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?"

2 comments:

  1. April3:18 AM

    hey tom

    we should talk evolutionary theory sometime... one of the thoughts right now is that an ability called 'theory of mind' (which not only aids in the prediction of behavior of conspecifics, and therefore leads to the ability to manipulate them, but also plays a key role in language acquisition) is what makes us 'superior.' i am currently exploring its evolutionary origins by studying other primates, so drop me an email sometime. ar354@st-andrews.ac.uk

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  2. Evolutionary theory is great!

    Not too long ago I realized that in order to advance the field of Machine Learning and Artificial Intelligence we (the researchers) must study fellow organism a little bit more and algorithms a little bit less.

    I am particuarly interested in how evolutionary theories could be used to develop better algorithms (how the processes of selection and reproduction could be used to develop algorithms), and since I am a computer scientist I frequently draw analogies between optimization theory and evolution. The traditional approach to Computer Vision is the {write code, analyze experiments} loop, but I would like to see how evolutionary theory could be used to breed algorithms in a less stochastic way then Genetic Programming (whose crossover operator isn't much more than a random perturbation).

    I find myself reading cognitive science (psychology) papers about human vision (and even sometimes pigeon vision!). This is great because it shows how the problem of 'Computer Vision' has deep philosophical roots as opposed to some engineering toy problem.

    I'll definitely drop you an email sometime.

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