Saturday, March 8, 2008

Prof. Ray C. Dougherty's Research

A few weeks ago I attended a Wolfram Research event called Mathematica Publishers Day. The goal of the event was to highlight the capabilities of Mathematica 6 as a platform for technical publishing. I really enjoyed this event but was also pleasantly surprised by a talk that did not quite fit into the overall theme of the event but nevertheless was quite fascinating to me.

The presenter was Prof. Ray C. Dougherty, NYU Linguistics researcher. He used Mathematica to model all possible sine wave based communications systems. The presentation is available via Wolfram. Unfortunately, as with many interesting presentations, you needed to hear the talk to get the most out of it. Here are some interesting excerpts that I remember:

  • The Cochlea is computing the second derivative of the auditory input.
  • The most mathematically complex communication system is one where the transmitter and receiver have the same anatomy (e.g., wings of insects).
  • Bats can hear phase changes because they can rotate their ears. A human can not hear a change in the rotation of a tuning fork but a bat can.
  • Prof Dougherty believes he has a Chomsky generative grammar that enumerates all possible animal communication systems.
  • He also believes he can map each possible system onto the integers in a natural way.
  • From this he concludes that evolution must proceed in jumps.
  • He relates this idea to the evolution of all possible Tic Tac Toe Games to illustrate the notion that all such games are not unique and similarly the space of all possible communication systems contains many redundant systems as well.
  • He goes on to visualising distributions of the primes to illustrate that there are systems that are not random but whose patterns are too complex for us to model in a simple fashion. Explains how this is related to the ideas in Stephen Wolfram's NKS.

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