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cousin_it comments on Kevin T. Kelly's Ockham Efficiency Theorem - Less Wrong
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Comments (81)
Haven't thought too hard about this question. In my mind complexity is filed away as a "mystery", on the same shelf as frequentism vs Bayesianism, decision theory and other things. I know the state of the art and am convinced that it's unsatisfactory, but how to fix it is unclear. You could carve out a nice research area for yourself if you took any of these questions and ran with it :-)
I have a vague idea that one shouldn't look for a single correct notion of complexity, but instead try to find some reasonable properties that any measure should have, and study them all at once. For instance, if I propose a measure that turns out to be equivalent to square-root of K-complexity, who's to say it's better or worse? More seriously, one could imagine complexity measures like "the time it would take to explain in English", "the time it would take to explain in Japanese", "the time it would take a smart person to explain", "the time it would take a stupid person to explain"...
But when I try to think about "properties a measure should have" all I can come up with is a kind of monotonicity: a complexity measure is a real-valued function on strings whose value on a given string is larger than the value on an (initial?) substring. That is not even true of K-complexity. (E.g. if N is an integer with high complexity, but less than 10 to the one-hundred, then a string of N repeated zeroes will have higher complexity than a string of 10 to the one-hundred zeroes.)
So many topics, so little time! :)
It's amazing how much a person can do if some topic manages to interest them more than the Internet, even for a little while.
A timely reminder. I'd better go back to obsessing about nootropics and see if I cannot amaze myself somewhat.
Damn Lesswrong and its "Recent Comments:" and its orange envelope icon.
When you reach a result, be sure to post it and make the Internet a little more alluring for all of us :-)
This suggests a new focus - drugs to treat internet addiction and promote procrastination resistance. The experimental procedure seems obvious. The double-blind, placebo controlled T4ET (Tv Tropes - Time To Exit Test).