But on another note; the Clarkkkkson number kind of cheats because it isn’t a solid unchanging number.

“Much larger” itself being a laughable understatement. Consider:
G1 = 3^^^^3 = 3^^^(3^^^3)

3^^^3 =
3^3^…^3^3
\_________/
3^3^3 //This is the LENGTH of the layer above.
\____/
3

Where 3^3^3 is 7.6 trillion, 3^3^3^3 is larger than a googol (which is larger than the number of elemental particles in the universe), 3^3^3^3^3 is larger than a googolplex (more 0s than there are elemental particles in the universe) and each of the 7.6 trillion 3s is another complete and total change in scope. Then we substitute that in:

3^^^(here)

3^^^(that big number) means:

3^3^…^3^3
\_________/
3^3^…^3^3
\_________/
3^3^…^3^3
\_________/
…
… Using the ‘big number’ as the number of layers.
…
3^3^3
\____/
3

That’s G1. G2 has G1 arrows.
3^^^^^3 = 3^^^^(3^^^^3)
3^^^^^^3 = 3^^^^^(3^^^^^3)
…
3^^^… G1 times … ^^^3
Each additional arrow makes the previous step trivial by comparison.
G3 has G2 arrows.
Etc.

And yet, given all that, much larger numbers have been devised, where G64 itself is insufficient for describing how much of an understatement “much larger” is. If you wish to see a cleaner visual representation of G1, you can check the wiki entry here:
http://en.wikipedia.org/wiki/Graham’s_number

Grahams number is so large because it is an upper bound on the concept of forming a sub graph in one of an arbitrary number of dimensions in a graph so large that even a purely chaotic distribution must have some small sections of order within it.

It’s the technical way of saying “the biggest describable number + 1″. Literally.

I’ve been playing with a computable function (I call it the up function) I made that can generate some numbers larger than can be represented even by itself with smaller terms combined with any notation I have ever heard of. The nifty thing is it can also represent many NORMAL numbers. For example, up(1,0,3) = 4, up(3,0,3) = 12, up(1,0,m,n) ~ A(m,n) – it’s almost exactly equal, but a tiny bit off on larger m values.

On the other hand, the only way I have come up with to describe the scale of up(3,2,3) is up(3,2,3). The second term of it is a real doozie – I call it the hyperrepeater – such that up(3,3,3) cannot be described in even in relation to up(3,2,3). Not even up(3,2,up(3,2,up(3,2,3))), or any traditionally way of noting how many times you substitute it into the third or first term.
Not even something like this:

up(3,2,up(3,2,up…up(3,2,3)…))
\________________/
L^up(3,2,3)(up(3,2,3))

- using the L function mentioned in a previous post here. That’s up(3,2,3) being called recursively into the L function “up(3,2,3) times” as the base for how many times to recursively call up(3,2,3) into it’s third term. Still insignificant next to up(3,3,3).

Calling a larger number into the second term is quite meaningless.

It does not call on any other functions, it is fully computable, and the only operator it uses is addition. If I can ever formalize my notes on it (and make sure I keep all the credit!… and figure out how to describe the numbers it makes… or even understand them.) I may try to publicize it some day.

By the way, L grows somewhat like Grahams numbers. Gn > L(n) > G(n+1)

Foxx released hissecond studio disc, Unpredictable, winter 2005. It positioned at #2, selling 598,000 discs in its first week….

Let n be the largest number that is the unique number satisfying
some formula in the first order language of arithmetic with less
than a google characters.

This beats anything you can generate by busy beaver applications…