Scientific theorizing is indeed about finding something reliable in the world — if we’re lucky something reliable enough to be called a law. Why do we want something that doesn’t change? Deep question. Here’s a practical reason: we aim to capture it with something that doesn’t change, namely with ink on paper. Stability, stationarity, ergodicity… are the holy grail of science.
This is how Cédric Villani puts it [Birth of a theorem, p.38]:
Michael Mauboussin recently re-tweeted an article by Jason Zweig in the Wall Street Journal titled “Disturbing New Facts About American Capitalism”.
The article summarizes reports of an increasing concentration of economic power (market capitalization, profits etc) in ever smaller numbers of American companies, so-called super-star companies in their respective sectors. Well-known examples are Google (or Alphabet) and Apple. But the trend, Zweig says, is broader, also occurring in supermarkets and real estate services.
This post is about mindset, culture, implicit assumptions. The big assumption in neoclassical economics is ergodicity, or equilibrium, or stationarity, or stability — basically the idea that nothing ever changes fundamentally. Things may fluctuate but they always return to some state of normality. Naively, that doesn’t fit with the idea of a growing economy, innovation, and change. So something’s up. I’ll explore what that is by replacing the mental image of stability with something that doesn’t return to normality: a nuclear explosion.
The term “weak ergodicity breaking” helps categorize things by their ergodic properties:
This list is chronological, in that there used to be an implicit belief that everything was ergodic (from 1654), then the realization that some things are strongly non-ergodic (1850s — 1870s), and then the discovery that things can be a lot more subtle (with Jean-Philippe Bouchaud coining the term “weak ergodicity breaking” in 1992).
Continue reading “Reproducibility and weak ergodicity breaking”
