Can anyone give me another example of outrageous large numbers in the real universe? Here is the best I can do for now.

The number of tiny Planck Volumes in the observable universe is about 10 to the power of 185. The number of Planck Volumes in a level teaspoon is about a googol (10 to the power of 100). But here is what surprised me some more. The number of Planck Volumes in a level teaspoon is a quadrillion times the number of teaspoons in the observable universe, and if you subtract 10 to the power of 85 from a googol, the remainder is very, very nearly a googol.

Now please surprise me with some big numbers. Graham's number is incredibly large but if you subtract Graham's number from TREE(3) the answer is very, very nearly TREE(3).

Edited August 25Aug 25 by Airbrush

1 hour ago, Airbrush said:

Now please surprise me with some big numbers. Graham's number is incredibly large

You have probably already seen the numberphile you tube videos on this?

They cover fast growing hierarchies w.r.t. functions and TREE is right up there if not the biggest.

2 hours ago, Airbrush said:

Now please surprise me with some big numbers.

There are a few videos on this but this one covers the fast growing hierarchies.

https://youtu.be/0X9DYRLmTNY?si=GGVE3oRmePaqYAmp

An example I can think of is: Numbers of states are "combinatorial" wrt numbers of "entities" (I hope the quoted terms are more or less clear).

For any number of things/entities etc you can think of, say N, combinatorial numbers are built out of factorials of those. Entropies go like logs of these numbers, which "keeps hugeness at bay" in a manner of speaking, because logs grow very slowly, but phase space gets you back to the hugeness of the combinatorial number, as phase space is roughly \( \exp{S} \) with S= entropy

Phase spaces are huge indeed. That's roughly why the chances of something happening again are zero to all intents and purposes.