed so as to do the most > damage. > This is because you're putting the cart before the horse. > The 4CT says that if you have a specific graph H first, then there is a > 4-coloring afterwards. > If you ruin the graph by adding edges, so that the coloring is no > longer valid, you get a new graph, but that NEW graph will have its own > 4-coloring. > There are lots and lots of colorings of G-v (2^(5-2) of them, according > (2^(5-2) = 8. Doesn't seem like lots and lots to me? > That's only a lower bound. > to Lorenz Friess). The point is you can't eliminate all of them > SIMULTANEOUSLY. > Most 4-colorings of G-v will not support a 5-coloring of G. > I'm not 100% sure I know what you mean. But any 4-coloring of G-v leads > to a 5-coloring of G. (Color the vertices of G, other than v, with > their color in H. Color v with a fifth color.) > That is not true if G is not minimal. In a sense, only one coloring of > (G-v) can make Chi(G) = 5. > In a sense? > Any 4-coloring of (G-v) where the neighbors of v are colored with 4 > colors will lead to to a 5-coloring. Now you might ask how many > 4-colorings of (G-v) there are where the neighbors of v are colored > with 4 colors. > I do not understand why I would need to know how many 4-colorings > (G-v) there are where ... . ? Well, you would care whether there are 0 or more than 0. If there aren't any colorings with this property, then G is 4-colorable. --- Christopher Heckman === Legal Multi-Level Marketing Opportunity To Make Money With Very Little Investment !!!!!$$$$$$ EASY MONEY, AND IT REALLY WORKS!!!!!! 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Now here is how and why this system works: Out of every block of 200 posts made, let's say you'll get 5 responses. Yes, that's right, only 5. You make $5.00 in cash, not checks or money orders. The real cash starts rolling in when your name is near the top of the six names on the list. Each additional person who sent you $1.00 now also makes 200 additional postings with your name at #5, and thus additional postings are being made by others joining the venture as your name moves up towards the #1 position and along with additional postings the cash starts to roll in. take the latest posting you can find and start all over again. The end result depends on you. You must follow through you make, the more people will see your ad and participate thus more cash ends up in your mailbox. It's too easy and too cheap to pass up!!! So that's it. Pretty simple sounding stuff, huh? There are millions of people surfing the net every day, all day, all over the world. And 100,000 new people get on the net every day. You know that, you've seen the stories in the paper. So read and follow the simple instructions and play fair. That's the key, and thats all there is to it. Try to keep an eye on all the postings you made to make sure everyone is playing fairly. You know where your name should be. If you're really not sure or still think this can't be for real, then you know who really needs the money, and see what happens. REMEMBER, HONESTY IS THE BEST POLICY. YOU DON'T NEED TO CHEAT THE BASIC IDEA TO MAKE THE MONEY! GOOD LUCK TO ALL AND PLEASE PLAY FAIR YOU WILL MAKE SOME REAL INSTANT FREE CASH! By the way, if you try to deceive people by posting the messages with your name in the list and not sending the money to the people already included, you will not get much. Someone tried this and only got about $150. (And that's after two months.) Then the person sent the 6 bills, people added him to their lists, and in 4-5 weeks the person had over $10,000! === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method I am trying to figure out why in the Indirect method of Infinitude of Primes proof that N is necessarily prime from the earlier step that all the primes that exist are on the list that compose N. Yet for the direct method, we cannot have an earlier step of listing all the primes that exist, but simply grab a few primes in a finite list or all the primes in a finite list, construct N which result in and *either or*. Either N is prime or it has a prime factor not on the list. So in the Indirect method we have the Existential quantifier producing a N that is necessarily prime, yet in the Direct method we have the universal quantifier of any list yielding an N that is either or. So is this typical Symbolic Logic that the existential quantifier yields a necessary result and the universal quantifer yields a either or result. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method > [...] > I will wait for this book to arrive to begin posting a Symbolic Logic > proof. Instead of the strange symbols for every I will just use A > instead of the familar upside down A, and for existence I will use E > instead of the reverse E. The Internet is not conducive to logic > symbols so will improvise. Actually, the Internet is. It's _Usenet_ that isn't. --- Christopher Heckman Sloppy speech is a symptom of sloppy speech. -- Aristotle === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method > I just ordered the book SYMBOLIC LOGIC by Thomason, which is the book I > used some 30 years ago (gee time sure flys) and will try to use the > same symbolism as I post a Symbolic Logic proofs of Infinitude of > Primes both Direct and Indirect. > We need to pinpoint the exact steps for which N is necessarily prime > and cannot be a prime factor search for a Q. > I believe the steps will be: > (i) Every prime in existence is listed as such 2,3,5,....P where P is > the last and final prime > (xxx) Construct N = ((2x3x5x...xP)+1), where all the primes that exist > are multiplied together and add 1. > (xxxx) a number N can be only prime or composite (skip 1 since it is > not 1) > (xxxxx) N is not composite because of Unique Prime Factorization > theorem for all the primes that exist leave a remainder of 1 Hmmm. You've always claimed that step (xxxxx) is unneeded. Now you're flip-flopping. > (xxxxxxx) N is necessarily a new prime not on the list of all primes in > existence > So basically, I sense that the step in the Formal Symbolic Logic Proof [...] You should also know that there can be more than one correct proof of a result, so speaking of THE formal symbolic logic proof is pompous and further proof of your closed-mindedness. --- Christopher Heckman === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method Hmmm. You've always claimed that step (xxxxx) is unneeded. Now you're flip-flopping. > (xxxxxxx) N is necessarily a new prime not on the list of all primes in > existence > So basically, I sense that the step in the Formal Symbolic Logic Proof [...] You should also know that there can be more than one correct proof of a result, so speaking of THE formal symbolic logic proof is pompous and further proof of your closed-mindedness. Apparently you are now making up things, for I do not recall where I claimed that step as unneeded. Granted there are several proofs of infinitude of primes outside of the area of Number Theory such as a topological proof of IP. This treatise is about Infinitude of primes specifically within Number theory. And none of these other proofs is able to use the same technique to prove infinitude of twin primes. Yet, as I reveal, that Euclid's method is able to prove Infinitude of twin primes. Does anyone know if Euclid himself was aware of Twin Primes and whether Euclid himself attempted a proof. Or, when was the first awareness of a twin prime infinitude conjecture. The Formal Symbolic Logic proof of Euclid Infinitude of Primes is needed because it is the referee and final arbiter and final judge as to whether it is valid or invalid. When I was in college taking mathematics, it was amazing to me that back then and still in the present that mathematics majors were not required to take Symbolic Logic. The misconception in 1970 and 2006 is that people who major in mathematics have an inbuilt store of logical reasoning and that they never need a study course of Symbolic Logic. That is a crass and false perception because that is the reason so many mathematicians foist their fake proofs onto the world public. Appel and Haken with their model of 4CM and not a proof. Wiles with his hidden assumption that finite integers have a reality in Fermat's Last Theorem. The plethora of invalid proofs of Infinitude of Primes of Euclid written in over 30 textbooks and books all because most mathematicians have the slightest idea of Symbolic Logic. Cantor and Goedel proofs with their hidden assumptions. You see, the trouble is that mathematicians do not appreciate a judge and jury of their work by Symbolic Logic. And all majors of mathematics should have a heavy dose of advanced Symbolic Logic. Before the textbook of Thomason's SYMBOLIC LOGIC arrives for which I am going to model after. I need to layout the Euclid IP proof as much as possible and then fill in with Symbolic Logic symbols. Direct Method of Infinitude of Primes (1) Statement: Given any finite collection of primes 2,3,...,pn possessing a cardinality n Reason: given (2) Statement: we find another prime by considering W+1 = (2x3x...xpn)+1 Reason: can always operate on given numbers (3) Statement: Either W+1 itself is a prime or else it has a prime factor not equal to 2,3,...,pn Reason: numbers are either unit, composite or prime (4) Statement: If p is not prime, we find that prime factor Reason: Unique Prime Factorization theorem (5) Statement: Thus the cardinality of every finite set can be increased Reason: from steps (3) through (4) (7) Statement: Since all/any finite cardinality set can be increased by 1 more therefore the set of primes is an infinite set. Reason: going from the existential logical quantifier to the universal quantification Here is the valid Indirect proof of IP. (Using Hardy's terminology) Infinitude of Primes Proof, *INDIRECT Method* (1) The prime numbers are the numbers 2,3,...,pn,... of set S Reason: definition of primes (2) Suppose finite, then 2,3,...,pn is the complete series set Reason: supposition step (3) Set S are the only primes that exist Reason: from step (2) Note: This step follows immediately from the Suppose primes are finite. And it is a very important step and because it is so much like the statement Suppose the set S of primes is finite, for it is this statement The set S is all the primes that exist. And it is this step that disallows any other prime factor search once W+1 is formed. W+1 is your only allowable prime candidate in the indirect method, otherwise you are self-contradicting your own logic. The math logic is supposed to get you the contradiction, not you, in your own illogic.) (4) Form W+1 = (2x3x,...,xpn) + 1 Reason: can always operate and form a new number (5) Is W+1 prime? yes Reason: Unique Prime Factorization theorem combined with the definition of what prime is. (6) Contradiction Reason: pn was supposed the largest prime yet we constructed a new prime larger than pn (7) Reverse supposition step and primes are infinite Reason: steps (1) through (6) So when this book comes in, I will have the chore of rendering the above into Symbolic Logic Format. The key statement is one of Existence: in that the finite set are the only primes that exist. This key statement eliminates the either or of the Direct method and causes the new number W+1 to be necessarily prime. The importance of all of this is that not only for the first time do we completely correct Euclid's proof, but we also now have a clear path to the proof of the Infinitude of Twin Primes. The reason we never had a Twin primes proof is because we never cleared the mud and fog of Euclid's ancient method. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method > [...] > When I was in college taking mathematics, it was amazing to me that > back then and still in the present that mathematics majors were not > required to take Symbolic Logic. [...] Well, students who get a Bachelor of SCIENCE degree have to. (I personally learned Symbolic Logic in junior high, so I didn't need it.) --- Christopher Heckman === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method >>When I was in college taking mathematics, it was amazing to me that >>back then and still in the present that mathematics majors were not >>required to take Symbolic Logic. [...] > Well, students who get a Bachelor of SCIENCE degree have to. (I > personally learned Symbolic Logic in junior high, so I didn't need it.) This depends rather hugely on both the institution awarding the degree, and on just what you mean by Symbolic Logic (which could mean just about anything from constructing a few truth tables through to a thorough course on predicate calculus). === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method <46pc72FcalkgU1@individual.net >>When I was in college taking mathematics, it was amazing to me that >>back then and still in the present that mathematics majors were not >>required to take Symbolic Logic. [...] > Well, students who get a Bachelor of SCIENCE degree have to. (I > personally learned Symbolic Logic in junior high, so I didn't need it.) > This depends rather hugely on both the institution awarding > the degree, and on just what you mean by Symbolic Logic > (which could mean just about anything from constructing > a few truth tables through to a thorough course on predicate > calculus). Well I used one of Quine's logic books (can't remember which) in a freshman logic course leading to a B.A. See, liberal arts colleges CAN do math. Ken === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method > Hmmm. You've always claimed that step (xxxxx) is unneeded. Now you're > flip-flopping. > (xxxxxxx) N is necessarily a new prime not on the list of all primes in > existence > So basically, I sense that the step in the Formal Symbolic Logic Proof [...] > You should also know that there can be more than one correct proof of a > result, so speaking of THE formal symbolic logic proof is pompous and > further proof of your closed-mindedness. > Apparently you are now making up things, for I do not recall where I > claimed that step as unneeded. > Granted there are several proofs of infinitude of primes outside of the > area of Number Theory such as a topological proof of IP. This treatise > is about Infinitude of primes specifically within Number theory. And > none of these other proofs is able to use the same technique to prove > infinitude of twin primes. Yet, as I reveal, that Euclid's method is > able to prove Infinitude of twin primes. > Does anyone know if Euclid himself was aware of Twin Primes and whether > Euclid himself attempted a proof. Or, when was the first awareness of a > twin prime infinitude conjecture. This sounds like a question for Ken Pledger and sci.math.history. Are you out there Ken? Who first postulated the twin primes infinitude conjecture, and what's the history of proof attempts? Ken (no pun intended) > The Formal Symbolic Logic proof of Euclid Infinitude of Primes is > needed because it is the referee and final arbiter and final judge as > to whether it is valid or invalid. > When I was in college taking mathematics, it was amazing to me that > back then and still in the present that mathematics majors were not > required to take Symbolic Logic. The misconception in 1970 and 2006 is > that people who major in mathematics have an inbuilt store of logical > reasoning and that they never need a study course of Symbolic Logic. > That is a crass and false perception because that is the reason so many > mathematicians foist their fake proofs onto the world public. Appel and > Haken with their model of 4CM and not a proof. Wiles with his hidden > assumption that finite integers have a reality in Fermat's Last > Theorem. The plethora of invalid proofs of Infinitude of Primes of > Euclid written in over 30 textbooks and books all because most > mathematicians have the slightest idea of Symbolic Logic. Cantor and > Goedel proofs with their hidden assumptions. You see, the trouble is > that mathematicians do not appreciate a judge and jury of their work by > Symbolic Logic. And all majors of mathematics should have a heavy dose > of advanced Symbolic Logic. > Before the textbook of Thomason's SYMBOLIC LOGIC arrives for which I am > going to model after. I need to layout the Euclid IP proof as much as > possible and then fill in with Symbolic Logic symbols. > Direct Method of Infinitude of Primes > (1) Statement: Given any finite collection of primes 2,3,...,pn > possessing a cardinality n Reason: given > (2) Statement: we find another prime by considering W+1 = > (2x3x...xpn)+1 > Reason: can always operate on given numbers > (3) Statement: Either W+1 itself is a prime or else it has a prime > factor not equal to 2,3,...,pn > Reason: numbers are either unit, composite or prime > (4) Statement: If p is not prime, we find that prime factor > Reason: Unique Prime Factorization theorem > (5) Statement: Thus the cardinality of every finite set can be > increased > Reason: from steps (3) through (4) > (7) Statement: Since all/any finite cardinality set can be increased > by 1 more therefore the set of primes is an infinite set. > Reason: going from the existential logical quantifier to the > universal quantification > Here is the valid Indirect proof of IP. (Using Hardy's terminology) > Infinitude of Primes Proof, *INDIRECT Method* > (1) The prime numbers are the numbers 2,3,...,pn,... of set S > Reason: definition of primes > (2) Suppose finite, then 2,3,...,pn is the complete series set > Reason: supposition step > (3) Set S are the only primes that exist > Reason: from step (2) > Note: This step follows immediately from the Suppose primes are > finite. > And it is a very important step and because it is so much like the > statement > Suppose the set S of primes is finite, for it is this statement > The set S is all the primes that exist. > And it is this step that disallows any other prime factor search once > W+1 > is > formed. W+1 is your only allowable prime candidate in the indirect > method, > otherwise you are self-contradicting your > own logic. The math logic is supposed to get you the contradiction, not > you, in your own illogic.) > (4) Form W+1 = (2x3x,...,xpn) + 1 > Reason: can always operate and form a new number > (5) Is W+1 prime? yes > Reason: Unique Prime Factorization theorem combined with the > definition of what prime is. > (6) Contradiction > Reason: pn was supposed the largest prime yet we constructed a new > prime larger than pn > (7) Reverse supposition step and primes are infinite > Reason: steps (1) through (6) > So when this book comes in, I will have the chore of rendering the > above into Symbolic Logic Format. > The key statement is one of Existence: in that the finite set are the > only primes that exist. This key statement eliminates the either or > of the Direct method and causes the new number W+1 to be necessarily > prime. > The importance of all of this is that not only for the first time do we > completely correct Euclid's proof, but we also now have a clear path to > the proof of the Infinitude of Twin Primes. The reason we never had a > Twin primes proof is because we never cleared the mud and fog of > Euclid's ancient method. > Archimedes Plutonium > www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method > [...] > Does anyone know if Euclid himself was aware of Twin Primes and whether > Euclid himself attempted a proof. Or, when was the first awareness of a > twin prime infinitude conjecture. > This sounds like a question for Ken Pledger and sci.math.history. > Are you out there Ken? Who first postulated the twin primes > infinitude conjecture, and what's the history of proof attempts? According to Wikipedia: The twin prime conjecture is a famous problem in number theory that involves prime numbers. It was first proposed by Euclid around 300 B.C. Furthermore: In 1849 de Polignac made the more general conjecture that for every natural number k, there are infinitely many prime pairs p and p' such that p - p' = 2k. The case k = 1 is the twin prime conjecture. And: In 1940, Paul Erdos showed that there is a constant c < 1 and infinitely many primes p such that p' - p < c ln p where p' denotes the next prime after p. ... In 2005, Goldston, Pintz and Y????? established that c can be chosen arbitrarily small. ... a 38-page proof that there are, in fact, infinitely many twin primes. On June 3, Michel Balazard of University Bordeaux reported that Lemma 8 on page 35 is false. As is typical in mathematical proofs, the defect may be correctable or a substitute method may repair or replace the defect. As to hexaprimes, quadprimes, etc: In 1966, Chen Jingrun showed that there are infinitely many primes p such that p + 2 is either a prime or a semiprime (i.e., the product of two primes). --- Christopher Heckman === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method your problem is that there is *no* real difference between direct & inductive proofs. UCLA (e.g.) has the full- text of Mathematics Magazine articels online; you ccan fine the 2.5-page proof of the isomorphism between the two kinds of proof (and the formula for converting one to the other). the question is, could you even follow *that* simple proof? and, again, I apologize for critiquing what cannot really be critiqued, or even understood. > Hardy's proof is invalid because his has the Hidden Assumption of > violating his earlier steps. Any proof that has hidden assumptions that > affect the proof, becomes an invalid proof. > What Hardy should have said is that his newly constructed number of > multiply the lot and add 1 is necessarily a prime and end his proof. > I do not even know if someone has already written up Infinitude of > Primes proof in Symbolic Logic Format with its symbols of P, Q, R, S, T > and its quantifiers of existence and every and its operators of and, > or, negation etc. > The reason a Symbolic Logic proof is in demand is because of this > important resolution of whether N is necessarily prime and that a Prime > Factor Search invalidates the proof. --Welcome ot the Googolplex; you can login any time, like, you, but.... http://tarpley.net/bush23.htm http://www.benfranklinbooks.com/ http://members.tripod.com/~american_almanac http://www.wlym.com/pdf/iclc/howthenation.pdf http://www.rand.org/publications/randreview/issues/rr.12.00/ http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html === Subject: Re: Symbolic Logic proofs of Infinitude of Primes, both direct and indirect method your problem is that there is *no* real difference between direct & inductive proofs. UCLA (e.g.) has the full- text of Mathematics Magazine articels online; you ccan fine the 2.5-page proof of the isomorphism between the two kinds of proof (and the formula for converting one to the other). Not so. There is a large school of thinkers who cast dispersions on the law of excluded middle which forms a basis of Indirect Proof Method. They are called intuitionists. Basically there is a huge difference in the direct method of constructing a proof of existence, and the indirect method which does not hand over the existing object and plays around with the concept that the object does not exist. So the two methods are asymmetrical with respect to the quantifier of existence. Also, there is a difference in the Space of the proving elements of the proof. In the direct method a proof can and often occurs in a remote tiny section of mathematics without involvement of other areas of mathematics. The indirect method involves the entire field of mathematics every time it proves something. So the two methods of direct and indirect are not isomorphic. And many mathematics proofs have only one method of proof, yet if they were isomorphic as you believe, then why do those proofs still have only one method, indicating that they are not isomorphic. Many proofs of geometry are constructive which have no indirect method. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: quotient group of a closed surface is a closed surface > Let G be a finite group acting freely on a closed surface S. Show that > S/G is a closed surface. > How to show that each point of S/G has a neighbourhood homeomorphic to > R^2? > Give an example that S is orientable but S/G is not. I'm trusting this is not homework, although it looks like a standard problem. G is finite, so each orbit of G is a finite point set. The surface S is a Hausdorff space, so distinct points have disjoint open neighborhoods. It is not difficult to show that each point s in S has a neighborhood U_s in S which is disjoint from all its translates under the action of G. Any open neighborhood of s contains a (possibly smaller) open neighborhood of s that is homeomorphic to R^2, so we can assume U_s is such an open set. The quotient map sends each U_s homeomorphically to its image in S/G, since all the sets gU_s are disjoint. Try S^2 with the antipodal map. I'll leave the issue of orientation up to you. Dale. === Subject: Re: quotient group of a closed surface is a closed surface <4BxNf.18207$2O6.6611@newssvr12.news.prodigy.com> It isn't homework. I'm not a math major and I am learning topology myself. === Subject: Re: quotient group of a closed surface is a closed surface <4BxNf.18207$2O6.6611@newssvr12.news.prodigy.com> Give an example that S is orientable but S/G is not. > Try S^2 with the antipodal map. It might be worth adding that the quotient of S^2 after identifying antipodal points is the projective plane (which is not orientable). We could also use a torus, consisting of points (x,y) mod 1, and a two-element group G={1,f} where f is the mapping of (x,y) to (x+ 1/2, -y). The quotient this time is the Klein bottle or twisted torus. LH === Subject: Re: Their tactics >> Now that I have an even simpler proof that I am right, where I >> can >> James (or anybody else): >> In the Uk the Reese's Nutrageous bar has recently up-sized from 56g >> to >> 60g. What is the weight of a Reese's Nutrageous in the USofA? > In the USA the bars always have net weight listed in ounces, > followed > by grams in parentheses. I've seen 1.6 oz (45 g), 1.92 oz (54 g), > and > it seems the current version is 1.8 oz (51 g). > Are you calling JSH nutrageous? No, not at all. I just happened to be eating a Nutrageous bar. Although, now you mention it, I suppose it would be a fitting description. Anyway, thank you for that weight info. I suppose that in the US the legal weight is the one given in ounces, which is then converted to grams and rounded down to an integer. I wonder why the 1.92 ounce bar is the only one with a second place of decimals. Perhaps they wanted to be able to say 54g, but in that case why didn't they go for 1.91 ounces... Hmm... -- Clive Tooth www.clivetooth.dk === Subject: Re: Their tactics The Last Danish Pastry a .8ecrit : >>Now that I have an even simpler proof that I am right, where I >>can >James (or anybody else): >In the Uk the Reese's Nutrageous bar has recently up-sized from 56g >to >60g. What is the weight of a Reese's Nutrageous in the USofA? >>In the USA the bars always have net weight listed in ounces, >>followed >>by grams in parentheses. I've seen 1.6 oz (45 g), 1.92 oz (54 g), >>and >>it seems the current version is 1.8 oz (51 g). >>Are you calling JSH nutrageous? > No, not at all. I just happened to be eating a Nutrageous bar. > Although, now you mention it, I suppose it would be a fitting > description. > Anyway, thank you for that weight info. I suppose that in the US the > legal weight is the one given in ounces, which is then converted to > grams and rounded down to an integer. > I wonder why the 1.92 ounce bar is the only one with a second place of > decimals. Perhaps they wanted to be able to say 54g, but in that case > why didn't they go for 1.91 ounces... Hmm... Mmm.. Google gets http://www.soundstage.com/revequip/shunyata_hydra_8.htm, where Gould's (Phyletic Size Decrease in Hershey Bars) apply to Nutrageous. And it === Subject: Re: Their tactics > http://www.soundstage.com/revequip/shunyata_hydra_8.htm This is truly hilarious, so much that you have to wonder if it is really a put-on. Here are some of the words used to describe the effect of this glorified power-strip on the music: clarity ... naturalness ... organic flow ... resolution ... ease and rightness ... lucid ... civilized ... nimbleness ... transparency ... speed It certainly sounds worth every penny of $1995. === Subject: Re: Their tactics > Mmm.. Google gets > http://www.soundstage.com/revequip/shunyata_hydra_8.htm Proprietary Teflon-insulated silver wire, top-grade cryogenically treated Hubbell outlets The Model-8's buss bars are machined from cryogenic-grade CDA-101 copper, reportedly the highest purity available, and each is over five inches long and one and a half inches thick. The funniest bit... the power cable that costs 1995 US dollars! There's one born every minute. Mark Atherton === Subject: Re: Their tactics <46mlqiFbn8hqU1@individual.net> <46nobuFc0ga4U1@individual.net> <440742d6$0$1153$7a628cd7@news.club-internet.fr> <5l3kd3-mkl.ln1@hippolyta.theathertons > Mmm.. Google gets > http://www.soundstage.com/revequip/shunyata_hydra_8.htm > Proprietary Teflon-insulated silver wire, top-grade cryogenically > treated Hubbell outlets > The Model-8's buss bars are machined from cryogenic-grade CDA-101 > copper, reportedly the highest purity available, and each is over five > inches long and one and a half inches thick. Harrumph, copper. Is there some reason why gold wouldn't be better here? === Subject: We cure any desease! boundary=------------ms060009030000080706030506 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k2293T327743 for ; Thu, 2 Mar 2006 04:03:29 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: Re: We cure any desease! > Cheapest If your cures are no better than your spelling, one would have to be a fool to try them, === Subject: Re: We cure any desease! >>Cheapest > If your cures are no better than your spelling, one would have to be a > fool to try them, I thought the mis-spellings were to sneak past spam filters. === Subject: Re: We cure any desease! <46ouijFbpk8oU1@individual.net >>Cheapest > If your cures are no better than your spelling, one would have to be a > fool to try them, > I thought the mis-spellings were to sneak past spam filters. Also, phartmacy could be merely a Freudian typo. === Subject: Re: Minimal Counter-example to the 4CT. > In one sense, the Minimal Counter-example to the 4CT says that there > exists a 4-colorable planar graph, to which you can add a vertex and > get a 5-colorable planar graph. If the idea is to prove 4CT by induction, then any counterexample is only hypthetical, and what exactly constitutes minimal will _depend_ on how the proof will go. There are lots of ways in which a graph can be minimal. LH === Subject: Re: Minimal Counter-example to the 4CT. We can equivalently say that if G is a minimal counterexample then for any four coloring of G-v cannot be extended to a four coloring of G. There as in the Kempe's argument re-coloring of G may end up with another four coloring of G. The historical difficulty is that no one able to show that that when Kempe argument fails there exits a well-defined way of obtaining four coloring of G from the existing one. Cahit === Subject: Re: Minimal Counter-example to the 4CT. > In one sense, the Minimal Counter-example to the 4CT says that there > exists a 4-colorable planar graph, to which you can add a vertex and > get a 5-colorable planar graph. > Perhaps this is hair splitting, but a minimal counterexample to the > four color conjecture (now theorem) involves a 4-colorable planar > graph to which one adds a vertex and gets a planar graph that is > not 4-colorable. > Every 4-colorable graph is also 5-colorable. > Literally a minimal counterexample would be a planar graph that is > not 4-colorable, but in which the removal of any vertex produces a > 4-colorable (necessarily planar) graph. > That's what I meant when I said [being a minimal counterexample to the > 4CT] says a lot more than [there existing a 4-colorable planar graph, > where if you add a vertex, you get a 5-colorable planar graph], bill. > OK! You start out with a 4-colorable graph, add a vertex and get a > graph that is not > 4-colorable! > Call the 5-chroma graph G and the 4-C graph (G-v) and the added vertex > v_1. > If you remove vertex v_i, (where i = 2,3,4, ... n) from G; do you > always get a 4-colorable graph or do you sometimes get a graph that is > not 4-colorable? > Hypothetically? Yes, without using the planarity of the graphs involved > and the 4 Color Theorem, you might have a situation in which adding > a vertex turns a 4-chroma graph into a 5-chroma graph, and removing > a _different_ vertex leaves you with a 5-chroma graph. > Would it be helpful to give an example on a torus (genus 1 surface), > where there can actually be 5-chroma graphs? > Of course it is _sufficient_ to prove 4CT if you can show inductively > that adding a vertex to a 4-chroma graph always results in another > 4-chroma graph, provided the result is planar. A posteriori we know > that to be true, as a consequence of 4CT. However no one knows > how to prove 4CT in that fashion. But if we assume that the graphs are planar and the 4CT is involved, what then? Consider only those cases for which G is an mce? Let me try to explain my position again (G-v) is 4-Colorable. If we add a vertex it becomes 5-chroma.. Is it possible that (G-v) can also be made 5-chroma by adding one or or more edges, but without adding any more vertices? All I understand of you position is that graph G without vertex v is 4-colorable. Presumably G is planar, and has one or more edges connecting v to other vertices in G (otherwise removing v is not very interesting as far as the chromatic number goes). If we add a vertex it becomes 5-chroma is unnecessarily imprecise. If you are assuming G is a minimal counter- example to the four color theorem then you are assuming G is 5-chroma. Take away any vertex or edge, and it stops being 5-chroma. That's the meaning of minimal counterexample, at any rate (not that one exists). It's not about adding stuff to a 4-colorable graph, at least not in a direct sense, but about taking something/anything away from the minimal non-4-colorable graph. (Of course the 5-color theorem was already proved for planar graphs by pretty elementary methods.) I'm confused what you are asking. Minimal counterexample has a pretty clearly defined in meaning with respect to 4CT, which was covered above. Other than clarifying what that meaning is, I seem not to have anything to contribute here. best wishes, chip === Subject: Re: Minimal Counter-example to the 4CT. > [...] > I'm confused what you are asking. Minimal counterexample > has a pretty clearly defined in meaning with respect to 4CT, Or in any other proof. A graph G is a minimal counterexample to a proposition T if (1) T is not true for G, and (2) If H has fewer vertices than G, then T is true for H. The idea is similar to that of Infinite Descent. --- Christopher Heckman === Subject: Re: Minimal Counter-example to the 4CT. > [...] > I'm confused what you are asking. Minimal counterexample > has a pretty clearly defined in meaning with respect to 4CT, > Or in any other proof. A graph G is a minimal counterexample to a > proposition T if > (1) T is not true for G, and > (2) If H has fewer vertices than G, then T is true for H. > The idea is similar to that of Infinite Descent. > --- Christopher Heckman Actually this is a bit different from the sense in which I took minimal counterexample, namely that no subgraph of G is a counterexample. My pretty clearly phrase corresponds to choosing a (possibly partial) ordering to place on candidates (planar graphs here). Your ordering (number of vertices) wouldn't address directly any intention that eliminating an edge of G, as opposed to eliminating a vertex, will also remove it from being a counterexample. Of course that feature might not be needed for an argument by contradiction, but it might come in handy. On the other hand counting the vertices allows one to pick a minimum size versus a merely minimal object to analyze. This too could prove handy. === Subject: Re: Minimal Counter-example to the 4CT. > [...] > I'm confused what you are asking. Minimal counterexample > has a pretty clearly defined in meaning with respect to 4CT, > Or in any other proof. A graph G is a minimal counterexample to a > proposition T if > (1) T is not true for G, and > (2) If H has fewer vertices than G, then T is true for H. > The idea is similar to that of Infinite Descent. > Actually this is a bit different from the sense in which > I took minimal counterexample, namely that no > subgraph of G is a counterexample. Well, any subgraph of G (other than G itself) has fewer vertices than G. > My pretty clearly > phrase corresponds to choosing a (possibly partial) > ordering to place on candidates (planar graphs here). > Your ordering (number of vertices) wouldn't address > directly any intention that eliminating an edge of G, > as opposed to eliminating a vertex, will also remove > it from being a counterexample. > Of course that feature might not be needed for an > argument by contradiction, but it might come in handy. > On the other hand counting the vertices allows one > to pick a minimum size versus a merely minimal > object to analyze. This too could prove handy. What you're doing is putting a total ordering on the planar graphs (which is also a well-ordering, of course; otherwise you might not have a minimal element of a nonempty set). My definition would say that you can totally order the graphs in any manner, as long as: (1) If G has more vertices than H, then G > H is true. Yes, it might also make a difference on how the graphs with n vertices are ordered, and the number of edges may play a role. (every planar graph on n nvertices without triangles and maximum degree <= 3 has an independent set with size >= 3/8 * n) that I came up with involved ordering the graphs according to (1) and the interesting condition: (2) If G has more vertices of degree 2 than H, and G and H have the same number of vertices, then G > H. The idea being that if you have a minimal counterexample G and connect two vertices incident with a common face, you get a graph H which is not simple (which was a case that was considered), has a triangle (which means two vertices of degree 2 share a neighbor, which was also considered), or has fewer vertices of degree 2 (which means H less than G, so G is not a minimal counterexample). We later found another, shorter proof, which didn't require condition (2) in the definition of a minimal counterexample. --- Christopher Heckman === Subject: Re: Minimal Counter-example to the 4CT. > In one sense, the Minimal Counter-example to the 4CT says that there > exists a 4-colorable planar graph, to which you can add a vertex and > get a 5-colorable planar graph. > Perhaps this is hair splitting, but a minimal counterexample to the > four color conjecture (now theorem) involves a 4-colorable planar > graph to which one adds a vertex and gets a planar graph that is > not 4-colorable. > Every 4-colorable graph is also 5-colorable. > Literally a minimal counterexample would be a planar graph that is > not 4-colorable, but in which the removal of any vertex produces a > 4-colorable (necessarily planar) graph. > That's what I meant when I said [being a minimal counterexample to the > 4CT] says a lot more than [there existing a 4-colorable planar graph, > where if you add a vertex, you get a 5-colorable planar graph], bill. > OK! You start out with a 4-colorable graph, add a vertex and get a > graph that is not > 4-colorable! > Call the 5-chroma graph G and the 4-C graph (G-v) and the added vertex > v_1. > If you remove vertex v_i, (where i = 2,3,4, ... n) from G; do you > always get a 4-colorable graph or do you sometimes get a graph that is > not 4-colorable? > Hypothetically? Yes, without using the planarity of the graphs involved > and the 4 Color Theorem, you might have a situation in which adding > a vertex turns a 4-chroma graph into a 5-chroma graph, and removing > a _different_ vertex leaves you with a 5-chroma graph. > Would it be helpful to give an example on a torus (genus 1 surface), > where there can actually be 5-chroma graphs? > Of course it is _sufficient_ to prove 4CT if you can show inductively > that adding a vertex to a 4-chroma graph always results in another > 4-chroma graph, provided the result is planar. A posteriori we know > that to be true, as a consequence of 4CT. However no one knows > how to prove 4CT in that fashion. > But if we assume that the graphs are planar and the 4CT is involved, > what then? > Consider only those cases for which G is an mce? > Let me try to explain my position again > (G-v) is 4-Colorable. If we add a vertex it becomes 5-chroma.. > Is it possible that (G-v) can also be made 5-chroma by adding one or > or more edges, > but without adding any more vertices? > All I understand of you position is that graph G without vertex v > is 4-colorable. Presumably G is planar, and has one or more > edges connecting v to other vertices in G (otherwise removing > v is not very interesting as far as the chromatic number goes). > If we add a vertex it becomes 5-chroma is unnecessarily > imprecise. If you are assuming G is a minimal counter- > example to the four color theorem then you are assuming > G is 5-chroma. I am NOT assuming that G is a mce! I am assuming only that G is planar and 5-chroma! If G is an mce, then there are no 5-chroma planar graphs with fewer vertices. If we remove a vertex from G we have a planar graph (G-v) with fewer vertices. Therefore, If G is an mce, then (G-v) must be 4-colorable. . . Since every vertex in G is at least degree 5, (G-v) cannot be maximal!. It has not been proven that maximizing (G-v) cannot make it 5-chroma! There does not seem to be any rule against maximizing (G-v). If (G-v) can be made 5-chroma without adding any vertices; then G cannot be an mce! I am merely investigating the possibility of proving that (G-v) can always be made 5_chroma by maximizing it. > Take away any vertex or edge, and it > stops being 5-chroma. That's the meaning of minimal > counterexample, at any rate (not that one exists). It's not > about adding stuff to a 4-colorable graph, at least not in a > direct sense, but about taking something/anything away > from the minimal non-4-colorable graph. (Of course the > 5-color theorem was already proved for planar graphs > by pretty elementary methods.) What were they? > I'm confused what you are asking. Minimal counterexample > has a pretty clearly defined in meaning with respect to 4CT, > which was covered above. Other than clarifying what that > meaning is, I seem not to have anything to contribute here. > best wishes, chip === Subject: Re: Minimal Counter-example to the 4CT. > In one sense, the Minimal Counter-example to the 4CT says that there > exists a 4-colorable planar graph, to which you can add a vertex and > get a 5-colorable planar graph. > Perhaps this is hair splitting, but a minimal counterexample to the > four color conjecture (now theorem) involves a 4-colorable planar > graph to which one adds a vertex and gets a planar graph that is > not 4-colorable. > Every 4-colorable graph is also 5-colorable. > Literally a minimal counterexample would be a planar graph that is > not 4-colorable, but in which the removal of any vertex produces a > 4-colorable (necessarily planar) graph. > That's what I meant when I said [being a minimal counterexample to the > 4CT] says a lot more than [there existing a 4-colorable planar graph, > where if you add a vertex, you get a 5-colorable planar graph], bill. > OK! You start out with a 4-colorable graph, add a vertex and get a > graph that is not > 4-colorable! > Call the 5-chroma graph G and the 4-C graph (G-v) and the added vertex > v_1. > If you remove vertex v_i, (where i = 2,3,4, ... n) from G; do you > always get a 4-colorable graph or do you sometimes get a graph that is > not 4-colorable? > Hypothetically? Yes, without using the planarity of the graphs involved > and the 4 Color Theorem, you might have a situation in which adding > a vertex turns a 4-chroma graph into a 5-chroma graph, and removing > a _different_ vertex leaves you with a 5-chroma graph. > > Would it be helpful to give an example on a torus (genus 1 surface), > where there can actually be 5-chroma graphs? > > Of course it is _sufficient_ to prove 4CT if you can show inductively > that adding a vertex to a 4-chroma graph always results in another > 4-chroma graph, provided the result is planar. A posteriori we know > that to be true, as a consequence of 4CT. However no one knows > how to prove 4CT in that fashion. > But if we assume that the graphs are planar and the 4CT is involved, > what then? > Consider only those cases for which G is an mce? > Let me try to explain my position again > (G-v) is 4-Colorable. If we add a vertex it becomes 5-chroma.. > Is it possible that (G-v) can also be made 5-chroma by adding one or > or more edges, > but without adding any more vertices? > All I understand of you position is that graph G without vertex v > is 4-colorable. Presumably G is planar, and has one or more > edges connecting v to other vertices in G (otherwise removing > v is not very interesting as far as the chromatic number goes). > If we add a vertex it becomes 5-chroma is unnecessarily > imprecise. If you are assuming G is a minimal counter- > example to the four color theorem then you are assuming > G is 5-chroma. > I am NOT assuming that G is a mce! I am assuming only that G is planar > and 5-chroma! The significance of the distinction eludes me. If you assume G is a counterexample to the four color theorem, then some subgraph of G will necessarily be a minimal counterexample. [Note that the approach is cutting down from a big counterexample to get a minimal one, rather than expanding a non-counterexample (a 4-chroma planar graph) somehow into a counterexample.] > If G is an mce, then there are no 5-chroma planar graphs with fewer > vertices. If we remove a vertex from G we have a planar graph (G-v) > with fewer vertices. Therefore, > If G is an mce, then (G-v) must be 4-colorable. . . I would quibble about the first of these three statements. Claiming that G is a minimal counterexample to the four color theorem means that no subgraph of G is a counterexample. However it is possible a priori that nonisomorphic minimal counterexamples exist, and possible that some have fewer vertices than others. You could always pick one that has a minimum number of vertices, among counterexamples to the 4CT, for your graph G, and then the first statement would be justified. To elaborate the description, such G would be a minimal counterexample to the 4CT with a minimum number of vertices. > Since every vertex in G is at least degree 5, (G-v) cannot be maximal!. I don't know how to prove what you claim in the antecedent portion of this statement. Note that it is possible to construct a minimal 4-chroma planar graph (not one with minimum number of vertices but nonetheless minimal with respect to requiring four colors among planar graphs) in which there are as many vertices of degree 3 as one wishes. Even if we assume G is a minimal counterexample with a minimum number of vertices I do not know how to prove that every vertex in G has degree at least 5. The only reason I know the corresponding fact for minimal 4-chroma planar graphs with minimum number of vertices is because it is possible to have K4, four mutual adjacent vertices, in the plane, but since K5 is not planar, no similar proof would work for the 5-chroma proposition. have such a graph In the consequent portion of this statement you introduce the word maximal. I don't understand the context of that adjective. With respect to what property is (G-v) not maximal? > It has not been proven that maximizing (G-v) cannot make it 5-chroma! > There does not seem to be any rule against maximizing (G-v). If (G-v) > can be made 5-chroma without adding any vertices; then G cannot be > an mce! > I am merely investigating the possibility of proving that (G-v) can > always be made 5_chroma by maximizing it. [more discussion of maximizing] I had written: Of course the 5-color theorem was already proved for planar graphs by pretty elementary methods > What were they? In 1879 Alfred Kempe published what he thought was a proof of the Four Color Theorem. More than ten years later, Percy Heawood showed that Kempe's proof contained a subtle but fatal error, and he showed that what one is actually able to obtain by the method of Kempe's argument is the weaker result that five colors at most are needed for any planar graph. http://en.wikipedia.org/wiki/Five_color_theorem === Subject: Integration Question -- Acceleration to Velocity I am using MATLAB to calculate velocity from acceleration data. I know that velocity is the integral of acceleration, but I don't know how to perform this. I tried using the polyfit and polyint functions, but am coming up with some off values. That is, I have acceleration and time data, but I do not know how to calculate velocity. Is there an equation that I can use to calculate === Subject: Re: Integration Question -- Acceleration to Velocity > I am using MATLAB to calculate velocity from acceleration data. I know > that velocity is the integral of acceleration, but I don't know how to > perform this. > I tried using the polyfit and polyint functions, but am coming up with > some off values. > That is, I have acceleration and time data, but I do not know how to > calculate velocity. Is there an equation that I can use to calculate This is the wrong group - try comp.soft-sys.matlab However, two possibilities: 1) For a crude result, use cumsum (if the data is equally spaced). 2) Fit a spline and analytically integrate the results. === Subject: Two questions about projective variety hello I'm stuck to solve these two problems... 1. Prove P^n x P^m is not isomorphic to P^(n+m) where P^n is a projective space of dimension n 2. P^2{q} is not affine variety where q is a single point of P^2. this means that there is no affine variety X in A^2 s.t f(X) is not isomorphic to P^2{q}. affine variety is an open subset of affine algebraic variety and f is a homeomophism from A^2 to U_0 where A^2 is affine plane and U_0 is an open subset of P^2, the first coordinate is not zero. === Subject: Re: Electric charge SiGN isN'T conserved. $$ Electric charge SiGN isN'T conserved. $$ The CHARGE SiGN of a battery terminal can be COMPLETELY reversed $$ ..by COMPLETELY discharging the battery and STARTiNG to reCHARGE. $$ [Note the point of zero (0) FLOW where the CHARGE reverses SiGN]. $$ Net CHARGE isN'T conserved in any system with NET CHARGE of zero. $$ $$ CHARGE is NOT perfectly conserved where the NET CHARGE is zero. $$ $$ Electric charge SiGN isN'T conserved where it's NOT (+) ..OR (-). $$ $$ PERHAPs this will help, ```Brian A M Stuckless, Ph.T (Tivity). > $$ Electric charge SiGN isN'T conserved. > $$ Electric CHARGE is NOT perfectly conserved ..it changes sign. > $$ There's no AC (i.e. alternating DC), if + current is conserved. > $$ Clearly the CHARGE must fall to zero between the + & - signs. > $$ Hope this helps, ```Brian A M Stuckless, Ph.T (Tivity). > There is a theoretical prediction that depends on the mass of a > photon being zero. That electric charge is perfectly conserved. > -=- > FrediFizzx > Re: is there a theoretical mass for a photon ??? > Re: Electric charge SiGN isN'T conserved. > Re: Elementary CHARGE (+ OR -), {e}. > Re: SiGNETiC mass. > What, are you on crack? > Alternating current is CURRENT flow, A.K.A electron flow. Electrons > have negative charge. The +/- alternation simply has to deal with the > directon of electron flow. > The voltage is simply a measure of the pressure which is pushing on the > electrons. Re: Electric charge SiGN isN'T conserved. === Subject: Re: Planck PRESSURE Pp ..a VARiABLE. > I say photons ARE their own medium....individual packages > of 'aether' if you like. $$ UNiVERSAL Planck PRESSURE Pp = no*h*fL ..a VARiABLE; $$ = nL*no*h*c / wl $$ = Na*h*fL / vm $$ = Ra*h*fL / vm*k $$ = Na*na*hbar*c / vm*rA $$ = Ra*na*hbar*c / vm*k*rA $$ Volume, vm constant. $$ Radius, rA = (+ OR -) sqrt{G*M1 / (n-1)*g} = G*M1 / (n-1)*v1^2. $$ Radius, rA = (+ OR -) sqrt{G*M1 / (n-1)*g} = G*M1 / (n-1)*rA*g. $$ Loschmidt NUMBER, no = Na / vm = Ra / vm*k -> (mol part) / m^3. $$ $$ Solar energy VARiABLE, Pp*vm. $$ Planck PRESSURE*Molar Volume, Pp*vm ..MOLAR Planck, SOHO energy; $$ = no*vm*h*fL ..1400 Watt/m^2 @ 1*AU; $$ = Na*h*fL ..Avagadro's NUMBER Na; $$ = Ra*h*fL / k ..the PARTiTiON, k; $$ = F*h*fL / {e} ..the Faraday, F. $$ $$ PERHAPs this ought help, ```Brian A M Stuckless, Ph.T (Tivity). Re: Ballistic Theory and the Sagnac Experiment Re: Planck PRESSURE Pp ..a VARiABLE. === Subject: Decomposable functions of independent variables Let X and Y be independent random variables, with mean 0 and variance 1. Consider the following subspaces of L^2(X,Y): E = L^2(X) + L^2(Y), F = L^2(X+Y). How to prove that the intersection of E and F is the 2-dimensional subspace spanned by 1 (constant r.v.) and X+Y ? Morally : among functions of X+Y, only affine functions can be decomposed as a function of X plus a function of Y. I ask the question in L^2 since it is usually simpler, but it can also be asked in L^p (assuming if necessary that X, Y have finite p-th moment). === Subject: Re: Decomposable functions of independent variables >Let X and Y be independent random variables, with mean 0 and variance >Consider the following subspaces of L^2(X,Y): >E = L^2(X) + L^2(Y), >F = L^2(X+Y). >How to prove that the intersection of E and F is the 2-dimensional >subspace spanned by 1 (constant r.v.) and X+Y ? >Morally : among functions of X+Y, only affine functions can be >decomposed as a function of X plus a function of Y. >I ask the question in L^2 since it is usually simpler, but it can also >be asked in L^p (assuming if necessary that X, Y have finite p-th >moment). It is even more general. Suppose that Z = f(X,Y) is a function of X plus a function of Y almost everywhere, and is also a function of X+Y almost everywhere. Then for almost all X_1, X_2, f(X_1, Y) - f(X_2, Y) is a function of X_1 and X_2 for almost all Y. For these non-exceptional X's, this is g(X_1) - g(X_2). Do the similar thing for Y; we get h(Y_1) - h(Y_2). So f(X, Y) = g(X) + h(Y) + c for almost all (X, Y). If it is a function of X+Y almost everywhere, one can take g(X) = X + u and h(Y) = Y + v almost everrywhere. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: the uniqueness of one > My mathematics is roughly that of a high school graduate. > No, it isn't. How do you know? > A competent high school student knows that > 1 is the multiplicative identity. The rest of your observations follow > from > 1st year JUNIOR HIGH SCHOOL algebra. So *this* mathematics is 1st year junior high. That says nothing about the rest of the OP's mathematics. -- Larry Lard Replies to group please === Subject: Re: the uniqueness of one <28997649.1141215952847.JavaMail.jakarta@nitrogen.mathforum.org> 03/01/2006 >How do the first two properties follow from 1 being the >multiplicative identity? They don't; they follow from R being an Archimedean field. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org === Subject: Re: the uniqueness of one <28997649.1141215952847.JavaMail.jakarta@nitrogen.mathforum.org> <44062e0b$2$fuzhry+tra$mr2ice@news.patriot.net matt271829-news@yahoo.co.uk said: >How do the first two properties follow from 1 being the >multiplicative identity? > They don't; they follow from R being an Archimedean field. What two properties? === Subject: Sums of i...d.r.v. with infinite invariance Hello everybody, Let X be i.i.d.r.v with infinite variance.Let Sn is the random walk based on X and assume that EX=0 and EX^2=inf and escpecially E(min(X,0)^2)=infinity. Is there any information about the behaviour of the following series Sum(P(-1<=S1<=0,.....,-n<=Sn<=0);n=1......infinity) === Subject: dedanoe sponging hard; am looking for .exe maker i spoke with prof.dr. vanco kusakatov from institute of informatics at www.pmf.ukim.edu.mk he told me how 4D vector are being crossed. take a look at the latest from http://dedanoe.tripod.com/sponge === Subject: Re: A problem about differences in reduced residue system. It's not very precise. For M= 2*3*5*7*11*13*17*19 = 9699690, the maximal difference is 34=2*17 For M= 2*3*5*7*11*13*17*19*23 = 223092870, the maximal difference is 40>19*2 For M= 2*3*5*7*11*13*17*19*23*29, the maximal difference is 46=23*2. There may be an upper bound for the difference. No more than twice the largest factor of M? The research of gaps of primes is a hot topic. The consecutive difference of minimal reduced residue system module M may describe the dynamical character of prime system. My short paper for it could be found in http://arxiv.org/abs/math.DS/0601517, may be interesting. === Subject: Re: topological volume theory or 21-color theorem nobody ?? === Subject: Re: topological volume theory or 21-color theorem <14850126.1141302252819.JavaMail.jakarta@nitrogen.mathforum.org> Doing coloring in 3-d without any extra restrictions has no upper bound on the number of colors. Think of having a woven piece of cloth, where each 'thread' is a single 3d peice of the puzzle. You would be able to have an arbitrarily large number of threads all touching each other. === Subject: Weird casus irreducibilis Hello all, Doing some research on geometric figures I stumbled on this rather unusual cubic, x^3+ 2x^2 = (1/phi)^2 where phi is the golden ratio. This equation has three REAL roots, approx: -1.89346, -0.50556, 0.39902. The funny thing is that these roots CAN be expressible in terms of _REAL radicals_! Of course it may be argued that the cubic casus irreducibilis applies only when coefficients are rational. Since the above is obviously a factor of a sextic with rational coefficients (which btw has 4 real roots) then the challenge is to express these sextic roots in terms of real radicals. Care to give it a shot? P.S. Let's focus on the root x approx 0.39902. You can't use Cardano's formula for cubics to express this in terms of real radicals. But nonetheless it can be done. --Titus === Subject: expected number of draws for selecting all random items with replacement I am struggling with a probability type problem that is as follows: I have a random search algorithm that takes an integer to find as input (x) as well as an array of randomly arranged integers (A) and a number of items in the array (n). This search takes a random number from 1 to n as the index to search for and continues to do this until either the number (x) is found or all items in array (A) have been checked. The expected value of finding the item in the array (given that it exists) is n (sum of k times the probability of finding it ((n - 1/n)^k-1 times 1/n) for k = 1 to n). What I am struggling to find is the expected number of tries, given that the number doesn't exist in the array, before the entire array has been checked. I know that this algorithm is not efficient. I believe that the answer to this is: 2nlogn + n. I have verified this by writing the algorithm in c and using repeated tries. What I need help in is setting up the expected value formula. I just can't get my head around it. A similar problem woould be: given a set of n numbered balls in an urn with fair random selection and replacement after each selection what would be the expected number of draws to select each ball at least once. Any help would be greatly appreciated. === Subject: Re: expected number of draws for selecting all random items with replacement > I am struggling with a probability type problem that is as follows: > I have a random search algorithm that takes an integer to find as input > (x) as well as an array of randomly arranged integers (A) and a number > of items in the array (n). This search takes a random number from 1 to > n as the index to search for and continues to do this until either the > number (x) is found or all items in array (A) have been checked. > The expected value of finding the item in the array (given that it > exists) is n (sum of k times the probability of finding it ((n - > 1/n)^k-1 times 1/n) for k = 1 to n). > What I am struggling to find is the expected number of tries, given > that the number doesn't exist in the array, before the entire array has > been checked. > I know that this algorithm is not efficient. > I believe that the answer to this is: 2nlogn + n. I have verified this > by writing the algorithm in c and using repeated tries. > What I need help in is setting up the expected value formula. I just > can't get my head around it. > A similar problem woould be: given a set of n numbered balls in an urn > with fair random selection and replacement after each selection what > would be the expected number of draws to select each ball at least > once. > Any help would be greatly appreciated. For the balls-and-urns question I make the expected number of draws equal to n*(1 + 1/2 + 1/3 + ... + 1/n) After you have got the (i - 1)'th different number, there are n - i + 1 different numbers out of the n that will give you the next (i'th) different number. The probability of getting this number after x further tries is therefore (1 - (n - i + 1)/n)^(x - 1) * (n - i + 1)/n, which is a geometric distribution with expected value of x equal to n/(n - i + 1). Then we can, I think, just add all the expectations together over i = 1 to n, to get n/n + n/(n -1) ... + n/1 = n*(1 + 1/2 + 1/3 + ... + 1/n). === Subject: Re: expected number of draws for selecting all random items with replacement > For the balls-and-urns question I make the expected number of draws > equal to > n*(1 + 1/2 + 1/3 + ... + 1/n) > After you have got the (i - 1)'th different number, there are n - i + 1 > different numbers out of the n that will give you the next (i'th) > different number. The probability of getting this number after x > further tries is therefore (1 - (n - i + 1)/n)^(x - 1) * (n - i + 1)/n, > which is a geometric distribution with expected value of x equal to > n/(n - i + 1). Then we can, I think, just add all the expectations > together over i = 1 to n, to get n/n + n/(n -1) ... + n/1 = n*(1 + 1/2 > + 1/3 + ... + 1/n). Hi matt, Tom === Subject: Re: Primes: Randomness and Prime Twin Proof On 1 Mar 2006 14:12:14 -0800, Martin Winer Actually the probability is 0 or 1, we just don't know it yet. >No way man! :) Seriously, it's not 0 or 1 because there are some >Pat(n)'s whose P(n)..P(n)^2 region does not subtend a prime twin >candidate, and there are some that do. Thus, the probability can't be >0 or 1. >However the compounded probability is 1. Meaning... suppose we have a >slot machine that starts out giving odds of 1 in 2 of winning. Each >time played, the odds decrease by 1 (1 in 3, 1 in 4, ...). Each play, >the odds of winning are NOT 1 in 1 nor are they zero. However, if you >are patient enough, and play long enough... you WILL for sure win. No. If the probability that you win eventually is 1 it does not follow that you WILL for sure win eventually. That's one of at least two reasons why you can't prove things about primes using probability arguments - probability = 1 does not imply certainty. (There's another much simpler reason: primes are not random, as people have been trying to point out. Thinking about the distribution of the primes in probabilistic terms can be very useful heuristically, and it could even lead to an insight that then led to a proof, but by itself it can't prove anything.) >Thus the compounded probability is 1. ************************ David C. Ull === Subject: Re: Primes: Randomness and Prime Twin Proof <31788282.1141237268175.JavaMail.jakarta@nitrogen.mathforum.org> <0mqd025nv6egfbmsagcth6euuqchehlqd0@4ax.comNo. If the probability that you win eventually is 1 it does not >follow that you WILL for sure win eventually. Suppose I call 'heads' for two coin flips. My probability is 1 that I'll get a head on one of the two flips. I think your point is that despite that probability, each flip has a 50-50 chance, and it's still possible that I'll lose, despite my probability of 1. Great, but there is a flipside to that coin :). There is a fundamental tenet of probabilities (I wish I could find the exact quote) which says that anything with a non-zero probability, given enough time, will occur. Thus, given an infinite number of flips and any non-zero probability, I'll eventually get heads and win. My proof relies on this non-zero probability given enough chances will eventually 'hit', not on the fact that the probability is = 1. So, to reiterate, my proof relies on the fact that in every turn, we have a non-zero probability that there will be a prime twin candidate between P(n) and P(n)^2 for any Pat(n), AND we have an infinite number of 'tries'. === Subject: Re: Primes: Randomness and Prime Twin Proof <31788282.1141237268175.JavaMail.jakarta@nitrogen.mathforum.org> <0mqd025nv6egfbmsagcth6euuqchehlqd0@4ax.com >No. If the probability that you win eventually is 1 it does not >follow that you WILL for sure win eventually. > Suppose I call 'heads' for two coin flips. My probability is 1 that > I'll get a head on one of the two flips. [...] I don't think so. 1 is the expected number of heads, but the probability that you call at least one right is 3/4. --- Christopher Heckman === Subject: Re: Primes: Randomness and Prime Twin Proof >Actually the probability is 0 or 1, we just don't know it yet. > No way man! :) Seriously, it's not 0 or 1 because there are some > Pat(n)'s whose P(n)..P(n)^2 region does not subtend a prime twin > candidate, and there are some that do. Thus, the probability can't be > 0 or 1. > However the compounded probability is 1. Meaning... suppose we have a > slot machine that starts out giving odds of 1 in 2 of winning. Each > time played, the odds decrease by 1 (1 in 3, 1 in 4, ...). Each play, > the odds of winning are NOT 1 in 1 nor are they zero. However, if you > are patient enough, and play long enough... you WILL for sure win. > Thus the compounded probability is 1. Great argument. The same form of proof shows that a random integer or even list of integers (finite or infinite) must contain the number 3, as if we pick a large enough integer the probability of it not containing the digit 3 is zero. Inspired by your paper, I now submit the proof that there are an infinite number of even primes: In the range 1..10, there are 4 primes, so statistically 2 of them should be even. (not far off). In the range 1 .. n, there should be 0.5* n/log(n) primes. This clearly goes to infinity, so there are an infinite number of even primes. === Subject: Re: Primes: Randomness and Prime Twin Proof <31788282.1141237268175.JavaMail.jakarta@nitrogen.mathforum.org> <44064c18$0$1256$afc38c87@news.optusnet.com.auGreat argument. The same form of proof shows that a random integer or even >list of integers (finite or infinite) must contain the number 3, as if we >pick a large enough integer the probability of it not containing the digit 3 >is zero. It seems a higher probability event that you haven't read my paper at all. I've said NONE of what you claim here. === Subject: Re: Primes: Randomness and Prime Twin Proof > Inspired by your paper, I now submit the proof that there are an infinite > number of even primes: > In the range 1..10, there are 4 primes, so statistically 2 of them should be > even. (not far off). In the range 1 .. n, there should be 0.5* n/log(n) > primes. This clearly goes to infinity, so there are an infinite number of > even primes. Not to mention an even number of infinite primes. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Primes: Randomness and Prime Twin Proof <31788282.1141237268175.JavaMail.jakarta@nitrogen.mathforum.org >Actually the probability is 0 or 1, we just don't know it yet. > No way man! :) Seriously, it's not 0 or 1 because there are some > Pat(n)'s whose P(n)..P(n)^2 region does not subtend a prime twin > candidate, and there are some that do. Thus, the probability can't be > 0 or 1. > However the compounded probability is 1. Meaning... suppose we have a > slot machine that starts out giving odds of 1 in 2 of winning. Each > time played, the odds decrease by 1 (1 in 3, 1 in 4, ...). Each play, > the odds of winning are NOT 1 in 1 nor are they zero. However, if you > are patient enough, and play long enough... you WILL for sure win. > Thus the compounded probability is 1. For any particular region the probability is 0 for 1. For example, between 10 and 15 the probability of there being a prime twin is 1. Between 30 and 40 the probability is 0. Between r and s, the probably of their being a prime twin is not so much random as it is unknown. I'm saying the probability aurgument doesn't work because it's not random. === Subject: Re: A question on C^infinity functions > For general C^infty function f, define > g(x)= f(x)/x for x not equal 0, = 0 for x=0. > Use L'Hopital Rule to prove that g is C^infty. > What if f(x)=1 for all x? read the original question, not quoted by TLC === Subject: Re: A question on C^infinity functions First statement only i.e. > Let f: R-->R be a C^infty function with f(0)=0. Then it is quite easy > to > find a C^infty function g such that > f (x)= x g(x) > For example, > f(x) = sin x is a C^infinity function. So what has to be function g(x), > such that sinx = x g(x) In your example, g is just the sinc function, which is defined as follows: sinc(x) = sin(x)/x if x <> 0 sinc(0) = 1 (the limit of sin(x)/x as x approaches 0). By construction, the sinc function is continuous everywhere. Moreover, a simple power series argument shows that the sinc function is an entire function (analytic on the entire complex plane) and is therefore infinitely differentiable. The sinc function is a well-studied function which plays an important role in information theory, sinc interpolation, sinc approximation, sinc quadrature, etc. For example, see http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem -- Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo http://www.scg.uwaterloo.ca/~fwchapman/ === Subject: C1alis 10 Pills 20 mg $89.95 boundary=------------ms020508060206050309020406 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k22DBX327092 for ; Thu, 2 Mar 2006 08:11:33 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! 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All here! === Subject: Re: Factor this differential operator > Write D for d/dt, and D^2 for d/dt(d/dt). > If v is a known solution of > D^2 y +p(t)Dy +q(t)y =0 > try to factor the differential operator D^2 + pD + q in terms of v, p, > q. > Anyone? I get: [vD + (2v'+pv)] [(1/v)D - (v'/v^2)] y = 0 -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Polynomials and Prime Numbers Mail-To-News-Contact: abuse@dizum.com >Actually, just the statement There's no rational polynomial P(x) such >that P(z) is >prime for every z in Z is true, with the proviso that P(x) is not a >constant. Here's a hint. Prove that > P(x + y*P(x)) is divisible by P(x) for every pair of integers x >and y. I played around with this last night. I used the following conditions: 1. P(x) is a polynomial with rational coefficients 2. x,y e Z I easily found cases where P(x + y*P(x)) and P(x) were both non-integral, with a non-integral quotient. Are there other conditions implied in your statement besides the ones that I used? -- Michael F. Stemper #include A bad day sailing is better than a good day at the office. === Subject: Re: Polynomials and Prime Numbers <15805881.1141132376717.JavaMail.jakarta@nitrogen.mathforum.org> <200603021349.k22Dn5p22546@walkabout.empros.com >Actually, just the statement There's no rational polynomial P(x) such >that P(z) is >prime for every z in Z is true, with the proviso that P(x) is not a >constant. Here's a hint. Prove that > P(x + y*P(x)) is divisible by P(x) for every pair of integers x >and y. > I played around with this last night. I used the following conditions: > 1. P(x) is a polynomial with rational coefficients > 2. x,y e Z > I easily found cases where P(x + y*P(x)) and P(x) were both non-integral, > with a non-integral quotient. Are there other conditions implied in your > statement besides the ones that I used? If you are using non-integral (rational?) values, then it is still true that P(x) divides P(x + y*P(x)) in the rationals. The Original Poster's application deals with a polynomial P that takes integer values at integer arguments (since it is desired to produce only prime values for these arguments). So the result by JoeS addresses this with the context of divisibility in the integers. More is true however. Let X be an indeterminate. Then P(X) divides P(X + y*P(X)) for any constant y as polynomials, with polynomial coefficients in any commutative ring. Sketch of proof: Use binomial expansion on terms in P(X + y*P(X)) and discard those which involve y*P(X) as obviously being divisible by P(X). What remains? Then, taking x,y as integers and P a rational polynomial whose values are integer for every integer argument, we have the application that is needed to show rational polynomials cannot produce only prime values unless the polynomial is a constant. === Subject: Re: Polynomials and Prime Numbers Mail-To-News-Contact: abuse@dizum.com >> Here's a hint. Prove that >> P(x + y*P(x)) is divisible by P(x) for every pair of integers x >>and y. >> I played around with this last night. I used the following conditions: >> 1. P(x) is a polynomial with rational coefficients >> 2. x,y e Z >> I easily found cases where P(x + y*P(x)) and P(x) were both non-integral, >> with a non-integral quotient. Are there other conditions implied in your >> statement besides the ones that I used? >If you are using non-integral (rational?) values, then it is still >true that P(x) divides P(x + y*P(x)) in the rationals. Well, as you specified, I was using integers for x and y. I initially tried integer polynomials, and they worked out as stated. When I started trying polynomials with rational (but non-integer) coefficients, that's when I started getting results whose quotients were also not integers. Sorry about the dumb questions, but I haven't gone very far in algebra -- I got hung up on permutation groups. What does it mean for two numbers to be divisible in the rationals? In the integers, i|j means that there is a k such that i*k =j. In the rationals, there's such a k for every i,j (i!=0), so there must be some additional restrictions. >More is true however. Let X be an indeterminate. Then >P(X) divides P(X + y*P(X)) for any constant y as polynomials, >with polynomial coefficients in any commutative ring. >Sketch of proof: Use binomial expansion on terms in >P(X + y*P(X)) and discard those which involve y*P(X) >as obviously being divisible by P(X). What remains? I think that I can flesh this out. I started down a proof by induction on the degree of the polynomial last night, but the expansiions got ugly too quickly for my relatively short attention span. This sounds more straightforward. >Then, taking x,y as integers and P a rational polynomial >whose values are integer for every integer argument, Ah-hah! I think that this was the missing (or implied) restriction. I was using polynomials such as P(x) = x/3 + 1/2, which certainly do not meet that constraint. -- Michael F. Stemper #include No animals were harmed in the composition of this message. === Subject: Re: Polynomials and Prime Numbers <7383567.1141251985929.JavaMail.jakarta@nitrogen.mathforum.org > Let me add to this. There does exist a polynomial in > 26 variables (not > one) > whose positive values EXACTLY coincide with the > primes. Look up the > 'Jones > Polynomial' > The polynomial found by Jones, Sato, Wada and Wiens has > the following property: the set of primes coincide with > the set of positive values of the polynomial when the > variables range over non negative integers. > Unfortunately, if we conbsider also negative integers, > then we have positve values that are not primes. > Is there a polynomial with this additional property? I think I see what you're asking, and the answer is 'yes'. Replace each variable with a sum of the squares of four new variables, e.g. replace x with a^2 + b^2 + c^2 + d^2. Every non-negative integer is the sum of four squares of integers, so the new polynomial will be prime whenever it is positive, for any positive or negative values of the new variables. === Subject: Signons I'm not sure if anyone has a name for these things so I'm calling them signons. They are not quite polygons but certainly can be mapped to them. http://bandtechnology.com/PolySigned/Lattice/Lattice.html I remember someone claiming that there is no object that packs in a tetrahedral lattice. Though I don't have a formal proof I think you will see that there is such a shape and that it exists in general for any dimension. Please let me know if you see any errors. Low bandwidth users: the animation is around 0.5 meg. -Tim === Subject: Re: My mind is more beautiful than John Nash's climate.Maggie wasn't there. The lions are camouflaged: SUVs with tinted windows mostly. But you see them in great display at election time when the next King of the Jungle will be elected. === Subject: Re: My mind is more beautiful than John Nash's IIRC tigers live in jungles and lions live on the savannah...... These lions live in the jungle.... the Asphalt Jungle that is. === Subject: Re: My mind is more beautiful than John Nash's >> Do lions live in jungles? >> IIRC tigers live in jungles and lions live on the savannah...... > These lions live in the jungle.... the Asphalt Jungle that is. Are they asphalt lions? Why aren't they tigers if they are living in the jungle? === Subject: Re: My mind is more beautiful than John Nash's > Do lions live in jungles? >> IIRC tigers live in jungles and lions live on the savannah...... > These lions live in the jungle.... the Asphalt Jungle that is. > Are they asphalt lions? Why aren't they tigers if they are living in the > jungle? Simply because these lions are --or claim to be-- the Kings of the Jungle. If it was for me though I'd put him in cages and make them eat the monkey's banana. Well, that's another story... ;) Anyone wants to know??? === Subject: Re: My mind is more beautiful than John Nash's >> Do lions live in jungles? >> IIRC tigers live in jungles and lions live on the savannah...... >> These lions live in the jungle.... the Asphalt Jungle that is. >> Are they asphalt lions? Why aren't they tigers if they are living in the >> jungle? > Simply because these lions are --or claim to be-- the Kings of the > Jungle. Really? If the lions are talking can you ask them what they are doing in the jungle and why the tigers arent killing them? > If it was for me though I'd put him in cages and make them eat the > monkey's banana. Well, that's another story... ;) The lion or the monkey is the other story? > Anyone wants to know??? Not really no. === Subject: Re: My mind is more beautiful than John Nash's OK, this is getting fun now... > John Nash stated that Adam Smith was wrong! The best result comes > from doing the best for one's self and for the group! > The economic self-interest of individuals, however, did not clash with the > general interest, but was, on the contrary, identical with it, at least as a > general rule. Behind the doctrine of the Physiocrats, and of Adam Smith too, > was the assumption of a natural harmony between self-interest and the > general interest, and of an equilibrium between economic supply and demand, > provided the Natural Order was adhered to. In the words of Condorcet, also > an economic liberal, there existed, in spite of apparent chaos, a general > law of the moral world which causes the efforts of everyone in his own > behalf to serve the interests of all; and which, despite the apparent > conflict, the common interest demands that everyone should understand his > own interest and be permitted to pursue it without opposition. Interesting lesson, but didn't see any role for the Hungry Lion in Smith theory. Throughout history there's been a chief, a pharaoh, a sheikh, a king or a president who to a greater or lesser degree procures the lion's share for himself (or herself, to honor feminists) and * the others* if you will, and there lies the problem. So the whole balance of a true jungle is thrown off-balance and it becomes a savannah of sorts where the big fish eats the little fish, speaking in parable of course. Well, sometimes the predator is too successful and overhunts his (or her) prey to extinction and then he (or she) starves himself (or herself). And you have such an extreme case happening in human society, for example in Easter Island... So the interest of the Hungry Lion and the little animals are at odds and in that it reminds us of the class struggle. Well, communism turned out to be as Darwinian as capitalism, but there remains the good old fashion way of defense of the sardines: In Union there's Strength. PS: For the record: the hunting lions are female. :) Easter Island example... Greed and the desire for social prestige dictated decisions. (I guess the Hungry Lion was there too.) how some people do not see the obvious parallels between what their society did and what we are currently doing to the environment. Easter Island was a virtually inaccessible island in the Pacific Ocean that was at one point in history populated by a flourishing civilization. As Ponting describes, Easter Island is a striking example of the dependence of human societies on their environment and of the consequences of irreversibly damaging that environment. The people were originally Polynesian and arrived at the island by traveling in double canoes. They created a very advanced society with access to only a very limited range of resources. The climate of Easter Island made it difficult to grow most plants, and most of the animals on the island had been brought by the people. With time though, the people figured out a simple diet that allowed a large amount of free time leftover. The people prospered and created a system of family clans each of which had their own specific religious shrines. Rituals and ceremonies became central to life on the island and as it was manifested in their communities, required the building of huge platforms and statues. Unfortunately, the people on Easter Island failed to consider their effect on the delicate ecosystem. They completely deforested the island and were left with even less resources than they had started with. The separate clans had to guard what little resources they had and became engaged in continual combat. They people even had to turn to cannibalism. The groups eventually unable to sustain themselves or the environment around them. The story of Easter Island is a shocking one, but what most affected me were the similarities between then and now. Resources were used without and the desire for social prestige dictated decisions. I would not doubt that there were people on Easter Island who questioned what the inhabitants were doing to the environment, but their voices went deforestation happened very suddenly, but I cannot believe that the people on the island did not notice the dwindling amount of trees growing on the island. Despite this, they continued to cut them down for their own selfish needs. This is incredibly similar to what groups of people have done throughout history. We used wood and deforested extensively even after we realized it was becoming scarce. Only the economics of the situation caused people to slow down and it seems like we will run into the same problems with oil. I wonder what it will take for humans to realize the damage they are causing the environment and have this be enough impetus to change the way we run our society.' http://fubini.swarthmore.edu/~ENVS2/rpattni1/essay1.html === Subject: Re: My mind is more beautiful than John Nash's <68mdncH3EPq-iZvZRVnyjw@pipex.net >> Well, Beauty is in the eye of the beholder, but I got good reasons to >> say so. >> Well, I think the newsgroups that you cross posted this to says a lot. > You forget I've been scientific about it. I put John Nash in the > newsgroups search, and whatever group popped up, there I posted. > There should be laws against Google groups. Let Big Brother alone. He's busy enough eavesdropping. === Subject: Re: Proability Question === Subject: Representation of Analytic Functions I came across a very difficult question, which I put to you, in the hope somebody solved it: is there a continuous function f(x,c_1, ...,c_n):R^(n+1)->R such that,fixing opportunely the values of c_1,...,c_n, one can obtain any analytic function of x? If we replace any analytiv function with any continuous function, then the answer is no (take g(x)=f(x,s(x))+1, where s(x) is space-filling curve). If someone has some idea, I'll be very very ... grateful. Maury === Subject: Re: Representation of Analytic Functions > I came across a very difficult question, which I put to > you, in the hope somebody solved it: > is there a continuous function > f(x,c_1, ...,c_n):R^(n+1)->R such that,fixing > opportunely the values of c_1,...,c_n, one can obtain > any analytic function of x? > If we replace any analytiv function with any > continuous function, then the answer is no (take > g(x)=f(x,s(x))+1, where s(x) is space-filling curve). > If someone has some idea, I'll be very very ... grateful. No. You are essentially trying to find a surjective map from R^n (the space of all c_n's) to the space of analytic functions (on the real line, I presume). However, the latter space is infinite dimensional (e.g. the functions 1,x,x^2,... are all linearly indpendent). So it will be impossible to find a surjective map onto it from the finite dimensional space R^n. Hope this helps. Igor === Subject: Re: Representation of Analytic Functions > No. You are essentially trying to find a surjective map from R^n (the > space of all c_n's) to the space of analytic functions (on the real > line, I presume). However, the latter space is infinite dimensional > (e.g. the functions 1,x,x^2,... are all linearly indpendent). So it will > be impossible to find a surjective map onto it from the finite > dimensional space R^n. Why? What you say is true, but infinte dimensional is not the reason. There is a surjective map from the one-dimensional space [0,1] onto the infinite-dimensional space [0,1]^T, with T countably infinite. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Representation of Analytic Functions > > No. You are essentially trying to find a surjective > map from R^n (the > space of all c_n's) to the space of analytic > functions (on the real > line, I presume). However, the latter space is > infinite dimensional > (e.g. the functions 1,x,x^2,... are all linearly > indpendent). So it will > be impossible to find a surjective map onto it from > the finite > dimensional space R^n. > > Why? > What you say is true, but infinte dimensional is > not the reason. Are you saying that the answer to my original question is No? > There is a surjective map from the one-dimensional > space [0,1] > onto the infinite-dimensional space [0,1]^T, with T > countably infinite. > -- > G. A. Edgar > http://www.math.ohio-state.edu/~edgar/ Maury === Subject: Re: Representation of Analytic Functions > There is a surjective map from the one-dimensional space [0,1] > onto the infinite-dimensional space [0,1]^T, with T countably infinite. even a continuous surjective map -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Representation of Analytic Functions > > There is a surjective map from the one-dimensional > space [0,1] > onto the infinite-dimensional space [0,1]^T, with T > countably infinite. > even a continuous surjective map > -- > G. A. Edgar What is this map? Maury > http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Representation of Analytic Functions > On 2006-03-02, Maury Barbato > I came across a very difficult question, which I > put to > you, in the hope somebody solved it: > is there a continuous function > f(x,c_1, ...,c_n):R^(n+1)->R such that,fixing > opportunely the values of c_1,...,c_n, one can > obtain > any analytic function of x? > If we replace any analytiv function with any > continuous function, then the answer is no (take > g(x)=f(x,s(x))+1, where s(x) is space-filling > curve). > If someone has some idea, I'll be very very ... > grateful. > No. You are essentially trying to find a surjective > map from R^n (the > space of all c_n's) to the space of analytic > functions (on the real > line, I presume). However, the latter space is > infinite dimensional > (e.g. the functions 1,x,x^2,... are all linearly > indpendent). What do you exactly mean by space (vector, topological, ...)? > So it will > be impossible to find a surjective map onto it from > the finite > dimensional space R^n. Hmm, I am not so sure that the answer is so simple. > Hope this helps. > Igor Maury === Subject: Men Health boundary=------------ms020508060206050309020406 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k22FFd311573 for ; Thu, 2 Mar 2006 10:15:39 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: Re: Applications of Mathematics <81qNf.62049$PL5.5464@newssvr11.news.prodigy.com Sci.math research project: Does there exist a genuine > paired with 'W' gives zero hits? >> fractal misanthrope > A few more: > fractal adjunct > fractal spoon > fractal hysterectomy [snip rest of list] I was thinking of non-phrase searches, which is why I used the term 'paired'. Several people have pointed out that some web pages are little more than dictionaries for various purposes, so a better challenge would be to find no hits for fractal paired with 'W', except for webpage(s) that are essentially lists of words. This classification of web pages would probably lead to some pages for which there would be no consensus on, however. One way to avoid this is to restrict the I suspect it wouldn't be difficult to find an example here, although my first try shows this might be more difficult than I expected, since fractal AND bathtub gave me 86 hits, and fractal AND hysterectomy gave me 35 hits: Dave L. Renfro === Subject: Re: Applications of Mathematics On 2 Mar 2006 07:21:00 -0800, Dave L. Renfro Sci.math research project: Does there exist a genuine >> paired with 'W' gives zero hits? > fractal misanthrope >> A few more: >> fractal adjunct >> fractal spoon >> fractal hysterectomy >[snip rest of list] >I was thinking of non-phrase searches, which is why I >used the term 'paired'. Several people have pointed out >that some web pages are little more than dictionaries >for various purposes, so a better challenge would be >to find no hits for fractal paired with 'W', except >for webpage(s) that are essentially lists of words. >This classification of web pages would probably lead >to some pages for which there would be no consensus >on, however. One way to avoid this is to restrict the >I suspect it wouldn't be difficult to find an example >here, although my first try shows this might be more >difficult than I expected, since fractal AND bathtub >gave me 86 hits, and fractal AND hysterectomy >gave me 35 hits: There is a common pastime called 'Google whacking', which consists of attempting to find a pair words that together produce exactly one hit on Google. The difficulty in producing a word pair which produces no hits has been observed by other posters. If we take the definition of a proper English word W to be one that appears in OED, Webster, or some such, then there exists many pages which list all such words. Ergo, for a word pair to appear with no hits on Google, at least one of the words must not be widely recognized by the most common English dictionaries, or must appear in a conjugated form not included in wordlists. Hence, I conjecture that choosing any specialist term, say from medical jargon not commonly known, and combining it with 'fractal' will sooner than later produce an example of no hits. === Subject: Re: Applications of Mathematics >> I would like to have a list of examples of applications >> of Mathematics to areas which, at first sight, might >> seem to be very non-mathematical. One good example: cryptography. > I suspect searches using either fuzzy or fractal > will turn up a lot of these. However, I'm guessing that > by at first sight you also mean but not at second sight, > which will eliminate a lot of what these searches will > likely uncover. Your guess is correct. Jose Carlos Santos === Subject: Re: Applications of Mathematics > A good little book for this is A. Friedman and W. Littman, Industrial > with such topics as Crystal Precipitation, Air Quality Modeling, > Electron Beam Lithography, Development of Color Film Negatives, > Catalytic Converters, and Photocopy Machines. Most of the > models/analyses are of the DE, PDE or Fourier flavor, and not > combinatorial like cryptography. there's a copy at the library of my department. Jose Carlos Santos === Subject: Re: Applications of Mathematics >> I would like to have a list of examples of applications of Mathematics >> to areas which, at first sight, might seem to be very non-mathematical. >> One good example: cryptography. > Why does cryptography seem nonmathematical to you? It doesn't, but for most people there's no connection whatsoever. Jose Carlos Santos === Subject: Re: Applications of Mathematics <46o0laFbu843U1@individual.net Why does cryptography seem nonmathematical to you? It doesn't, but for most people there's no connection whatsoever. Actually for the average person on the street, they are so totally disconnected from ALL technical subjects that their viewpoint [of connections that might exist among various subjects] has no meaning whatsoever. === Subject: Re: Applications of Mathematics > I would like to have a list of examples of applications > of Mathematics to areas which, at first sight, might > seem to be very non-mathematical. One good example: cryptography. > Theology - Pascal's Wager. Ok, if that counts, then how about the decryption of Linear B (the writing system of the Cretans) done around 1952? Or would that count as a sub-case of cryptography? Then there's David Cope's work in music (automatized composing). And there was a time when human reasoning was considered 'at first sight, to be very non-mathematical'. Nowadays, this is a rather bizarre thought, but that's a relatively new development. The idea that a formal system could somehow represent human, correct reasoning is ridiculed, for example, in 'Gulliver's Travels'. And it wouldn't surprise me if many still find it nonsense, today. -- Herman Jurjus === Subject: Re: Applications of Mathematics >Sci.math research project: Does there exist a genuine >paired with 'W' gives zero hits? Since Google searches some rather big word lists, the answer may well be no. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Applications of Mathematics > I would like to have a list of examples of applications > of Mathematics to areas which, at first sight, might > seem to be very non-mathematical. One good example: cryptography. > I suspect searches using either fuzzy or fractal > will turn up a lot of these. However, I'm guessing that > by at first sight you also mean but not at second sight, > which will eliminate a lot of what these searches will > likely uncover. Here are some examples using fractal, > each of which gives over 100,000 hits: > Sci.math research project: Does there exist a genuine > paired with 'W' gives zero hits? fractal crackpot === Subject: Re: Applications of Mathematics On Wed, 01 Mar 2006 18:37:26 -0800, The World Wide Wade >> I would like to have a list of examples of applications >> of Mathematics to areas which, at first sight, might >> seem to be very non-mathematical. One good example: cryptography. >> I suspect searches using either fuzzy or fractal >> will turn up a lot of these. However, I'm guessing that >> by at first sight you also mean but not at second sight, >> which will eliminate a lot of what these searches will >> likely uncover. Here are some examples using fractal, >> each of which gives over 100,000 hits: >> Sci.math research project: Does there exist a genuine >> paired with 'W' gives zero hits? >fractal crackpot If you include the two words in quotes then yes, you get no hits. That's searching for the exact phrase fractal crackpot, not for pages that contain both words. If you leave out the quote marks you find plenty of pages containing both words. ************************ David C. Ull === Subject: Re: Applications of Mathematics > I would like to have a list of examples of applications of Mathematics > to areas which, at first sight, might seem to be very non-mathematical. How about the use of the statistical analysis of word frequencies to authenticate writings of Shakespeare. === Subject: Re: Applications of Mathematics > How about the use of the statistical analysis of word frequencies to > authenticate writings of Shakespeare. Jose Carlos Santos === Subject: Re: Applications of Mathematics > I would like to have a list of examples of applications of Mathematics > to areas which, at first sight, might seem to be very non-mathematical. > How about the use of the statistical analysis of word frequencies to > authenticate writings of Shakespeare. The perfect ratio and it's apparent application to art/beauty/architecture. DK === Subject: Re: Applications of Mathematics > I would like to have a list of examples of applications of Mathematics > to areas which, at first sight, might seem to be very non-mathematical. > How about the use of the statistical analysis of word frequencies to > authenticate writings of Shakespeare. > The perfect ratio and it's apparent application to > art/beauty/architecture. If you're talking about the Golden Ratio, that's more an example of misapplication (as has been discussed here on a number of occasions). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Short, cute problem In an imaginary world, half of 6 is 4. In that world, what is one-third >of 12? > It is 5 1/3 > w. > That's an interesting solution, and not the one I came up with. How did > you arrive at it? > FWIW, here is what occured to me: > Draw a number line with two marks at 0 and 6. > Halfway along the line, draw a mark and label it 4. > Now ask: What is the number that should sit halfway between 0 and 4? > PD To extend this a bit further, the mark that is midway between 0 and 4 is 8/3, and the mark that is midway between 0 and 8/3 is then 16/9. I believe this is a consistent (but non-commutatitve) way of defining the multiplication. By this same rule, half of 12 is 8, and with just a little work in figuring out the nonlinearity of the line, you can deduce that one-third of 12 is 6. PD === Subject: Relativity a ... Short, cute problem was ------- Re: Short, cute problem ----------- >>In an imaginary world, half of 6 is 4. In that world, >>what is one-third of 12? >> It is 5 1/3 >> w. [PD] >> That's an interesting solution, and not the one >> I came up with. How did you arrive at it? >> FWIW, here is what occured to me: >> Draw a number line with two marks at 0 and 6. >> Halfway along the line, draw a mark and label it 4. >> Now ask: What is the number that should sit halfway between 0 and 4? > To extend this a bit further, the mark that is midway between 0 and 4 > is 8/3, and the mark that is midway between 0 and 8/3 is then 16/9. I > believe this is a consistent (but non-commutatitve) way of defining the > multiplication. By this same rule, half of 12 is 8, and with just a little work in > figuring out the nonlinearity of the line, you can deduce that > one-third of 12 is 6. > PD [hanson] ahahahaha....see, all those different answers you and a host of other posters came up with in this thread, in your *imaginary world*, applying willfully, ad hoc, different rules for the prediction of an outcome? See how you get into each other's hair over these different procedures and out comes in your imaginary worlds?... As long as you keep it in the realm of the unreal, fine... But the relativists, meaning the Einstein disciples, viciously advocate to carry such type of mental masturbations over into the normal, empirically experienced 3DT reality without thought, qualms and inhibitions. That makes these relafans out to be CRANKS,... the original cranks & crack pots! That is cool as long as they stay masturbating in the darkness of their Albertian cul de sac and keep on ejaculating in there.... Have fun!... ahahahaha... AHAHAHAHAHA.... ahahahaha.... Androcles just posted a few interesting lines in this regard: Re: Invalidity of Special Theory of Relativity >What difference to physics does it make what somebody's expectation > happens to be? [Androcles] > Exactly. > Physics doesn't give a what Einstein's expectation happens to be. > Time is a universal constant no matter what mathematical games you play > with speed, and experimental evidence from the Cassini probe at Saturn > proves > (PROVES!) that Einstein's guesses are 28 seconds a year off, a far greater > error than 38 microseconds a day from GPS. > Androcles. [hanson] then kk If one sets a = b, where a =/= b, then you can derive division by zero or all kinds of wierd things. Let 1 = 2, and see what happens. Now, we dont say that 1 = 2 is undefinfed, but 1/0 sure is. So, what's so special about 1/0 that it gets this white glove treatment ? We dont roll out the red carpet for 1 = 2 ? === Subject: Re: Short, cute problem or all kinds of wierd things. > Let 1 = 2, and see what happens. > Now, we dont say that 1 = 2 is undefinfed, but 1/0 sure is. I'm pretty sure I've never said that anything was undefinfed, or definfed for that matter. Not to mention finfed. > So, what's so special about 1/0 that it gets this white glove treatment > ? We dont roll out the red carpet for 1 = 2 ? 1 = 2 is an equation, which happens to be false. 1/0 is an expression, not an equation. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Cracking 7 digit passwords <119cbceeo6nrm$.18xck0xa3bcxw$.dlg@40tude.net> No, Swain. You said, and it is here on Google, that Hi and Corey were not the same person. Wrong. Asiya confirmed this. I said that Corey, Hi and the Corey's from alt.tarot were the same. You said nothing about that, darling dear. Asiya said it wasn't the same person. To which I replied that although I want to believe her I had seen too much evidence pointing to the contrary. You are sticking your nose into other people's conversations. Whatsa matter, neglected much? Never said it as a big deal to Hi. Obviously it isn't. Doesn't take a Candian to tell me that much. I never said it was a big deal, either. I simply said Corey was Hi and etc etc etc Learn how to read, girlpants. === Subject: Re: ordinary differential equation help z^2/2*x^2*(1-x)^2*y''[x]-lam*x*y'[x]-r*y[x]= f[x] (for 0following 2nd order ODE has an explicit analytical solution I can >use? (or if there's a recipe I could follow to get one) >z^2/2*x^2*(1-x)^2*y''[x]-lam*x*y'[x]-r*y[x]=0 (for 0 S with F(f)(u) = s. Let the functor F be F(S) = S x S, F(f) = f x f. 1) For 2 = {1, 2}, prove that (1,2) in 2 x 2 is a universal element for the functor F. 2) For 3 = {1, 2, 3}, prove that (1,2) in 3 x 3 is not a universal element for the functor F, 3) For 1 = {1}, prove that (1,1) in 1 x 1 is not universal for F. === Subject: Re: universal element for the functor days. My association with the Department is that of an alumnus. Before you reply: 1. Mathforum does not insert line breaks properly; please insert them manually. Otherwise, your lines run off at the end of the screen just as bad on text based newsreaders like mine. 2. When you reply, be sure to quote the message you are replying to. On mathforum this can be achieved by clicking on the Quote original button over the reply box. >A universal element for a functor F is an ordered pair (u,R) >consisting of a set R and an element u in F(R) with following >property: I guess your functor goes from Set to some category whose objects are sets and whose arrows are functions on the underlying sets... >To any set S and any element s in F(S) there is exactly one function >h: R -> S with F(f)(u) = s. >Let the functor F be F(S) = S x S, F(f) = f x f. >1) For 2 = {1, 2}, prove that (1,2) in 2 x 2 is a universal element >for the functor F. Are you asking us to do your homework for you? To explain the question? To give a hint? What? What have you managed? What are you confused about? >2) For 3 = {1, 2, 3}, prove that (1,2) in 3 x 3 is not a universal > element for the functor F, >3) For 1 = {1}, prove that (1,1) in 1 x 1 is not universal for F. Likewise. -- === Subject: Re: universal element for the functor > <15793250.1141316667274.JavaMail.jakarta@nitrogen.math > forum.org>, > Before you reply: > 1. Mathforum does not insert line breaks properly; > please insert them > manually. Otherwise, your lines run off at the end > end of the screen > get displayed; it's > just as bad on text based newsreaders like mine. > 2. When you reply, be sure to quote the message you > are replying > to. On mathforum this can be achieved by clicking > ing on the Quote > original button over the reply box. >A universal element for a functor F is an ordered > pair (u,R) >consisting of a set R and an element u in F(R) with > following >property: > I guess your functor goes from Set to some category > whose objects are > sets and whose arrows are functions on the underlying > sets... >To any set S and any element s in F(S) there is > exactly one function >h: R -> S with F(f)(u) = s. >Let the functor F be F(S) = S x S, F(f) = f x f. >1) For 2 = {1, 2}, prove that (1,2) in 2 x 2 is a > universal element >for the functor F. > Are you asking us to do your homework for you? To > explain the > question? To give a hint? What? This is not a homework. > What have you managed? What are you confused about? F(2) = {(1,1), (1,2), (2,1), (2,2)} and try to define f as f(1)= 1, f(2)=2 then I have problem. Since we need a functor to be satisfied such that F(f)(1) = (1,2) etc. But F(f)(1) = (f x f)(1) = f(1)xf(1) = (1,1) F(f)(2) = (f x f)(2) = f(2)xf(2) = (2,2) I don't get (1,2) where it should be. How should I define f? >2) For 3 = {1, 2, 3}, prove that (1,2) in 3 x 3 is > not a universal > element for the functor F >3) For 1 = {1}, prove that (1,1) in 1 x 1 is not > universal for F. > Likewise. > -- > It's not denial. I'm just very selective about > what I accept as reality. > --- Calvin (Calvin and Hobbes) > Arturo Magidin > magidin@math.berkeley.edu === Subject: Re: universal element for the functor days. My association with the Department is that of an alumnus. >> <15793250.1141316667274.JavaMail.jakarta@nitrogen.math >> forum.org>, >> 2. When you reply, be sure to quote the message you are replying >> to. On mathforum this can be achieved by clicking on the Quote >> original button over the reply box. Okay, good. Now, you need to find a balance between quoting everything and quoting nothing. You want to trim your quotes so as to include only what is needed for context. Yes, it sounds like contradictory advise; but good posting is like good writing: you need to find a balance between putting in too little (and putting nothing is invariably too little) and too much. > A universal element for a functor F is an ordered pair (u,R) > consisting of a set R and an element u in F(R) with following > property: >> I guess your functor goes from Set to some category whose objects >> are sets and whose arrows are functions on the underlying sets... > To any set S and any element s in F(S) there is exactly one > function h: R -> S with F(f)(u) = s. What happened to h? What is f? Nonsense yet again. This should be F(h)(u) = s. > Let the functor F be F(S) = S x S, F(f) = f x f. > 1) For 2 = {1, 2}, This is TERRIBLE notation. Your 2 is playing two roles (either that, or your set theory is not well-founded). Much better to let 2 = {0,1}. > prove that (1,2) in 2 x 2 is a universal > element for the functor F. This is nonsense as written. According to the definition, a universal element is an ordered pair, (u,R), where u is an element of F(R). If R=2, and u = 1, then you need 1 to be an element of F(R)= R x R = 2 x 2, but 1 is not an element of F(R). So this is nonsense. Did you notice that? >> Are you asking us to do your homework for you? To explain the >> question? To give a hint? What? >This is not a homework. Sure seemed like you were assigning homework to this newsgroup. Perhaps next time you will bother to say things like I would like some help or Could someone help me with If it is not homework, then what is it? Please tell me you made up the problems; if you copied them from somewhere, you need to sue the author. The statements are a mess of confusing notation and nonsense statements. >> What have you managed? What are you confused about? >as f(1)= 1, f(2)=2 then I have problem. Since what you are trying to prove is nonsense, it is hardly surprising that you are having a problem. Not to mention the terrible use of notation, which is confusing. So, let us rephrase and see if we can figure out WHAT it is you want to prove, shall we? Let 2 = {0,1}, and let F:Set -> Set be the functor that sends each set R to R x R, and sends each function f:R->T to the function fxf:(RxR)->(TxT). You want to show that ( (0,1),2) is a universal element for F. Note that this makes pirma facie sense, since (0,1) is indeed an element of F(2)=2x2 = {(0,0), (0,1), (1,0), (1,1)}. What does that mean? It means that you want to show that: For any set S, and every element s in F(S)=S x S, there is exactly one function h: 2 -> S such that F(h)((0,1)) = s. So, let S be any set, and let s = (a,b) be an element of S x S. You want to find a function h:{0,1} -> S, such that F(h)(0,1) = (a,b). Now, by definition, F(h)(x,y) = (h x h)(x,y) = (h(x),h(y)). So, what should h be? Your example is a bit of nonsense again, because you seem to be trying to map to 2. >I don't get (1,2) where it should be. >How should I define f? You should first review the definitions and make sure they make sense. Then you should fix your notation so it is not such a mess. Then you might have a chance at solving the problem. > 2) For 3 = {1, 2, 3}, Yet again confusing notation. Rather, set 3 = {0,1,2} so that 3 does not play two roles. > prove that (1,2) in 3 x 3 is not a universal element for the > functor F Nonsense again. Universal objects are supposed to be ordered pairs, (u,R), where the first entry is an element of F(R). So in your case, your universal object should be a pair, where the first element is an ordered pair, and the second element is a set that contains the two entries of the first. So in this case, you mean perhaps: 2) For 3 = {0,1,2}, show that ( (0,1),3) is NOT a universal element for F. So: you want to show that there is a set S and an element s in SxS for which either there is NO function h:3->S such that F(h)(0,1)=s, or else that there is more than one function h:3->S such that F(h)(0,1)=s. Doing the first problem should give you a clue that the problem is that there may be more than one h, since the condition you have, namely, F(h)(0,1)=s, will only determine the value of h on 0 and on 1, leaving you free to pick the value of 2. So just make sure your set S is such that it allows you to define two different function h:{0,1,2}->S which have the same value on 0 and 1; that should tell you how to go about it. > 3) For 1 = {1}, prove that (1,1) in 1 x 1 is not > universal for F. More nonsese. WHERE are you getting these statements from? Probably rephrasement: 3) For 1 = {0}, prove that ( (0,0), 1) is not universal for F. In this case the problem is going to be that there are sets S and elements s in S x S for which there is NO function h:1->S for which F(h)(0,0)=s. It should be easy to see why, once you get the hang of the first two problems. -- === Subject: Full of health? Then don't click! boundary=------------ms010004010703090208040203 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k22GgO323852 for ; Thu, 2 Mar 2006 11:42:24 -0500 by support2.mathforum.org (8.12.10/8.12.10/The Math Forum, $Revision: 1.6 secondary) with ESMTP id k22GejF4019606 for ; Thu, 2 Mar 2006 11:40:50 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: Medicines before Valentine Day !!! boundary=------------ms050906030402080807050801 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k22H0c326330 for ; Thu, 2 Mar 2006 12:00:38 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: psuedorandom number generator A few years ago I came across a neat algorithm which would generate a repeatable sequence of numbers within a set bound. Ie for the range of (integer) numbers, it would find all the numbers in that range once each before it began repeating. The order of the numbers appearing was not linear. Can anyone point me to this algorithm, please === Subject: Formula for error bound for a aproximation p(x) of function f(x) Does anyone know the formula or equation to calculate the error bound for an aproximation of a function. I.E. f(x)=e^x and aproximation p(x)=(1/6)x^3 + (13/24)x^2 +x + 191/192 === Subject: Re: Formula for error bound for a aproximation p(x) of function f(x) > Does anyone know the formula or equation to calculate the error bound > for an aproximation of a function. Sure, but only if the approximation p(x) is obtained in some well-known way from f(x), such as via Lagrange interpolation, or via Chebychev approximation, etc. Different approximation methods give different error-bound formulas. On the other hand, if p(x) is just some totally random formula, then the answer is probably no. Suggestion: consult a Numerical Analysis book. R.G. Vickison > I.E. f(x)=e^x and aproximation p(x)=(1/6)x^3 + (13/24)x^2 +x + 191/192 === Subject: Re: Formula for error bound for a aproximation p(x) of function f(x) I have actual aproximation i want to find the bound, I used the roots of the Chebeshev T4 to to construct my polynomial which is this p3(x)=.1752x^3 + .5429x^2 + .9989x + .9946. That is the degree polynomial aproximation i got and it aproximates f(x)=e^x rather well. I have a numerical analysis book but it is not clear on the error bound, it shows truncation error but nothing else. === Subject: Re: Formula for error bound for a aproximation p(x) of function f(x) > I have actual aproximation i want to find the bound, I used the roots > of the Chebeshev T4 to to construct my polynomial which is this > p3(x)=.1752x^3 + .5429x^2 + .9989x + .9946. > That is the degree polynomial aproximation i got and it aproximates > f(x)=e^x rather well. > I have a numerical analysis book but it is not clear on the error > bound, it shows truncation error but nothing else. Well,aside from roundoff errors, truncation error IS what you are looking for. However, such errors are often written in terms of maximum absolute values of some higher-order derivatives on some interval, and obtaining exact values is not always easy. However, obtaining looser bounds is often helpful and may be a lot easier. RGV === Subject: Re: statistics silly question?? >hi everyone >here comes a possible silly question. >I like my other 2 posts better but i just had to ask :p >Gauss transformed the binomial distribution into the erf(x) This is false. >i don't know how , i suppose he used limits and integrals. >at least that's how i can explain it, so seems likely to me. It was done by de Moivre, long before Gauss was born. By using the leading term of Stirling's approximation to the factorial, the binomial probability is close to the density of a normal distribution with the same mean and variance. Just as the integral is approximated by the sum, so is the sum by the integral; see the Euler-Maclaurin summation formula. >is there another way ? There are many, none so enlightening. >and how about a generalization kind a like this: >transform the trinomial distribution ? >to understand trinomial distribution its like the gausscurve ( discreet) of the trinomial coefficients , there like binomium but instead of (1+x)^n ; it's (1+x+x^2)^n . No problem; use the same approximation to the factorial. It will work for arbitrary multinomial, and even for sampling with an infinite number of choices. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: statistics silly question?? again nobody :s why im i being ignored ! ? it is too obvious ? === Subject: Re: statistics silly question?? <19449817.1141302353502.JavaMail.jakarta@nitrogen.mathforum.org again nobody :s > why im i being ignored ! ? > it is too obvious ? To be brutally honest, the most likely reason is that your original post is so badly written that no-one can be bothered trying to figure out what you are trying to ask. === Subject: Re: Beal's conjecture > Also, it does not deserve the name 'Beal > Conjecture'. The extension > from the > Fermat conjecture to one of unequal exponents is one > that is obvious to > any number > theorist. And Mr. Beal isn't even a mathematician. > At a number theory conference in Arcata California in > 1985, I was > present when John Tate > gave a terrific presentation of the (then brand new) > connection between > Taniyama-Shimura > and FLT that was given by Frey's work. Tate > mentioned that there were > a couple of obstacles, > including a conjecture of Serre, (proved by Ken > Ribet) that stood in > the way. At the end > of the talk a member of the audience asked the > question: Does the > result also apply to the > case of unequal exponents? > Posing the question in such a casual manner shows > that the conjecture > is rather obvious. > If anything, whoever posed the question is more > deserving to have the > conjecture named > after him. I wish I could remember who it was. Fermat used to express some kind of marvelous demonstration to the case of powers bigger than 2. Is it written in his statement, that such powers should be equal ? There is really something unexpected and common for equal and not equal powers bigger than 2. I used to come back to some trivial transformation and just noticed once overlooked link to proof. It looks there for very significant simplifications of this conjecture and why: plotted parameter shows to be just rational number... Ro-bin P.S. Please do not mix me so much with my previous errors: my properties to square determinants falls to factorization of X=mk but k=1... if anybody used to read my previous posts... === Subject: Re: Beal's conjecture <13379167.1141321772052.JavaMail.jakarta@nitrogen.mathforum.org > Also, it does not deserve the name 'Beal > Conjecture'. The extension > from the > Fermat conjecture to one of unequal exponents is one > that is obvious to > any number > theorist. And Mr. Beal isn't even a mathematician. > At a number theory conference in Arcata California in > 1985, I was > present when John Tate > gave a terrific presentation of the (then brand new) > connection between > Taniyama-Shimura > and FLT that was given by Frey's work. Tate > mentioned that there were > a couple of obstacles, > including a conjecture of Serre, (proved by Ken > Ribet) that stood in > the way. At the end > of the talk a member of the audience asked the > question: Does the > result also apply to the > case of unequal exponents? > Posing the question in such a casual manner shows > that the conjecture > is rather obvious. > If anything, whoever posed the question is more > deserving to have the > conjecture named > after him. I wish I could remember who it was. > Fermat used to express some kind of marvelous > demonstration to the case of powers bigger than 2. > Is it written in his statement, that such powers > should be equal ? > There is really something unexpected and common > for equal and not equal powers bigger than 2. > I used to come back to some trivial transformation > and just noticed once overlooked link to proof. > It looks there for very significant simplifications > of this conjecture and why: plotted parameter shows > to be just rational number... > Ro-bin > P.S. Please do not mix me so much with my previous > errors: my properties to square determinants > falls to factorization of X=mk but k=1... > if anybody used to read my previous posts... I looked at two sources and the conjecture can be read one of two ways: (1) a^x + b^y = c^z and x,y,z > 2 implies a,b, and c have a common factor d > 1 (2) a^x + b^y = c^z and x,y,z > 2 implies (a,b), (a,c), and (b,c) are not all 1. Which is correct? === Subject: Re: Beal's conjecture <13379167.1141321772052.JavaMail.jakarta@nitrogen.mathforum.org > Also, it does not deserve the name 'Beal > Conjecture'. The extension > from the > Fermat conjecture to one of unequal exponents is one > that is obvious to > any number > theorist. And Mr. Beal isn't even a mathematician. > At a number theory conference in Arcata California in > 1985, I was > present when John Tate > gave a terrific presentation of the (then brand new) > connection between > Taniyama-Shimura > and FLT that was given by Frey's work. Tate > mentioned that there were > a couple of obstacles, > including a conjecture of Serre, (proved by Ken > Ribet) that stood in > the way. At the end > of the talk a member of the audience asked the > question: Does the > result also apply to the > case of unequal exponents? > Posing the question in such a casual manner shows > that the conjecture > is rather obvious. > If anything, whoever posed the question is more > deserving to have the > conjecture named > after him. I wish I could remember who it was. > Fermat used to express some kind of marvelous > demonstration to the case of powers bigger than 2. > Is it written in his statement, that such powers > should be equal ? > There is really something unexpected and common > for equal and not equal powers bigger than 2. > I used to come back to some trivial transformation > and just noticed once overlooked link to proof. > It looks there for very significant simplifications > of this conjecture and why: plotted parameter shows > to be just rational number... > Ro-bin > P.S. Please do not mix me so much with my previous > errors: my properties to square determinants > falls to factorization of X=mk but k=1... > if anybody used to read my previous posts... > I looked at two sources and the conjecture can be read one of two ways: > (1) a^x + b^y = c^z and x,y,z > 2 implies a,b, and c have a common > factor d > 1 > (2) a^x + b^y = c^z and x,y,z > 2 implies (a,b), (a,c), and (b,c) are > not all 1. > Which is correct? I believe these are equivalent. Suppose a,b have a common prime factor. Then this prime divides c^z and hence must divide c also. Similarly for any common factor of a,c or b,c... === Subject: Re: Ball and Urn with Multiple Colors? >Here's a ball and urn question; Suppose I have a single urn, with m >balls, painted x different colors, and there are m_i of each color. >The sum of m_i is of course m. >I choose n balls without replacement- what is the probability of each >combination of colors? Basically, I want a hypergeometric distribution >with more than one category of ball. The trials are no longer >bernoulli, because there's more than 2 colors- they are x-bernoulli, >bernoulli with x different types and the probability of types is given >by the number of balls of each color. >Is there a name for this distrbution tha tI can go look up and read I believe it is sometimes called multivariate hypergeometric. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Fourier Transform to find the answer/or help to my question. I've recently been doing some work on fourier analysis. X-ray patterns. i started with the problem T is my distribution. T=[summation {(on k, k is an element of the intergers)} dirac delta_k] So the graph will look like spikes at every integer. Then i went through a normal procedure to find the fourier transform, And found it to be equal to 2*pi* [summation {(m element of integers)} dirac delta_2*pi*m*i] (spikes with a gap of 2Pi) Im fairly confident that this is all correct. My problem occurs when i increase the dimensions to a 2D space for example take Z to be a 2D lattice spanned by v_1=(1,0), v_2=(0.5,j) so Z={z element of R^2| z=a_1*v_1+a_2+v_2, where a_1,2 element of the integers) I want to find the fourier transform of this distribution T_Z = [summation {(z element of Z)} dirac delta_z] So i thought i would write Z=matrix(B)*any matrix 2x2 so B=[1 0] [ 0.5 h] i then thought it would be easier to find the fourier transform of T_with any 2x2 matrix 2x2 matrix is my test functions by the way. I have no idea how to compute the fourier transform of the distribution T_Z, or even if im heading in the right directions. Any help would be very much appreciated. also if any one can recommend any x-ray/crystal diffraction with fourier analysis books, it would be great === Subject: Re: Why are Asians so good at math? >> Well said. To specifically respond to the false claim: Nobody can pass for >> white, because there are no whites,. >Mankind is a bunch of mutts. >If a small group of African Bushmen were bred with a small bunch of tall >blonde Swedes within 20 generations over 85 percent of the variability >of the human genome would reassert itself. >Bob Kolker This is quite possible, but without mutations, the remainder of the variation would never be seen. It does not take many generations for a breed of dogs to be registered with the appropriate group. There are genes which indicate that there has been little mixing with sub-Saharan Africa for 50,000 years. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Why are Asians so good at math? >HI PPL >DOnt forget the numeric symbols(including zero) which Newton and all other western scientists used were developed in India(Asia) and before that roman symbols were used to do calculations. U can imagine its an herculean task to do a simple calculation with roman symbols. So we gave platform to all. >Westerners were very comman students in Nalanda, Taxila UNiversities in India. And I am talkin in BCs and early ADs guys. >Dont discriminate try to appreciate. Egyptian and Greek decimal calculations were done much as using the Hindu-Arabic system; they did not have a zero symbol, and used different representations for different powers of 10, or multiples of such, but the calculations were much the same, and Roman numerals do not make it that much harder. But even before that, we have the Sumerian-Babylonian system with base 60, using the same symbols, and occasionally using their 0 symbol to indicate power of 60 which did not occur in the representation. This is over 4000 years old, and it is believed that those in India who developed the current system for base 10 adapted the Babylonian base 60. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Why are Asians so good at math? === Subject: Re: Why are Asians so good at math? <0tavv11eno9kd99k9l1v33cqoshneflfun@4ax.com> <6NfMf.1$25.87@news.uchicago.edu> <0001HW.C028C7A40008C05BF0284550@family.alibis.com> <0001HW.C02A687F0003DBC4F0284550@family.alibis.com> <8soa02t27jsh2i1cst49uiss98d7k2m85m@4ax.com> <46lijqFb9r7nU4@individual.net> <79ob021jegr1e2vp1qgg9q2t8e6db29sku@4ax.com> <46ml7qFc165lU5@individual.net> They know how to multiply. Also, they love puns, so are quite happy about it. You know what I recommend to you: Windows, and research. If you're serious about mathematics, you should sit down and read math PDF's for days. Post to usenet, go for it, learn. I might approach it in a slightly different way than I recommend. Maybe Not Windows, and research. I work with UNIX supercomputers, with the mathematics. I'll tell you, there's nothing you can't learn from the Internet. It's not just a bad idea, it's the law! Women are like high performance sports cars, uh, hopefully. Parts, are parts. Truth in advertising. I shall call the null axiom theory A theory. Don't take a gun to a knife fiight. Ross === Subject: Re: Why are Asians so good at math? <43EB0216.8BC3CEA6@yahoo.com> <%Q4Mf.52$45.1821@news.uchicago.edu> if everyone is the same race, racism is moot because the racist cannot tell who is what. === Subject: Re: Why are Asians so good at math? I am a racist, I hate all humans who are racists. :) === Subject: Re: Why are Asians so good at math? I thought white people believed in their devine origin and superiority. Japan was just trying to protect themselves. >> Not even close. You must've forgotten that Germany was involved in WWII. > Historically, Germany was not all that racist. The Japanese believed in > their devine origin and superiority for thousands of years. Another > variant of the Chosen People disease. > Anti-Jewish racism was stoked up after the Germans lost WWI so > disasterously. There were no racial laws operative in Germany prior to > the Nazis, whereas the Japanese required their people to have pedigrees > (literally!). That is still followed to this day as a custom so there > will be no gai jin in the woodpile. > Bob Kolker === Subject: Re: Why are Asians so good at math? ): > I thought white people believed in their devine origin and superiority. Some people thought that. Some people think that. They are not however white, whatever they may think. There are no races -- Love, Jim http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =---- === Subject: Re: Why are Asians so good at math? > I thought white people believed in their devine origin and superiority. > Japan was just trying to protect themselves. The Jap Shinto cult teaches that Japs are descended from a goddess Amaterasu and are superior to all other peoples. The Japs considered westerners barbarian gaijin and incapable of standing up their betters. We showed them otherwise on August 6 and August 9 of 1945. Banzai motherers! Hirohito eats ! Google Bob Kolker === Subject: Re: Why are Asians so good at math? Wasn't Adam and Eve created by God? >> I thought white people believed in their devine origin and >> superiority. Japan was just trying to protect themselves. > The Jap Shinto cult teaches that Japs are descended from a goddess > Amaterasu and are superior to all other peoples. The Japs considered > westerners barbarian gaijin and incapable of standing up their betters. > We showed them otherwise on August 6 and August 9 of 1945. Banzai > motherers! Hirohito eats ! > Google Wasn't Adam and Eve created by God? No. -- Love, Jim http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =---- === Subject: Re: Why are Asians so good at math? Then Adam and Eve truely are Japanese. >>Wasn't Adam and Eve created by God? > No. === Subject: Re: Why are Asians so good at math? >Wasn't Adam and Eve created by God? Whose God? -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: Why are Asians so good at math? > On Wed, 01 Mar 2006 16:51:02 -0800, Zuo Tung >Wasn't Adam and Eve created by God? > Whose God? > -- > Dorothy > There is no sound, no cry in all the world > that can be heard unless someone listens .. > The Outer Limits I think it's weird that people sit around and talk about their God as in their version of God. If God exists, which I believe He does, do you think He runs around changing who He is so He can be their god to every different person who decides the Real God isn't good enough or do you think He's made it clear who He is and He's waiting for those people to drop their god and go to the Real God... whether you believe or not, logically, which do you think is more likely? === Subject: Re: Why are Asians so good at math? <15228248.1141286676645.JavaMail.jakarta@nitrogen.mathforum.org > On Wed, 01 Mar 2006 16:51:02 -0800, Zuo Tung >Wasn't Adam and Eve created by God? > Whose God? > -- > Dorothy > There is no sound, no cry in all the world > that can be heard unless someone listens .. > The Outer Limits > I think it's weird that people sit around and talk about their God as in their version of God. If God exists, which I believe He does, do you think He runs around changing who He is so He can be their god to every different person who decides the Real God isn't good enough or do you think He's made it clear who He is and He's waiting for those people to drop their god and go to the Real God... whether you believe or not, logically, which do you think is more likely? === Subject: Re: Why are Asians so good at math? > Wasn't Adam and Eve created by God? Adam was the (mythological) forerunner of the entire human race. Eve was just a side effect. Bob Kolker === Subject: Re: Why are Asians so good at math? Then Adam and Eve must of been Japs. >> Wasn't Adam and Eve created by God? > Adam was the (mythological) forerunner of the entire human race. Eve was > just a side effect. > Bob Kolker === Subject: Re: Why are Asians so good at math? <%Q4Mf.52$45.1821@news.uchicago.edu> <46lidgFb9r7nU2@individual.net> <46mtp7FbuooqU1@individual.net> <46mtviFbuooqU2@individual.net> the correct prounciation is japanese, speakee englisheee. === Subject: Re: Why are Asians so good at math? I don't think Japan was racist at all. >> Seems to me that many asian societies have been, or remain, racist. >> Certainly the Japanese fall into this category. Although anecdotal, >> I've seen rather violent reactions from people of Chinese extraction >> when they were mistakenly referred to as Korean (or vice-versa). >> Racism is simply overt notice that someone is other. > The War in the Pacific pitted the two most racist nations on earth > against each other. The Japs said very nasty things about gai jin in > general and white folks in particular. The Americans said even nastier > things about the Japs. In American propaganda Japs were demonsized and > portrayed as rats or insects. Just about anything but human. I saw a lot > of this when I was a kid (I was six years old when the Japs attacked > Pearl Harbor). > Bob Kolker === Subject: Re: Why are Asians so good at math? >I don't think Japan was racist at all. Interesting. There are four groups which are traditionally considered as minorities in Japan. They are Korean, Ainu, Ryukyuan, and Burakumin. Zainichi are foreign permanent residents of Japan, most of whom are Korean or Chinese. Japanese law doesn't allow dual citizenship and until the 1980s required adoption of a Japanese name for citizenship. The Ryukyuan are the people of Okinawa. Whether Okinawans are Japanese or not is debated quite intensely throughout Okinawa and recently in Japan. Linguistically, Okinawan is unintelligible to other Japanese but still actually a distant dialect of Japanese. Culturally, Okinawa is much closer to South East Asia and South China reflecting their long history of trade with these regions. The Ainu are considered to be the original inhabitants of Japanese islands. As the Japanese government encouraged immigration of ethnic Japanese to populate Hokkaido, Ainu were increasingly marginalised in their own land. Many establishments in Hokkaido had signs stating Dogs and Ainu not allowed. Burakumin refers to a Japanese social minority group and therefore, is not part of the Japanese ethnic issue. Unlike Indian Dalits, they do not have any distinct cultural heritage. Rather, their status is derived from caste policy introduced in the Tokugawa Shogun era. The system was political and was never as rigid as the Indian caste system. Nevertheless, the Tokugawa Shogun government designated certain workers such as leather workers, certain entertainers or executioners as eta (filth) or hinin (non person) and imposed various restrictions on their life including the clothes they were allowed to wear or areas they were allowed to visit. Unlike nations like the U.S.A. racism in Japanese is not directed so much at people of a particular race or ethnic group but rather those who are non-Japanese. ****************** A total of 38,935 Chinese males between the ages of 11 and 78 were forcibly brought to Japan and made to perform harsh physical labor at mines, construction sites and docks from Kyushu to Hokkaido beginning in April 1943. While the overall death rate was 17.5 percent, at some sites half of all workers perished. Brutality was standard practice and there was little or no pretense of payment of wages. Food, clothing and shelter were provided at or below survival threshold levels. In the Chinese City of Nanking, Japanese soldiers butchered anywhere between 300,000 to 750,000 civilians. Japanese soldiers quickly turned murder and execution of innocent men, women, and children into a game. ************************ http://www.webenglish.com.tw/encyclopedia/en/wikipedia/e/et/ethnic_issues_in _japan.html Racism faced by non-Japanese Asians * Japanese children who are not born in Japan, or whose parents are not 100% Japanese, experience racism from a very young age and can even be subject to beatings or stonings by their peers and adults. One recent example is of a 9 year old boy of 1/4 American heritage whose teacher aggresively pulled his nose while yelling Pinochio, Pinochio until his nose bled. Initially the school refused to confront the issue until the boy's parents became incessantly vocal. The confused child was quoted as asking his parents if he was dirty because he was 1/4 American. * Recently there has been an upsurge in hate-crimes towards Koreans with many buildings being terrorized and even exploded with bombs. This stems from the abduction of Japanese nationals (often as teenagers or young adults) by North Korea in the late 1970s and early 1980s from Japan's western shores. These abductions were long denied by North Korea and often considered a conspiracy theory by observers. Although some abductees have been returned to Japan, many of their families are being held in North Korea as tensions between the two countries persist. (see external links) * There are many Koreans who were imported as slaves during WWII but who never returned to Korea after the war. Some of these people originate in what is now North Korea and openly support North Korea's current government hence their becoming a target for hate-crimes by Japanese people. The upsurges typically coincide with the yearly arrival of a North Korean ferry which docks in the free-port of Niigata for supplies. * Okinawans, despite being of the same background as Japanese, were regarded as non-Japanese prior to WWII. Their islands were later claimed by Japan, occupied by the U.S.A following the war, and have since been returned to Japan. * Prime Ministers and high ranking officials have repeatedly visited Yasukuni Shrine, a burial place for Japan's war dead, including many infamous war criminals such as Hideki Tojo. These visits have been considered troubling and provocative by many Asians, and some Japanese, who are concerned that the visits might indicated rising Japanese nationalism. Racism faced by non-Asians * It is not uncommon to be denied the right to rent a dwelling based on race in parts of Japan and some for-rent notices explicitly state gaijin-dame (???? lit: Foreigners not acceptable). The common reason stated for this policy is that foreigners are associated with being overly loud and more likely to host parties or other disruptive events. * A small minority of hot-springs, especially in areas of Hokkaido frequented by Russian sailors, may deny access to their facilities based on the belief that foreigners are more likely to clean themselves in the bath water rather than washing in a shower prior to entering the bath. Japanese only relax in bath water after washing or rinsing, and do not wish soap or dirt to be present in the water. Most foreigners understand this but some onsens, citing problems in the past, refuse to allow them to prove it. -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: Why are Asians so good at math? If you want to count civilian deaths, let's compare how many were killed in Japan by US bombers. How many innocent civilians were killed or, using your terms, butchered in Nagasaki and Hiroshima compared to the number of innocent civilians killed in Nanking? It is illegal to discriminate against foreign permanent residents of Japan, indigenous peoples, or burakumin. Racism is illegal in Japan. >>I don't think Japan was racist at all. > Interesting. > There are four groups which are traditionally considered as minorities > in Japan. They are Korean, Ainu, Ryukyuan, and Burakumin. > Zainichi are foreign permanent residents of Japan, most of whom are > Korean or Chinese. Japanese law doesn't allow dual citizenship and > until the 1980s required adoption of a Japanese name for citizenship. > The Ryukyuan are the people of Okinawa. Whether Okinawans are > Japanese or not is debated quite intensely throughout Okinawa and > recently in Japan. Linguistically, Okinawan is unintelligible to other > Japanese but still actually a distant dialect of Japanese. Culturally, > Okinawa is much closer to South East Asia and South China > reflecting their long history of trade with these regions. > The Ainu are considered to be the original inhabitants of Japanese > islands. As the Japanese government encouraged immigration of > ethnic Japanese to populate Hokkaido, Ainu were increasingly > marginalised in their own land. Many establishments in Hokkaido > had signs stating Dogs and Ainu not allowed. > Burakumin refers to a Japanese social minority group and > therefore, is not part of the Japanese ethnic issue. Unlike > Indian Dalits, they do not have any distinct cultural heritage. > Rather, their status is derived from caste policy introduced > in the Tokugawa Shogun era. The system was political and > was never as rigid as the Indian caste system. Nevertheless, > the Tokugawa Shogun government designated certain workers > such as leather workers, certain entertainers or executioners > as eta (filth) or hinin (non person) and imposed various > restrictions on their life including the clothes they were allowed > to wear or areas they were allowed to visit. > Unlike nations like the U.S.A. racism in Japanese is not directed > so much at people of a particular race or ethnic group but rather > those who are non-Japanese. > ****************** > A total of 38,935 Chinese males between the ages of 11 and 78 were > forcibly brought to Japan and made to perform harsh physical labor at > mines, construction sites and docks from Kyushu to Hokkaido beginning > in April 1943. While the overall death rate was 17.5 percent, at some > sites half of all workers perished. Brutality was standard practice > and there was little or no pretense of payment of wages. Food, > clothing and shelter were provided at or below survival threshold > levels. > In the Chinese City of Nanking, Japanese soldiers butchered anywhere > between 300,000 to 750,000 civilians. Japanese soldiers quickly turned > murder and execution of innocent men, women, and children into a game. > ************************ > http://www.webenglish.com.tw/encyclopedia/en/wikipedia/e/et/ethnic_issues_in _ japan.html > Racism faced by non-Japanese Asians > * Japanese children who are not born in Japan, or whose parents > are not 100% Japanese, experience racism from a very young age and can > even be subject to beatings or stonings by their peers and adults. One > recent example is of a 9 year old boy of 1/4 American heritage whose > teacher aggresively pulled his nose while yelling Pinochio, Pinochio > until his nose bled. Initially the school refused to confront the > issue until the boy's parents became incessantly vocal. The confused > child was quoted as asking his parents if he was dirty because he > was 1/4 American. > * Recently there has been an upsurge in hate-crimes towards > Koreans with many buildings being terrorized and even exploded with > bombs. This stems from the abduction of Japanese nationals (often as > teenagers or young adults) by North Korea in the late 1970s and early > 1980s from Japan's western shores. These abductions were long denied > by North Korea and often considered a conspiracy theory by observers. > Although some abductees have been returned to Japan, many of their > families are being held in North Korea as tensions between the two > countries persist. (see external links) > * There are many Koreans who were imported as slaves during WWII > but who never returned to Korea after the war. Some of these people > originate in what is now North Korea and openly support North Korea's > current government hence their becoming a target for hate-crimes by > Japanese people. The upsurges typically coincide with the yearly > arrival of a North Korean ferry which docks in the free-port of > Niigata for supplies. > * Okinawans, despite being of the same background as Japanese, > were regarded as non-Japanese prior to WWII. Their islands were later > claimed by Japan, occupied by the U.S.A following the war, and have > since been returned to Japan. > * Prime Ministers and high ranking officials have repeatedly > visited Yasukuni Shrine, a burial place for Japan's war dead, > including many infamous war criminals such as Hideki Tojo. These > visits have been considered troubling and provocative by many Asians, > and some Japanese, who are concerned that the visits might indicated > rising Japanese nationalism. > Racism faced by non-Asians > * It is not uncommon to be denied the right to rent a dwelling > based on race in parts of Japan and some for-rent notices explicitly > state gaijin-dame (???? lit: Foreigners not acceptable). The common > reason stated for this policy is that foreigners are associated with > being overly loud and more likely to host parties or other disruptive > events. > * A small minority of hot-springs, especially in areas of Hokkaido > frequented by Russian sailors, may deny access to their facilities > based on the belief that foreigners are more likely to clean > themselves in the bath water rather than washing in a shower prior to > entering the bath. Japanese only relax in bath water after washing or > rinsing, and do not wish soap or dirt to be present in the water. Most > foreigners understand this but some onsens, citing problems in the > past, refuse to allow them to prove it. > -- > Dorothy > There is no sound, no cry in all the world > that can be heard unless someone listens .. > The Outer Limits === Subject: Re: Why are Asians so good at math? > It is illegal to discriminate against foreign permanent residents of And just how well is that law enforced? > Japan, indigenous peoples, or burakumin. > Racism is illegal in Japan. But nationalism and chauvanism are not. Bob Kolker === Subject: Re: Why are Asians so good at math? > (snip) > Racism is illegal in Japan. Is there any country in the world today, where racism is actually legal? Even in Israel, where Zionists discriminate openly against the Palestinians, you can't say that they are practising racism, because the Jews and the Arabs are of the same race. J. === Subject: Re: Why are Asians so good at math? In Japan, there are laws that state discrimination is illegal. In Israel there are no anti-discrimination laws for Palestinians and Arabs. >>(snip) >>Racism is illegal in Japan. > Is there any country in the world today, where racism is actually legal? Even in Israel, where Zionists discriminate openly against the Palestinians, you can't say that they are practising racism, because the Jews and the Arabs are of the same race. > J. === Subject: Re: Why are Asians so good at math? > In Japan, there are laws that state discrimination is illegal. In > Israel there are no anti-discrimination laws for Palestinians and Arabs. J. === Subject: Re: Why are Asians so good at math? > I don't think Japan was racist at all. You are ignorant of history. Go learn some. Bob Kolker === Subject: Re: Why are Asians so good at math? I have learned Japanese history in China which is true, unlike the history written by the Western world, which is full of lies and missing truths. >> I don't think Japan was racist at all. > You are ignorant of history. Go learn some. > Bob Kolker === Subject: Re: Why are Asians so good at math? > I don't think Japan was racist at all. >> You are ignorant of history. Go learn some. > I have learned Japanese history in China which is true, > unlike the history written by the Western world, > which is full of lies and missing truths. [hanson] ahahahaha.... ahahahaha... ahahaha.... AHAHAHA... Robert, Zuo is not ignorant of history. The poor sod has been brainwashed, at a tender age, like the rest of us, by his local pedagogic environments and thus believes in the data presented to him. You can't blame him for that. We are all exposed to these biases of cultural, natrional & religious inflections. No way out of that. One may eventually become lucky in time and begin to make judgments based on one's own real world experiences, instead of eating the party line and lapping up the notions from the media and books and websites... only to discover that most of the stereotypes, which the goodie-2-shoers so desperately try to do away with, are (un)fortunately largely true..... ahaha.... ahahahaha... AHAHAHAHA... Everybody knows it, but everybody too also brushes the following under the carpet, namely that anytime, in ANY group of humans, when you give to some selected individuals, some power over others there will be some pervert assholes in that ruling group who behave like swine.... be that in ancient Rome, in Nanking, the KZ, in Israeli jails, in Hussein's dungeons, or in Abu Grhaib... or with some of your local cops... or even within a family... ahaha... Prof. Fraunfelder, in Physics 101, started his 1st lecture with: Mankind is a vast herd of swine. And when everybody chuckled, he hollered: ...and you are members thereof!... Don't you ever forget that !... nobody laughed any more. Already 2600 years ago someone warned against this type of institutionalized feed acceptance, when he said: Do not believe simply because you have heard it. Do not believe because it is written in your books. Do not believe in the authority of your teachers and elders. Do not believe in traditions that were handed down for generations. Believe only what you yourself do judge to be true. -- Buddha ahahaha... ahahahanson === Subject: Re: Why are Asians so good at math? I am no more brainwashed than Kolker. >>I don't think Japan was racist at all. >You are ignorant of history. Go learn some. >>I have learned Japanese history in China which is true, >>unlike the history written by the Western world, >>which is full of lies and missing truths. > [hanson] > ahahahaha.... ahahahaha... ahahaha.... AHAHAHA... > Robert, Zuo is not ignorant of history. The poor sod > has been brainwashed, at a tender age, like the rest > of us, by his local pedagogic environments and thus > believes in the data presented to him. You can't blame > him for that. We are all exposed to these biases of > cultural, natrional & religious inflections. No way out of that. > One may eventually become lucky in time and begin to > make judgments based on one's own real world experiences, > instead of eating the party line and lapping up the notions > from the media and books and websites... only to discover > that most of the stereotypes, which the goodie-2-shoers so > desperately try to do away with, are (un)fortunately largely true..... > ahaha.... ahahahaha... AHAHAHAHA... > Everybody knows it, but everybody too also brushes the > following under the carpet, namely that anytime, in ANY > group of humans, when you give to some selected individuals, > some power over others there will be some pervert assholes > in that ruling group who behave like swine.... be that in > ancient Rome, in Nanking, the KZ, in Israeli jails, in Hussein's > dungeons, or in Abu Grhaib... or with some of your local cops... > or even within a family... ahaha... > Prof. Fraunfelder, in Physics 101, started his 1st lecture with: > Mankind is a vast herd of swine. And when everybody > chuckled, he hollered: ...and you are members thereof!... > Don't you ever forget that !... nobody laughed any more. > Already 2600 years ago someone warned against this type > of institutionalized feed acceptance, when he said: > Do not believe simply because you have heard it. > Do not believe because it is written in your books. > Do not believe in the authority of your teachers and elders. > Do not believe in traditions that were handed down for generations. > Believe only what you yourself do judge to be true. -- Buddha > ahahaha... ahahahanson === Subject: Re: Why are Asians so good at math? >I have learned Japanese history in China which is true, unlike the >history written by the Western world, which is full of lies and missing >truths. So you learned about the Rape of Nanking? Do you think that was not motivated in part by racism? -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: Why are Asians so good at math? The Rape of Nanking is a book written by Iris Chang, who wasn't even born during WWII. Her books took historical events and exagerrated them so they would become bestsellers. The misery she caused toward the younger Japanese generation and the guilt of exageration soon paid it's toll, she committed suicide at age 36. Liars often die early. >>I have learned Japanese history in China which is true, unlike the >>history written by the Western world, which is full of lies and missing >>truths. > So you learned about the Rape of Nanking? Do you think that was > not motivated in part by racism? > -- > Dorothy > There is no sound, no cry in all the world > that can be heard unless someone listens .. > The Outer Limits === Subject: Re: Why are Asians so good at math? >The Rape of Nanking is a book written by Iris Chang, who wasn't even >born during WWII. Her books took historical events and exagerrated them >so they would become bestsellers. The misery she caused toward the >younger Japanese generation and the guilt of exageration soon paid it's >toll, she committed suicide at age 36. Liars often die early. And you were born when? -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: Why are Asians so good at math? When has Japan been racist? Nationalistic, but not racist. >>I agree. But why do white people continue racism? > Seems to me that many asian societies have been, or remain, racist. > Certainly the Japanese fall into this category. Although anecdotal, > I've seen rather violent reactions from people of Chinese extraction > when they were mistakenly referred to as Korean (or vice-versa). > Racism is simply overt notice that someone is other. === Subject: Re: Why are Asians so good at math? > When has Japan been racist? Nationalistic, but not racist. The treatment of the Eta (Bonrun) is clear evidence of Jap racism. Their disdain of gaijin is legendary. The treatment of Chinese by the Japs puts them in the top run of racist maniacs. Bob Kolker === Subject: Re: Why are Asians so good at math? The treatment of Eta or Burakumin people in Japan is exagerated in Western society. It is illegal to discriminate against Burakumin in Japan. The treatment of Chinese is also exagerated. My parents are from Shanghai and were not mistreated during the Japanese occupation. >> When has Japan been racist? Nationalistic, but not racist. > The treatment of the Eta (Bonrun) is clear evidence of Jap racism. Their > disdain of gaijin is legendary. The treatment of Chinese by the Japs > puts them in the top run of racist maniacs. > Bob Kolker === Subject: Re: Why are Asians so good at math? > The treatment of Eta or Burakumin people in Japan is exagerated in > Western society. It is illegal to discriminate against Burakumin in Japan. > The treatment of Chinese is also exagerated. My parents are from > Shanghai and were not mistreated during the Japanese occupation. Have them tell you about the Rape of Nanking. Bob Kolker === Subject: Re: Why are Asians so good at math? The Rape of Nanking is fictional. Just like Mai Lai in Vietnam. Just like Thanh Phong in Vietnam. Ask Sen. Bob Kerrey about Thanh Phong. >> The treatment of Eta or Burakumin people in Japan is exagerated in >> Western society. It is illegal to discriminate against Burakumin in >> Japan. >> The treatment of Chinese is also exagerated. My parents are from >> Shanghai and were not mistreated during the Japanese occupation. > Have them tell you about the Rape of Nanking. > Bob Kolker === Subject: Re: Why are Asians so good at math? >The Rape of Nanking is fictional. Just like Mai Lai in Vietnam. Just >like Thanh Phong in Vietnam. Ask Sen. Bob Kerrey about Thanh Phong. So the pictures and records in this book are lies? http://www.tribo.org/nanking/ The Rape of Nanking by James Yin and Shi Young For the second edition of the book, published on December 13, 1997 -- the 60th anniversary of the Rape of Nanking -- the authors carefully reviewed the records of Japanese military units, the puppet municipal government of Nanking established under Japanese occupation, and Chinese and international burial societies. These records conclusively demonstrate that no fewer than 369,366 bodies of Chinese men, women, and children were buried or otherwise disposed of by these agencies. The records leave open the possibility that there were in fact many more victims, but the authors eliminated from their tally any reports that might conceivably have been overlapping or unreliable. Links to pictures. http://www.metroactive.com/papers/metro/12.12.96/cover/china3-9650.html Links to journals and first person accounts http://www.metroactive.com/papers/metro/12.12.96/cover/china2-9650.html -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: Why are Asians so good at math? Yes. Some are propaganda photos. This has been proven by American historical researchers. Even the numbers are in question. Nanking had less than 200,000 people - total population. These books claim up to about. In China we do not teach these types of lies. >>The Rape of Nanking is fictional. Just like Mai Lai in Vietnam. Just >>like Thanh Phong in Vietnam. Ask Sen. Bob Kerrey about Thanh Phong. > So the pictures and records in this book are lies? > http://www.tribo.org/nanking/ > The Rape of Nanking by James Yin and Shi Young > For the second edition of the book, published on December 13, 1997 -- > the 60th anniversary of the Rape of Nanking -- the authors carefully > reviewed the records of Japanese military units, the puppet municipal > government of Nanking established under Japanese occupation, and > Chinese and international burial societies. These records conclusively > demonstrate that no fewer than 369,366 bodies of Chinese men, women, > and children were buried or otherwise disposed of by these agencies. > The records leave open the possibility that there were in fact many > more victims, but the authors eliminated from their tally any reports > that might conceivably have been overlapping or unreliable. > Links to pictures. > http://www.metroactive.com/papers/metro/12.12.96/cover/china3-9650.html > Links to journals and first person accounts > http://www.metroactive.com/papers/metro/12.12.96/cover/china2-9650.html > -- > Dorothy > There is no sound, no cry in all the world > that can be heard unless someone listens .. > The Outer Limits === Subject: Re: Why are Asians so good at math? > Yes. Some are propaganda photos. This has been proven by American > historical researchers. Even the numbers are in question. Nanking had > less than 200,000 people - total population. These books claim up to > about. In China we do not teach these types of lies. Oh. What other types of lies do you teach then? Incidentally, you are not posting from China, but from Berkeley, CA. J. === Subject: Re: Why are Asians so good at math? Are you saying that all concert-level violinists and people who cannot succeed in a marriage are equal to einstein? >>ramanujan had below average intelligence in every subject except for >>his particular brand of math. the man could barely utter a complete >>sentence, and i bet he could not write a decent essay or explain simple >>algebra to a 10th grader. he could not appreciate art. he did not >>play sports. in short, he was a one-trick pony. > Whether he could explain mathematics, he could understand it. > He certainly did not play sports, so? His writings are a > reasonable sample of English mathematical writing. > My son, at age 6, had a strong understanding of logic and > ordinary algebra, but could not explain it to his baby > sitter, who was taking algebra. >>einstein was also a one-trick pony. you take away physics and what >>does einstein know about? art? law? literature? theatre? women? >>clothes? buahahahahaa! > Einstein was an concert-level violinist, even at an early > age. As to what he knew about women, he got married twice. > He had a much better understanding of literature than you > seem to think possible. === Subject: Re: Why are Asians so good at math? >Are you saying that all concert-level violinists and people who cannot >succeed in a marriage are equal to einstein? You are confusing two posts. Humperdinck stated that Einstein was ONLY a physicist. I pointed out that he was also a concert-level violinist and was married twice, to indicate that he was not a one-trick pony. >ramanujan had below average intelligence in every subject except for >his particular brand of math. the man could barely utter a complete >sentence, and i bet he could not write a decent essay or explain simple >algebra to a 10th grader. he could not appreciate art. he did not >play sports. in short, he was a one-trick pony. >> Whether he could explain mathematics, he could understand it. >> He certainly did not play sports, so? His writings are a >> reasonable sample of English mathematical writing. >> My son, at age 6, had a strong understanding of logic and >> ordinary algebra, but could not explain it to his baby >> sitter, who was taking algebra. >einstein was also a one-trick pony. you take away physics and what >does einstein know about? art? law? literature? theatre? women? >clothes? buahahahahaa! >> Einstein was an concert-level violinist, even at an early >> age. As to what he knew about women, he got married twice. >> He had a much better understanding of literature than you >> seem to think possible. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Why are Asians so good at math? One trick or two tricks, he was an idiot savant. >>Are you saying that all concert-level violinists and people who cannot >>succeed in a marriage are equal to einstein? > You are confusing two posts. Humperdinck stated that > Einstein was ONLY a physicist. I pointed out that he > was also a concert-level violinist and was married twice, > to indicate that he was not a one-trick pony. >>ramanujan had below average intelligence in every subject except for >>his particular brand of math. the man could barely utter a complete >>sentence, and i bet he could not write a decent essay or explain simple >>algebra to a 10th grader. he could not appreciate art. he did not >>play sports. in short, he was a one-trick pony. >Whether he could explain mathematics, he could understand it. >He certainly did not play sports, so? His writings are a >reasonable sample of English mathematical writing. >My son, at age 6, had a strong understanding of logic and >ordinary algebra, but could not explain it to his baby >sitter, who was taking algebra. >>einstein was also a one-trick pony. you take away physics and what >>does einstein know about? art? law? literature? theatre? women? >>clothes? buahahahahaa! >Einstein was an concert-level violinist, even at an early >age. As to what he knew about women, he got married twice. >He had a much better understanding of literature than you >seem to think possible. === Subject: Re: Why are Asians so good at math? so if a person isn't interested in science and math, they are not as intelligent as Einstein? What are you trying to say? > On Tue, 28 Feb 2006 20:52:15 +0800, Jim Walsh >On Mon, 27 Feb 2006 15:13:40 +0800, Jim Walsh >>In 1894 Einstein's family moved to Milan but Einstein remained in Munich. >>In >>1895 Einstein failed an examination that would have allowed him to study >>for >>a diploma as an electrical engineer at the Eidgen.9assische Technische >>Hochschule in Zu..... >Because he did not study the material that was covered on the exam. >>I see we totally agree that Einstein had troubles in school. > His grades were not poor, however, even in subjects he was not > really interested in. He got average grades in those and high marks > in math and science. > -- > Dorothy > There is no sound, no cry in all the world > that can be heard unless someone listens .. > The Outer Limits === Subject: Re: Why are Asians so good at math? Considering the numbers of people who people in such stuff, 90% have become zombies already.... >>They are all true. Racism, God and Ghosts all exist in the minds of people. > Are you proposing that we should be human beings without minds of our own? Zombies? > J. === Subject: CP^n, CW-complex structure help. I am having trouble with understanding some final important details about the construction of the CW-structure of CP^n. Let f : D^(2n) ------> CP^n be the map (z_1, ..., z_n) |----> [ z_1, ..., z_n, ( 1 - |z|^2 )^(1/2) ] where [ ] represents class in CP^n, and |z| denotes the norm of (z_1, ..., z_n). Also I am looking at D^(2n) as sitting in C^n. Denote the boundary of D^(2n) by bd(D^(2n)). Then, f maps bd(D^(2n)) to elements whose last entry is 0. In fact, since every element of CP^(n-1) can be represented by an element whose norm is 1, it is true that bd(D^(2n)) maps (via f) ONTO an isomorphic copy of CP^(n-1) sitting in CP^n. Thus, f factors through the space CP^(n-1) /_g D^(2n), where g denotes the restriction of f to bd(D^(2n)). (so bd(D^(2n)) gets identified with CP^(n-1) in CP^(n-1) /_g D^(2n)). Now the claim is that f maps D^(2n) - bd(D^(2n)) homeomorphically to CP^n - CP^(n-1), that is, homeomorphically to the classes of CP^n whose last entry is non-zero. I have been trying and trying to understand this claim, but to no avail. All I really want to see is bijectivity, in particular surjectivity. Please please assist me and if you could provide as much detail as you can, I would highly appreciate it. James === Subject: 2006 International Conference on Complex Systems I thought you all may be interested in this event, scheduled for June 2006. INTERNATIONAL CONFERENCE ON COMPLEX SYSTEMS (ICCS) Further Information: http://www.necsi.org/events/iccs6/ This conference has two major aims: first, to investigate those properties or characteristics that appear to be common to the very different complex systems now under study; and second, to encourage cross fertilization among the many disciplines involved. Topics to be addressed include: * Networks & Structural Themes * Systems biology * Socio-economic systems * Engineering systems * Evolution and Ecology / Population change * Nonlinear dynamics and Pattern formation * Physical systems, Quantum and Classical * Learning / Neural, Psychological and Psycho-Social Systems * Concepts, Formalisms, Methods and Tools * Analysis and Expression in the Arts and Humanities Early Registration by: March 15, 2006 Registration by: To be announced Paper submission by: May 12, 2006 Conference: June 25-30, 2006 Marriott Boston Quincy, Boston, MA, USA June 25-30, 2006 === Subject: Re: JSH: Oh, forgot, remember Decker? >>7(A'(x) + 1)(B'(x) + 1) = (A(x) + 7)(B(x) + 1) >>and by the distributive property >>A(x) = 7A'(x) and B'(x) = B(x). > -------------- > I'm reasonably new to this discussion so maybe I'm missing an > assumption here about these functions... but that line does not appear > to follow, at all, from the distributive property. Hah. That's because you don't understand the distributive property the way JSH understands it. === Subject: Re: JSH: Oh, forgot, remember Decker? > Hah. That's because you don't understand the distributive property the > way JSH understands it. To be fair, he's hardly alone in that respect. === Subject: Re: JSH: Oh, forgot, remember Decker? <46othdFc4mvlU1@individual.net > Hah. That's because you don't understand the distributive property the > way JSH understands it. > To be fair, he's hardly alone in that respect. But you can understand it the way he does ... Just hit yourself in the head repeatedly with a Malleus Jamesharrisum (which looks a lot like a common hammer). --- Christopher Heckman === Subject: Re: JSH: Oh, forgot, remember Decker? >Hah. That's because you don't understand the distributive property the >way JSH understands it. >>To be fair, he's hardly alone in that respect. > But you can understand it the way he does ... Just hit yourself in the > head repeatedly with a Malleus Jamesharrisum (which looks a lot like a > common hammer). Sorry: I'm saving myself for Maxwell's Silver Hammer. === Subject: Re: Example to show a limitation of the Runge-Kutta Method That Hubbard-West example and similar ones showing spurious RK asymptotic behavior are studied in detail in the following UWO thesis: http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq28470.pdf cf pages 22ff. === Subject: Re: Example to show a limitation of the Runge-Kutta Method >The Runge-Kutta Method of order 4 (RK4) can determine a numerical >approximation of the solution of an ODE, y(t), on a closed interval >[a,b]. I am looking for an example of a ODE such that the solution >provided by RK4 seem to stabilize as t approaches b, although the exact >solution diverge as t tends to infinity. Huh? You said t is on the closed interval [a,b], what's it doing tending to infinity? Do you mean the exact solution goes to infinity as t -> b? One of my favourite examples, but maybe not what you want, is dy/dt = 1 - 4 y^2, y(0) = 0 where RK4 with step size 1 shows a spurious constant solution y = 0, while the correct solution has y -> 1/2 as t -> infinity. > In short, I am looking for an >example to illustrate that the RK4 is unable to show that there is a >steady state as t tends to infinity. Huh? You just said the exact solution diverges as t tends to infinity, while RK4's solution seems to stabilize as t approaches b . Please tell us exactly what you're looking for. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Example to show a limitation of the Runge-Kutta Method The Runge-Kutta Method of order 4 (RK4) can determine a numerical >>approximation of the solution of an ODE, y(t), on a closed interval >>[a,b]. I am looking for an example of a ODE such that the solution >>provided by RK4 seem to stabilize as t approaches b, although the exact >>solution diverge as t tends to infinity. > Huh? You said t is on the closed interval [a,b], what's it doing tending > to infinity? Do you mean the exact solution goes to infinity as t -> b? > One of my favourite examples, but maybe not what you want, is > dy/dt = 1 - 4 y^2, y(0) = 0 > where RK4 with step size 1 shows a spurious constant solution > y = 0, while the correct solution has y -> 1/2 as t -> infinity. >> In short, I am looking for an >>example to illustrate that the RK4 is unable to show that there is a >>steady state as t tends to infinity. > Huh? You just said the exact solution diverges as t tends to infinity, > while RK4's solution seems to stabilize as t approaches b . > Please tell us exactly what you're looking for. wants to show that the solution of a ODE tends to a certain constant and that one wants to use RK4 for that purpose. What I want to illustrate with an example is that the stated procedure is not safe in the sense that one may get a solution from RK4 which looks like stabilizing as t tends to b, i.e., the curve of the RK4's solution looks like approximately flat near b, but notwithstanding if one is able to find the exact solution of the ODE, one can see that the exact solution diverges at infinity. In short, as Carlos poses the point, I want to show that RK4 is not reliable to determine the long term behavior of the solution of a ODE. Clearer now? Paul === Subject: Re: Example to show a limitation of the Runge-Kutta Method >The Runge-Kutta Method of order 4 (RK4) can determine a numerical >>approximation of the solution of an ODE, y(t), on a closed interval >>[a,b]. I am looking for an example of a ODE such that the solution >>provided by RK4 seem to stabilize as t approaches b, although the exact >>solution diverge as t tends to infinity. > Huh? You said t is on the closed interval [a,b], what's it doing tending > to infinity? Do you mean the exact solution goes to infinity as t -> b? > One of my favourite examples, but maybe not what you want, is > dy/dt = 1 - 4 y^2, y(0) = 0 > where RK4 with step size 1 shows a spurious constant solution > y = 0, while the correct solution has y -> 1/2 as t -> infinity. >> In short, I am looking for an >>example to illustrate that the RK4 is unable to show that there is a >>steady state as t tends to infinity. > Huh? You just said the exact solution diverges as t tends to infinity, > while RK4's solution seems to stabilize as t approaches b . > Please tell us exactly what you're looking for. > wants to show that the solution of a ODE tends to a certain constant > and that one wants to use RK4 for that purpose. What I want to > illustrate with an example is that the stated procedure is not safe in > the sense that one may get a solution from RK4 which looks like > stabilizing as t tends to b, i.e., the curve of the RK4's solution > looks like approximately flat near b, but notwithstanding if one is > able to find the exact solution of the ODE, one can see that the exact > solution diverges at infinity. In short, as Carlos poses the point, I > want to show that RK4 is not reliable to determine the long term > behavior of the solution of a ODE. Clearer now? Is your ODE supposed to be autonomous? Otherwise, why would one ever conclude something about the behaviour as t -> infinity from the fact that the solution is approximately flat near b? Anyway, if you're happy with the example Carlos quoted, I won't pursue the point. Note, however, that in this example the exact solution blows up at a finite t. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Example to show a limitation of the Runge-Kutta Method ever conclude something about the behaviour as t -> infinity from the > fact that the solution is approximately flat near b? My ODE has the form y'(t)=f(y(t)). I am aware of the fact that RK4 gives an approximation of the solution on an interval [a,b] and that, from a purely logical point of view, one cannot extrapolate the conclusion that the exact solution stabilizes when t-> infinity even if it is apparently flat near b, but I do want to show it with an example. Carlos's quoted example has not the form of my ODE. Perhaps, I can show the point by choosing an interval [a,b] with b small enough to produce the illusion that the RK4's solution seems to stabilize near b, but it would be funny if one could find an example with an exact solution that only blows up at infinity (not sure whether only blows up at infinity makes sense). With such an example the illusion of stability would be produced for whatever interval [a,b] considered. Paul === Subject: Re: Example to show a limitation of the Runge-Kutta Method Is your ODE supposed to be autonomous? Otherwise, why would one > ever conclude something about the behaviour as t -> infinity from the > fact that the solution is approximately flat near b? > My ODE has the form y'(t)=f(y(t)). OK, that's called autonomous. > I am aware of the fact that RK4 gives an approximation of the solution > on an interval [a,b] and that, from a purely logical point of view, one > cannot extrapolate the conclusion that the exact solution stabilizes > when t-> infinity even if it is apparently flat near b, but I do want > to show it with an example. Carlos's quoted example has not the form of > my ODE. Perhaps, I can show the point by choosing an interval [a,b] > with b small enough to produce the illusion that the RK4's solution > seems to stabilize near b, but it would be funny if one could find an > example with an exact solution that only blows up at infinity (not sure > whether only blows up at infinity makes sense). With such an example > the illusion of stability would be produced for whatever interval [a,b] > considered. Well, my example y' = 1 - 4 y^2, y(0) = 0 may be pretty close, in that it appears to have a stationary solution at y = 0 but the true stationary solutions are y = 1/2 and y = -1/2. In this case the spurious solution is unstable (i.e. if you used an initial value near 0 but not exactly 0 the RK4 solution would move away from 0), but examples can be given where it would be stable, e.g. y' = 1 + 2 y - 8 y^2 - 2 y^3 + 4 y^4, where the RK4 solution (with step size 1) approaches 0 if the initial value |y(0)| < 0.005. Note that if f is continuous and the exact solution to y' = f(y), y(0) = 0 goes to +infinity, either as t -> +infinity or t -> b- where b > 0, then we must have f(y) > 0 for all y > 0. But in that case it's not hard to show that the RK4 approximate solution must also go to +infinity as t -> +infinity. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Is Complex Set isomorphic to Modular Group? Modular Group can be represented by 2*2 matrices; ((a,b),(c,d)) with; ad-bc=1. Where a,b,c,d are integers. Note that Stern-Brocot Tree has the same condition. The matrix format is obviously polarised, i.e. each element knows where it sits. But the symmetry suggests an unpolarised form. Consider the sequence; {} [] 0 {,{}} [,[]], [[],] -1, +1 {,{,{}}} [,[,[]]], [,[[],]], [[,[]],], [[[],],] -1, +1, -i, +i Note that this sequence has a 1-step memory (OSM) aspect due to iterating on the previous step. OSM can be seen in; ad-bc=1 since this condition vertically ties a rational node to the next, thus defining a fully-addressed binary tree. OSM is in MSet; x(n+1) = x(n)^2+c since (n+1)st step remembers (n)th step. I suggested HFractal and MSet relationship in a previous posting. OSM is in Schrodinger's Equation; (d/dt)W(x,t) = (-iH/h)W(x,t) -i represents a delay of pi/2 since; -i = exp(-i*pi/2) OSM is the temporal aspect of the iteration. The sequence above has two aspects; temporal (TA) and spatial (SA). TA expands the tree and gives it a direction. SA is realised explicitely after polarisation. TA defines a HFractal while the SA defines a coordinate system. TA is like algebra while SA is like geometry. Newton's third law reiterated; For every action, there is an equal and opposite reaction, and subsequent lateral ones for each. H2 seems to be isomorphic to our universe. === Subject: Re: Is Complex Set isomorphic to Modular Group? > Modular Group can be represented by 2*2 matrices; > ((a,b),(c,d)) > with; > ad-bc=1. > Where a,b,c,d are integers. Okay, but the matrices ((a,b),(c,d)) and ((-a,-b),(-c,-d)) are regarded as identical in the modular group. More precisely, the modular group is the quotient of SL2(Z) by the subgroup {1,-1}. That is not isomorphic to the multiplicative group of nonzero Gaussian integers (e.g. because the latter is commutative). But if we map x+iy to ((x,y),(-y,x)) the mapping is injective and preserves the laws of addition and multiplication. The extra condition that the matrix is unimodular: ad-bc=1 (i.e. xx+yy=1) would now mean that the matrix is the image of a complex number on the unit circle. LH === Subject: Re: partial derivative > Of course some books are sloppy about this, and expect you > to answer the second question although the way they > phrase the problem sounds like they're asking the > first question... OK. Here is an example from my textbook: find partial_z/partial_u and partial_z/partial_v of: z = x*e^y x = ln(u) y = v It has some answer for those that is not 0. Is my textbook wrong here? If not, what am I missing? === Subject: Re: partial derivative Of course some books are sloppy about this, and expect you > to answer the second question although the way they > phrase the problem sounds like they're asking the > first question... > OK. Here is an example from my textbook: > find partial_z/partial_u and partial_z/partial_v of: > z = x*e^y > x = ln(u) > y = v > It has some answer for those that is not 0. Is my textbook wrong here? If > not, what am I missing? To use Ull's term, this is clearly an example of the second question, and indeed the partials are not zero. Of course here, there are no explicit (i.e. no formal) function definitions. All we know -- implicitly, from the question -- is that u and v are independent variables and that z depends on them as defined implicitly by the three simultaneous equations. IOW we have z = g(u,v) for some g consistent with the three equations. Sure, there could be a function f such that z = f(u,v,x,y) and all four variables are independent, but since nobody has defined such a function here, we're not interested in it. (*If* someone had defined this f, and *if* you were asked to find df/du etc. instead of dz/du, then it would be an example of what Ull called the first question. But frankly, even then that would be a bit silly; in a way I guess you are supposed to assume that the problem as stated is not silly, especially since you're given no particular reason to think that it is!) Anyhow, if you just rewrite the first equation as z = ln(u)e^v you'll see that you haven't changed its meaning, and in that form it's clear enough how to get the partials wrt u and v. Explicit use of the chain rule of course would give the same results. === Subject: Re: partial derivative Of course some books are sloppy about this, and expect you > to answer the second question although the way they > phrase the problem sounds like they're asking the > first question... > OK. Here is an example from my textbook: > find partial_z/partial_u and partial_z/partial_v of: > z = x*e^y > x = ln(u) > y = v > It has some answer for those that is not 0. Is my textbook wrong here? If > not, what am I missing? > To use Ull's term, this is clearly an example of the second > question, and indeed the partials are not zero. A better way to put it is simply that there's no reason at all here to assume that x and y are to be considered as independent variables. And plenty of reason to assume that they are *not*. Putting it that way makes my whole explanation a lot shorter, and more importantly it avoids any hint of putting my own inexpert words into David Ull's mouth. === Subject: pseudonorm confusion This is a problem from Royden -- Chapter 10, problem 10. I'm utterly confused about the problem itself and also what it's asking me to solve in particular. It's very long: (Here let == mean is equivalent to -- I can't make the normal symbol) A nonnegative real valued functin || || defined on a vector space X is called a pseudonorm if ||x+y|| <= ||x|| + ||y|| and ||ax|| = |a|*||x||. Show that the relation x == y defined by ||x-y|| = 0 is an equivalence relation compatible with addition and multiplication by scalars and that if x==y, then ||x||=||y||. Let X' be the set of equivalence classes of X under ==. Then X' becomes a normed vector space if we define ax'+by' as the unique equivalence class which contains ax+by for x in x' and y in y' and define ||x'|| = ||x|| for x in x'. The mapping f of X onto X' that takes each element of X into the equivalence class to which it belongs is a homomorphism (called the natural homomorphism) of X onto X. What is the kernel of f? Illustrate this procedure iwth the L^p spaces on [0,1]. James === Subject: Re: pseudonorm confusion > This is a problem from Royden -- Chapter 10, problem 10. I'm utterly > confused about the problem itself and also what it's asking me to solve > in particular. It's very long: > (Here let == mean is equivalent to -- I can't make the normal > symbol) > A nonnegative real valued functin || || defined on a vector space X is > called a pseudonorm if ||x+y|| <= ||x|| + ||y|| and ||ax|| = |a|*||x||. > Show that the relation x == y defined by ||x-y|| = 0 is an equivalence > relation compatible with addition and multiplication by scalars and > that if x==y, then ||x||=||y||. Let X' be the set of equivalence > classes of X under ==. Then X' becomes a normed vector space if we > define ax'+by' as the unique equivalence class which contains ax+by for > x in x' and y in y' and define ||x'|| = ||x|| for x in x'. The mapping > f of X onto X' that takes each element of X into the equivalence class > to which it belongs is a homomorphism (called the natural homomorphism) > of X onto X. What is the kernel of f? Illustrate this procedure iwth > the L^p spaces on [0,1]. Do the L^p case first. Let X = {measurable functions f : [0,1] -> R with int_[0,1] |f|^p < oo}. What do you think X' is in this case? === Subject: pseudonorm confusion This is a problem from Royden -- Chapter 10, problem 10. I'm utterly confused about the problem itself and also what it's asking me to solve in particular. It's very long: (Here let == mean is equivalent to -- I can't make the normal symbol) A nonnegative real valued functin || || defined on a vector space X is called a pseudonorm if ||x+y|| <= ||x|| + ||y|| and ||ax|| = |a|*||x||. Show that the relation x == y defined by ||x-y|| = 0 is an equivalence relation compatible with addition and multiplication by scalars and that if x==y, then ||x||=||y||. Let X' be the set of equivalence classes of X under ==. Then X' becomes a normed vector space if we define ax'+by' as the unique equivalence class which contains ax+by for x in x' and y in y' and define ||x'|| = ||x|| for x in x'. The mapping f of X onto X' that takes each element of X into the equivalence class to which it belongs is a homomorphism (called the natural homomorphism) of X onto X. What is the kernel of f? Illustrate this procedure iwth the L^p spaces on [0,1]. James === Subject: Re: JSH: Their tactics > Now that I have an even simpler proof that I am right, where I can... I would suggest contacting the mass media, e.g. major news papers, network/cable news, news hows (20/20, 60 minutes, etc.). The mathematics community conspiring againsts an outsider to block from the world one or more major discoveries is certainly newsworthy. I am gambling the journalism industry would be much more open to the truth. === Subject: Re: JSH: Their tactics > Your system is broken. I can tell you what's broken, Harris. You are. > Consider, my research proves that Andrew Wiles did not prove Fermat's > Last Theorem. The difference between a liar and a pathological liar is that a pathological liar says things that no one COULD believe for an instant. You do that every day. === Subject: Re: JSH: Their tactics >[...] >Remember, I have already contacted top mathematicians like Barry Mazur >and Andrew Granville. Why don't you ever tell us what they _said_ when you contacted them? A more interesting question would be this: How many emails were exchanged in each case before they simply stopped replying? What? I'm aware of the fact that at some point they simply stopped replying to your emails? No, I haven't been in contact with them, and no, I don't have psychic powers. >[...] >Consider, my research proves that Andrew Wiles did not prove Fermat's >Last Theorem. What? Don't know how I could remember this, since this is the first time I've heard you make this claim. >But do you think he'll come out and admit that? If it were true that there was an error in the proof then yes he _would_ come out and admit it. How do I know? Because there _was_ an error in the first version of the proof, and he didn't try to hide it (as though that would be possible). Nor, curiously, did he start making posts on the internet explaining that the world would end if people didn't agree he was right. >Would you if you were in his position? (Not saying I'm certain he >knows, but it wouldn't surprise me by now if he did know.) >If you were him and you found out, would you tell the truth? >I do seem to remember hearing that he and Barry Mazur were close >colleagues. >What if he's known for years now? >James Harris ************************ David C. Ull === Subject: Re: JSH: Their tactics <1lmd02di7d5k93d4tdmdt7kcj7sj93gbeb@4ax.com >[...] >Remember, I have already contacted top mathematicians like Barry Mazur >and Andrew Granville. > Why don't you ever tell us what they _said_ when you contacted > them? > A more interesting question would be this: How many emails > were exchanged in each case before they simply stopped replying? > What? I'm aware of the fact that at some point they simply > stopped replying to your emails? No, I haven't been in contact > with them, and no, I don't have psychic powers. >[...] >Consider, my research proves that Andrew Wiles did not prove Fermat's >Last Theorem. > What? Don't know how I could remember this, since this is the > first time I've heard you make this claim. Don't you remember all that cun hoc, ergo propter hoc nonsense? About a year and a half ago. >But do you think he'll come out and admit that? > If it were true that there was an error in the proof then > yes he _would_ come out and admit it. > How do I know? Because there _was_ an error in the first > version of the proof, and he didn't try to hide it (as > though that would be possible). Nor, curiously, did he > start making posts on the internet explaining that the > world would end if people didn't agree he was right. >Would you if you were in his position? (Not saying I'm certain he >knows, but it wouldn't surprise me by now if he did know.) >If you were him and you found out, would you tell the truth? >I do seem to remember hearing that he and Barry Mazur were close >colleagues. >What if he's known for years now? >James Harris > ************************ > David C. Ull === Subject: Google's ad: first 10-digit prime found in consecutive digits e i know that many of you are familiar with this problem. Could you please explain the problem to me, and show me how they solved it? The way that I interpret the problem is this: Give me the 10-digit prime number, which appears in the number 'e' (=~2.718281828459045...). My logic is that the answer should be the *FIRST* and smallest 10-digit prime. since e goes out to infinity places, *ANY* combination of numbers should be there at some point...including the digits of pi! The answer, btw, is 7427466391. === Subject: Re: Google's ad: first 10-digit prime found in consecutive digits e >My logic is that the answer should be the *FIRST* and smallest 10-digit >prime. since e goes out to infinity places, *ANY* combination of >numbers should be there at some point...including the digits of pi! Obviously they meant the first one you'd find by looking in e sequentially. Even if they didn't, it isn't known whether e is normal in any base. If it's normal in base 10^10, it would have to contain the lowest 10-digit prime, which is 1000000007. >The answer, btw, is 7427466391. --Keith Lewis klewis {at} mitre.org The above may not (yet) represent the opinions of my employer. === Subject: Re: Google's ad: first 10-digit prime found in consecutive digits e > i know that many of you are familiar with this problem. Could you > please explain the problem to me, Group digits of the base-10 expansion of e into groups of 10 digits. Interpret that as a number. What is the first position in the expansion where this 10-digit number is prime? > and show me how they solved it? Look at digits 1-10 of e. Is it prime? If no, look at digits 2-11 of e. Is it prime? If no, look at digits 3-12 of e. Is it prime? etc. > The answer, btw, is 7427466391. I used Matlab's variable precision arithmetic to give me some modest number of digits of e, like 1000. I then went through that sequence in order, doing a prime test, until it passed. I don't recall where the above sequence occurs in e, but it was within that modest chunk somewhere. - Randy === Subject: Re: Google's ad: first 10-digit prime found in consecutive digits e > since e goes out to infinity places, *ANY* combination > of numbers should be there at some point...including > the digits of pi! The decimal expansion of one third, 1/3, goes out to infinitely many places, and yet it doesn't even contain the single digit 5, let alone any combination of numbers. Also, the only way a decimal expansion can contain all the digits of pi (in order) is if we're talking about a finite decimal expansion followed by the decimal digits of pi, in other words, a rational number (of a certain special type) plus pi. Dave L. Renfro === Subject: Re: Google's ad: first 10-digit prime found in consecutive digits e >> since e goes out to infinity places, *ANY* combination >> of numbers should be there at some point...including >> the digits of pi! > The decimal expansion of one third, 1/3, goes out to > infinitely many places, and yet it doesn't even contain > the single digit 5, let alone any combination of numbers. > Also, the only way a decimal expansion can contain all > the digits of pi (in order) is if we're talking about a > finite decimal expansion followed by the decimal digits > of pi, in other words, a rational number (of a certain > special type) plus pi. Looking back over this, I'm not sure my very last remark is correct. For example, 0.01001010010100101 ... plus 0.09009090090900909 .. equals 0.1001010010100101 ... Although these are rational numbers (each of their decimal expansions have a period of 5), this example tells me that my conclusion a rational number (of a certain special type) plus pi is not as obvious as I had thought it to be. (It may still be true for all I know. For that matter, it might be obvious as well, but it's not obvious in the way that I was thinking it was obvious.) Dave L. Renfro === Subject: Father of ISS Publishes Structure of the Atomic Nucleus! GlobalC << Global Consciousness >> Thursday, February 23, 2006 World BlueStar Awakes With (ElectroDynamic) Start! press release for all peoples of the world ... birth of Electrodynamic Blue Star, Global Consciousness! the overarching COMPLETENESS of the global corporate media banking *gag-sputte*r chem-dissolution State -- gives witness, birth, to our aggregate voluntaryist awakening-planetwide world heart/mind/body collectivity. the Blue Star, world consciousness, integrity, knowing-ness, sensitivity, gentility ... nurturing respect! MT ~~~~~~ ~~~~~~~~~ Re: Gentlest Awakening For Our Divine World Family! ~~ ~~~ for your Wire Service! this is the 'release' on the Nuclear Structure publication! for a WORLD in collaboration ... we just sent this announcement to the BBC, with a special sharing Climate 'Hottest for Millennium' with a world ready for simple, caring, truths. the BBC interviewed me live from New Zealand -- years ago -- and now we are back in California, my wife Megumi and I. then the news was my X49 Scramjet spaceplane design, for which we were conducting preliminary tests in New Zealand, and had distributed the business plan for. now the news is my publication of the Structure of the Atomic Nucleus -- putting an end to a hundred years of disinfo & fear-tactics by the 20th century corporate consumer state. putting an end to that ignorance-based media programming of conflict and combat focused around the nuclear industry commitment to nuclear fission energy and arsenals. as your science education will tell you, the global nuclear fission industry is deadly -- and is based on the forceful breaking of large and radioactive nuclei (heavy atomic elements) and the neutrons, etc.) and further radioactive decay products. fusion, CREATION of the smallest, healthiest, elements of the periodic table is not only a natural and organic process -- but also can produce a hundred times more energy for a whole collaborative world, a hundred times more energy and safety than deadly atomic nuclear fission. fusion, not fission. creation, not violence. to repeat, I have now published the Electrodynamic Structure of the Atomic Nucleus ... for ANY scientist, engineer, student, journalist or other to download, discuss and understand, WORLDWIDE. entitled NucleonSong, it can be downloaded or discussed at: http://groups.yahoo.com/group/NuclearStructure/ or from a few dozen other groups and locations orbiting in cyberspace. http://groups.yahoo.com/group/StarShipChina/ http://groups.yahoo.com/group/Nuclear-Physics/ http://groups.yahoo.com/group/NaturalPhilosopHER/ for three examples. yes, the paper includes the electrodynamic structures of the helium, lithium, berylium, boron, carbon, nitrogen & oxygen nucleon groups (nuclei). i.e., it reveals a new paradigm in our world -- the realm of creation, not destruction. nature, and the light elements of the periodic table, are all assembled in nurturing healthy processes ... setting an example for global humanity in the era of the arrival of the soon-to-be well-articulated Blue Star ... Manido, Maitreya, Messiah, Maschiak, Madi. and of course, I can email you it as a 2.4 Meg PDF file. for all our sacred relations, Millennium Twain father of the US/International Space Station Program, Who's Who in the Frontiers of Science & Technology, designer of the X49 Scramjet 'Electra' Spaceplane, publisher of The Undiscovered Physics organic, green, vegan, car-free ... refining ... http:/unamity.com cc: Ian Wishart, Investigate Magazine .. . === Subject: Re: JSH: Functions and the distributive property > So posters have been acting as if it's really complicated how the > distributive property works--if you have functions. > they are playing on the belief that functions are these powerful and > uncontrollable mystical entities which have super-duper-mathematical > powers! > That's bogus. > It IS easy to understand the mathematics, even with the distributive > property and functions. > Consider > a(b+c) = ab + ac > is the distributive property, where the math doesn't care if you use > functions: True. The distributive property holds for functions. No-one disputed this. However, you assumed that a factorization of a certain form into algebraic-integer-valued functions exists. That's what's being disputed. === Subject: Re: JSH: Functions and the distributive property > When f(x) equals 0, you just have > a(0 + b) = a(0) + ab > so you can see what b is You can see what b is when f(x) equals 0. I agree. The problem is, what happens when f(x) doesn't equal 0? In this trivial equation, above, if we assume b is constant, then we can find it by setting x such that f(x) becomes 0 (assuming that f(x) ever becomes 0)... but that logic does not apply if b is not constant, and is instead a function in x. In fact, all you are doing is solving for b(x) at the point x, when f(x) equals 0. That is not the same as the function b(x). === Subject: Re: JSH: Functions and the distributive property > So posters have been acting as if it's really complicated how the > distributive property works--if you have functions. No, it's not complicated how the distributive property works. What posters have been saying is that your conclusion does not follow from the distributive property, and there are now many examples out there of things which violate your theorem. They aren't mysterious. > as > they are playing on the belief that functions are these powerful and > uncontrollable mystical entities which have super-duper-mathematical > powers! No, they are simply illustrations that 7(A'(x) + 1)(B'(x) + 1) = (A'(x) + 7)(B(x) + 1) Does not imply A(x) = 7A'(x), B'(x) = B(x). > It IS easy to understand the mathematics, even with the distributive > property and functions. > Consider > a(b+c) = ab + ac > is the distributive property, where the math doesn't care if you use > functions: > a(f(x) + b) = a f(x) + ab Yes, yes. This is why it is valid to conclude that 7(A'(x)+1) = 7A'(x) + 7 That much is the distributive property. The remainder: A'(x) = 7A(x), B'(x) = B(x) is NOT the distributive property and is not in general true. > When f(x) equals 0, you just have > a(0 + b) = a(0) + ab > so you can see what b is, and now you can see how things are going, > even with functions. Yes, if it were required that 7A'(x) + 7 = A(x) + 7, then it would also be required that A(x) = 7A'(x). However requiring the two products (7A'(x) + 7)(B'(x) +1) = (A(x)+7)(B(x)+1) does not require that the two first terms be equal for all x, or that the two second terms be equal for all x. There is no theorem or axiom that requires that to be true and there are many counterexamples. There are infinitely many ways to make these two products equal for all x, even with A(0) = B(0) = A'(0) = B'(0) = 0, but not with A(x) = 7A'(x), B(x) = B'(x). This is of course an old tactic with you. You have a short argument. The first couple of lines are trivial, and everybody agrees. Then you make an unjustified leap and when people call you on it, you pretend the problem is with the first couple of lines. Here's the part which is not true: (7A'(x) + 7)(B'(x) +1) = (A(x)+7)(B(x)+1) DOES NOT IMPLY 7A'(x) + 7 = A(x) + 7 B'(x) + 1 = B(x) + 1 OK? More simply: f(x)*g(x) = r(x)*s(x) does not imply f(x) = r(x), g(x) = s(x). Not even if f(0) = r(0), g(0) = s(0). - Randy === Subject: Re: JSH: Functions and the distributive property > (7A'(x) + 7)(B'(x) +1) = (A(x)+7)(B(x)+1) > DOES NOT IMPLY > 7A'(x) + 7 = A(x) + 7 > B'(x) + 1 = B(x) + 1 And this is quite easy to show: A(x) = B(x) = x B'(x) = 0 A'(x) = 1/7 ( x^2 + 8x) Also note that A(0) = B(0) = A'(0) = B'(0) = 0. The top equation is true for my equations, however the bottom pair fail miserably. === Subject: Re: Functions and the distributive property <4405ed19$0$73224$892e7fe2@authen.yellow.readfreenews.net > Consider > a(b+c) = ab + ac > is the distributive property, where the math doesn't care if you use > functions: > a(f(x) + b) = a f(x) + ab > SO WHAT, TROLL? Posters have made claims that reduce to the distributive property behaving differently with functions, where they say that when the function goes to 0 is a special case. That case is a(0 + b) = a(0) + ab and I say that case is NOT just a special case, in that the distributive property changes, as it just allows you to clear out the function to see what is constant with respect to x. They say function and people get stupid. Here's a key proof now that is little different from the basic case: In the complex plane, given 7C(x) = (A(x) + 7)(B(x) + 1) true for all x, where A(0) = B(0) = 0 let C(x) = (A'(x) + 1)(B'(x) + 1) where A'(0) = B'(0) = 0 and making that substitution, gives 7(A'(x) + 1)(B'(x) + 1) = (A(x) + 7)(B(x) + 1) and by the distributive property A(x) = 7A'(x) and B'(x) = B(x). Notice it doesn't matter what the functions are beyond those on the right going to 0 at x=0 as it's just a slightly more complicated demonstration of the distributive property. Let's examine the function argument more closely, by considering 42(f(x) + 1) as notice I can have 6( 7f(x) + 7) or 2( 21f(x) + 21) or 3( 14f(x) + 14) along with a couple of other cases and AT NO TIME does the value of f(x) matter. Notice that even if you have something like 7(x/7 + 1) you can STILL multiply through, by the distributive property to get 7(x/7 + 1) = x + 7 as the function HAS NO IMPACT ON THE DISTRIBUTIVE PROPERTY. So the mathematics proving I am correct is trivial. The problem though is the ability of many of you to just lie, like calling me a troll, when I'm talking easy algebra. You can do that to any mathematics people. You can take any mathematical proof out there and just claim it's wrong. James Harris === Subject: Re: Functions and the distributive property >> Consider >> a(b+c) = ab + ac >> is the distributive property, where the math doesn't care if you use >> functions: >> a(f(x) + b) = a f(x) + ab >> SO WHAT, TROLL? > Posters have made claims that reduce to the distributive property > behaving differently with functions, where they say that when the > function goes to 0 is a special case. > That case is > a(0 + b) = a(0) + ab WRONG. CLEAN UP YOUR NOTATION. a* (f(x) + b) = a * f(x) + a * b If f(x) = 0 for all x then, a * ( 0 + b ) = a * 0 + a * b and that is NOT equal to your a(0) + ab A good Learning Lesson for you. (Get a good beginning middle school algebra book and read it throughly). === Subject: Re: Functions and the distributive property > That case is > a(0 + b) = a(0) + ab Whoa! You have been using a(0) to denote the value of the function a, at 0. In that case, there is no distributive property. It's not true that for an artibtrary function a, a(0+b) = a(0) + a(b). === Subject: Re: Functions and the distributive property > Posters have made claims that reduce to the distributive property > behaving differently with functions, where they say that when the > function goes to 0 is a special case. Provide *one* example in which someone actually said that. > That case is > a(0 + b) = a(0) + ab > and I say that case is NOT just a special case, in that the > distributive property changes, as it just allows you to clear out the > function to see what is constant with respect to x. > They say function and people get stupid. You do, at least. > Here's a key proof now that is little different from the basic case: > In the complex plane, given > 7C(x) = (A(x) + 7)(B(x) + 1) > true for all x, where A(0) = B(0) = 0 > let > C(x) = (A'(x) + 1)(B'(x) + 1) > where A'(0) = B'(0) = 0 Again: what are A'(x) and B'(x)? You did not define them. > and making that substitution, gives > 7(A'(x) + 1)(B'(x) + 1) = (A(x) + 7)(B(x) + 1) > and by the distributive property > A(x) = 7A'(x) and B'(x) = B(x). Again: how is it that the distributive property allows you to deduce this? Hint: it doesn't. > Let's examine the function argument more closely, by considering > 42(f(x) + 1) > as notice I can have > 6( 7f(x) + 7) > or > 2( 21f(x) + 21) > or > 3( 14f(x) + 14) > along with a couple of other cases and AT NO TIME does the value of > f(x) matter. Correct. > Notice that even if you have something like > 7(x/7 + 1) > you can STILL multiply through, by the distributive property to get > 7(x/7 + 1) = x + 7 > as the function HAS NO IMPACT ON THE DISTRIBUTIVE PROPERTY. Nobody said otherwise. > So the mathematics proving I am correct is trivial. If it is trivial, why dont you explain in detail how do you prove that A(x) = 7A'(x) and B'(x) = B(x)? > The problem though is the ability of many of you to just lie, like > calling me a troll, when I'm talking easy algebra. I *never* called you a troll. You're a crank, that's what you are (well, and a few other things too). > You can do that to any mathematics people. You can take any > mathematical proof out there and just claim it's wrong. Yes, that's easy. So easy, that you have been doing it for years. Jose Carlos Santos === Subject: Re: question about orthogonal transformation Then how to compute such Q? I was thinking we only need n-1 such pairs. Of course they must be independent. Since orthogonal matrix preserves orthogonality. So if you know the action on the (n-1)-dim subspace, then you know the action on the orthogonal complementary one dimension. Is this wrong? === Subject: Re: question about orthogonal transformation 1. Then how to compute such q? 2. I was thinking we only need n-1 such pairs. Of course, there pairs must be independent. Since orthogonal matrix preserves orthogonality. So if you know the action on the (n-1)-dim subspace, then you know the action on the orthogonal complementary one dimension. Is this wrong? Roy === Subject: Re: question about orthogonal transformation >2. I was thinking we only need n-1 such pairs. Of course, there pairs >must be independent. >Since orthogonal matrix preserves orthogonality. So if you know the >action on the (n-1)-dim subspace, then you know the action on the >orthogonal complementary one dimension. Yes, but you only know the subspace. The last vector could still be turned to either direction (+ or -). Take the vectors e1 = [1; 0], e2 = [0; 1] and the matrices: A = [1 0; 0 1], B = [1 0; 0 -1]. Then both A and B are orthogonal and A*e1 = B*e1 = [1; 0], but A*e2 = -B*e2. You cannot know which one you have by simply looking at the action on e1. === Subject: Why seek? Choose any love pi11 you want! boundary=------------ms030105060001030709090100 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id k22Mcn314741 for ; Thu, 2 Mar 2006 17:38:49 -0500 --------------------------------------------------------------------- Cheapest medications based LICENSED online phartmacy! Cialis Soft Tabs as low as $4.72 Viagra Professional as low as $3.8 Viagra Soft Tabs as low as $3.8 Cialis as low as $5.67 Valium as low as $2.85 Generic Viagra as low as $3.5 Need medicine? All here! === Subject: Probability question: runs of consecutive digits A sequence of the digits 0 through 9 is generated, with each digit having independent equal probability of being selected at each position. What is the expected position of the first run of n consecutive zeros? Should be easy, but can I do it? It looks as if the expected starting position of the first such run might be Int(10^(n + 1)/9) - n, where Int means integer part, but I do not see how to prove it. Any ideas? And, if it's not an intermediate step in the above answer, can anyone find a tractable expression for the probability that the first run will start at position x, or, failing that, an approximation with some known error bound? I have a recurrence relation that I think I can solve in principle, but for anything greater than about n = 3 it becomes horrendous to do in practice. === Subject: Re: Probability question: runs of consecutive digits >A sequence of the digits 0 through 9 is generated, with each digit >having independent equal probability of being selected at each >position. What is the expected position of the first run of n >consecutive zeros? Should be easy, but can I do it? If all else fails, construct a Markov chain with n+1 states: 0 <-> 0 consecutive zeros 1 <-> 1 consecutive zeros etc. Then you have transition probabilities p(j,0) = 9/10 for all j Nicely handled, Arturo. I had programmed a heat-seeking missile to lock > into Ray Steiner's brain waves, but your way is much cleaner. Actually, the missile should have been for Thomas Mautsch (who posted a solution, which fortunately is at best incomplete), not Ray Steiner (who should get only a slap on the wrist). Sorry, Ray. 8-) --- Christopher Heckman === Subject: Re: Diophantine problem from current MONTHLY <44039887$1@news1.ethz.ch schrieb : > MONTHLY: > Find all nonnegative integers n such that n^3 + n^2 + n + 1 is a > square. > I can reduce the problem to finding all members of the Pell sequence > (i.e., 1, 3, 7, 17 ...) of the form 2y^2 -1. Is there an easier way > to solve this problem? > Don't know. - I also get the same equation in an intermediate step. > Are there any solutions other than n = 0 , 1 and 7? > No. > [Spoilerspace] > Sketch of solution: > Factorize the term (n^3 + n^2 + n + 1): > (n+1)(n^2+1). > The g.c.d. of the factors (n+1) and (n^2+1) is either 1 or 2. > In the case that the g.c.d. is 1, both (n^2+1) must be a square numbers. > The difference between the two squares - (n^2+1) and n^2 - > can only be 1 if the numbers are 1 and 0; > thus n=0 is the only solution in this case. > In the case that the g.c.d. is 2, > (n+1)/2, and (n^2+1)/2 must be square numbers: > n = 2m^2 - 1 > n^2 = 2k^2 - 1 > Yet to be solved: > m^2 - 1 = [ (2k^2-1)^2 + 1 ] / 2 - 1 > Factorize: > (m-1)(m+1) = 2 k^2 (k-1) (k+1) > Again by g.c.d.-considerations, > either (m-1) or (m+1) must be divisible by k^2. > Thus, there must hold: > m = +/- 1, which yields the solution n=1, > or > m = k^2 +/- 1, which yields the solution n=7, > or > m >= 2k^2 - 1. > In the latter case, there follows: > 2 k^2 (k-1) (k+1) <= (2k^2 - 2) * 2k^2, > and this leaves only k = -1, 0, 1 as possibilities, > leading back to the already discussed case m = +/- 1. Well, here's the bloke with the heat seeking missile in the brain. Without discussing the solution further, I just want to comment that the solution given above is wrong. Let's look at the faulty part of it. In the case that the g.c.d. is 2, > (n+1)/2, and (n^2+1)/2 must be square numbers: > n = 2m^2 - 1 > n^2 = 2k^2 - 1 > Yet to be solved: > m^2 - 1 = [ (2k^2-1)^2 + 1 ] / 2 - 1 (*) Look at the solution n = 7. Then m = 2 and k = 5. But then (*) doesn't hold! The k and m are reversed here. Further, the solution has > Factorize: > (m-1)(m+1) = 2 k^2 (k-1) (k+1) > Again by g.c.d.-considerations, > either (m-1) or (m+1) must be divisible by k^2. Again, we should have (k-1)(k+1) = 2m^2(m-1)(m+1) which gives m^2 | k^2 - 1 Finally, and even more important, the statement that either k-1 or k+1 must be divisible by m^2 sorely needs proof. It is not true in general that if a^2 | b^2 -1 and (a,b)=1 then a^2 divides b+1 or b -1. Take a = 4 and b = 7. Then 16 divides 48 but 16 divides neither 6 nor 8. See you all on 1 June with a different and hopefully correct proof. Ray Steiner === Subject: Re: multivalued lower semicontinuous mapping and G - delta graph multivalued lower semicontinuous mapping, when, moreover, F(x) is a > closed (bounded) interval for every x from R. > Yes, in this case it is a G_delta. > Let's say F(x) = [A(x), B(x)]. > Lower semicontinuity of F says for any c, > {x: A(x) < c} = {x: F(x) intersects (-infty, c)} and > {x: B(x) > c} = {x: F(x) intersects (c, infty)} are open, > i.e. A is upper semicontinuous and B is lower semicontinuous. > Let Q be the set of rationals and N the natural numbers. > Note that a <= y iff for every q in Q, a <= q or q <= y. > Thus the graph of F is > G(F) = {(x,y): A(x) <= y <= B(x)} > = intersection_{q in Q} (C_q intersect D_q) > where C_q = {(x,y): A(x) <= q or q <= y} and > D_q = {(x,y): q >= y or q <= B(x)}. > But C_q = intersection_{n in N} {(x,y): A(x) < q + 1/n or q < y + 1/n} > is a G_delta. Similarly D_q is a G_delta, and so G(F) is a G_delta. More generally, suppose each F(x) is a closed set. For each pair of rationals c < d, let C_{c,d} = {(x,y): y <= c or y >= d or F(x) intersects (c,d)}. Then G(F) = intersection_{c,d} C_{c,d}, and since C_{c,d} = intersection_{n in N} {(x,y): y < c + 1/n or y > d - 1/n or F(x) intersects (c,d)} this is a G_delta. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Pleaz Help Me > thank you > i mean : 3^(x^2) +3^(x) -90=0 > is there way (method)without numerical solution ? Not that I'm aware of. I'm surprised that nobody has mentioned that there are _two_ real solutions, one positive and one negative. The positive real solution, x = 2, can be found by inspection, as Robert indicated. I'll show how to approximate both real solutions easily by an iterative method. Begin by solving 3^(x^2) - 90 = 0, ignoring the 3^x term in the original equation. This gives x_0- = -Sqrt(log_3(90)) and x_0+ = +Sqrt(log_3(90)), which we will use as the initial values in our iterations. Now back to the original equation. Rewrite it as 3^(x^2) = 90 - 3^x x^2 = log_3(90 - 3^x) x = +/- Sqrt(log_3(90 - 3^x)) Of course, we haven't solved for x actually, since x appears on both sides. But we have put it in a form suitable for iteration: x_(n+1) = +/- Sqrt(log_3(90 - 3^x_n)) To approximate the negative solution, beginning with x_0- = -Sqrt(log_3(90)), we then get x_1- = -Sqrt(log_3(90 - 3^x_0-)), which is approximately -2.02356317. This is surprisingly(?) accurate already. The negative solution is actually -2.02356309... To approximate the positive solution, beginning with x_0+ = +Sqrt(log_3(90)), we then get x_1+ = +Sqrt(log_3(90 - 3^x_0+)), which is approximately 1.999328. We had already noted, by inspection, that the positive solution is exactly 2. Of course, if greater accuracy is desired for either positive or negative root, just iterate more... David === Subject: Re: Pleaz Help Me > U can get the numerical solution . > And the last Equation: > (3^x)^2+3^x-90 [ 1 ] > Or > 3^(x^2)+3^x-90 [ 2 ] > If it is like [2] > Y can do like this > y=3^x. > And: > y^2+y=90 [ 3] That is true if it is like equation [1], not if it is like equation [2]. If y=3^x, then y^2 = 3^{2x}, not 3^{x^2}. So equation [1] is equivalent to equation [3] (modulo y = 3^x), but equation [2] is not. Arturo Magidin, sans .sig === Subject: Re: Pleaz Help Me pleaz help me i founded a solution for : 3^(x^2) +3^(x) -90=0 3^(x^2)-9+3^(x)-81=0 (3^x+3)(3^x-3)+3^x-81=0 (y+3)(y-3)+y-81=0 then y=9 then x=2 is there another way (method)? pleaz help me hus === Subject: Re: Pleaz Help Me days. My association with the Department is that of an alumnus. >pleaz help me Sure thing. It's spelled Please. There is a key labeled Shift or with an up-arrow in your keyboard. If you press it simultaneously with a letter key, it will print a capital letter; try it. >i founded a solution for : I found. >3^(x^2) +3^(x) -90=0 >3^(x^2)-9+3^(x)-81=0 >(3^x+3)(3^x-3)+3^x-81=0 This is incorrect. (3^x + 3)(3^x -3) = (3^x)^2 - 9 = 3^{2x} - 9. That is: 3^x times 3^x is NOT 3^{x^2}; it is 3^{2x}. >(y+3)(y-3)+y-81=0 >then y=9 y^2 + y - 90 = 0 which gives y = 9 or y = -10. Of course, y=-10 is not a solution to the original problem, since y = 3^x means y must be positive. >then x=2 You got lucky that 2^2 happens to be the same thing as 2*2, so your answer turns out to be correct. However, the process you used is incorrect since you messed up the algebra, as noted above. >is there another way (method)? Are you sure you have 3^(x^2)? If so, this is in general a difficult problem. Note that 3^(x^2) = (3^x)^x, not (3^x)^2. If you let y = 3^x, then the equation becomes y^x + y - 90 = 0 or y^{log_3(y)} + y - 90 = 0. Such equations are in general nontrivial to solve. --