Terence Tao

all the atoms in a box of air.

That's, like, Avogadro's number is humongous, right?

There's a huge number of particles.

If you actually have to track each one, it'll be ridiculous.

But certain laws emerge at the microscopic scale that almost don't depend on what's going on at the macroscale, or only depend on a very small number of parameters.

So if you want to model a gas of, you know,

quintillion particles in a box.

You just need to know its temperature and pressure and volume and a few parameters, like 5 or 6.

And it models almost everything you need to know about these 10 to 23 or whatever particles.

So we have...

We don't understand universality anywhere near as we would like mathematically, but there are much simpler toy models where we do have a good understanding of why universality occurs.

The most basic one is the central limit theorem that explains why the bell curve shows up everywhere in nature, that so many things are distributed by what's called a Gaussian distribution, a famous bell curve,

There's not even a meme with this curve.

Even the meme applies broadly, the universality to the meme.

Yes, you can go meta if you like.

But there are many processes.

For example, you can take lots of independent random variables and average them together in various ways.

You can take a simple average or more complicated average, and we can prove in various cases that these bell curves, these calciums emerge, and it is a satisfying explanation.

Sometimes they don't.

So if you have many different inputs and they're all correlated in some systemic way, then you can get something very far from a bow curve show up.