Terence Tao

There's no reason why they should unmix.

But in principle, because of all the collisions between them, there could be some sort of weird conspiracy.

Like maybe there's a microscopic demon called Maxwell's demon that will, every time an oxygen and nitrogen atom collide, they will bounce off in such a way that the oxygen sort of drifts onto one side and the nitrogen goes to the other.

And you could have an extremely improbable configuration emerge.

which we never see, and statistically it's extremely unlikely, but mathematically it's possible that this can happen, and we can't rule it out.

And this is a situation that shows up a lot in mathematics.

A basic example is the digits of pi, 3.14159 and so forth.

The digits look like they have no pattern, and we believe they have no pattern.

On the long term, you should see as many 1s and 2s and 3s as 4s and 5s and 6s.

There should be no preference in the digits of pi to favor, let's say, 7 over 8.

But maybe there is some demon in the digits of pi that every time you compute more and more digits, it biases one digit to another.

And

This is a conspiracy that should not happen.

There's no reason it should happen, but there's no way to prove it with our current technology.

Okay, so getting back to Navier-Stokes, a fluid has a certain amount of energy.

And because the fluid is in motion, the energy gets transported around.

And water is also viscous.

So if the energy is spread out over many different locations, the natural viscosity of the fluid will just damp out the energy and it will go to zero.

And this is what happens in...

when we actually experiment with water.