alt Hacker NewsHot 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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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.
any good resources to understand more about them?
The CLT is everywhere because convolution/adding independentish random variables is a super common thing to do.
Most things aren't infinite or extreme, though. Almost by definition, most phenomena aren't extreme phenomena.
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
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…