[math-fun] Re: radio math
From: James Propp <jpropp@cs.uml.edu>
I've been invited to speak on a college morning radio program next week, on the topic of mathematical proof and infinity. It'll be a conversation with two interviewers (no call-ins).
I've not notice anyone mention proofs of the infinitude of primes yet. That should be simple enough for anyone reasonably awake to understand, and introduces both important techniques used in mathematical proof as well as an infinity. Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed [stolen with permission from Daniel B. Cristofani] __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
I strongly second Phil's suggestion. The mathematical world didn't have to wait for Cantor to deal with infinity. Euclid and co. knew exactly what they were saying about the prime numbers and so would the average radio listener. You can get quite a bit of mileage out of this area. After describing Euclid's PROOF it's natural to think about possible primality for Fermat and Mersenne numbers. You can tell lots of interesting stories, how Euler factored F5, current results about finding large Mersenne's and factoring large Fermat's the intriguing fact that there are probably INFINITELLY many M's but only a finite number of F's, -we may know them all already. I would stay away from Cantorian infinity, much as we love it. People, as opposed to mathematicians, find it hard to digest and it really doesn't play a role in most of the rest of mathematics. DG
From: James Propp <jpropp@cs.uml.edu>
I've been invited to speak on a college morning radio program next week, on the topic of mathematical proof and infinity. It'll be a conversation with two interviewers (no call-ins).
I've not notice anyone mention proofs of the infinitude of primes yet. That should be simple enough for anyone reasonably awake to understand, and introduces both important techniques used in mathematical proof as well as an infinity.
Phil
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David Gale Professor Emeritus Department of Mathematics University of California, Berkeley
PS. and of course there is THE example of finite verses INFINITE, the twin prime problem. Query. Is there an easily described sequence which has been PROVED to be finite but we don't know what the last term is? At 03:11 AM 10/27/2007, you wrote:
I strongly second Phil's suggestion. The mathematical world didn't have to wait for Cantor to deal with infinity. Euclid and co. knew exactly what they were saying about the prime numbers and so would the average radio listener. You can get quite a bit of mileage out of this area. After describing Euclid's PROOF it's natural to think about possible primality for Fermat and Mersenne numbers. You can tell lots of interesting stories, how Euler factored F5, current results about finding large Mersenne's and factoring large Fermat's the intriguing fact that there are probably INFINITELLY many M's but only a finite number of F's, -we may know them all already. I would stay away from Cantorian infinity, much as we love it. People, as opposed to mathematicians, find it hard to digest and it really doesn't play a role in most of the rest of mathematics.
DG
From: James Propp <jpropp@cs.uml.edu>
I've been invited to speak on a college morning radio program next week, on the topic of mathematical proof and infinity. It'll be a conversation with two interviewers (no call-ins).
I've not notice anyone mention proofs of the infinitude of primes yet. That should be simple enough for anyone reasonably awake to understand, and introduces both important techniques used in mathematical proof as well as an infinity.
Phil
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David Gale Professor Emeritus Department of Mathematics University of California, Berkeley
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David Gale Professor Emeritus Department of Mathematics University of California, Berkeley
At 03:11 AM 10/27/2007, David Gale wrote:
I would stay away from Cantorian infinity, much as we love it. People, as opposed to mathematicians, find it hard to digest and it really doesn't play a role in most of the rest of mathematics.
Cantor-type diagonalization is the major tool Goedel's work and in computational complexity, so Cantor's work does find a role in certain parts of computer science. It's an interesting challenge to figure out what role diagonalization might play in "real" life.
On 10/27/07, Henry Baker <hbaker1@pipeline.com> wrote:
At 03:11 AM 10/27/2007, David Gale wrote:
I would stay away from Cantorian infinity, much as we love it. People, as opposed to mathematicians, find it hard to digest and it really doesn't play a role in most of the rest of mathematics.
Cantor-type diagonalization is the major tool Goedel's work and in computational complexity, so Cantor's work does find a role in certain parts of computer science.
It's an interesting challenge to figure out what role diagonalization might play in "real" life.
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On 10/27/07, Henry Baker <hbaker1@pipeline.com> wrote:
Cantor-type diagonalization is the major tool Goedel's work and in computational complexity, so Cantor's work does find a role in certain parts of computer science.
It's an interesting challenge to figure out what role diagonalization might play in "real" life.
I'm not entirely convinced that the similarity of the Cantor diagonal argument to the Russell paradox / Goedel proof / Cretan liar et al is sufficient grounds for drawing the latter into a discussion about infinities. Perhaps it might be argued that diagonalisation leads to a new object in an open-ended system (e.g. the continuum in the cardinals); but in a closed system it leads to a contradiction. At any rate, I am convinced that diagonalisation by itself does impinge very immediately on "real life", in a manner which does not seem well appreciated. There is an obscure corner of mathematical logic and computer science known as "situation theory" [one reason for its low profile may well be that none of its practitioners will actually admit to being a situation theorist!]. Situation theory employs axiomatic set theory to model the concept of truth in a closed universe where the active agents are capable of self-reference. The central revelation is that (loosely) in such situation, either there is are questions whose answers are unknown to some agents, or else there are answers about which agents must disagree. There is a very readable account of all this material in Jon Barwise & John Etchemendy's book "The Liar". Failure to appreciate the ramfiications of this theorem have resulted elsewhere in the generation of an enormous amount of otherwise (possibly) well-informed and entertaining twaddle --- a situation which will doubtless persist, whatever I say! [Apologies for earlier empty message --- rodent problem!] Fred Lunnon
I'm looking for a simple derivation of the probability that a random walk starting at 0, with unit steps, will ever end up to the left of 0. Probability that the person goes to the left (towards the negative) at any step is p. Thanks, Bill C.
participants (5)
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Cordwell, William R -
David Gale -
Fred lunnon -
Henry Baker -
Phil Carmody