Turned up to eleven: Fair and Balanced

Friday, July 19, 2002


"Godless Capitalist", in the comments below, casts aspersions on my mathematical capabilities, suggesting that my skepticism about genetic engineering of complex traits is rooted in (to paraphrase) "being a mathematically illiterate molecular biologist"; ok, he didn't quite, but close enough. He suggests that the future of biological modeling is analogous to current electrical circuit theory. Now, I was really bad at electric circuit diagrams, but I do remember the basics of impedance, capacitance, resistance, voltage, and current, and I agree that for simple biological systems, this model is adequate, if oversimplified.

"Godless" misses the point, however, in arguing that this is a case of mathematical inadequacy. The question is not whether or not I can do it, but whether or not it is 1) theoretically possible, and 2) practical.

Was Godel (no umlauts in Blogger) a naysayer, when he proved that no sufficiently powerful logical system could be consistent and complete?

Was Heisenberg just not so good at solving equations, or did he find a fundamental physical limitation?

I suspect that most of my readers understand that these rhetorical questions illustrate that fundamental limitations exist, and sometimes, we find them. I don't know for a fact that such a limitation exists in this instance, although smarter people than me or Godless have argued that case (Penrose, and John Searle, just to name a couple in a particular field).

I won't spend any more time on this till next week, but here is some food for thought:

Suppose we define complexity as the ratio of the description of a system to the system itself. It is a bit tricky, but we can think of the system itself as taking up space within a defined solution space S. If that system's set of solutions fills the space, then it is "maximally complex". If not, then a ratio can describe that complexity. The ratio can be approximated for the three general types of solutions to dynamical systems; point solutions, limit cycles, and "strange attractors". Think about it...

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