Opinion of Graham's number

[I spent the winter writing songs about getting better]

http://en.wikipedia.org/wiki/Graham's_number

[I spent the winter writing songs about getting better]

What's this have to do with politics?

As much as the Cambrian Explosion.

[I spent the winter writing songs about getting better]

I'm kind of wondering how he calculated it. There isn't enough hard drive space in the world to hold all the digits so even computers wouldn't be very useful. It appears though that we don't even know the first digits, just the last ones.

[I spent the winter writing songs about getting better]

This thread reminds me how much my maths skills & knowledge have declined since I left secondary school. Though I LOL at the idea of a number being unexpressable due to the limitations of the universe, I also second what PiT said.

Well googelplex (a 1 followed by googel 0's, where googel equals a 1 followed by 100 zeroes, also expressed as 10^10^100) can't be expressed due to lack of space in the universe also. And Graham's number is far larger apparently. I would just like to know how many digits there are in the number.

Yes but a googleplex can be easily expressed by shorthand notation like you have there. This can't.

[I spent the winter writing songs about getting better]

This thread reminds me how much my maths skills & knowledge have declined since I left secondary school. Though I LOL at the idea of a number being unexpressable due to the limitations of the universe, I also second what PiT said.

Well googelplex (a 1 followed by googel 0's, where googel equals a 1 followed by 100 zeroes, also expressed as 10^10^100) can't be expressed due to lack of space in the universe also. And Graham's number is far larger apparently. I would just like to know how many digits there are in the number.

     If I grasp the concept of up-arrow notation as well as I think, the first layer is equal to 3¹⁹⁶⁸³. The next layer's number of arrows is equal to the previous layer's value, so the second layer is a power tower of threes, 3¹⁹⁶⁸³ terms high. There are 62 more layers after that. Suffice it to say it's huge.

Can you guess how many digits?

[I spent the winter writing songs about getting better]

So I read up on the arrow notation, and basically with four arrows between the 3s, you already have a number larger than a google. The next layer is calculate the same...except with the results of the first layer being the number of arrows. Repeat 62 times. So yeah, even the number of digits is a number so large we don't have a name for it.

The amusing thing is that this is the upper bound in a range where the lower bound is 6. Basically any number between 6 and this could answer a certain problem.