Thursday, July 12, 2012

mathematical modeling

Mathematical modeling's most important purpose is to formalize logic, so that lines of reasoning can't be led astray by false intuition. Game theoretic signaling models, for example, are often so hard to think about intuitively that math is flat out necessary to understand what's going on.

Through modeling, I may have convinced myself, over the past month or so, that the costly signaling story I've been in love* with for the last year is misleading, nearly to the point of being wrong. By exploring what happens when I change one set of assumptions in various ways, correcting an early error in my original model**, and formalizing one more aspect of what's going on, it seems like costliness of signals is a minor issue in only certain circumstances.

That, however, leads to new insights, and hopefully new models of those insights. That's progress. And hopefully that will make up for the time lost pursuing something that wasn't quite right.

I love the objectivity of math. It's hard, and a brutal judge, but there's less room for error, less room for pointless pursuit of invalid arguments, less room for arguing over reasoning that people interpret differently, and it's easier to pinpoint mistakes and move on from sunk costs.

*Huh, I feel like I've blogged on that topic a lot more than once, but I can't find them.

**Doh. I really need a mathematical collaborator who can check my work, and vice versa. It's phenomenal how much time I waste over simple math mistakes, and I hear I'm definitely not alone in this. I can only hope it gets better with experience.

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