December 2013 - mathfun@mailman.xmission.com

[math-fun] Group theory question
by Eugene Salamin 26 Dec '13

26 Dec '13

Let G be a group, and let S be the permutation group on G. For a in G, let L(a) be the permutation that sends x to ax, and let R(b) be the permutation that sends x to xb' (' denoting inverse). Then im L and im R are isomorphic copies of G in S, and each is the centralizer in S of the other. I have a vague memory of having seen a proof of the statement concerning centralizers, but can't pin it down. Can someone point me to either a proof, or a counterexample? -- Gene

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[math-fun] Better late than never? Turing has been pardoned.
by Mike Speciner 26 Dec '13

26 Dec '13

http://edition.cnn.com/2013/12/24/world/europe/alan-turing-royal-pardon/ind…

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[math-fun] Turing -- world's fastest mathematician?
by Warren D Smith 26 Dec '13

26 Dec '13

The page http://www.turing.org.uk/scrapbook/run.html give's Turing's marathon time (August 1947) as 2hr 46min 03sec and the winner J.T.Holden's time as 2hr 33min 20sec. Contrasting this with wikipedia re the 1948 London Olympic marathon http://en.wikipedia.org/wiki/Athletics_at_the_1948_Summer_Olympics_–_Men's_marathon we see that Turing's time would have been good enough for him to place 15th out of the 30 finishers (41 starters), whereas Holden's time would have been good enough to just win gold. The Olympic course and/or conditions presumably were tougher, but even assuming that is worth 5 minutes, which is probably an overestimate, then Turing still would have placed 20th in the Olympics. Not too shabby! Turing was probably the world's fastest mathematician, (before say, 1970, anyhow).

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[math-fun] Alan Turing pardon
by Guy Haworth 25 Dec '13

25 Dec '13

I was of course delighted to hear this news. My wife said exactly the same as Andy Latto, straight of the bat - and she's always right. Kudos, Andy. I agree too. Guy

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Re: [math-fun] Better late than never? Turing has been pardoned.
by Henry Baker 25 Dec '13

25 Dec '13

[Not math, and not fun.] Actually, Americans share some of the blame for Turing's troubles. After Burgess defected in 1951, I suspect that things got pretty hot for any British homosexuals in secret positions who had contact with the U.S., since McCarthy & Hoover already thought that homosexuality was incompatible with secrecy: http://en.wikipedia.org/wiki/Lavender_Scare "... President Dwight D. Eisenhower to sign an Executive Order on April 29, 1953, that barred homosexuals from obtaining jobs at the federal level." http://en.wikipedia.org/wiki/J_Edgar_Hoover The British intensely desired the "Special Relationship" with the U.S., and so Turing (as an open homosexual) became an embarrassment to the British. Since Turing's work was so instrumental in saving lives & shortening the war, and he full well knew it, this shabby treatment (which he must have assumed would last the rest of his career) indicated that Turing's professional life going forward was not going to be particularly pleasant. Turing died in June 1954, possibly having committed suicide, although there are also darker theories about the cause of his death. Note also that many in both Britain & the U.S. considered Turing's code-breaking activities to be THE secret of WWII -- far more secret than the atomic bomb, which had already been copied at that point. At 10:41 AM 12/25/2013, Andy Latto wrote: >On Wed, Dec 25, 2013 at 6:35 AM, David Makin <makinmagic(a)tiscali.co.uk>wrote: > >> Also it hasn't been applied to all the others..... > >Yes, that was my thought. Shouldn't they be offering a blanket pardon and >apology to *everyone* convicted under those laws? Otherwise, aren't they >sending a message of "well, I guess we can put up with homosexuality if >you're brilliant and famous and a war hero,. Otherwise..."

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[math-fun] It's about time!
by meekerdb 24 Dec '13

24 Dec '13

This comes over 60 years too late <http://www.nytimes.com/2013/12/24/world/europe/alan-turing-enigma-code-brea…>. But at least it came.

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[math-fun] Speaking of spirals
by Bill Gosper 23 Dec '13

23 Dec '13

(Which I was if you got my rhumb addendum to the sin 1/x discussion) https://www.youtube.com/watch?v=LH8G7atCFSQ https://www.youtube.com/watch?annotation_id=annotation_2287679251&feature=i… Neglecting gravity (not by laying the thing flat!), shouldn't it be possible to eliminate the Archimedean spiral stator by replacing the straight rotor with a very particular curve a la a jai alai basket? Reproducibility might be a problem. --rwg (sin(1/x): What about spiralling into a black hole?)

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[math-fun] Fw: Mathematica 9.0 puzzle
by Wouter Meeussen 23 Dec '13

23 Dec '13

I tried Transpose[ Partition[ FromCharacterCode[#] & /@ Range[63488, 63488 + 55], 5]] // Grid but that doesn’t cut it. What’s the answer (on your system)? W.

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[math-fun] problem: intersecting annuli
by Warren D Smith 22 Dec '13

22 Dec '13

Consider an annulus in Euclidean D-space with inner radius R and outer radius R+W. (If D=2 this means the region inside R+W circle and outside R circle. If D=3 then spheres not circles.) Now consider the set-intersection of D such annuli, respectively centered at the D vertices of a (D-1)-dimensional simplex. What is the AREA (if D=2, or VOLUME if D=3) of this region, as a function of R,W and the simplex? An exact formula should be attainable but complicated when D=2 and D=3. (Trivial answer 2W when D=1.) But I am interested in the LIMIT of large R and small W with simplex fixed, and in this limit there should be a fairly simple asymptotically correct inexact formula. -- Warren D. Smith http://RangeVoting.org

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[math-fun] News article - RSA collaboration with NSA
by Eugene Salamin 21 Dec '13

21 Dec '13

http://news.yahoo.com/exclusive-secret-contract-tied-nsa-security-industry-… -- Gene

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