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.
In June 1946 Max Planck spoke in the Göttingen physics colloquium. Planck was 88 years old, had received the highest honors of his community, including a Nobel Prize in 1918 for his discovery of the quantum, and had profoundly changed how we think about physical reality. He knew something about problems, both in science and in life. He postulated the quantum, famously, “in an act of desperation.” His first wife died young, as did four of his five children, the fourth, Erwin, killed by the Gestapo in 1945. Having lived through all of this, Max Planck decided to talk about problems that are nothing but distraction — scheinproblems.
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.
This is a bit of LML jargon that we felt is worth promoting, even though it’s terribly unfair to a great mathematician. So please, you admirers of Laplace, don’t take offense. What’s the story?
In 1738 Daniel Bernoulli wrote his famous paper that introduces expected utility theory and thereby defines the basis of neoclassical economics — macro and micro. Since you ask: this paper is famous for its treatment of the St. Petersburg paradox. The “paradox” goes like this:
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.