March 2009 - mathfun@mailman.xmission.com

[math-fun] Free will ...
by Guy Haworth 27 Mar '09

27 Mar '09

c.f. 'Words, words, words' from Bernstein's Candide. Track 21 of 28 on the (UK) National Theatre's 1999 Performance. CDs but regrettably not DVDs (missed that one) still available. If any production ever sets the bar higher, I want to be there! As in Candide, the 'best of all possible worlds' seems to have been replaced lately by a need to 'make our garden grow' :-( Guy

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[math-fun] promic numbers or pronic numbers?
by James Buddenhagen 27 Mar '09

27 Mar '09

Numbers of the form n(n+1), where n is a positive integer are sometimes called "pronic numbers". See: http://en.wikipedia.org/wiki/Pronic_number However, in Sloane's OEIS both Richard Guy and Michael Somos say this is incorrect and it should be "promic numbers". See http://www.research.att.com/~njas/sequences/?q=2%2C6%2C12%2C20%2C30&sort=0&… I can't find either in any of my dictionaries. Which is correct? And what are the roots? Jim

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Re: [math-fun] If We Have Free Will, Then So Do Electrons
by Henry Baker 27 Mar '09

27 Mar '09

Hopefully, these upcoming lectures will appear as Princeton University podcasts, which you can get for free & automatically using iTunes (or other podcast receiver): http://www.princeton.edu/WebMedia/podcasts/ At 01:24 PM 3/20/2009, Ray Tayek wrote: >http://science.slashdot.org/article.pl?sid=09/03/20/1229233 > >snahgle writes "Mathematicians John Conway (inventor of the Game of Life) and Simon Kochen of Princeton University have proven that if human experimenters demonstrate 'free will' in choosing what measurements to take on a particle, then the axioms of quantum mechanics require that <http://arxiv.org/abs/quant-ph/0604079>the free will property be available to the particles measured, or to the universe as a whole. Conway is giving <http://www.princeton.edu/main/news/archive/S23/69/84A24/index.xml?section=a…>a series of lectures on the 'Free Will Theorem' and its ramifications over the next month at Princeton. A followup <http://www.ams.org/notices/200902/rtx090200226p.pdf>article strengthening the theory (PDF) was published last month in Notices of the AMS." > >--- >vice-chair http://ocjug.org/

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Re: [math-fun] Freeman Dyson integer problem
by Eric Angelini 26 Mar '09

26 Mar '09

Let's try to "cycle": Is there an integer with digits abcdefg...klm where mabcdefg...kl is m times abcdefg...klm then lmabcdefg...kl is l times mabcdefg...kl then klmabcdefg...kl is k times mabcdefg...k then (etc.) Best, É. -----Message d'origine----- De : math-fun-bounces(a)mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Cordwell, William R Envoyé : jeudi 26 mars 2009 18:57 À : math-fun Objet : Re: [math-fun] Freeman Dyson integer problem Using the same idea, start with 2, and consecutively divide by 3, to obtain 3*2068965517241379310345827586 = 6206896551724137931037482758 -----Original Message----- From: math-fun-bounces(a)mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Allan Wechsler Sent: Thursday, March 26, 2009 11:16 AM To: math-fun Subject: Re: [math-fun] Freeman Dyson integer problem For some reason I haven't quite figured out the algebra, but permit me to report that 923076/3 = 307692, with two digits moving to the back. On Thu, Mar 26, 2009 at 12:12 PM, Cordwell, William R <wrcordw(a)sandia.gov>wrote: > So, one can just start with a digit and start working backwards, at > each point dividing by 2 and seeing if it "works" when the digit > repeats? E.g., > 315789473684210526 will also work; 421052631578947368, etc. > > Bill C. > > -----Original Message----- > From: math-fun-bounces(a)mailman.xmission.com [mailto: > math-fun-bounces(a)mailman.xmission.com] On Behalf Of Veit Elser > Sent: Thursday, March 26, 2009 9:17 AM > To: math-fun > Subject: Re: [math-fun] Freeman Dyson integer problem > > 421052631578947368 / 210526315789473684 = 2 > > smallest k, such that 10^k - 2 is divisible by 2 x 10 - 1 = 19, is k = > 17 > > Veit > > > On Mar 26, 2009, at 3:52 PM, Henry Baker wrote: > > > http://www.nytimes.com/2009/03/29/magazine/29Dyson-t.html > > > > "At Jason, taking problems to Dyson is something of a parlor trick. > > A group of scientists will be sitting around the cafeteria, and one > > will idly wonder if there is an integer where, if you take its last > > digit and move it to the front, turning, say, 112 to 211, it's > > possible to exactly double the value. Dyson will immediately say, > > "Oh, that's not difficult," allow two short beats to pass and then > > add, "but of course the smallest such number is 18 digits long." > > When this happened one day at lunch, William Press remembers, "the > > table fell silent; nobody had the slightest idea how Freeman could > > have known such a fact or, even more terrifying, could have derived > > it in his head in about two seconds." The meal then ended with men > > who tend to be described with words like "brilliant," "Nobel" and > > "MacArthur" quietly retreating to their offices to work out what > > Dyson just knew." > > > > Is this correct? > > > > > > _______________________________________________ > > math-fun mailing list > > math-fun(a)mailman.xmission.com > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ 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] Everett & self-aware observers
by sw＠tiac.net 26 Mar '09

26 Mar '09

>From: Rowan Hamilton <rowan(a)arctic.org> > >But it does seem to me that tossing out the old Copenhagen interpretation >of the collapse of the wave function (which is what I was taught in >college), and accepting the Everett interpretation (which I know a bit >about) *does* seem to imply, at least in my naive perspective, the >requirement of a self-aware observer. (Is there any other kind of >observer?) Hmm, maybe you could describe how. I thought Everett *got rid of* any special role for measurement, observer, etc. Instead what you get by with is correlation. So, two particles that haven't interacted, or a particle and a detector, start out having independent distributions of (phasey) states they can be in, but once they interact, their distributions are correlated. So you might start with particle spin up or spin down, crossed with detector detects it or not, so the world is spread over all four combinations: yes | ????? | ?????? detector ---+-------+-------- no | ????? | ?????? ---+-------+-------- | up | down particle But then they interact and it narrows down to (say): yes | ????? | detector ---+-------+-------- no | | ?????? ---+-------+-------- | up | down particle Which divides the distribution into two parts that aren't going to interact anymore. I am missing a lot here but the point is that this is just following the regular rules for the evolution of the wave function and yet the world has split into two separated worlds, one where the particle went one way and was detected, and one, where it went the other way and wasn't and won't be. And sure, if there are observers, in one world they'll see (the effects of) the event definitely happening, and in the other, definitely not, but any observers are latecomers to the action as it were, not particularly involved in or necessary to how it works. The world just really splits, and we inhabitants of the splinters just see (individual examples of) the results. --Steve

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[math-fun] Freeman Dyson integer problem
by Henry Baker 26 Mar '09

26 Mar '09

http://www.nytimes.com/2009/03/29/magazine/29Dyson-t.html "At Jason, taking problems to Dyson is something of a parlor trick. A group of scientists will be sitting around the cafeteria, and one will idly wonder if there is an integer where, if you take its last digit and move it to the front, turning, say, 112 to 211, its possible to exactly double the value. Dyson will immediately say, Oh, thats not difficult, allow two short beats to pass and then add, but of course the smallest such number is 18 digits long. When this happened one day at lunch, William Press remembers, the table fell silent; nobody had the slightest idea how Freeman could have known such a fact or, even more terrifying, could have derived it in his head in about two seconds. The meal then ended with men who tend to be described with words like brilliant, Nobel and MacArthur quietly retreating to their offices to work out what Dyson just knew." Is this correct?

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Re: [math-fun] Freeman Dyson integer problem
by Henry Baker 26 Mar '09

26 Mar '09

Very elegant! At 08:57 AM 3/26/2009, Dave Blackston wrote: >My solution is a little different... > >suppose x is our number, and it has last digit d. Further, let X be the >rational number formed by repeating x after a decimal point, i.e., if x is >112, then X is .112112112112... > >The constraints imply that X/10 + d/10 = 2X, or X=d/19. Clearly X>.1, so >d>1. This means the smallest such X occurs for d=2, X=2/19, and x is the >repeated block for the decimal 2/19, which has 18 digits since 10 is a >primitive root mod 19. > >On Thu, Mar 26, 2009 at 8:32 AM, victor miller <victorsmiller(a)gmail.com>wrote: > >> The explanation is that Freeman Dyson (who started his career as a Number >> Theorist in case you've forgotten) remembered that 10 was a primitive root >> mod 19, and observed that 2*10 = 1 mod 19, so that 2 would have to be a >> "tail end" of the powers of 10 mod 19. >> >> Victor >> >> On Thu, Mar 26, 2009 at 11:29 AM, victor miller <victorsmiller(a)gmail.com >> >wrote: >> >> > Suppose that the number in question is 10n + a (where a is the lowest >> > digit). The transformed number is a*10^r + n. If that's equal to double >> > the original we get >> > >> > a(10^r - 2) = 19 n, so that 19 has to divide 10^r-2 (since it's prime and >> > bigger than a). 10 is a primitive root mod 19, and you can check that 2 = >> > 10^17 mod 19, so that r must be 17 mod 18. You can check >> > that (10^17 - 2)/19 = 2*q, where q is a prime. Thus the number in question >> > is 10*q + 2. >> > >> > Victor >> > >> > ---------- Forwarded message ---------- >> > From: Henry Baker <hbaker1(a)pipeline.com> >> > Date: Thu, Mar 26, 2009 at 10:52 AM >> > Subject: [math-fun] Freeman Dyson integer problem >> > To: math-fun(a)mailman.xmission.com >> > >> > http://www.nytimes.com/2009/03/29/magazine/29Dyson-t.html >> > >> > "At Jason, taking problems to Dyson is something of a parlor trick. A >> > group of scientists will be sitting around the cafeteria, and one will idly >> > wonder if there is an integer where, if you take its last digit and move it >> > to the front, turning, say, 112 to 211, its possible to exactly double the >> > value. Dyson will immediately say, Oh, thats not difficult, allow two >> > short beats to pass and then add, but of course the smallest such number is >> > 18 digits long. When this happened one day at lunch, William Press >> > remembers, the table fell silent; nobody had the slightest idea how Freeman >> > could have known such a fact or, even more terrifying, could have derived it >> > in his head in about two seconds. The meal then ended with men who tend to >> > be described with words like brilliant, Nobel and MacArthur quietly >> > retreating to their offices to work out what Dyson just knew." >> > >> > Is this correct?

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[math-fun] Free will ...
by Guy Haworth 26 Mar '09

26 Mar '09

I have decided to let you brighter minds argue the toss and let me know. I think that was free will. "I think I have free will: therefore I have". Haworth (2009) [ Who knows: I might be right. ] G

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Re: [math-fun] If We Have Free Will, Then So Do Electrons
by Dan Asimov 26 Mar '09

26 Mar '09

Ever since I learned from Dennett's "Understanding Consciousness" that he does not believe in the existence of qualia (aka conscious experience*), I have seriously wondered whether it's worth the trouble to read anything else he wrote. (He later summarized his argument in "Quining qualia", online at < http://ase.tufts.edu/cogstud/papers/quinqual.htm >.) --Dan ___________________________________ * See, e.g., < http://plato.stanford.edu/entries/qualia/ > Steve Witham wrote: << I agree that Dennett's "Elbow Room" does a pretty good job of disentangling (heh) quantum whatsit issues from more sensible ponderings about free will. . . . >> _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] If We Have Free Will, Then So Do Electrons
by Steve Witham 25 Mar '09

25 Mar '09

I agree that Dennett's "Elbow Room" does a pretty good job of disentangling (heh) quantum whatsit issues from more sensible ponderings about free will. Anyway, the term "free will" in the recent paper is just a special technical term for the purpose of the paper, provides no useful connection to philosophy, and is either a conscious joke or dig at the theories it's criticizing, or is a really bad choice that mainly serves to confuse conversations about the result. |http://arxiv.org/PS_cache/quant-ph/pdf/0604/0604079v1.pdf | |Mind you |- it's not really about free will, free will is a |stronger and fuzzier |claim than non determinism |- it doesn't really disprove determinism because then the |experiment itself |is a deterministic event. | |The main result seems to be disproving ( special |relativity ^ GRW ) and |Yah, that terminology is a distraction. | ||The main result seems to be disproving ( special ||relativity ^ GRW ) | |And also a variety of hidden variable theories. :) GRW as I understand it is a theory where individual particles actually collapse their state, but very rarely. --Steve -- My apples and oranges are beyond compare!

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