This was sort of my reading as well: I took "clumping" to mean "bump-shaped".

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.

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