Sunday, January 29, 2012

Good solution vs. "the" solution

Most interesting problems have more than one solution; it's also usually the case that you can do pairwise comparisons and determine if one solution is better (faster, or simpler, or more reliable, or what have you) than some other one. For some problems, there exist something that is the solution. It's a solution that does much more than solve the problem: it makes the problem go away. It dissolves the problem. When you find the solution to some problem, you'll wonder why anyone ever thought it was a problem in the first place. For example, the imaginary unit first appeared as part of a piecemeal solution of the problem of finding general roots of a cubic equation. But if you imagine someone who grew up in a reality where complex numbers were discovered and used before real numbers, you'll probably agree that that someone couldn't even understand why finding roots of cubic equations should be any more difficult than quadratic equations.

Now I'll do something all of us do but rarely admit to: I'll talk about something I really don't have the first clue about. Quantum mechanics! I think that the "many worlds" meta-theory of quantum mechanics is the solution to what's known in other interpretations as the "measurement problem" (i.e. the empirical fact that apparently identical quantum systems behave differently depending on whether they are observed or not). The many worlds interpretation dissolves the problem completely: It shows why, given that quantum systems don't really behave differently when they're measured than when they're not, it appears to us that they do. If by some historical accident the many worlds interpretation were the first meta-theory of quantum mechanics to be developed, no one would have even coined the phrase "measurement problem".

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