Thursday, April 2, 2009

Mathematical Laws or Trivial Patterns?

Philip Ball offers an entertaining summary of a recent paper in Science on how data can be analyzed to propose laws. The kinds of examples discussed, from physics through biology, show the need for some philosophical clarification:
As Schmidt and Lipson point out, some of the invariants embedded in natural laws aren't at all intuitive because they don't actually relate to observable quantities. Newtonian mechanics deals with quantities such as mass, velocity and acceleration, whereas its more fundamental formulation by Joseph Louis Lagrange invokes the principle of minimal action — yet 'action' is an abstract mathematical quantity that can be calculated but not really 'measured'.
And many of the seemingly fundamental constructs of natural law — the concept of force, say, or the Schrödinger equation in quantum theory — turn out to be mathematical conveniences or arbitrary (if well motivated) guesses that merely work well. Whether any physical reality should be ascribed to such things, or whether they should just be used as theoretical conveniences, remains unresolved in many of these constructs.

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