tea.mathoverflow.net - Discussion Feed (Graham number and beyond)

Andres Caicedo comments on "Graham number and beyond" (20884)

Andres Caicedo — Mon, 17 Dec 2012 22:46:39 -0800

Thank you, Scott. :-)

Scott Carnahan comments on "Graham number and beyond" (20883)

Scott Carnahan — Mon, 17 Dec 2012 21:53:24 -0800

@Andres: done.

Edit: I see now that even editing deleted answers bumps the question.

Andres Caicedo comments on "Graham number and beyond" (20882)

Andres Caicedo — Mon, 17 Dec 2012 20:46:25 -0800

Hmm... I had forgotten about that one. (But while we are at it, would a moderator please edit the sweary deleted answer so 10K people don't have to suffer it?)

grp comments on "Graham number and beyond" (20881)

grp — Mon, 17 Dec 2012 18:37:21 -0800

I think the question is morally (if not technically) a duplicate of other MathOverflow
questions, and that those questions instead should be resurrected.
http://mathoverflow.net/questions/11934/magnitude-of-grahams-number is one
where I suggested a comparison with some numbers Harvey Friedman proposed.

If you want to make a brand new question that covers a particular aspect left
out of the present questions, I encourage you to do so after you have convinced
yourself that it is not addressed in an extant MathOverflow question.

Gerhard "Ask Me About System Design" Paseman, 2012.12.17

Andres Caicedo comments on "Graham number and beyond" (20879)

Andres Caicedo — Mon, 17 Dec 2012 17:03:25 -0800

The question http://mathoverflow.net/questions/116648/thoughts-about-a-number-much-larger-than-grahams-number-closed was recently closed.

I think it has potential, and have voted for it to be reopened.

Having spent some time playing with fast growing hierarchies, I see why the OP struggles trying to comprehend the magnitudes involved. On the other hand, there are mathematical reasons why these large numbers become harder and harder to grasp (as more and more induction is needed to prove that functions in fast growing hierarchies are total).

H. Friedman has some interesting comments about "large finite numbers". In the paper of that name, for example, he talks about the Ackermann hierarchy A_n and says that k=A_5(5) is "incomprehensibly large". Since the number A_k(k) is claimed as an upper bound for what he calls n(3) (see page 7 in http://www.math.osu.edu/~friedman.8/pdf/EnormousInt112201.pdf ), we may actually want to come to terms with these incomprehensible magnitudes.

The question gives us a chance to see explanations that may help us with such a task.