View Full Version : Graham's Number Or A Googleplex?
Psilocybe
2008-07-11, 22:13
Which is larger, Graham's number or a googleplex? Does anyone actually know?
Grahams Number is much larger
Psilocybe
2008-07-11, 22:47
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.
"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."
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
2008-07-12, 14:16
Whats bigger out of a googleplex to the power of a googleplex or graham's number?
thebigmoney
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
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
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
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.
thizz all day
2008-07-24, 19:00
What's so hard to grasp the length of a fucking number?
That's no where near as mind boggling as the size of the largest stars or just the mass of the universe itself.
Here's an idea, Gramah's number x Graham's number OoOoOooo. Can easily say numbers, but things that actually exist in that size are much much more crazy.
10000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 There you go THiZZ's number.
What's so hard to grasp the length of a fucking number?
That's no where near as mind boggling as the size of the largest stars or just the mass of the universe itself.
Here's an idea, Gramah's number x Graham's number OoOoOooo. Can easily say numbers, but things that actually exist in that size are much much more crazy.
10000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 There you go THiZZ's number.
The main point of this thread is that things in nature like the mass of the universe actually do not compare to large numbers such as googolplex and Graham's number. For example, in that number you wrote, you have a 1 followed by a large number of zeros. If you were to consider a similar number, being a 1 followed by many zeros, with the number of zeros being equal to the number of atoms in the whole universe, you would not even have a googolplex, and a googolplex is absolutely nothing compared to Graham's number. Even googolplex^googolplex would be absurdly tiny compared to Graham's number.
However, you are completely correct that we can make numbers as large as we want, like in your post graham's number times graham's number, would certainly be larger than just graham's number. However, the reason that graham's number is considered so amazing is not just its stupendous size, but the fact that it was actually used in a mathematical proof of a very reasonable nature, in an area of math known as Ramsey theory.
That's why googolplex is not really that amazing since even though it is large, it was constructed for the sole purpose of being large. Whereas with Graham's number, it came up in a math proof (as an upper bound of something) and only later was it realized how large it really was.
thebigmoney
2008-07-24, 22:40
What's so hard to grasp the length of a fucking number?
That's no where near as mind boggling as the size of the largest stars or just the mass of the universe itself.
...
Can easily say numbers, but things that actually exist in that size are much much more crazy.
I think you skipped the end of the first page, because we have just gone over the fact that the number is MUCH greater than all the particles in the universe put together, thereby making it impossible to write down. That's why it's hard to grasp how big it is. At least you can write "THIZZ's number."
thizz all day
2008-07-26, 06:28
I think you skipped the end of the first page, because we have just gone over the fact that the number is MUCH greater than all the particles in the universe put together, thereby making it impossible to write down. That's why it's hard to grasp how big it is. At least you can write "THIZZ's number."
Ok, I see your point.
Graham's number is so unfathomably large you can't even begin to comprehend it. Not only could you not write it normally, you can't write it as powers, or a tetrational product.
XtomJames
2008-08-01, 01:35
Graham's number can be expressed through Null mathematics though.
([]i)^(n^64)
This can also be seen as a Prime number reducer.
Edit: Also looking at the Graham number more I'd write it in a simpler notation.
Use a fractalization structure. 3!Φ^(3!^64!)
9.70820394^(6^(1.26886932 × 10^89))
That is:
9.70820394^(6^(12688693200000000000000000000000000 00000000000000000000000000000000
0000000000000000000000)
which is: 9.70820394^(97134218000000000000000000000000000000 00000000000000000000000000000
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00000000000000000000000000000000000000000000000000 *continued on next post*
XtomJames
2008-08-01, 07:31
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XtomJames
2008-08-01, 07:31
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XtomJames
2008-08-01, 07:39
A note: that is 18480 zeros in that power. A googolplex is 10^10,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000
Which is only 100 zeros in the power.
thebigmoney
2008-08-01, 16:15
A note: that is 18480 zeros in that power. A googolplex is 10^10,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000
Which is only 100 zeros in the power.
Dy-no-miiiite! nice post, the arrow notation gives you some idea, but seeing it written out as an exponent makes it somewhat easier to fathom how unfathomably huge it is.
XtomJames
2008-08-02, 14:36
The funny thing is that Wikipedia still says you can't write it in normal notation....
xXPhoenixFireXx
2008-08-02, 21:59
The funny thing is that Wikipedia still says you can't write it in normal notation....
Because you haven't written out Graham's number ^-^. Or even close to it for that matter ^-^.
The number you wrote isn't even greater than 3 ^^^^ 3, treating the ^ as the up arrow in up arrow notation. In the definition of this number this corresponds to the first layer. If you look at the definition for graham's number this is the number of up arrows in the second layer. Not just 5 up arrows, 3^^^^3 up arrows. On the second layer. Out of 64.
XtomJames
2008-08-03, 06:00
Um, that number is the number of 3^^^... in the 64th layer.
Yea, that number you wrote isn't even remotely close to Graham's number. I'm wondering where you got it from though, because its sort of a random number to just think of, and no serious mathematician would ever attempt to write Graham's number in scientific notation.
Discounting the long number of zeros you wrote, you say that number is equal to 9.70820394^(6^(1.26886932 × 10^89)) and that both of these are equal to Graham's number. And if you look at the construction of Graham's number on wikipedia or something, it should be easy to see 9.70820394^(6^(1.26886932 × 10^89)) isn't anywhere close to it.