Ridiculously Huge Numbers [video]

Sometimes it's fun to bask in the unimaginable largeness of really big numbers: a googolplex, power towers, Knuth's up-arrow notation.

How big can we go? There's something called the Fast-growing hierarchy[0] that quickly makes even anything expressed with Knuth's up-arrow notation completely puny.

Not only do Really Big Numbers™ tickle some childlike fancy in us, but a sharp exploration of them actually cuts into some deep questions about the foundations of math.

This 46 video playlist is the most in-depth and accessible exploration of the depths this rabbit-hole goes that I know.

[0]:https://en.wikipedia.org/wiki/Fast-growing_hierarchy