How to think about Grahams Number

Tim Urban erklärt, wie man ziemlich große Zahlen zusammenbaut und mit denen dann per exponentieller Exponentialismusdingens noch größere Zahlen, und irgendwann landet man dann bei Power Towers und Sun Towers in einem Psychofestival mit Zahlen, die ausgeschrieben circa hunderttausend Universen füllen würden. Wie Powers of Ten on Steroids. Toll!

Remember, a googol and its universe-filling microscopic mini-sand is only a 100-digit number. So all it takes is a power tower of 3s stacked 4 high to dwarf a googol, as well as 10185, the number of Planck volumes to fill the universe and our physical world maximum. It’s not as big as a googolplex, but we can take care of that easily by just adding one more 3 to the stack:

33333 = 3(3333) = 3(3.6 trillion-digit number) = way bigger than a googolplex, which is 10(100-digit number). As for a googolplex itself, power towers allow us to immediately humiliate it by writing it as:

1010100 or, more typically, 1010102. So you can imagine what kind of number you get when you start making tall power towers. Tetration is intense.

From 1,000,000 to Graham’s Number (via Kottke)