The Axiom of Choice and Predicting the Future

Abstract:

Meteorologists routinely attempt to predict the weather based on observations made in the recent (and distant) past. They can do this because the weather tends to follow certain patterns and obey certain physical laws. Suppose, though, that the weather could be an arbitrary function of time, possibly switching between raining, snowing, and sunny infinitely many times per second, without having to follow any particular pattern or law. Where would the meteorologists turn? They might turn to the Axiom of Choice. The Axiom of Choice is an indispensable part of mathematics, but it is known for producing some very counterintuitive results. One consequence of the Axiom of Choice is that we can produce a strategy for guessing future weather from past weather which almost always correctly predicts some interval of the future, even if the weather is a completely arbitrary function of time (not necessarily even continuous). The talk will make this precise and explain how it is done. Along the way, we will look at the Axiom of Choice, well-orderings, and, time permitting, how to get out of prison.

Union College Math Department Home Page Comments to: math@union.edu Created automatically on: Fri Apr 20 22:03:28 EDT 2018