Bell curves are everywhere because all distributions of any properties clump in some way at some level. The basics of any probability shows this. The result is you “seeing” bell curves everywhere. Aka clumps.
If sums of independent identically distributed random variables converge to a distribution, they converge to a Levy stable distribution [0]. Tails of the Levy stable distribution are power law, which makes them not Gaussian.
Yes but really what our brains do is use Gaussian Mixture model to cut up those distributions into more granular bell curves which we then call “normal”. Because we find what we are tuned to find.
Eg we find bell curves because we look for bell curves. And given infinite resolution we can find them at some granularity.
As I'm sure tsunamifury would agree, it is incredibly common for people to label "bell curves" by eyeball, regardless of whether they are normal curves. To most people, "clumping" in a one-dimensional spectrum is all they mean by the phrase "bell curve".
This completely misses the point, which is that the central limit theorem says that it isn't just any old clumping, it's always the normal distribution. tsunamifury dismissed this strong finding as "tautology" because clumping is obvious ... but that it's always precisely a bell curve is far from obvious. Again,
> your "aka" is incorrect --- there is all sorts of clumping that is not a normal distribution.
That it's "incredibly common for people to label "bell curves" by eyeball, regardless of whether they are normal curves" is not just not relevant, it's anti-relevant ... the central limit theorem says that the distribution of the means is always a bell curve--a normal distribution--not merely a "bell curve".
Anyway, this is covered in far more detail in other comments and material elsewhere, so this is my last contribution.
Wow aside from the fact that none of that support is in the article it still boils down to
Normal curves are everywhere normal curves are -- which are an observational tautology -- and a fundamental over our observation of "stuff". You're dismissive as if im some illiterate, but you'd be surprised at the contributions on math I've made to the world.
Yup. And in general more heavy-tailed bumps are in fact better models (assuming normality tends to lead to over-confidence). Really think the universality is strictly mathematical, and actually rare in nature.
This is a tautology to the extreme.