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KenChen comments on Rationality Quotes: April 2011 - Less Wrong
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– Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid
Doesn't that spiral out to infinity?
It can just asymptotically approach the right value. It's probably more metaphorical, though.
It always takes longer than you expect, even when you take into account the limit of infinite applications of Hofstadter's Law.
Even further:
Hofstadter's Law+: It always takes longer than you expect, even when you take into account the limit of infinite applications of Hofstadter's Law+.
For all ordinal numbers n, define Hodstadter's n-law as "It always takes longer than you expect, even when you take into account Hofstadter's m-law for all m < n."
For all natural numbers n, define L_n as the nth variation of Hofstadter's Law that has been or will be posted in this thread. Theorem: As n approaches infinity, L_n converges to "Everything ever takes an infinite amount of time."
Actually it takes longer than that.
I've got a truly marvelous proof of this theorem, but it would take forever to write it all out.
Hofstadter's Shiny Law: It always takes longer than you expect, especially when you get distracted discussing variants of Hofstadter's Shiny Law.
...which then forces things to take an infinite amount of time once you get to n=omega_1, so thankfully things stop there.
EDIT April 13: Oops, you can't actually "reach" omega_1 like this; I was not thinking properly. Omega_1 flat out does not embed in R. So... yeah.
Yes. Hofstadter is like that.