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Jay_Schweikert comments on Open Thread, November 1-15, 2012 - Less Wrong
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This is a random question, and I have poked around a bit on Google looking for the answer: what's the convention for pronouncing particular instances of Knuth's up-arrow notation? Like, if you had 3^^^3, how would you actually say that out loud? I always find myself stumbling through something like "three three-up-arrows three," but that seems terribly clunky. I also read somewhere that "3^^^3" would read as "three threes," which is more elegant, but doesn't seem to work when the numbers are different -- e.g., how would you say "3^^^4"? Anyway, I figured someone here would know.
Regardless of the specific numbers, or the number of up-arrows, the correct pronunciation is "kajillion".
2^2?
Well, 2^2 is closer to 3^^^3 than almost every other positive integer, so we can round it up to 3^^^3 and then call it "kajillion".
Gazzillion feels bigger to me
I've heard "three up up up three", which is concise and not easily confused with other operations. If I heard "three threes", I'd interpret that as meaning 9.
It's been a few years since I heard this pronounced aloud, but my old undergrad prof's pronunciation of "3^^^3" was "3 hyper5 3". The "hyper5" part refers to the fact that three up-arrows is pentation. Similarly, "x^^y" is "x hyper4 y", because two up-arrows indicate tetration.
In general, add 2 to the number of up-arrows, and that's the hyper number you'd use.
(I should mention that I've never heard it used by anyone other than him, so it might have been just his way of saying it, as opposed to the way of saying it.)
Thanks to everyone for all the answers. I'd say this one makes the most sense to me -- pretty quick to say and easily scalable for any number -- but I guess there's just not one, well-accepted convention.
The ^^ operation is called tetration, so I'd guess ^^^ is pentation. So 3^^^3 would be “three pentated to three”, or something like that.
I don't care what the convention is, but I say "three to the to the to the three!".
That implies exponentiation; up-arrow notation is two steps beyond that.
(Not serious:)
Instead of the third power of three, it's the "third triforce of three"!
"Three triple-caret four" is what I've heard. I'm not a math person though, so take it with a grain of salt.
I would say "power of"
So "three to the power of the power of the power of three"
Those '^'s are being used in up-arrow notation, not exponentiation.