April 2014 - mathfun@mailman.xmission.com

Re: [math-fun] everything that exist from nothing...
by W. Edwin Clark 11 Apr '14

11 Apr '14

In the Discussion and Conclusion to the paper "Spontaneous creation of the universe from nothing" http://arxiv.org/pdf/1404.1207v1.pdf the authors say, "In summary, we have presented a mathematical proof that the universe can be created spontaneously from nothing." If they have a proof then they must start with axioms and undefined terms. Their "nothing" appears to have lots of properties. Perhaps they should just say what their assumptions are and avoid the word "nothing". See the book by Jim Holt http://www.amazon.com/dp/0871403595/ref=rdr_ext_tmb for some interesting riffs on the question of something from nothing including interviews with David Deutsch and others on the question. Philosophers have a field day with this business of nothingness: http://plato.stanford.edu/entries/nothingness/ Edwin On Fri, Apr 11, 2014 at 4:37 PM, Simon Plouffe <simon.plouffe(a)gmail.com>wrote: > > Hello, > > > see this. > > https://medium.com/the-physics-arxiv-blog/ed7ed0f304a3 > > > There is an interesting article on the concept of > the universe being created from nothing, > > > BEst regards, > > Simon Plouffe > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >

1 0

[math-fun] everything that exist from nothing...
by Simon Plouffe 11 Apr '14

11 Apr '14

Hello, see this. https://medium.com/the-physics-arxiv-blog/ed7ed0f304a3 There is an interesting article on the concept of the universe being created from nothing, BEst regards, Simon Plouffe

1 0

[math-fun] sketched proof of Knight distance formula
by Warren D Smith 11 Apr '14

11 Apr '14

I think the argument below (admittedly sketchy) now proves it. 1. Recall the problem comes down to proving that g(x,y)=1 for all x,y except x=y=0, and g(0,0)=-1. Here g(x,y) is a certain known formula I stated in an earlier post. 2. Computer verifies that for all x,y with max(|x|,|y|)<2999999. This should require less than a day of computing. I'd already done it up to 20000. 3. Divide into the following cases: Case1[k,v,w]: k<=y, y+k<=x, x mod 24=v, y mod 24=w Case2[k,v,w]: 0<=y<k, y+k<=x, x mod 24=v, y mod 24=w Case3[k,v,w]: k<=y<=x<y+k, x mod 24=v, y mod 24=w Here k can be anywhere from 0 to 49, and v and w each anywhere in {0,1,...,23}, so this is 86400=3*50*24*24 cases in all. 4. Within each of the above cases, the formula for g(x,y) simplifies. Specifically, all the floor functions can be removed since floor(linear polynomial) in each of these cases just becomes (the polynomial plus a known constant). All polynomials have all coefficients equal to integers divided by 24. Further, the max and min functions inside the formula also can be removed since in each case it can be deduced a priori which argument of the min or max is the one that wins. 5. We do not actually need to do any of that simplifying ourselves(!) -- we merely need to know that it could in principle be done. Because of this combined with the fact verification worked in step (2) we can deduce from (4) that the polynomials must in fact simplify, in every single case, to: 1. If even one did not, the computer would have detected that in step (2). 6. Theorem proven. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

2 4

Re: [math-fun] Tiling trompe l'oeil
by Bill Gosper 11 Apr '14

11 Apr '14

(Apologies to any repeat recipients) (An active version of my G11 exchange gift.) > Stare at (don't click) the "infinite" periodic tessellation > http://gosper.org/sqartri1.html . Can it be broken > up (along color boundaries) into a tessellation by > A) Regular hexagons? > B) Squares? > C) Equilateral triangles? > D) None of the above? > --Bill > Answer: click on larger image (forward) > and smaller image (back). > >

2 1

Re: [math-fun] math-fun Digest, Vol 134, Issue 26
by Warren D Smith 10 Apr '14

10 Apr '14

> Subject: Re: [math-fun] sketched proof of Knight distance formula > The screed at > https://www.dropbox.com/s/nzmzjswtctju23f/knights_path.txt > has been updated (and substantially shortened). > Fred Lunnon --I'm not accepting: your lemma 4, near end of its proof.

1 0

Re: [math-fun] What if Turing/Shannon/Bekenstein were wrong?
by Henry Baker 10 Apr '14

10 Apr '14

I did a Google search on "photon conservation" & came up with nothing (there were discussions of _preserving_ as many photons as possible in detectors, but that was completely different). If there is such a notion of photon conservation, that would be a valuable insight. Do you have any links or references? At 11:14 AM 4/9/2014, Eugene Salamin wrote: >As the universe expands, the number of photons is conserved, and the wavelength of each photon lengthens proportionally to the expansion.

4 3

Re: [math-fun] Kale
by Adam P. Goucher 10 Apr '14

10 Apr '14

I propose the following experiment: For varying values of r, cut discs of radius r out of the kale. Then measure the area A (or, equivalently, weigh them, assuming kale is of uniform thickness and density). You are looking for a relationship of the following form: A = 2 pi s^2 (cosh(r/s) - 1) where s is the characteristic length-scale of kale (and, I believe, the reciprocal of the absolute value of the curvature). Sincerely, Adam P. Goucher > ----- Original Message ----- > From: Fred Lunnon > Sent: 04/10/14 04:04 AM > To: math-fun > Subject: Re: [math-fun] Kale > > Jim, stop playing with your food, and eat up your greens! WFL > > > > On 4/10/14, James Propp <jamespropp(a)gmail.com> wrote: > > Does kale have constant (negative) curvature? > > > > Jim Propp > > _______________________________________________ > > math-fun mailing list > > math-fun(a)mailman.xmission.com > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

4 3

[math-fun] 32-bit reversal speed tests
by Warren D Smith 10 Apr '14

10 Apr '14

I tested several 32-bit reversors for speed. Arndt32BitReverseA: 0.598 like Freed but without explicit constants Arndt32BitReverseB: 0.492 uses 31=5*3+1+5*3, 32=31+1 Freed32BitReverse: 0.484 uses 32,16,8,4,2,1 WDS32BitReverseA: 0.526 uses 32=27+5; 5 handled using multiply/mask tricks WDS32BitReverseB: 0.500 uses 32=27+5; 5 handled via 32-byte table lookup The winner is the comparatively boring: uint32 Freed32BitReverse(uint32 v){ //Edwin Freed in Dr. Dobb's Journal 1983. v = ((v >> 1) & 0x55555555) | ((v & 0x55555555) << 1); // swap odd and even bits v = ((v >> 2) & 0x33333333) | ((v & 0x33333333) << 2); // swap consecutive pairs v = ((v >> 4) & 0x0F0F0F0F) | ((v & 0x0F0F0F0F) << 4); // swap nybbles v = ((v >> 8) & 0x00FF00FF) | ((v & 0x00FF00FF) << 8); // swap bytes v = ( v >> 16 ) | ( v << 16); //swap 2-byte long pairs return(v); } -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

2 3

[math-fun] Search the digits of pi
by Michael Kleber 10 Apr '14

10 Apr '14

Surely all funsters carrying smartphones in their pockets immediately see the need for the "Find this sequence of digits in pi" app available at http://fathom.info/pi. This seems to be implemented in the obvious way: the app itself is 47.68 MB large, which is precisely what you would need to store 100,000,000 digits at two decimal digits in each byte. Loading and searching both take a while. At the other end of the spectrum, the app could be tiny and just include an algorithm to generate the digits itself. It would end up quite slow, certainly. But for some trade-off between data transmission time and cpu speed, that would be the right implementation. Are there any other interesting points on this trade-off curve? What might one want to do, other than pre-compute all or none of the digits? --Michael -- Forewarned is worth an octopus in the bush.

7 9

[math-fun] Kale
by James Propp 10 Apr '14

10 Apr '14

Does kale have constant (negative) curvature? Jim Propp

2 1