totse.com | Graham's Number Or A Googleplex?

Psilocybe · #1 2008-07-11, 22:13

Which is larger, Graham's number or a googleplex? Does anyone actually know?

Azure · #2 2008-07-11, 22:18

Grahams Number is much larger

Psilocybe · #3 2008-07-11, 22:47

Quote:

Originally Posted by Azure View Post

Grahams Number is much larger

Meh, that's what I thought. How do you know though? I know trippy notations are required for it but yeah.

Azure · #4 2008-07-11, 22:51

"Graham's number is much larger than other well-known large numbers such as a googol and a googolplex, and even larger than Skewes' number and Moser's number, other well-known large numbers."

danreil · #5 2008-07-12, 05:34

Its basically impossible for anyone to imagine just how immensely large Graham's Number is, and a googolplex does not compare one iota to Graham's Number. If your interested, try to understand how Knuth's up arrow notation works (and the related topic of the hyper operator) by reading about it on wikipedia and planet math and other sites. I say read about it several times on several sites, because even though it seems like a simple concept, it can be really hard to grasp just how quickly (and I mean really fucking quickly) it grows.

Then look up the expression for Graham's Number in the Knuth up arrow notation (or equivalently hyper operator notation) and see if you can possibly comprehend what it means, because I know I can't come close even though I fully understand the notation.

You can also try to read about Conway chained arrow notation, which leads to a nice definition of Graham's Number. In my opinion though, this is much harder to understand, not nearly as intuitive, and also does not make the number seem as large as in the hyper operator notation, (even though it, of course, is as large).

l33t-haX0r · #6 2008-07-12, 14:16

Whats bigger out of a googleplex to the power of a googleplex or graham's number?

thebigmoney · #7 2008-07-12, 16:23

On the wiki page, it says something to the effect of "due to its size, Graham's Number is impossible to denote given the limitations of the universe" in the intro paragraph. Does that mean it is physically impossible to write the number in standard numeration? Or does that just mean it's impossible to plug into a calculator? If it's the former, that's a total mindfuck. If the latter, that's a little more believable.

l33t-haX0r · #8 2008-07-12, 17:38

Yeah it means its impossible to write out fully using normal notation. Think a googol is 10^100 or 10000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0. So a googol plex is 10^googol or 1 with a googol zeros after it. This is obviously impossible to write out fully, like one of the other guys said an estimate of the number of particles in the universe is 10^80 and i think someone estimate that if u packed the universe with neutrons there would only be 10^120 or so which is tiny compared to a googolplex. Then you consider Graham's Numbers which is massively bigger than a googolplex.

And obviously its impossible to plug these numbers into a caluclator or computer cause of the memory requirements.

thebigmoney · #9 2008-07-12, 19:41

Wow, found this quote by a guy named David Wells on google:

"If all the material in the universe was turned into pen and ink it would not be enough to write the number down."

that IS a mindfuck.

royce.beat.man · #10 2008-07-14, 04:15

this is much related to the planetary systems beyond ours,
the stars that incomparison to earth are of undescibeable size, Just blows my mind, nearly if not impossible to grasp mentally.