I recently stumbled across this number, and then (foolishly, most likely) decided to try to describe it in a blog post
http://frothygirlz.com/2010/01/14/big-numbers-part-2/
Q – Are there any comparisons of Graham's Number, hell, even G1, to other well known "big" numbers, such as googolplex?
I'd just like to have some way, however abstract, to be able to pretend that I have some sort of idea of the magnitude of this number.
Any help and/or tips would be much appreciated.
Best Answer
I think all that can really be said is that a googolplex is much, much smaller.
This isn't a direct comparison of a googolplex with Graham's number, but maybe it will help give some perspective:
Some back-of-the-envelope/Mathematica calculations tell me that
$10^{(10^{100})}\approx 3^{(3^{(3^{4.86})})}$
and so a googolplex is between $3\uparrow\uparrow 4=3^{(3^{(3^{3})})}$ and $3\uparrow\uparrow 5=3^{(3^{(3^{27})})}$ (much closer to $3\uparrow\uparrow 4$, obviously).