August 2007 - mathfun@mailman.xmission.com

[math-fun] reminder - this is a family list
by Richard Schroeppel 27 Aug '07

27 Aug '07

The Math-Fun list is a family list. We have several teenage subscribers. Referring to the Prom Theorem, there are several things that could spoil it: a) Averages must match, but medians don't need to. Nothing says that the distributions of the two groups are the same. b) There could be recall bias, especially at higher numbers. c) The Prom Theorem assumes a definite beginning and end to the dance. If it's a permanent on-going affair, snapshots don't have to add up. d) Interview subject selection bias. Some people have left the dance early and moved out of state. They don't get interviewed. e) Ambiguity about "What's a dance?". f) Assumption of a bipartite graph, with edges. g) Possible confusion between number of dances, and number of different dance partners. I'm sure that Prof. Gale knows all of these, but perhaps Ms. Kolata has overlooked some of them. Rich

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[math-fun] Re: Sexual activity and mathematics: a math-funner appears in a Vancouver Sun editorial
by Dan Asimov 26 Aug '07

26 Aug '07

This was already mentioned in the New York Times, but now that it's hit the local paper I can no longer keep its existence a secret: < http://www.canada.com/vancouversun/news/editorial/story.html?id=4668b9b9-72… >. Alas, the New York Times article has slipped behind its paywall, but what appears to be the selfsame article .can for now be found at < http://www.dallasnews.com/sharedcontent/dws/dn/opinion/points/stories/DN-ko… >. --Dan

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Re: [math-fun] Constructivist logic
by Eugene Salamin 26 Aug '07

26 Aug '07

----- Original Message ---- From: Fred lunnon <fred.lunnon(a)gmail.com> To: math-fun <math-fun(a)mailman.xmission.com> Sent: Saturday, August 25, 2007 5:18:45 PM Subject: Re: [math-fun] Constructivist logic On 8/25/07, Eugene Salamin <gene_salamin(a)yahoo.com> wrote: > Could some constructivists or intuitionists answer the following. There are two summits on a mountain ridge. You are a peak bagger; you need to hike to the highest peak. The two peaks look equally high, and the map says they have the same elevation. So you just hike up both of them. Can you truthfully assert that you have climbed to the high point of the ridge? Why might this question be expected to receive different answers from intuitionists vis-a-vis nonconstructivists? WFL I thought that for an intuitionist, to prove A or B, it is necessary to either prove A or to prove B. I was curious as to how an intuitionist would apply that principle to real life situations. Gene ____________________________________________________________________________________ Need a vacation? Get great deals to amazing places on Yahoo! Travel. http://travel.yahoo.com/

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Re: [math-fun] Constructivist logic
by Eugene Salamin 26 Aug '07

26 Aug '07

Could some constructivists or intuitionists answer the following. There are two summits on a mountain ridge. You are a peak bagger; you need to hike to the highest peak. The two peaks look equally high, and the map says they have the same elevation. So you just hike up both of them. Can you truthfully assert that you have climbed to the high point of the ridge? Gene ____________________________________________________________________________________ Yahoo! oneSearch: Finally, mobile search that gives answers, not web links. http://mobile.yahoo.com/mobileweb/onesearch?refer=1ONXIC

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Re: [math-fun] Doppler shift and relativity
by Eugene Salamin 25 Aug '07

25 Aug '07

----- Original Message ---- From: Gary McGuire <gary.mcguire(a)ucd.ie> To: math-fun <math-fun(a)mailman.xmission.com> Sent: Friday, August 24, 2007 4:31:33 AM Subject: Re: [math-fun] Doppler shift and relativity On 8/23/07, Eugene Salamin <gene_salamin(a)yahoo.com> wrote: > Let's look at the Doppler shift in light due to the velocity v of an observer..... I've been wondering from time to time about a different question about Doppler: Suppose you are driving along a motorway exceeding the speed limit, and you notice a cop with a speed gun aimed at you and he/she is about to take a reading of your speed. You jam on the brakes, and the reading is actually taken as you are deccelerating. How is the reading on the gun affected? Could it appear that you are below the speed limit when in fact you are above it? This happened to, er, a friend of mine who didn't get a ticket. (Of course there are many other possible explanations as to why he didn't get a ticket.) Gary McGuire The answer depends on the details of the radar gun, mainly its response time and display update time. Hard and sudden braking for no apparent reason is unsafe and that might attract undesired attention from the cop. Here's my technique for avoiding speeding tickets: Don't exceed the speed limit. Then you need not be alert for the highway patrol, can give your full attention to driving safely. Gene ____________________________________________________________________________________Ready for the edge of your seat? Check out tonight's top picks on Yahoo! TV. http://tv.yahoo.com/

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Re: [math-fun] Doppler shift and relativity
by James Propp 25 Aug '07

25 Aug '07

>Suppose you are driving along a motorway exceeding the speed limit, >and you notice a cop with a speed gun aimed at you and he/she is about >to take a reading of your speed. You jam on the brakes, and the >reading is actually taken as you are deccelerating. How is the >reading on the gun affected? Could it appear that you are below the >speed limit when in fact you are above it? This question remind me of the way Prof. Dan Kleitman at MIT says he once tried to beat a speeding ticket: he claimed in court that the radar gun was (or could have been) at least partly aimed at the very top of his tire, whose velocity in the forward direction would be TWICE the velocity of the car, leading the radar gun to overestimate his speed by a factor fo 2. Kleitman's theory didn't convince the judge, and he ended up having to pay the speeding ticket, but it's still a good story, and one that's fun to tell at the start or end of a calculus class. There's a nice way to see that when a wheel is moving forward with velocity v, the top of the wheel is moving forward with velocity 2v: use the fact that the hub is always midway between the top and bottom, and the fact that the bottom of the wheel is moving forward with velocity zero. Jim Propp

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Re: [math-fun] Constructivist logic
by Dan Asimov 25 Aug '07

25 Aug '07

Jason asked what[math-fun thinks of constructivist logic. I'm very "maximal" about what qualifies as set having real existence. Anything that can exist does exist, as far as I'm concerned. I think asking what can be computed in a finite sense, as the Constructivists do, is a worthy endeavor. But that to me is no reason to ignore all the mathematics that views countable and continuum as sets of unequal size (because of Cantor's diagonal proof, yes). To try to understand what human beings can and cannot ever know and in what way -- this is a worthy endeavor. But there must exist some proposition of number theory which can be proved neither true nor false by axiomatic reasoning, despite the fact that checking the proposition over all combinations of integers could, in priciple, be done in a finite amount of time by a computer that could compute arbitrarily fast. And that check would settle the truth of the proposition once and for all. Do the Constructionsists not mind having to view ostensibly really-true (or really-false, whichever the case may be) propositions as undecidable? --Dan

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[math-fun] the rising ratio
by Thane Plambeck 25 Aug '07

25 Aug '07

>From The Economist, 28 July 2007, pg 25, "Japan's changing demography:" * * * By 2030, demographers say, Japan will have just two working-age people for each retired one; by mid-century, short of a rapid and unlikely return to fecundity, the ratio will rise to three for every two retirees. * * * [ seems wrong to me, but i guess a reading that has it comparing 1/2 to 2/3 is possible ] -- Thane Plambeck tplambeck(a)gmail.com http://www.plambeck.org/ehome.htm

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[math-fun] Re: glyph
by Steve Witham 24 Aug '07

24 Aug '07

>From: Bill Gosper <rwmgosper(a)yahoo.com> > > PS, p 73: IMPROVING YOUR REASONING SKILLS >A glyph is a symbol that presents information nonverbally. > > No it isn't. It's a carving, e.g. petroglyph or dermatoglyphics. >They probably mean ideogram. Way to go, Accuracy Checker. On this page a couple dictionaries back up their use as well as yours: http://www.answers.com/glyph&r=67 A particular shape for a character is a called glyph, too. The wikipedia page included there has some etymology. --Steve

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[math-fun] article at the new statesman
by Thane Plambeck 24 Aug '07

24 Aug '07

snip * * * Complicite's latest production is inspired by the life of the Indian mathematician Srinivasa Ramanujan. Nikita Lalwani traces his short life and extraordinary story http://www.newstatesman.com/200708230027 -- Thane Plambeck tplambeck(a)gmail.com http://www.plambeck.org/ehome.htm

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