User blog comment:Swooped me in one hit/silly number/@comment-29310326-20170213214931/@comment-30754445-20170213230503

The number of planck volumes in the universe is something like 10↑180. The largest number which (barely) has any physical meaning is something like 10↑↑5  or 10↑↑6 (the poincare recurrence time of the entire universe).

10↑↑↑10 is so much larger than both of these, that it's not even funny.

Think about it this way:

10↑↑6 has a managable description is a power tower of 6 tens.

10↑↑↑10, on the other hand, is a power tower of 10↑↑↑9 tens! The height of the tower is just as unfathomable a number as 10↑↑↑10 itself.

Another way to "get" just how big 10↑↑↑10 is, is to try and visualize a sequence of smaller numbers leading to it:

10↑↑100 is a tower of 100 tens. That's easy enough to imagine, right?

10↑↑1000000 is a tower of a million tens.

10↑↑10↑↑2 is a tower of ten billion tens.

Still with me? Well then, take a look at this:

10↑↑↑3 = 10↑↑10↑↑10. That's a tower of 10↑↑10 tens. A power tower 'whose height is - in itself - a power tower fo 10 tens''. '''

Whoa! This is getting quickly way out of hand, and we are nowhere near 10↑↑↑10 yet.

Does this answer your question of how such number compares with the largest numbers in astronomy (which are - if we are generous - comparable to a power tower of 5 or 6 tens?)

Of-course, googologically speaking, numbers like 10↑↑↑10 are tiny. Even Graham's number (which is much much larger) is considered relatively small in the world of googology. It's a completely different (and immesnly vast) world, which is one of the reasons it is so exciting.