1. ## The largest number

I've been idly speculating about what would be the largest number to have any meaning, and I figured it would be the number of universes created via the "many worlds hypothesis" since the dawn of time.

I'm not a physicist, but there are some thoughts I'd had on sketching it out:

The number of elementary particles created in the big bang (1088?)

The number of ways in which they can interact. (based on the laws of physics)

The total number of initial interactions within the first planck time after creation

The number of possible conseqences to those interactions

The number of possible consequences to those consequences, consequences to the consequences to those consequences, consequences to the consequences to the consequences to those consequences etc. in each planck time from the Big Bang until now.

The number of planck times since the Big Bang. (8 x 1060)

Have I missed anything?
Last edited by parallaxicality; 2006-Sep-19 at 09:24 AM.

2. Infinity+1?

3. Originally Posted by BigDon
Infinity+1?
That's still infinite, infinity is wierd that way although I believe Cantor showed you could get different sizes of infinity it just doesn't behave quite how you might expect (please don't ask me to explain, I picked this up from a book on infinity and don't really understand the underpinnings myself but you can find the wikipedia article on it here).

4. According to my dictionary of numbers (a dictionary that starts with the smallest known useful number and ends with the highest known useful number) the largest useful number is called Graham's number. Parallaxicality your number pales into insignificant nothingness compared to Graham's number.

The World Champion largest number, listed in the latest Guinness Book of Records, is an upper bound, derived by R. L. Graham, from a problem in a part of combinatorics called Ramsey theory.

Graham's number cannot be expressed using the conventional notation of powers, and powers of powers. If all the material in the universe were turned into pen and ink it would not be enough to write the number down. Consequently, this special notation, devised by Donald Knuth, is necessary.

3^3 means '3 cubed', as it often does in computer printouts.

3^^3 means 3^(3^3), or 3^27, which is already quite large:

3^27 = 7,625,597,484,987

but is still easily written, especially as a tower of 3 numbers: 3^(3^3).

3^^^3 = 3^^(3^^3) = 3^^7,625,597,484,987 = 3^(7,625,597,484,987^7,625,597,484,987)

which makes a tower of exponents 7,625,597,484,987 layers high.

3^^^^3 = 3^^^(3^^^3).

Even the tower of exponents is now unimaginably large in our usual notation, but Graham's number only starts here.

Consider the number 3^^^...^^^3 in which there are 3^^^^3 arrows. A largish number!

Next construct the number 3^^^...^^^3 where the number of arrows is the previous 3^^^...^^^3 number.

An incredible, ungraspable number! Yet we are only two steps away from the original ginormous 3^^^^3. Now continue this process, making the number of arrows in 3^^^...^^^3 equal to the number at the previous step, until you are 63 steps, yes, sixty-three, steps from 3^^^^3.

That is Graham's number.

There is a twist in the tale of this true fairy story. Remember that Graham's number is an upper bound, just like Skewes' number. What is likely to be the actual answer to Graham's problem? Gardner quotes the opinions of the experts in Ramsey theory, who suspect that the answer is: 6

clop

5. Wasn't Graham's number considered by someone as the worst estimate in human history? I recall reading that somewhere...

6. Originally Posted by parallaxicality
The number of elementary particles created in the big bang (1088?)
That's nothing compared to the number of possible games of chess.

From mathworld:
Hardy (1999, p. 17) estimated the number of possible games of chess as 10^(10^(50)). In a game of 40 moves, the number of possible board positions P(40) is at least 10^(120) according to Peterson (1996). However, this value does not agree with the 10^(40) possible positions given by Beeler et al. (1972),
As you can read there are different estimates, but nevertheless I think 10^(10^(50)) is a very large number.

7. Take an infinite number of numbers and list all the possible subsets of those numbers, twice!

8. Theoretical number of strings in the universe. That would be one damn big number as well.

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The number of sets in the set of all subsets of the set of all sets. Since the set of all subsets of a set has sets that aren't in the original set it means the set of all subsets of the set of all sets has sets that aren't in the set of all sets. That's a lot of sets.

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Of course, we all know that the real largest number is 1 / ( 1 - 0.999999... )

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Originally Posted by Chuck
Of course, we all know that the real largest number is 1 / ( 1 - 0.999999... )
Oh gods... do not... I repeat... do not... start down this path!!!!!

12. Well, Planck length is the shortest meaningful to science unit of length, but does that mean that nothing smaller exists, just because its of no use to us?

Last I checked, the Universe is everything that exists, whether many/parallel Universes or just this one. So, keeping in mind that numbers are imaginary...does this not just become a game of how many chunks I can divide the Universe into? In other words, who can think of a bigger number...

Would this also not mean that "one" is the only real number existing independently of anything else, and therefore is the only meaningful number in the grand scheme of things?

I mean...Taking the entire existance into account...there is only one, not 2, not 0.9, not 0, not 1.00000000000000000001....just one (and as exactly as it gets one) existence. Furthermore, it exists independantly of anything else, unlike the various and infinite subdivisions of the Universe. That is why 1 is the only, and therefore the largest meaningful number there is. And that, ladies and gentlemen, is what it is.

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Read Rudy Rucker's INFINITY AND THE MIND

Best book on the subject.

14. Graham's number is only for sissies.

Real men use Conway's chained arrow notation.

For example 3 -> 3 -> 3 -> 3 is by far larger than Graham's number.

15. Max Tegmark says that if universe is isotropic and infinite, your exact copy should be no further than 101029 meters away. Of course, there should be mind-boggling number of near-copies much more nearby.

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Originally Posted by Kullat Nunu
Graham's number is only for sissies.

Real men use Conway's chained arrow notation.

For example 3 -> 3 -> 3 -> 3 is by far larger than Graham's number.
Tetration has that beat.

17. Originally Posted by Kullat Nunu
Graham's number is only for sissies.

Real men use Conway's chained arrow notation.

For example 3 -> 3 -> 3 -> 3 is by far larger than Graham's number.
Well the OP did say that the number "had to have meaning". And Graham's number does have a meaning, which I included in my post about it.

So Mr Nunu, what is the meaning of your number hmmm?

clop

18. For a very large number, how about the number of unique combinations of Planck space-time volumes in all universes.

19. Originally Posted by Kullat Nunu
Graham's number is only for sissies.

Real men use Conway's chained arrow notation.

For example 3 -> 3 -> 3 -> 3 is by far larger than Graham's number.
Try doing that one in Roman Numerals...

20. Originally Posted by clop
So Mr Nunu...
My nick is the obscure name of the star Eta Piscium, not a real name. Babylonian, no idea what it means.

Originally Posted by clop
...what is the meaning of your number hmmm?
It is the answer. To find out the question, you might like to consult the Margatheans.

21. Originally Posted by Kullat Nunu
It is the answer. To find out the question, you might like to consult the Margatheans.

Rubbish. It is widely known that no universe or form of existance can ever know both the question and the answer at the same time.

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