Wednesday, October 12, 2005

Discovering Laguerre Polynomials and Shortcomings of Darwinian Evolution

I was recently playing with the Gamma Function, and realized how it could be used to help evaluate a certain type of weighted inner product between polynomials defined over [0,inf). After a few hours of playing, I finally googled this type of expansion and was non-surprised to find these polynomials called Laguerre Polynomials. These orthonormal polynomials could be used to define a Laguerre-Fourier expansion of functions with a wider support than the other orthonormal polynomials such as the Legendre polynomials.

I recently had a interesting conversation with my friend Mark about the 'missing link' in evolutionary theory. We both agreed that one problem with Darwinian Evolution is that it requires some special mechanism for humans to possess that would explain their superiority in the modern world. We pretty much agreed on the fact that an advanced theory of mating partner selection can be ruled out on the basis of empirical evidence. Although a theory of intelligent partner selection could explain man's dominance in the modern world, the empirical evidence shows that modern man's selection algorithm is rather arbitrary. It brings back the 'big' question, "Why are we so advanced?"