I'm not a mathematician - far from it. Every time I come back to Graham's number I can't get my head around Knuth's up-arrow notation. I interpreted it in my own way, but I have a feeling I've got it wrong. The way I thought of it is that:

Step 1: 3^3 = 27. Take that result (27) and make it the new power:

Step 2: 3^27 = 7.6 trillion. Take that result (7.6T) and make it the new power:

Step 3: 3^7.6T = ? (An "Impossibly Huge Number.") Take that result (I.H.N) and make it the new power:

Step 4: 3^I.H.N = ? (A "Savagely Huge Number.") Take that result (S.H.N) and make it the new power:

Step 5: 3^S.H.N = ? And so on, and so on. (I forget which one would be "G1", step 4 or step 5 maybe)

- What I'd like to know is whether this way of looking at it is right or not. Obviously you can't write anything down without coming up with "Magnificently Ridiculous Names" for these numbers so it defeats the object, but I'm trying to get my head around the process.

Thanks in advance for any help, I really appreciate it.