Tuesday, 17 August 2010

Seminars I wish I had time to attend: infinite monkeys edition

Over in the Maths and Stats Department on Thursday:
Subject: Mathematics & Statistics Department Seminar - Thursday 19 August

Thursday, 19 August 2010
Erskine Room 446

Maarten McKubre-Jordens (University of Canterbury)

Infinity in Computable Probability: Logical Proof that William Shakespeare probably was not a Dactylographic Monkey

The "Infinite Monkey Theorem" has frequently been used to emphasize the danger of reasoning about probability when infinity is involved. The theorem states that at least one of infinitely many monkeys, producing a character string equal in length to the collected works of Shakespeare by striking typewriter keys in a uniformly random manner, will with probability one reproduce the collected works.

The bad news: classically, finding the champ chimp will take A Very Long Time. But there is worse news, constructively. Surprisingly, it is possible to assign to an infinite number of monkeys probabilities of reproducing Shakespeare's collected works in such a way that while it is impossible that no monkey reproduces the collected works, the probability of any finite number of monkeys reproducing the works of Shakespeare is arbitrarily small. This result potentially destroys any hope of completing such a project with as much computing power as we could ever hope to have.

However, the news is not all bad. For sufficiently large troops of monkeys, the fraction among all possible probability distributions of such pathological distributions is vanishingly small; so the chances of running into one of these distributions in practice is negligible.
I suspect that the seminar would get into mathy stuff rather than the perils that come from having infinite monkeys, one of whom may be Mojo Jojo. But if there were an infinite number of such seminars, and if they all varied a bit from each other, then maybe...

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