Comments on: CG. Graham’s Number http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/ The Math Factor Podcast Site Wed, 20 Aug 2008 12:47:02 +0000 http://wordpress.org/?v=2.5.1 By: strauss http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-136 strauss Sat, 03 Nov 2007 03:07:12 +0000 http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-136 I typed things in wrong way round initially--- it's fixed now. The hyperfive of 3 and 3 is 3^^^3, a mere 3^^3^^3 = 3^^( 3^3^3) = 3^^ (3^27) which is about 3^^(7.5 trillion) or 3^3^3^...^3 with about 7.5 trillion 3's--- a stack of exponents 7.5 trillion high. Now the number of particles in the universe has caused us some trouble in the past, but there are perhaps 10^80, or perhaps 10^120. Either way, the number of <b> digits </b> in 3^^5 = 3^3^3^3^3, a stack of 3's just five high, is MUCH greater than the number of particles in the universe; 3^^^3 is just incomprehensibly huge. And we're not even up to 3^^^4. As far as a <i> fractional </i> number of arrows goes, as discussed in the comic, well, ya got me there. I typed things in wrong way round initially— it’s fixed now. The hyperfive of 3 and 3 is 3^^^3, a mere 3^^3^^3 = 3^^( 3^3^3) = 3^^ (3^27) which is about 3^^(7.5 trillion) or 3^3^3^…^3 with about 7.5 trillion 3’s— a stack of exponents 7.5 trillion high.

Now the number of particles in the universe has caused us some trouble in the past, but there are perhaps 10^80, or perhaps 10^120. Either way, the number of digits in 3^^5 = 3^3^3^3^3, a stack of 3’s just five high, is MUCH greater than the number of particles in the universe; 3^^^3 is just incomprehensibly huge.

And we’re not even up to 3^^^4.

As far as a fractional number of arrows goes, as discussed in the comic, well, ya got me there.

]]> By: Swalkyr http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-133 Swalkyr Mon, 29 Oct 2007 09:22:19 +0000 http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-133 So, how <i>would</i> the "hyper<b>five</b> of <b>3</b> and <b>3</b>" be expressed? 3^^^^^3? So, how would the “hyperfive of 3 and 3” be expressed?

3^^^^^3?

]]> By: strauss http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-127 strauss Thu, 25 Oct 2007 13:54:31 +0000 http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-127 Here is an amusing, mind-blowing comic strip, sent to us by a listener: <a href = 'http://www.absurdnotions.org' rel="nofollow"> <img src='http://www.absurdnotions.org/an20070914.gif' width = 450/></a> from <a href = 'http://www.absurdnotions.org' rel="nofollow"> www.absurdnotions.org</a> (kth operation in the sequence is k-2 arrows) Here is an amusing, mind-blowing comic strip, sent to us by a listener:


from
http://www.absurdnotions.org

(kth operation in the sequence is k-2 arrows)

]]> By: PA32R http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-53 PA32R Sun, 15 Apr 2007 00:09:56 +0000 http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-53 And then there are some functions that grow very fast - the busy beaver function for example. And it should be pointed out that, no matter what number is named or even recursively defined, almost every number is larger. And then there are some functions that grow very fast - the busy beaver function for example. And it should be pointed out that, no matter what number is named or even recursively defined, almost every number is larger.

]]> By: rmjarvis http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-44 rmjarvis Tue, 10 Apr 2007 15:21:54 +0000 http://mathfactor.uark.edu/2007/04/09/cg-grahams-number/#comment-44 It is worth noting that Geoff Exoo claims to have improved the lower limit to 11: http://isu.indstate.edu/ge/GEOMETRY/cubes.html Still a far cry from Graham's number, but higher than 6. :) It is worth noting that Geoff Exoo claims to have improved the lower limit to 11:

http://isu.indstate.edu/ge/GEOMETRY/cubes.html

Still a far cry from Graham’s number, but higher than 6. :)

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