the absurd observers

Thursday, March 10, 2005

Math persists, despite shortcomings.


Jordan Ellenberg, in his Math column on Slate, reviews a book on Godel and discusses the impact of Godel's incompleteness theory. The theory can be understood as "no system of logical axioms can produce all truths about numbers because no system of logical axioms can pin down exactly what numbers are. " JE points out that people have coopted this theory and stretched it out to include arguments against evolution.

In a clever passage, JE writes the following aphorism: "Any scientific result that can be approximated by an aphorism is ripe for missappropriation." This statement mirrors Godel's paradox: "P is not provable using the given axioms". This kind of trickery appeals to me.

However, what I really liked about the piece was the suggestion that the truly interesting thing about Godel's theory is that it exposed the lack of foundation for math, and yet, math survives. He uses the analogy of a country where the constitution is destroyed, and yet, the citizens lives do not change. Math seems like a fiction or maybe a dream. It is a system that operates without being attached to the ground.

So, things exist in the material world without a theoretical framework? Ideas based on intuition? That's right. Think of:
  1. Busses without schedules. Intuitively I know the bus comes at a certain time, but the schedule definitely does not exist.
  2. The goodness of Jello. Intuitively I know it tastes good, but I don't think I can prove it.
  3. Dick Cheney. Intuitively we know he exists but we can't prove it.


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