Terence Tao

But the mathematical point of the model is that you want to have fewer parameters in your model than data points in your observational set.

So if you have a model with 10 parameters that explains 10 observations, that is a completely useless model.

It's what's called overfitted.

But like if you have a model with two parameters and it explains a trillion observations, which is basically, so yeah, the dark matter model, I think it has like 14 parameters and it explains petabytes of data that the astronomers have.

You can think of a theory, like one way to think about a physical mathematical theory is it's a compression of the universe and a data compression.

So, you know, you have these petabytes of observations.

You'd like to compress it to a model which you can describe in five pages and specify a certain number of parameters.

And if it can fit to reasonable accuracy,

almost all of your observations.

I mean, the more compression that you make, the better your theory.

Einstein had a quote like that, the most incomprehensible thing about the universe is that it is comprehensible.

Right.

And not just comprehensible.

You can do an equation like E equals MC squared.

There is actually some mathematical possible explanation for that.

So there's this phenomenon in mathematics called universality.

So many complex systems at the macro scale are coming out of lots of tiny interactions at the macro scale.

And normally, because of the common form of explosion, you would think that the macroscale equations must be exponentially more complicated than the microscale ones.

And they are, if you want to solve them completely exactly.

Like, if you want to model...