November 2016 - mathfun@mailman.xmission.com

[math-fun] Draft of my November 2016 blog post
by James Propp 13 Nov '16

13 Nov '16

I started writing a new draft titled "Breaking Logic with Self-Referential Sentences" and would love to get your feedback. I plan on publishing it on the 17th and will continue to tinker with it over the coming week. Suggestions for references, and comments of all kinds, are welcome. I appreciate candid criticism from people who are sympathetic to my aims but think I've fallen short of them. My prose style is designed to make the material accessible, but my breeziness should not be interpreted as indicating indifference to scholarly correctness. I'm especially in need of a good illustration or two for this post. I like each of my essays to contain at least one visual. And I *don't* want my readers to have to see Escher's "Drawing Hands" for the gazillionth time. Surely there's something less familiar that I could include. Please leave your feedback at https://mathenchant.wordpress.com?p=1338&shareadraft=581cfacf126c7 keeping in mind that the comments of EVERYONE on math-fun will get funneled through the same email conduit; if you want me to know who you are, please sign your comments! If you sign your comments I'll assume (unless you indicate otherwise) that you don't mind my acknowledging your contribution. Title: Breaking logic with self-referential sentences Beginning: I don't especially like people who talk a lot about themselves, but I have a soft spot for sentences that do. Case in point: the self-referential sentence "This sentence is false." I really like that one. You may think you've seen this sentence before, but in fact you've seen other sentences, each m... Read more: https://mathenchant.wordpress.com?p=1338&shareadraft= 581cfacf126c7 Thanks, Jim Propp

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Re: [math-fun] Landau's function of 2^16
by Dan Asimov 13 Nov '16

13 Nov '16

An interesting question! Did not know of Landau's function. Any partition with repeated sizes has the same LCM as if all the extra duplicates are replaced by ones. So at least partitions with repetition — except for ones — can be ignored. Yikes, this seems a Herculean task. Can anyone come up with reasonable upper or lower bounds, even? Or some kind of asymptotic bounds? Here is at least some relevant info: https://oeis.org/A000793. —Dan ----- . . . a reasonable way to evaluate Landau's function (A000793) at 2^16 = 65536. This is the maximum least common multiple of any partition of 65536; equivalently it is the maximum order of any element of Sym(65536). I am sure there are lots of shortcuts, that save one from enumerating all the partitions of 65536. Can anyone suggest one? . . . -----

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[math-fun] Not particularly math, possibly fun, particularly particles
by Bill Gosper 12 Nov '16

12 Nov '16

>Date: 2016-11-05 09:51 >From: Mike Speciner <ms(a)alum.mit.edu> >https://ms0.github.io/gas.html This is a great toy! I delete everything except six identical balls (and maybe one wall), set one ball to bounce around for a while before disrupting the others, run it half a minute into the disruption, save it out, and show it time-reversed to some unsuspecting person. Or if I'm afraid they'll notice the negative time passage, I manually negate all the velocities before saving. (Is there a way to load one of those text files?) Unfortunately, neither of these reversal stunts is perfect, due to accumulated numerical errors, which I assume you've worked hard to minimize. So let's get particularly math-y and ask: Given rational positions and velocities, can we simulate one of these six-ball scenarios exactly and indefinitely, without runaway denominator buildup, nor irrational collision results? --rwg

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[math-fun] The base 2-i, digits 0,i^0..3 spacefill
by Bill Gosper 11 Nov '16

11 Nov '16

(whose?) underlying the pretty gosper.org/dana.PNG has only moderately interesting Fourier gosper.org/rt5-324.png and polygonal gosper.org/rt5.png approximations. --rwg

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[math-fun] Differential Privacy and Poll Sampling
by Henry Baker 11 Nov '16

11 Nov '16

The pollsters in the recent presidential election didn't do a very good job of predicting the result. Apparently, one of the better polls -- the LATimes poll -- was heavily criticized for having one sample that appeared to be an outlier, but who affected the result quite significantly in a way that produced (in this particular case) a more *correct* prediction. It occurred to me that it might be a good idea to use some of the ideas from *differential privacy* to reduce the possibility of having a single sample point significantly affect the result. After all, the whole point of differential privacy is to make sure that a single sample point can't be identified using a small number of questions. The polls have also been criticized for "oversampling" -- i.e., applying the wrong weighting factors to different sample points. So, my modest proposal is to *oversample* rare combinations, but then *underweight* these oversamplings in such a way as to produce the overall correct weighting. The amount of oversampling should be calculable from the basic equations of differential privacy, which try to minimize any change due to the inclusion or elimination of any single sample point. https://en.wikipedia.org/wiki/Differential_privacy "The definition [of differential privacy] gives a strong guarantee that presence or absence of an individual will not affect the final output of the algorithm significantly."

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[math-fun] The bombshell from yesterday
by Henry Baker 09 Nov '16

09 Nov '16

No, not THAT bombshell, but this one, regarding *dark matter* and the Holographic Principle: https://science.slashdot.org/story/16/11/09/0031212/new-theory-of-gravity-m… https://arxiv.org/pdf/1611.02269.pdf New Theory of Gravity Might Explain Dark Matter (phys.org) 111 Posted by BeauHD on Wednesday November 09, 2016 @02:00AM from the spacetime dept. vikingpower writes: Dutch prodigy and Amsterdam University Professor Erik Verlinde published a paper on arXiv yesterday, November 7, titled "Emergent Gravity and the Dark Universe." In the paper, Verlinde derives gravity from the so-called Holographic Principle, which -- simply put -- states that gravity emerges from the interplay between and entropy re-arrangement of sub-atomic "strings" that live in a negatively curved spacetime. At that level [...] spacetime and gravity are emergent from an underlying microscopic description in which they have no a priori meaning." Most importantly, Verlinde's paper has as a consequence that dark matter, nemesis of many an astronomer, is nothing more than an illusion.

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[math-fun] A visual riddle (hard)
by Joerg Arndt 09 Nov '16

09 Nov '16

The arrangement in the square grid shown below has four-fold rotational symmetry and none of its squares (apart from the central one) has more than two neighbors. Of course there are very many such arrangements. This one, however, has a very special property, unique within all such(*) arrangements of 289 squares. (*) edge-to-edge connected, four fold symmetry, and fewest possible number of neighbors. Which? > ................................................... > ................................................... > ................................................... > ................................................... > ..........................#####.................... > ..........................#...#.................... > ..........................#...#.................... > ..........................#...#.................... > ..........................#...#.................... > ..........................#...#.................... > ..........................#...#.................... > ..................#########...#.................... > ..................#...........########............. > ............###...#..................#............. > ............#.#...#..........#########............. > ............#.#...#..........#..................... > ............#.#...#..........#..................... > ............#.#...########...#..................... > ............#.#..........#...#...#######........... > ............#.#..........#...#...#.....#........... > ....#########.#..........#...#...#.....#........... > ....#.........########...#...#...#.....#........... > ....#....................#.......#.....#........... > ....#....................#.......#.....#........... > ....########.............#.......#.....#........... > ...........#.....#################.....#........... > ...........#.....#.......#.............########.... > ...........#.....#.......#....................#.... > ...........#.....#.......#....................#.... > ...........#.....#...#...#...########.........#.... > ...........#.....#...#...#..........#.#########.... > ...........#.....#...#...#..........#.#............ > ...........#######...#...#..........#.#............ > .....................#...########...#.#............ > .....................#..........#...#.#............ > .....................#..........#...#.#............ > .............#########..........#...#.#............ > .............#..................#...###............ > .............########...........#.................. > ....................#...#########.................. > ....................#...#.......................... > ....................#...#.......................... > ....................#...#.......................... > ....................#...#.......................... > ....................#...#.......................... > ....................#...#.......................... > ....................#####.......................... > ................................................... > ................................................... > ................................................... > ................................................... Best regards, jj Hints below, after some several blank lines. Hints: A) 289 = 15^2 + 8^2 B) Consider two copies of the arrangement C) Consider 289 copies of the arrangement P.S.: almost-spoiler at http://jjj.de/visual-riddle/visual-riddle.png

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Re: [math-fun] peculiar sequence
by Joerg Arndt 09 Nov '16

09 Nov '16

Nobody asked, shame! What is the proof? Best regards, jj P.S.: broke the thread in order to not bury this in old-ish messages. * Tomas Rokicki <rokicki(a)gmail.com> [Sep 04. 2016 19:07]: > David Wilson's assertion that > > The number of zeroes at the end of n! is equal in bases 10 and 16 iff > > > > 0 <= sum of base-5 digits of n - sum of base-2 digits of n <= 3. > > > has a very sweet proof! I admit I started looking for a counterexample > before a proof, but I should have had more faith. > > I'm omitting the proof because I don't want to spare anyone else the > joy of discovery. > > -- > -- http://cube20.org/ -- [ <http://golly.sf.net/>Golly link suppressed; > ask me why] -- > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] Dump time zones in favor of UTC everywhere?
by Bill Gosper 08 Nov '16

08 Nov '16

On 2016-11-06 08:05, Eugene Salamin via math-fun wrote: > I agree, daylight savings time year round. > > -- Gene > > > > From: Gareth McCaughan <gareth.mccaughan(a)pobox.com> > To: math-fun(a)mailman.xmission.com > Sent: Sunday, November 6, 2016 3:48 AM > Subject: Re: [math-fun] Dump time zones in favor of UTC everywhere? > > On 06/11/2016 09:18, Adam P. Goucher wrote: > >> As a first approximation, I think that we should ditch Daylight Saving Time. >> A corollary of this is that the UK will permanently reside in Greenwich Mean >> Time, which is *almost* identical to UTC. > > I would prefer to ditch not-Daylight-Saving Time. The proper term is Daylight Wasting Time. --rwg

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Re: [math-fun] Dump time zones in favor of UTC everywhere?
by Henry Baker 07 Nov '16

07 Nov '16

"China has established a single time zone across its breadth, overlapping six time zones in its northern and southern neighbors" The great leap-second forward ? At 01:41 PM 11/5/2016, Dan Asimov wrote: >James Gleick argues that we should: > >http://www.nytimes.com/2016/11/06/opinion/sunday/time-to-dump-time-zones.ht… > >ÂDan

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