## Tuesday, September 1, 2015

### Bachelier was no Einstein

It's been fun following David Warsh's series on the history of economic thought (I got a bit behind and only now read this one ... so now I'm obviously going to see what I can do about Black-Scholes in the information equilibrium framework).

Although this quote by Warsh from Davis and Etheridge:
[Bachelier] defined Brownian motion – predating Einstein by five years ...
doesn't make much sense to me. Brown 'defined' Brownian motion (a physical process) by observation. Einstein's contribution was to connect Brownian motion directly to atoms thereby confirming that atoms exist [1]. There is no sense in which Bachelier came up with the idea of Brownian motion first (it was observed) or predated Einstein's result about atoms in his 1905 paper.

...

Footnotes:

[1] Einstein's "annus mirabilus" papers (from 1905) are paradigm shifting because of the way they take theoretical models "seriously" in a modern sense. In 1928 Dirac writes down a relativistic Schrodinger equation that has an additional solution with the opposite charge. Before Einstein, this might have been taken as a mathematical curiosity or irrelevant solution. After Einstein, we get Dirac taking the solution seriously and proposing the existence of antimatter. Einstein's papers from 1905 have us taking the theoretical constructs of atoms, photons and Lorentz symmetry seriously.

1. Fair enough that Bachelier was no Einstein. However, he was credited by Mandelbrot among others as being groundbreaking in the study of statistical finance. According to the definitive source (Wikipedia):

He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900).

So I would give him some credit...

1. Hi Todd,

I swear I am reading the draft material you sent and will get back to you soon!

I think the issue here is confusing the mathematical model with the physical process -- Wikipedia has a good disambiguation on Brownian motion:

https://en.wikipedia.org/wiki/Brownian_motion