If we assume that a false proposition is true, we can prove anything (ex falso quodlibet). Bertrand Russell, so the story goes, once mentioned this in class. A student raised his hand and challenged: in that case prove that 1=0 implies that you’re the Pope. Russell promptly obliged, see below. Bernoulli 1738, as discussed in an earlier post, contains two contradictory definitions of expected utility theory. This contradiction amounts to a false proposition, and that means any statement can be proved using expected utility theory. As an illustration, let’s prove that Bertrand Russell is the Pope.
Not all academic fields have a clear starting point, a seminal paper that constitutes the foundation of the entire discipline. But economics does. The paper that defines modern formal economics was written by Daniel Bernoulli in 1738. It introduces expected utility theory. The main thrust of our work is, of course, to replace expected utility theory and instead work with time-average growth rates of wealth. I’ll mention how that works, but the focus of this post will be on something else. Bernoulli’s paper is not only conceptually misleading but also technically flawed in a sneaky way that keeps confusing everyone. Where Bernoulli determines the price to be paid for a risky prospect, he contradicts himself. I wouldn’t make such a fuss about this if the paper wasn’t so absolutely crucial. This basis of economics contains an error that invalidates commonly held beliefs and puts tens of thousands of studies into a different light. I recently encouraged people, using twitter, to read the paper and see for themselves. In this blog post I go through the relevant analysis step by step and address questions that came up in response to the tweet.
The most interesting scientific projects are those that surprise, when the mathematics, or the code, tells us something we didn’t expect. In our study of US wealth dynamics that’s what happened. We wrote it up in a paper, but that’s only the end product not the curious route by which we got there. Hence this post.
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.
The term “weak ergodicity breaking” helps categorize things by their ergodic properties:
- strongly non-ergodic
- weakly non-ergodic
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).