Sean Carroll

That means there is a horizon around us, and once we get rid of all the matter and galaxies and things like that, and we're just in empty space, there's a well-known calculable size to the horizon that is around us.

The horizon just means there are points that are so far away that space is expanding too fast,

If you're at one of those points, you can never return to where we are.

That's the horizon that is around us.

You'd have to move faster than the speed of light.

Stephen Hawking and his friends have shown that the horizon in the sitter space, a universe with a positive cosmological constant,

has an entropy and a temperature just like the horizon of a black hole does.

And the entropy of our desider horizon in the real world is something like 10 to the 122, okay?

A pretty big number, 10 to the 122.

The number of particles in the observable universe is only like 10 to the 88th by comparison.

So 10 to the 122 is a big number.

If you have a quantum system in thermodynamic equilibrium with a certain entropy, then there's a well-known fact that the dimensionality of Hilbert space is roughly speaking e to the entropy, okay?

So that's e to the 10 to the 122, which is a preposterously big number.

And I'm building up to the fact that the recurrence time is roughly again, very roughly speaking, because who cares?

These numbers are too big to be precise about it.

the recurrence time is something like e to the dimensionality of Hilbert space.

So e to the e to the 10 to the 122.

And by the way, when the numbers are big enough, it doesn't matter whether you use e or 10 or 2 as your base.

e to the e to the 10 to the 122 is approximately equal to 10 to the 10 to the 10 to the 122.

That's just how these exponentials really work out.