October 2011 - mathfun@mailman.xmission.com

Re: [math-fun] Zillions
by N. J. A. Sloane 12 Oct '11

12 Oct '11

Dan, You might also be amused by my sequence A000052, which dates from about 1965, and has a (marginally) more mathematical definition. Neil > Circa 1980 someone at MIT showed me a little pamphlet floating around, > created by Gian-Carlo Rota, of all the integers between I think > 1 and 1000, listed purely in English, alphabetically. The idea > that this could have any conceivable use struck me as so absurd > that I could not stop laughing for quite a while.

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[math-fun] fastest computer ? (single operation).
by Simon Plouffe 12 Oct '11

12 Oct '11

Hello, As you may know, the fastest computer is currently a japanese machine called K, which can do 10 petaflops (?) or something like that. These machines are made with ordinary components at the base like Intel processors or Opteron + many GPU like Nvidia. This is all very impressive but I am wondering, what is the fastest single operation computer on this planet ? A souped-up Intel machine running overclocked at 4 ghz ? Is there somebody that knows the answer to that question ? In other words, if someone wants to run let's say the Mersenne test for a prime which is not yet implemented in parallel then on which machine would that algorithm run the fastest ? Best regards and ha ve a nice evening. Simon Plouffe

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Re: [math-fun] somewhat related to "words for really long numbers
by Phil Carmody 12 Oct '11

12 Oct '11

Bill Gosper <billgosper(a)gmail.com>: > Yeah, what about 2*10^4679+3, (two zillion and three)-? It seems to precede 2*10^4772+2003 (two zillion two thousand and three) Phil -- [aside - I'm very pro- correct email usage, but use the digest so can't reply (header-wise) to a real post; I always try to manually get the subject line correct - does this mess up people's threading?]

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Re: [math-fun] Judge rules 'Bayes' can no longer be used ...
by Henry Baker 12 Oct '11

12 Oct '11

I hope that the judge will now throw away his computer; modern disk drive read heads are designed to take advantage of Bayes' Theorem. --- BTW, I've been meaning to ask math-fun this question for a long time. I seem to recall that someone solved the following problem, but I've been unable to locate the solution. Bayes' Theorem takes advantage of whatever a priori information you might have to refine that probability based on a new observation. Suppose that you don't have very good information about the shape of the a priori probability curve, but may know some simple facts -- e.g., the mean, standard deviation, etc. You then do an experiment & refine the shape, but still don't have a very good idea about the precise shape. I think that someone suggested a particular family of parameterized curves for a probability distributions that is particularly well suited for Bayesian analysis/computations, in that the experiments modify the parameters of the curve, but keep the subsequent curve in the same family. Does anyone know which family of curves might be useful in this regard and/or a link to some info ? At 09:26 AM 10/11/2011, Guy Haworth wrote: >Apologies if this surfaced before, but I haven't seen it go by. > >A formula for justice > >Bayes' theorem is a mathematical equation used in court cases to analyse statistical evidence. But a judge has ruled it can no longer be used. Will it result in more miscarriages of justice > >http://www.guardian.co.uk/law/2011/oct/02/formula-justice-bayes-theorem-mis… > >Guy

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[math-fun] Machine Go
by rcs＠xmission.com 12 Oct '11

12 Oct '11

Science Daily has a report of a recent success for a Go program. http://www.sciencedaily.com/releases/2009/05/090514083931.htm The program Huygens defeated two professional Go players. The program had handicaps of 6 or 7 stones. Question for the Go players among us: Does a handicap of 6 stones mean that the starting board has 6 stones added for the weaker player, or that 6 is added to the final score? Rich

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Re: [math-fun] Judge rules 'Bayes' can no longer be used ...
by Dan Asimov 11 Oct '11

11 Oct '11

Freudian slip? Her name is Angela Saini. --Dan << Can anyone find an error or garble in that column? I didn't. Perhaps we can use Bayesian analysis to estimate the probability that Angela Saint is a rare and welcome talent! >> Sometimes the brain has a mind of its own.

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Re: [math-fun] Judge rules 'Bayes' can no longer be used ...
by Bill Gosper 11 Oct '11

11 Oct '11

http://www.guardian.co.uk/law/2011/oct/02/formula-justice-bayes-theorem-mis… Can anyone find an error or garble in that column? I didn't. Perhaps we can use Bayesian analysis to estimate the probability that Angela Saint is a rare and welcome talent! --rwg

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Re: [math-fun] Judge rules 'Bayes' can no longer be used ...
by Dan Asimov 11 Oct '11

11 Oct '11

No, that's not what happened. Buried in the article is this sentence: << [The judge] decided that Bayes' theorem shouldn't again be used unless the underlying statistics are "firm". >> Which is quite different from tossing out Bayes's theorem entirely. Further, if less-than-certain statistics can be assigned to intervals with virtual certainty, then Bayes's theorem can still be used to get bounds on the conditional probability, which may be all that is needed. --Dan << A formula for justice Bayes' theorem is a mathematical equation used in court cases to analyse statistical evidence. But a judge has ruled it can no longer be used. Will it result in more miscarriages of justice http://www.guardian.co.uk/law/2011/oct/02/formula-justice-bayes-theorem-mis… >> Sometimes the brain has a mind of its own.

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[math-fun] Judge rules 'Bayes' can no longer be used ...
by Guy Haworth 11 Oct '11

11 Oct '11

Apologies if this surfaced before, but I haven't seen it go by. A formula for justice Bayes' theorem is a mathematical equation used in court cases to analyse statistical evidence. But a judge has ruled it can no longer be used. Will it result in more miscarriages of justice http://www.guardian.co.uk/law/2011/oct/02/formula-justice-bayes-theorem-mis… Guy

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[math-fun] Onward and Upward with the Arts: Moneyball
by Hilarie Orman 05 Oct '11

05 Oct '11

The movie "Moneyball" is about baseball statistics. Putting a human touch on this subject seems nearly impossible, but the movie is primarily about how people deal with the emotional side of taking a calculated risk. If I were younger I might think that it held great life lessons about determination, courage, and the triumph of glorious mathematics over stodgy old men. I recommend it today because it has some great moments of humor, and because it illustrates one step in what turns out to be a long and continuing saga of mathematics applied to sports. Baseball teams have finite budgets for player salaries, and the ratio can be as much as 5 to 1. In order to get into post-season play, a team needs to win more than 90 games. What is the least money needed to buy players who can assure that? That's the game of "moneyball". Surprisingly, until recently, the concept of maximizing return on player investment had little traction. Managers got the best (i.e., most highly paid) players that they could afford. More surprisingly, there has been plenty of mathematical and modeling information available to guide moneyball players (i.e., general managers) for decades. The movie "Moneyball" is about how "conventional" baseball wisdom finally started being displaced by statistical wisdom. What was the impediment to this displacement? It seems to me that there were two factors which are probably common to all group endeavors. The first is that the reward system was skewed. Teams that spent a lot but did not perform to expectation were still admired because they had good players, and teams that did well on low budgets aspired to buy expensive players. Secondly, the decision process for selecting players is consensus-based, and that is inherently conservative. Again, the reward for selecting a good team is too little --- the analysts themselves are like players that are not subjected to individual metrics. Are they doing well or not? Without the metric, they evaluate themselves and reward consensus over excellence. I was surprised to discover that there a model of human aversion to risk. See Prospect Theory, http://en.wikipedia.org/wiki/Prospect_theory This caused me to wonder about conventional wisdom about decision making. I've read that in general, "crowds" do well at Bayesian decisions. Apparently committees don't. As for Moneyball, it's effects are longlasting. This is a good article about it: http://www.grantland.com/story/_/id/6466015/cashing-new-moneyball Baseball isn't my game, though. I like NFL football. So, naturally I've wondered if there a version of moneyball for football, soccer, basketball, lacrosse, or Ultimate? Maybe not. Field-based team sports are harder to analyze. Baseball has some very simple metrics that are clearly tied to winning, e.g. "he gets on base." Having 10 to 22 people in motion at once is complicated. Which individual performance metrics most strongly predict success? As far as I know, this is an open question. For the most part, team sports on a playing field are about control of space. Strategies that can create open space adjacent to players are the most successful It is like chess. But, because everyone is in motion, the space is also in motion. There's also a premium for maintaining space around the player with the "ball" (like avoiding checkmate). If you can turn that into player metrics, then you could invent "Money Football" and be as famous as Bill James (read "Moneyball" the book). Hilarie

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