Ergodicity

Ole Peters

LML Resident Fellow

The mathematics of randomness began in 1654, with imagined parallel worlds where all possible events coexist. In 1657 Huygens declared that expectation values are all we ever need to know. This setup made it possible to keep concepts of time away from concepts of randomness. I will speculate that our choice of this specific formalisation of randomness has to do with the introduction of heliocentricity and its challenge to Aristotle’s concept of time. In the 18th century we discovered difficulties — related to extremes, risk, and human behaviour — inherent in the many-worlds view of randomness. In the case of human behaviour, these problems were superficially patched up by the introduction of utility theory. In the 19th century Boltzmann asked the crucial question: when do expectation values reflect what happens over time? This is the ergodicity problem. Because ergodic systems are so much easier to work with, ergodic models have been a constant temptation, even after Boltzmann had told us how unusual they are. I will argue that key problems in economics and evolutionary biology exist because we yielded to this temptation. But the good news is that we don’t have to. Without much technical effort we can solve these problems by studying temporal behaviour instead of ensemble-average behaviour in simple non-ergodic models.

Location

South Kensington Campus, Imperial College London

Date & Time

Tuesday 10th October 2017 at 12.00hrs