Hot take: bell curves are everywhere exactly because the math is simple.

The causal chain is: the math is simple -> teachers teach simple things -> students learn what they're taught -> we see the world in terms of concepts we've learned.

The central limit theorem generalizes beyond simple math to hard math: Levy alpha stable distributions when variance is not finite, the Fisher-Tippett-Gnedenko theorem and Gumbel/Fréchet/Weibull distributions regarding extreme values. Those curves are also everwhere, but we don't see them because we weren't taught them because the math is tough.

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atrettel 5 hours ago | parent | next [-]

I've often described this as a bias towards easily taught ("teachable") material over more realistic but difficult to teach material. Sometimes teachers teach certain subjects because they fit the classroom well as a medium. Some subjects are just hard to teach in hour-long lectures using whiteboards and slides. They might be better suited to other media, especially self study, but that does not mean that teachers should ignore them.

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BobbyTables2 7 hours ago | parent | prev | next [-]

It also took me a little while to realize “least squares” and MMSE approaches were not necessarily the “correct” way to do things but just “one thing we actually know how to do” because everything else is much harder.

We can use Calculus to do so much but also so little…

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orangemaen 6 hours ago | parent | prev | next [-]

The CLT is everywhere because convolution/adding independentish random variables is a super common thing to do.

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gowld 5 hours ago | parent | prev | next [-]

Most things aren't infinite or extreme, though. Almost by definition, most phenomena aren't extreme phenomena.

	▲	D-Machine 4 hours ago \| parent [-]
		No, but when you get into the nitty gritty of most things sometimes being influenced by extremely rare things, and also that the convergence rate of the central limit theorem is not universal at all, then much of the utility (and apparent universality) of the CLT starts to evaporate. In practice when modeling you are almost always better not assuming normality, and you want to test models that allow the possibility of heavy tails. The CLT is an approximation, and modern robust methods or Bayesian methods that don't assume Gaussian priors are almost always better models. But this of course brings into question the very universality of the CLT (i.e. it is natural in math, but not really in nature).

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AndrewKemendo 7 hours ago | parent | prev [-]

That’s exactly the right take and the article proves it:

Statisticians love averages so everywhere that could be sampled as a normal distribution will be presented as one

The median is actually more descriptive and power law is equally as pervasive if not more

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fsckboy 4 hours ago | parent [-]

combining repeated samples of any distribution* (any population density fuction including power law distributions) will converge to the normal distribution, that's why it appears everywhere.

* excluding bizarre degenerates like constants or impulse functions

	▲	abetusk 2 hours ago \| parent [-]
		No, that's not correct. Sums of power law distributions can converge to power low tailed distributions, not normal distributions.