Yes, I know Shannon's number is "small". The point was that it's been around for a while, and that with the right mathematical tools one can deal with such numbers without having their mind boggled.
Fair enough. I clicked on the link expecting to get something like graham's number or TREE(3) or some other monstrosity, and felt kind of cheated when it was only 10^43 ;)
Do those mathematical methods really allow us to comprehend these numbers though? They only really allow use to express them as configurations of other numbers don't they? Even if you understand hyperoperations and stuff you're not really gazing upon what those figures really entail.
I suppose all mathematics involves notation in the end.
Sure, but there is still something to be said for bound finite numbers. The universe is somewhere between 26 billion light years wide and infinity. From what we can observe it might be reasonable to guess that it's smaller than grahm's number of light years wide, but for all our hubris that's still just a reasonable guess.
