I'll just leave this here...

The number of digits in the exponent is beyond comprehension even in the early stages of getting to this number.

If I recall correctly, the size of the tower of exponents is greater than the total number of estimated atoms in the universe.

So 3^3^3 would be 3 numbers in the tower. 3^3^3^3 would be 4. And that goes on basically endlessly.

I do not believe, however big a number or however small a number you can discover when dealing with matter because you will always be playing the known/unknown game into infinity. You'll never reach the end. It exists but it doesn't!

Countable infinity vs actual infinity?

dds08 said:

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I do not believe, however big a number or however small a number you can discover when dealing with matter because you will always be playing the known/unknown game into infinity. You'll never reach the end. It exists but it doesn't!

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This doesn't have anything to do with matter. I could compare Graham's number to the number of atoms in the observable universe, but that's just a mere 10^80 particles. Or we could try comparing Graham's number to the number of configurations of 10^80 particles in the observable universe, but still it's just a paltry 10^10^122 according to Brian Greene's book "The Hidden Reality".

But you're right. Graham's number is nothing compared to infinity. It's just as far from infinity as is the number one.

For grins...

http://home.earthlink.net/~bobseller1/id89.html

There is a chapter in the book The River Why dedicated to 153 fish. The book is worth buying for that chapter alone.

I like the fact that these dudes actually prove that an understanding of Grahams number is so impossible, that the weight of the electrons that would be required to be in your head would be so large, that your head would become dense enough to create a black hole.

That is some seriously comic perspective.