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CronoDAS comments on Complexity of Value ≠ Complexity of Outcome - Less Wrong
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Comments (198)
Joke counterexample:
x^2 = -1 is a simple problem that only has complex solutions. ;)
(Of course, that's not the meaning of "complex" that you meant.)
Serious counterexample:
The four-color theorem is relatively simple to describe, but the only known proofs are very complicated.
Gah, don't over-qualify jokes! It's a supplicating behavior and seeking permission to be funny blunts the effect. Just throw the "X^2 = -1" out there (which is a good one by the way) and then go on to say "A more serious counterexample". That's more than enough for people to 'get it' and anyone who doesn't will just look silly.
This is the Right (Wedrifid-Laughter-Maximising) thing to do.
I'm sorry. :(
Was that a practical joke on wedrifid?
It is now!
Nice. Die. :P
But that complicated proof could be concisely provided via a universal proof algorithm and the statement of the four color theorem.
Exactly! The Kolmogorov complexity is not very high.