I know a similer thread was started by JonnyBeGood but...

I read in a book called "The Immortal Game" that there are  1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000 (10^120)  possible board positions in chess. I can hardly comprehend a number that huge.

wow

And that's just positions that could legally come to be, correct?

Yes

and that number is dwarfed by graham's number. It's so inconceivably large I can't even begin to understand the magnitude of it.

Basically to start forming this number, you add up a bunch of iterations of exponentiation. They start with 3, then the next number has three 3's, so it's 3^3^3, or 3^27= 7,625,597,484,987, so the next number has 7 TRILLION 3s in it. And this goes on for a little while....and that's the smallest number of a 64-step sequence to sum up.

http://en.wikipedia.org/wiki/Graham%27s_number

There are far larger numbers than this now, such as TREE(3), but it starts getting really abstract after that.

I know that there are bigger unimaginably huge numbers out there that I won't try to comprehend (I'm an English and History student), but as for this number, it is what is possible in Chess (how many different board positions) not just a randomly huge number.

And if I think about Graham's number too much, my brain will bleed.

There are also some more physically bound numbers that are gigantic, but they're not nearly as fun to think about. A smaller example is the database to store all the 40-character passwords is roughly 10^96, which is 1,000,000,000,000,000,000,000,000 times smaller.

Interestingly, one scientist/mathematician estimates the number of operations made if every particle in the universe was used for computation is roughly 10^120 as well.

This probably shows how little we know of chess. There are so many positions that will never occur, we are playing a very small part of the game. 

Imagine a human or computer who could calculate that. The game would change completely.