Terence Tao

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.

You splash around, there's some turbulence and waves and so forth, but eventually it settles down and the lower the amplitude, the smaller the velocity, the more calm it gets.

But potentially there is also a demon that keeps pushing

the energy of the fluid into a smaller and smaller scale.

And it will move faster and faster.

And at faster speeds, the effect of viscosity is relatively less.

And so it could happen that it creates some sort of what's called a self-similar blob scenario where, you know,

the energy of the fluid starts off at some large scale, and then it all sort of transfers its energy into a smaller region of the fluid, which then, at a much faster rate, moves into an even smaller region, and so forth.