I realize this thread is a from a year and a half ago (a possible spam post moved it into the current thread titles), but if anyone is still interested in these issues, about 9 years ago I posted in sci.math a lengthy essay on Graham's number and then followed it up with three more essays (and a promise for more, which I never got around to).
GRAHAM'S NUMBER AND RAPIDLY GROWING FUNCTIONS [2 March 2002] http://groups.google.com/group/sci.math/msg/0f3c8bab92145996
BIG NUMBERS #1 [8 April 2002] http://groups.google.com/group/sci.math/msg/403051f310ff3dfc
BIG NUMBERS #2 [8 April 2002] http://groups.google.com/group/sci.math/msg/d12962e3af2c74b7
BIG NUMBERS #3 [8 April 2002] http://groups.google.com/group/sci.math/msg/4f2ed8e0385b72f2