in reply to Re^2: Empirically solving complex problems
in thread Empirically solving complex problems

True, there are many problems which cannot be solved or even vaguely approached analytically, but this isn't one of them.

There are more problems that cannot be solved by or even vaguely approached analytically by a given person than ones that cannot be solved by or even vaguely approached analytically. I think that the original poster laid out a pretty good case that he couldn't tackle this analytically, while leaving it open as to whether someone else might succeed in doing so.

Therefore your success with an analytical approach takes nothing away from the value of the non-analytical approach in this case.

  • Comment on Re^3: Empirically solving complex problems

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Re^4: Empirically solving complex problems
by fizbin (Chaplain) on Mar 07, 2005 at 14:18 UTC
    While I see your point in general, I think that in this specific case the original poster gave up on the analytical approach too quickly, and came up with a solution that I don't think does what he thinks it does. (As I said, this particular problem didn't involve difficult, advanced mathematics -- it involved being able to solve a quadratic equation and plug the results into a black box pulled off the mathworld site)

    Among other things, the original solution is not symmetric with respect to the distributions: if I reverse distribution 1 and distribution 2, I should get the same answer, right? If not, I can hardly claim to be measuring something related to the union of two distributions. Also, I wonder whether measuring the area under two curves is in fact the appropriate thing to do given the problem. 

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