January 2019 - mathfun@mailman.xmission.com

[math-fun] Perfect nonlinear functions n=2m
by Henry Baker 20 Jan '19

20 Jan '19

In Nyberg's 1991 paper, she proves that a perfect nonlinear binary S-box must have an input dimension at least twice that of the output dimension. I'm trying to construct the most trivial versions of her theorem: i.e., n=2*m, m=1, 2, 3, etc. Has anyone here done such a thing?

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[math-fun] Subject: Re: e^(iπ)
by Bill Gosper 19 Jan '19

19 Jan '19

-------- Original Message -------- Date: 2019-01-18 21:19 From: Neil Sloane <njasloane(a)gmail.com> Reply-To: math-fun <math-fun(a)mailman.xmission.com> Adam Goucher wrote: "I'm firmly in the exp(i pi) = -1 camp." Me too, there is no argument. "Beauty is truth" is obviously better than "beauty - truth is zero" ---------- When I first saw e^(iπ) + 1 = 0, I gagged. If you like clutter, why not throw in a factor of GoldenRatio? But now I have a clincher. I asked a beginner to solve x^x = e^-(π/2), with the hint: "Try taking √ of the World's Most Beautiful Formula." He used the messy one and got stuck! —rwg (I actually asked for *two* solutions.) On Fri, Jan 18, 2019 at 10:05 PM Cris Moore <moore(a)santafe.edu> wrote: > > but those just imply e^(i pi) is +1 or -1. > > > On Jan 18, 2019, at 7:53 PM, Allan Wechsler <acwacw(a)gmail.com> wrote: > > > > Nobody for e^(2iπ) = 1 or e^(2iπ) - 1 = 0 ? > > > > On Fri, Jan 18, 2019 at 9:45 PM Thane Plambeck <tplambeck(a)gmail.com> > wrote: > > > >> The second one is more aesthetically pleasing, but the first one seems > >> (weirdly) more directly informative somehow, to me. > >> > >> On Fri, Jan 18, 2019 at 6:12 PM Bill Gosper <billgosper(a)gmail.com> > wrote: > >> > >>> At the risk of a protracted and rancorous political dispute, I'd > >>> like an informal vote on which is most "beautiful": > >>> e^(iπ) = -1 or e^(iπ) + 1 = 0 ? > >>> —rwg > >>> I get polarized just thinking about it. > >>> _______________________________________________ > >>> math-fun mailing list > >>> math-fun(a)mailman.xmission.com > >>> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > >>> > >> > >> > >> -- > >> Thane Plambeck > >> tplambeck(a)gmail.com > >> http://counterwave.com/ > >> _______________________________________________ > >> math-fun mailing list > >> math-fun(a)mailman.xmission.com > >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > >> > > _______________________________________________ > > math-fun mailing list > > math-fun(a)mailman.xmission.com > > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Think you're good at Trig?
by Bill Gosper 18 Jan '19

18 Jan '19

I gave ries ArcTan[1/2]/ArcTan[1/3`22] and it quickly found. Cos[\[Pi]/(x + 1)] == 7/25 Quick, is that right?-) But interestingly, it can't do ArcTan[1/2]/ArcTan[1/4`22] There's probably a way to turn on arctrigs, but my manual is ancient. —rwg

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[math-fun] New CPU does 4x4 *matrix* multiply-accumulate !
by Henry Baker 17 Jan '19

17 Jan '19

The new CPU from "Tachyum" (www.tachyum.com) claims to do full 64bit floating point 4x4 matrix multiply- accumulate operations; i.e., (R4x4) = (M4x4).(N4x4)+(P4x4) So we can now do full *quaternion* arithmetic as easily as real & complex arithmetic. Also, makes block matrix ops a lot easier.

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[math-fun] Deutsche Mathematiker essen keinen Maiskolben
by Henry Baker 16 Jan '19

16 Jan '19

"Germans use the word 'fressen' to describe the act of an animal feeding, as opposed to 'essen' for a human eating. Eating corn from the cob is pure 'fressen'." Boutard, Anthony. "Beautiful Corn: America's Original Grain from Seed to Plate". 2012. Gauss, Hilbert, Noether, etc. Not a kernel of truth to the rumor that they ate corn, much less on the cob. --- Joke about German cooking and corn: "My German grandmother boiled corn on the cob for 24 hours, and it was still hard in the middle." At 01:09 PM 1/16/2019, rcs(a)xmission.com wrote: > <The mailing-list software rejected this message from Thomas Colthurst. > I've deleted the image; presumably it's in the article. --rich> > >--- >Date: Wed, 16 Jan 2019 08:20:10 -0500 >Subject: Math preference / corn-eating correlation debunked? >From: Thomas Colthurst <thomaswc(a)gmail.com> > >From >https://slatestarcodex.com/2019/01/15/kernel-of-doubt-testing-math-preferen… > ><image of bar graph; text mentions algebraists, analysts, spirals, and rows> > >with no statistical significance in the difference according to chi-squared. > >-Thomas C

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Re: [math-fun] Math preference / corn-eating correlation debunked?
by Henry Baker 16 Jan '19

16 Jan '19

Perhaps Aussie mathematicians use corncobs for backdooring scytale encryption used on text messages sent via htTPs. https://en.wikipedia.org/wiki/Scytale https://www.newscientist.com/article/2140747-laws-of-mathematics-dont-apply… Mathematicians around the world are rushing to check millennia of calculations, as the Australian prime minister Malcom Turnbull has explained that their discoveries aren't as concrete as we thought. "The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia," said Turnbull. At 01:09 PM 1/16/2019, rcs(a)xmission.com wrote: > <The mailing-list software rejected this message from Thomas Colthurst. > I've deleted the image; presumably it's in the article. --rich> > >--- >Date: Wed, 16 Jan 2019 08:20:10 -0500 >Subject: Math preference / corn-eating correlation debunked? >From: Thomas Colthurst <thomaswc(a)gmail.com> > >From >https://slatestarcodex.com/2019/01/15/kernel-of-doubt-testing-math-preferen… > ><image of bar graph; text mentions algebraists, analysts, spirals, and rows> > >with no statistical significance in the difference according to chi-squared. > >-Thomas C

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Re: [math-fun] Math preference / corn-eating correlation debunked?
by Dan Asimov 16 Jan '19

16 Jan '19

Back when I began grad school at Berkeley, the math grad students used to joke about how some of us were gooey (topology, geometry, analysis, etc.) and others were crunchy (algebra, logic, combinatorics, etc.). (I was definitely gooey. Nowadays I'm both crunchy *and* gooey.) Even if (as in the linked paper) corn-eating style is not correlated to this dichotomy, I am certain there are some correlations between personality and math preference. It would be interesting to analyze the statistics on this. —Dan Thomas Colthurst wrote: ----- >From https://slatestarcodex.com/2019/01/15/kernel-of-doubt-testing-math-preferen… <image of bar graph; text mentions algebraists, analysts, spirals, and rows> with no statistical significance in the difference according to chi-squared. -----

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[math-fun] Math preference / corn-eating correlation debunked?
by rcs＠xmission.com 16 Jan '19

16 Jan '19

<The mailing-list software rejected this message from Thomas Colthurst. I've deleted the image; presumably it's in the article. --rich> --- Date: Wed, 16 Jan 2019 08:20:10 -0500 Subject: Math preference / corn-eating correlation debunked? From: Thomas Colthurst <thomaswc(a)gmail.com> From https://slatestarcodex.com/2019/01/15/kernel-of-doubt-testing-math-preferen… <image of bar graph; text mentions algebraists, analysts, spirals, and rows> with no statistical significance in the difference according to chi-squared. -Thomas C

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[math-fun] *linear* decoding of ECC code ?
by Henry Baker 16 Jan '19

16 Jan '19

The simplest form of ECC is that for a single bit: 0 -> 000, 1 -> 111. The decoding rule is also a simple majority test: 001/010/100 -> 0; 110/101/011 -> 1. My problem: I'd like an ECC code that can be computed *linearly* -- i.e., via a (chain of) matrix multiplication(s). Thus, codeword . R . P = decodedword Where R is an invertible matrix and P is some non-invertible matrix -- e.g., a projection matrix. I haven't been able to find a linear decoding for this version of ECC, nor have I been able to convince myself that it is impossible. If this type of ECC can't be decoded in a linear fashion, is there any other type of ECC that can?

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[math-fun] More examples of serious weirdness for higher integers?
by Dan Asimov 16 Jan '19

16 Jan '19

I'm interested in very natural examples in math where something goes askew in a big way after some low integers. In topology, it's known that the n-dimensional sphere (the unit sphere in R^(n+1) cannot have more than one smooth structure if n = 1, 2, 3, 5, 6. Almost every sphere of dimension >= 7 does have more than 1. (The case n = 4 is unresolved.) As Adam pointed out, the symmetric and alternating groups S_n, A_n, have some strange things happening for low n. Like A_n is simple, except not for n = 4. The outer automorphism group Out(S_n) is trivial for all n *except* for n = 6 (there is an outer automorphism). What are the best examples of this kind of thing in various branches of math? I'm not so interested in things like "Every integer greater than 127401 is the sum of 17 9th powers." I just made that up, but you get the idea. —Dan

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