October 2013 - mathfun@mailman.xmission.com

Re: [math-fun] Mathematics on a gravestone
by Henry Baker 23 Oct '13

23 Oct '13

In most graveyards, "freezing the animation" is redundant. But then again it IS coming up on Halloween... At 11:03 PM 10/22/2013, Bill Gosper wrote: >http://gosper.org/perigal.gif . At least in my Mac Firefox, you can freeze >the animation

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Re: [math-fun] Mathematics on a gravestone
by Bill Gosper 23 Oct '13

23 Oct '13

Charles>In less somber situations, it would be hilarious that council would think that this was their business. I can only hope that they soon find themselves unemployed. Charles Greathouse Analyst/Programmer Case Western Reserve University On Sat, Oct 19, 2013 at 1:24 AM, Stuart Anderson < stuart.errol.anderson(a)gmail.com> wrote: http://www.dailystar.co.uk/news/latest-news/345729/Grieving-widow-told-by-j… Standards? What standards _________________________________________ Perhaps they will also send a nasty letter to Perigal's heirs: http://plus.maths.org/content/dissecting-table --rwg

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[math-fun] Pick theorems
by Joerg Arndt 22 Oct '13

22 Oct '13

Pick's theorem (cf. http://en.wikipedia.org/wiki/Pick's_theorem): The area A of a simple polygon with all corners on a square grid is A = i + b/2 - 1 where i is the number of lattice points in the interior and b is the number of lattice points on the boundary. For the following A is the area as number of unit cells covered. Triangular lattice: A = 2*i + b - 2 Hexagonal lattice: A = i/2 + b/4 - 1/2 Square grid, every second column shifted by a half unit: A = i/2 + b/2 - 1 where b counts only the boundary points whose local neighborhood is not concave (i.e., 90 degrees of outside, 270 degrees of inside). I obtained these scribbling on a train ride yesterday. Best, jj P.S.: If anyone can access the following articles, then please email them to me. W. W. Funkenbusch, >From Euler's Formula to Pick's Formula using an Edge Theorem, The American Mathematical Monthly Volume 81 (1974) pages 647-648 Dale E. Varberg, Pick's Theorem Revisited, The American Mathematical Monthly Volume 92 (1985) pages 584-587 Branko Grünbaum and G. C. Shephard, Pick's Theorem, The American Mathematical Monthly Volume 100 (1993) pages 150-161

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Re: [math-fun] Exact Cover Solver
by Adam P. Goucher 22 Oct '13

22 Oct '13

In polynomial time? I think I have a reduction of 3-SAT to an exact cover problem, so this would be *really* useful. Sincerely, Adam P. Goucher http://cp4space.wordpress.com > ----- Original Message ----- > From: quad > Sent: 07/29/13 02:18 PM > To: math-fun > Subject: [math-fun] Exact Cover Solver > > Hello: > > I just wanted to announce that I wrote a program to find the exact > cover of a set S = {0, ..., n-1}. It uses Knuth's Algorithm X with > his Dancing Links strategy. > > The code is here in Lisp: https://bitbucket.org/tarballs_are_good/dancing-links > > Example: Given the sets > > A = {0, 3, 6} > B = {0, 3} > C = {3, 4, 6} > D = {2, 4, 5} > E = {1, 2, 5, 6} > F = {1, 6}, > > find all disjoint unions of the above that equals S. > > This is an exact cover problem for n = 7. Input into the program is easy: > > > (exact-cover 7 '((0 3 6) ; A > (0 3) ; B > (3 4 6) ; C > (2 4 5) ; D > (1 2 5 6) ; E > (1 6))) ; F > > It will think, and spit out > > Solution #1 at depth 3: > 6 1 > 5 2 4 > 3 0 > > and then return the total number of solutions found (1) and the total > number of "positions" checked (5). Note that the solution above > corresponds to F, D, and B respectively, just the elements were > permuted. Note that they are indeed disjoint and their union is S. > > > The program still needs a little polishing, but may be useful to some > people who want to solve pentomino or n-omino packing, sudokus, or > whatever. If anyone is interested in having it as a stand-alone binary > that takes a file as input, let me know, and I can probably > accommodate. :) > > Cheers, > > Robert Smith > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] GR black hole collider ?
by Henry Baker 22 Oct '13

22 Oct '13

People also used to think that the electrons going around atoms would very quickly fall into the nucleus due to electromagnetic radiation. But Quantum Man came to save the day! I suspect that if there is anything to this Milne universe idea, then something analogous in QM will save it. At 01:53 PM 10/22/2013, Charles Greathouse wrote: >Wouldn't an electron-black hole evaporate (essentially) instantly through >Hawking radiation? > >The Schwarzschild evaporation time would be >https://www.google.com/search?q=mass+of+an+electron^3+*+5120*2*pi^2*G^2%2F%… > >I don't know the equivalent Kerr-Newman equation (maybe someone can help me >out here?) but I wouldn't expect it to be much longer. Surely there is an >answer, else this solution would not have been proposed. > >Charles Greathouse >Analyst/Programmer >Case Western Reserve University > >On Tue, Oct 22, 2013 at 4:05 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> I did some more Googling & found that this is a subject of active research; >> i.e., no one knows what happens when a fast-spinning black hole acquires >> too >> much material. >> >> Specifically, a spinning black hole is known as a "Kerr black hole", and >> there is a "Kerr Limit" to how fast a Kerr black hole can spin. One of >> the problems of an "extreme" Kerr black hole (a Kerr black hole having >> maximum spin) is that the singularity -- which is a circular ring for >> a Kerr black hole -- approaches the event horizon from the inside and >> lies on the surface for an extreme Kerr black hole. >> >> But nature is apparently modest; "cosmic censorship" is invoked to hide >> all singularities behind event horizons. Cosmic censorship would imply >> that extreme Kerr black holes cannot exist. >> >> So what happens to a Kerr black hole that somehow gets too big? How >> does it disintegrate? No one knows. >> >> Apparently, a Kerr black hole cannot accumulate material incrementally; >> the physics seems to push particles away when the Kerr black hole >> approaches the Kerr limit. But no one knows if similar sized black >> holes can merge to form an extreme Kerr black hole. >> >> Kerr black holes carry up to 29% of their energy in their spin; ALL of >> this energy can be extracted (thereby producing a spinless black hole) >> using techniques such as a "Penrose process"; however, extracting all >> of this energy may take an infinite amount of time. >> >> Kerr black holes "frame drag" their surrounding space-time, so that it >> is impossible to remain stationary next to a Kerr black hole, no matter >> how much thrust your rocket has. Since all of the spin energy of a >> Kerr black hole can be extracted, this energy obviously lies OUTSIDE >> the event horizon within the "dragged frame". Ditto for the angular >> momentum ?? >> >> Because the singularity of a Kerr black hole is a circular ring, it >> should be possible to go through it. Unfortunately, all of this happens >> inside the event horizon so you wouldn't be able to communicate any >> results to anyone outside. >> >> There are apparently "closed timelike curves" (CTC's) associated with >> Kerr black holes, which might conceivably be connected with "time travel". >> >> http://en.wikipedia.org/wiki/Closed_timelike_curve >> >> There's even a really cool, but really far-out proposal called "A symmetric >> matter-antimatter Milne Universe", in which particles like electrons are >> little Kerr black holes (with charge, obviously): >> >> From: http://www.icranet.org/talks/WeeklySeminars/2008/March/Chardin.pdf >> To: D:\Downloads\Chardin.pdf >> Size: 11.2 MB (11,731,792 bytes) >> >> From: http://moriond.in2p3.fr/J08/trans/sunday/benoit-levy.pdf >> To: D:\Downloads\benoit-levy.pdf >> Size: 2.1 MB (2,116,521 bytes) >> >> From: >> http://indico.lal.in2p3.fr/getFile.py/access?resId=2&materialId=slides&conf… >> To: D:\Downloads\Milne_Chardin_LAL.pdf >> Size: 1.4 MB (1,451,264 bytes)

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[math-fun] GR black hole collider ?
by Henry Baker 22 Oct '13

22 Oct '13

After looking at all the formulae re black holes, I have another question: If you could somehow accelerate 2 approximately equal black holes in a counter-rotating ring like CERN and have them smash into one another, what would happen? I'm talking about _pure_ GR here, so I'm not concerned about all of the cascade of random particles that you'd get just from a high energy collision, but I'm interested in what happens to the black holes themselves. I can think of 3 possibilities: 1. The black holes merge, producing one extremely fast rotating black hole. 2. The black holes miss one another, but scatter elastically, generating a significant gravitational wave. 3. The black holes rip one another "apart" (whatever that means), producing a shower of smaller black holes. I'm particularly interested if there are any solutions in GR of type 3.

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[math-fun] arXiv suckitude clarification
by Warren D Smith 22 Oct '13

22 Oct '13

I mean, it is good they provide very cheap, very fast publication, far exceeding paper journals. It is just stupid that they do not also far exceed paper journals in the refereeing (=commenting) dimension. Which they easily could in terms of speed & volume, thus obsoleting paper journals. The alleged reason (they told me) for their refusal to implement commenting was it would have been "impolite". This presumably explains the arxiv overlay sites Mike Stay mentioned. Aha. Evidently created by people who do not care about politeness, thank god. But still stupid. Another aspect is this. A lot of papers do big computations, produce a lot of data, use some computer program, etc. This data or program could be posted. IN paper journals, it is not published since long. Electronic publication need not suffer that defect. But -- it is a fact, that in all, or perhaps 99% (I do not know), of ArXiv papers where they could publish such stuff as an auxiliary file, they do not. I do not know the reason, but it is a fact. And in some cases, this nonpublication makes their actually published paper be silly. I mean, it works something like this: OFFICIAL PAPER: we did a huge computation to find a few numbers. We'll offer some vague descriptions, but basically, just trust us, we got the numbers right since we're pros, so we have no need to provide any code or details. UNPUBLISHED COMPUTER PROGRAM: has full details. May have bugs, but since secret, you'll never find them. Historically, many papers on this topic, including sometimes by the same authors, have been erroneous due to bugs. IF YOU ASK THE AUTHORS FOR THE DETAILS: they won't respond. it is kind of science by reputation, not science by science.

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[math-fun] zeta irrationality baloney, arxiv suckitude
by Warren D Smith 22 Oct '13

22 Oct '13

Message: 7 Date: Tue, 22 Oct 2013 16:41:46 +0200 From: Joerg Arndt <arndt(a)jjj.de> To: math-fun <math-fun(a)mailman.xmission.com> Subject: Re: [math-fun] zeta(5) -- and all zeta(odd) -- irrational??? Message-ID: <20131022144146.GB19908(a)jjj.de> Content-Type: text/plain; charset=us-ascii From: http://oeis.org/A013663 In a widely distributed May 2011 email, Wadim Zudilin gave a rebuttal to v1 of Kim's 2011 preprint: "The mistake (unfixable) is on p. 6, line after eq. (3.3). 'Without loss of generality' can be shown to work only for a finite set of n_k's; as the n_k are sufficiently large (and N is fixed), the inequality for epsilon is false." In a May 2013 email, Zudilin extended his rebuttal to cover v2, concluding that Kim's argument "implies that at least one of zeta(2), zeta(3), zeta(4) and zeta(5) is irrational, which is trivial." - Jonathan Sondow, May 06 2013 --yeah, I thought it had to be bullshit. But the thing is, no retraction has been posted even 2 years later, and not only that, if the ArXiv had a commenting facility, this could have been commented by somebody besides the uncooperative author, but no. In short: THE ARXIV SUCKS. I have complained to them for 10-20 years they needed to add commenting and rating, and they always to me to go chew a log. They have the capability to make this have far better refereeing than any journal has ever had, but instead chose intentionally to make it have no refereeing. It is absurd. I think this is an intentional conspiracy to support obsolete ultra-expensive journals, supported by big money and big egos -- what is actually useful for humanity be damned. They have lost 20 years for all of humanity by their idiocy.

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[math-fun] zeta(5) -- and all zeta(odd) -- irrational???
by Warren D Smith 22 Oct '13

22 Oct '13

claims Yon-Cheol Kim http://arxiv.org/abs/1105.0730

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[math-fun] how not to handle equations in lectures
by Warren D Smith 21 Oct '13

21 Oct '13

When I give a lecture, if I write an equation, I explain all the meanings of the letters inside it, and what it says. If Nima Arkani-Hamed flashes an equation on screen, he never (?) defines the letters inside it, never explains what it says, and just sort of waves his hand at it, kind of as though pointing out a passing airplane, then moves on. Also, he never writes a theorem statement, nor even an explicit "CLAIM: xxxx." I would say "never" except maybe sometimes he does give a very partial stab at it for a small subset of equations, so perhaps we should give him partial credit on a few equations. I don't understand how one can adopt this lecture style, except as a joke. If other physicists imitate him in this respect (since he's a great $3M prize winner) it would be a disaster. just my opinion...

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