|Turned up to eleven: Fair and Balanced|
Friday, July 19, 2002
"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...