Feh, such a tiny inconsequential number

Post #401,968 by pwhysall 5/22/15 1:30:14 AM Reply	Feh, such a tiny inconsequential number You want a bit of Graham's Number, you do. the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume. Although I must confess that I would have never happened across Graham's Number, myself, as the following question has never raised itself in my mind: Connect each pair of geometric vertices of an n-dimensional hypercube to obtain a complete graph on 2n vertices. Colour each of the edges of this graph either red or blue. What is the smallest value of n for which every such colouring contains at least one single-coloured complete subgraph on four coplanar vertices?
Post #401,969 by static 5/22/15 5:33:35 AM Reply	I was thinking about Graham's Number, too. Though there does seem to be a kind of insanity to how you have to write it. Wade. Just Add Story http://justaddstory.wordpress.com/
Post #401,971 by Another Scott 5/22/15 8:36:58 AM Reply	Who needs to be constrained by the Universe? Kruskal's Tree Theorem: The latter theorem ensures the existence of a rapidly growing function that Friedman called TREE, such that TREE(n) is the length of a longest sequence of n-labelled trees T1,...,Tm in which each Ti has at most i vertices, and no tree is embeddable into a later tree. The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4),[] are extremely small by comparison.[1] A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of As is A(187196),[2] and A() is a version of Ackermann's function: A(x) = 2 [x + 1] x in hyperoperation. Graham's number, for example, is approximately A^64(4) which is much smaller than the lower bound A^A(187196)(1).* It can be shown that the growth-rate of the function TREE exceeds that of the function fΓ0 in the fast-growing hierarchy, where Γ0 is the Feferman–Schütte ordinal. Neat stuff. Cheers, Scott.
Post #401,991 by Ashton 5/23/15 1:44:56 AM 5/23/15 2:15:32 AM Reply	I suspect that Monty Python's send-up of these utterly surreal imaginations was the skit with the aged author/artist? sitting outdoors in a chair, as the reporter repeatedly refers to him by his full-name: {some thousands of mouth-noises long} ..as the subject finally expired amidst the final recitation: a tribute turned into a threnody, much like MAHLER: "Das irdische Leben" ("Earthly Life") [German text from the anthology Des Knaben Wunderhorn (The Youth's Magic Horn)] where the child dies as his mutter repeatedly tells him to wait-a-while ... as the bread bakes. I suppose that such ruminations may so occupy the grey cells in some homo saps as to preclude their otherwise emulating Dr. Moriarty or other fictional Mr. Hyde-grade outliers, becoming just another nasty menace as they age. (So this may be a good thing, in such cases.) But I fail to see how such MIne's Bigger exercises can take precedent over the efforts needed next by millions of the math-unafflicted: in mere repetitive, pedestrian labors towards planetary rescue from [Twain] The whole damned human race {/Twain] Do. That. ... and there will be time for mental masturbations, again. I wot. ie We are not amused. PS: Believe n! has been mentioned; it is al ye Need to know in imagineering such tempests in academic teapots; Teller was right: most people Fail in perceiving emotionally the consequences of exponentials (and n!) ... Now There is.. applied math for a species with short attention-span. ;^> Edited by Ashton May 23, 2015, 02:15:32 AM EDT Expand All History

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