The TV in my apartment flickered as I sat on my couch with a slice of cold mushroom pizza, idling away the hours on another lonely Friday night.

I missed Lisa. It felt like it had been months since I'd seen her. Not as many months as, say, Graham's number, which is the largest number ever used in a mathematical proof and can be constructed by taking the value of G(64) where G(1)=3^^^^3 (using Knuth's up-arrow notation, in which a double up-arrow operator denotes iterated exponentiation and in general an N-arrow operator expands into a right-associative series of N-minus-1-arrow operators) and G(n) for n>1 equals 3^^^^...^^^^3 where the number of up-arrows in each term is equal to G(n-1), because even calculating 3^^^3 (with only three arrows instead of four) produces a tower of 7,625,597,484,987 stacked exponents, and the value of G(64) itself couldn't be written even if you had really tiny handwriting and a piece of paper the size of all the universes that could ever possibly be imagined to exist even in a "Star Trek" movie, but still a long time. And yes, I know those are carets and not actual up-arrows. If it bothers you that much, print out a copy of this paragraph and draw a little vertical line under each one. Anyway, I did miss her, and as I sat on my couch pondering exactly what purpose a number as large as G(64) could possibly have, and whether my phone number would occur in any ten consecutive digits if you could somehow write out the entire value, the TV continued to flicker and the pizza got even colder.

Word count: 280
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Author's Note:

Yes, there really is such a number. Google it.

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  • Entered: 3/9/2010 7:12:51 PM
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