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somervta comments on Rationality Quotes January 2013 - Less Wrong
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I get the concept of hyperbole, but this:
Is ludicrously too far.
It's two tens with six supers between them! That's twice as much as 10^^^10, right!
</sarcasm>
I guess it just intuitively seems like there should be a useful not-impossible-just-rare event that has a probability in that range (long-term vacuum fluctuation appearance of a complex and useful machine on the order of 5kg, maybe?)
Not... quite.
Let's say there are 10^^10 particles in the universe, each one of them independently has a 1 in 10^^10 chance of doing what we want over some small unit of time, and we are interested in 10^^10 of those units of time. Then the probability that the event we want to observe happens is much better than 1 in 10^^12, and that was only two up-arrows.
(We can rewrite ((10^^10)^(10^^10))^(10^^10) as 10^(10^^9 x 10^^10 x 10^^10) which is less than 10^((10^^10)^3) which is less than 10^((10^^10)^10). This would be the same as 10^^12 if we took exponents in a different order, and the order used to calculate 10^^12 happens to be the one that gives the largest possible number. Actually if I were more careful I could probably get 10^^11 as a bound as well.)
And although I'm not entirely sure about the time-resolution business, I think the numbers in the calculation I just did are an upper bound for what we'd want in order to compute the probabability of any universe-history at an atomic scale.