October 2012 - mathfun@mailman.xmission.com

Re: [math-fun] Math paper generator
by Warren Smith 26 Oct '12

26 Oct '12

the "blog" at http://thatsmathematics.com/mathgen/ said that that at least one paper generated by their algorithm was accepted, by "advances in pure mathematics."

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[math-fun] Borromean string puzzle
by Adam P. Goucher 26 Oct '12

26 Oct '12

Here's an interesting group-theoretic puzzle with connections to Borromean rings, Brunnian braids et cetera: http://cp4space.wordpress.com/2012/10/26/borromean-strings/ I doubt the existence of Borromean strings, although I haven't been able to prove it. Sincerely, Adam P. Goucher

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Re: [math-fun] Math paper generator
by Henry Baker 26 Oct '12

26 Oct '12

At 01:51 AM 10/26/2012, Eric Angelini wrote: >... this is pure math-fun, >http://thatsmathematics.com/mathgen/ >Best, >Ã. Perhaps the number N=2^11-1 in this Proc. NAS paper indicates misconduct? --- From comp.risks: Date: Sun, 7 Oct 2012 10:37:17 -0400 From: Monty Solomon <monty(a)roscom.com> Subject: Misconduct Widespread in Retracted Science Papers, Study Finds (Carl Zimmer) Carl Zimmer, *The New York Times*, 1 Oct 2012 Last year the journal *Nature* reported an alarming increase in the number of retractions of scientific papers - a tenfold rise in the previous decade, to more than 300 a year across the scientific literature. Other studies have suggested that most of these retractions resulted from honest errors. But a deeper analysis of retractions, *** being published this week, *** challenges that comforting assumption. In the new study, published in the Proceedings of the National Academy of Sciences, two scientists and a medical communications consultant analyzed *** 2,047 *** retracted papers in the biomedical and life sciences. They found that misconduct was the reason for three-quarters of the retractions for which they could determine the cause. ... http://www.nytimes.com/2012/10/02/science/study-finds-fraud-is-widespread-i…

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Re: [math-fun] Math paper generator
by Henry Baker 26 Oct '12

26 Oct '12

Hmmm... This is the first time I've seen 42 references at the end of a 6-page non-biology paper. More usually, the reviewers have to ask for additional references. Mathgen needs to tweak their algorithm a little. At 01:51 AM 10/26/2012, Eric Angelini wrote: >... this is pure math-fun, >http://thatsmathematics.com/mathgen/ >Best, >Ã.

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[math-fun] Digit-Fibonacci
by Eric Angelini 25 Oct '12

25 Oct '12

I guess this is old hat (at least for the Fibonacci Quarterly); What could be the longest repeated pattern in a sequence where we just add the last two digits to produce the next term? Starting with 0,1, produces: 0,1,1,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11,... where the repeated pattern is = [2,3,5,8,13,4,7,11] This pattern is 8-term long (or 10-digit long). Could one find a longest pattern with another start? Best, É.

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[math-fun] Fooling with GmailTex
by Bill Gosper 24 Oct '12

24 Oct '12

http://dlmf.nist.gov/17.5#17.5.5 (or BHS (II.5)) gives [image: \, _1\phi _1\left(a;c;q,\frac{c}{a}\right)=\frac{\left(\frac{c}{a};q\right)_{\infty }}{(c;q)_{\infty }}] for |q|<1. This has the peculiar special case [image: \, _1\phi _1(q;q z;q,z)=1-z] independent of q. But this can be generalized to |q|≠1: [image: \, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q z};\frac{1}{q}\right)_{\infty }}-z+1] Can we similarly generalize BHS (II.5)? Maybe not. E.g., [image: \, _1\phi _1\left(q^2;c q^2;q,c\right)=(c-1) (c q-1) \left(\frac{c+q-c q}{c (q-1) \left(\frac{1}{c};\frac{1}{q}\right)_{\infty }}+1\right)] We seem to be off to a rough start. I just implemented the base reciprocation formula for general rφs, which I was surprised BHS and DLMF 17.5 omit. Now I'm less surprised--it's a typesetting challenge. --rwg If instead of typesetting you see the alternate text, e.g., [image: \, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q z};\frac{1}{q}\right)_{\infty }}-z+1] Then paste \, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q z};\frac{1}{q}\right)_{\infty }}-z+1 into the window at www.texify.com . (Thanks, Neil!)

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Re: [math-fun] Fooling with GmailTex
by Bill Gosper 23 Oct '12

23 Oct '12

Mike S>Pasting this into texify as directed yielded some of the worst-typeset math I've ever seen. On 2012-10-21 08:03, Bill Gosper wrote:> \, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q>> z};\frac{1}{q}\right)_{\infty }}-z+1 --------------- Puzzling. In Safari, Firefox, and Chrome, I see http://gosper.org/mathwurst.png which seems comparable to http://dlmf.nist.gov/17.5 How about http://texify.com/?$\, _1\phi _1(q;q z;q,z)=\frac{z}{\left(\frac{1}{q z};\frac{1}{q}\right)_{\infty }}-z+1$ ? Maybe q-series are just irretrievably ugly? --rwg

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[math-fun] Third cipher challenge, MathsJam
by Adam P. Goucher 22 Oct '12

22 Oct '12

Once again it has come to this time of month. In twelve hours' time, you can see the cipher here: http://cp4space.wordpress.com/2012/10/23/cipher-3-chess-cipher/ Of course, if you're slightly less patient, you can follow this direct link to download the image now: http://cp4space.files.wordpress.com/2012/10/chesscipher.png There's a MathsJam at 19:00 BST on Tuesday, which takes place internationally (mostly in Britain, but also in the USA, India and a few other countries). I might be able to attend the Cambridge one for a maximum of 20 minutes or so, since I have another agenda at 19:30. Sincerely, Adam P. Goucher http://cp4space.wordpress.com

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Re: [math-fun] Fooling with GmailTex
by Bill Gosper 22 Oct '12

22 Oct '12

GarethM>On Monday 22 October 2012 01:10:18 Mike Speciner wrote: > Well, maybe I'm just too fussy. (My first job, in the early '70s, was> writing software to typeset mathematics beautifully, and I always> thought that TeX was a big step backwards from the state of the art.)> Your png looks quite similar to what I see. Should I not expect the> first two 1s to be at the same height? Should I not expect the ; between> 1/qz and 1/q to be vertically centered around the fraction bars so that> the semicolon's dot doesn't look like a center dot? And should I not> expect the spacing to be a bit looser in several places? I'm fairly sure that texify.com is not in fact running TeX; it's doing some simpler cheaper thing, probably involving MathML or something. If you typeset that same formula in TeX then ... well, actually you still get something pretty ugly, but it's ugly in quite different ways. What was the state of the art of computerized mathematical typesetting before TeX? -- g ----------- Well, at Stanford AI there was P(rototype)O(verlay)X(erographics). The macrology was an absolute bear. For a quotient, you had to measure the numerator and denominator, max for the division bar, and do your own centering. I wrote my own list mapper. The simplest call required six consecutive open parens. I just restored <http://gosper.org/facfun.pdf> (scanned XGP output, pre-inkjet, pre-laser) from a server crash. --rwg MRob>What is the date (year of authorship) of these ancient (mostly) POX notes? I want to add this as a reference for OEIS sequence A2109:https://oeis.org/A002109 ------------------------- There's a handwritten letter in the binder dated 1979. It must have coincided with the dawn of TeX, since the later pages are TeXed. MRob> It would also be nice to add a sequence for the (Gosper's) second factorial with integer arguments, which I take to be 1, 1, 16, 122009559759792, 16358..68032 (169 digits, approx. 1.63588 x 10 ^ 168) but I don't like to add sequences without a reference. - Robert [Munafo] I'm sure there are better references, but J.W.L. Glaisher uses the function on p81-87 of Products and series involving prime numbers only, part II, The Quarterly Journal of Pure and Applied Mathematics, Vol. XXVIII and on p82 refers to an apparently more relevant article in The Messenger of Mathematics, Vol XXIII, p155, presumably also by Glaisher. I haven't checked, but I suspect his ilg_2 function is the closely related double integral of log gamma. (A negapolygamma.) Glaisher also treats prod k^k^n, n<0. Barnes and Kinkelin and perhaps Alexiewsky(sp?) almost certainly treated this function. --rwg On 5/7/12, Bill Gosper <billgosper(a)gmail.com <http://gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com> <http://www.gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com>> wrote:> By way of preservation, Neil has kindly scanned in my ancient,> (mostly) POX (pre-Tex), brief notes <http://gosper.org/facfun.pdf>> (3.7M) on higher factorials.> These stem from my astounding discovery that the dot at the> bottom of an exclamation point is actually hollow, representing> the number 0, and what happens when you change it to a 1.> --rwg On the subject of shapes with constant dissolution rates, there might be real monetary incentive from the drug companies, seeking to improve "timed release". To illustrate the lengths they've already reached, I take an expensive, insoluble plastic pill with a laser-punched pinhole, through which medication is pushed by a tiny expanding sponge. There must already be scads of patents on inhomogeneous pills, with solubility varying with internal depth, etc.

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[math-fun] syncing in waves
by Henry Baker 19 Oct '12

19 Oct '12

32 metronomes, eventually syncing... http://www.youtube.com/watch?v=JWToUATLGzs

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