alt Hacker NewsGreat article. Personally I have been learning more about the mathematics of beyond-CLT scenarios (fat tails, infinite variance etc)
The great philosophical question is why CLT applies so universally. The article explains it well as a consequence of the averaging process.
Alternatively, I’ve read that natural processes tend to exhibit Gaussian behaviour because there is a tendency towards equilibrium: forces, homeostasis, central potentials and so on and this equilibrium drives the measurable into the central region.
For processes such as prices in financial markets, with complicated feedback loops and reflexivity (in the Soros sense) the probability mass tends to ends up in the non central region, where the CLT does not apply.
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As to ye philosophy of “why” the CLT gives you normals, my hunch is that it’s because there’s some connection between:
a) the CLT requires samples drawn from a distribution with finite mean and variance
and b) the Gaussian is the maximum entropy distribution for a particular mean and variance
I’d be curious about what happens if you starting making assumptions about higher order moments in the distro
You (and others) may enjoy going down the rabbit hole of universality. Terence Tao has a nice survey article on this which might be a good place to start: https://direct.mit.edu/daed/article/141/3/23/27037/E-pluribu...
>natural processes tend to exhibit Gaussian behaviour
to me it results of 2 factors - 1. Gaussian is the max entropy for a distribution with a given variance and 2. variance is the model of energy-limited behavior whereis physical processes are always under some energy limits. Basically it is the 2nd law.
The key principle is that you get CLT when a bunch of random factors add. Which happens in lots of places.
In finance, the effects of random factors tend to multiply. So you get a log-normal curve.
As Taleb points out, though, the underlying assumptions behind log-normal break in large market movements. Because in large movements, things that were uncorrelated, become correlated. Resulting in fat tails, where extreme combinations of events (aka "black swans") become far more likely than naively expected.