Re: Graham's Number -- Practically Everyone Has It Wrong!?

mytg8_at_yahoo.com
Date: 12/09/04 

Date: 9 Dec 2004 10:19:35 -0800

Yeah, I know about the troubles with getting a copy of older articles.
:)

Years ago I did a little research on Graham's Number, including
xeroxing the SciAm article I mentioned. And I turned around and lost
it. So I can only recall, naturally, some portions, including the
*unpublished* (this caught my eye) remark of Gardner. And it makes
sense that he, Graham, would publish a recalculation of his earlier
work. I don't know. Maybe you could email Graham himself.

And I remember a thread here a couple of years ago where someone tried
to get the proof because he couldn't believe that such an immense
quantity could be the result of any realistic (I'm paraphrasing here
from memory :) ) mathematical proof. If interested, try searching sci
math "Graham's Number" for this post and thread.

Concerning the SciAm article, it was the first time the so-called
Graham's Number was mentioned in the popular press, and it was
definitely the same problem in Ramsey Theory about the lowest dimension
of a hypercube such that if the lines joining all pairs of corners are
two-colored, a planar graph Kv[4} of one color will be forced.

The number in the SciAm article is the same as Wolfram's and, as you
said before, the same as most representations online. Gardner
represented it in an informal graph, something like this- (hope this
comes out okay)

/ 3^^^^3 arrows
| ______^_______
| / \
| 3^^^...........^^3 arrows
| ______^_______
| / \
| 3^^............^^3 arrows
64 layers< .
| .
| .
| _______^_______
| / \
\ 3^^.............^^3

HTH

-cs

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