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The humble parameter

As any software engineer will know, it is often easier and better to design a system that is too general for the particular task at hand and then to govern the actual behavior with a parameter. At one extreme you get sort functions with the comparator supplied as a parameter to the sort. At the other extreme you get entire policy-based frameworks where the parameters that govern the system are represented as rules.

A similar phenomenon occurs in mathematics: it is often simpler to solve a more general problem than to solve the particular problem. The more general solution is often parameterized in such a way that the particular solution falls out of the general case.

Recently, I learned of a use that Nature has put to the parameter, it seems that Finches' beaks may also be governed by one or two genes (BMP4) which show up in many wildly different animals (Finches, fish, butterflies, ...). I would suggest that what is going on here is that we have a general mechanism (the HOX genes) with a system of parameterization that is easily modified.

There seems to be a general principle at work here -- that the pattern of having a general mechanism tied to a parameter to give particular instances -- applies to many things and in many areas of the world. Perhaps this is one of those natural joints that philosophers love to carve.

Perhaps a Math grad student would be interested in designing an algebra of parameters?
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