Nature evolves in saltations -- genetic mutations that produced significant changes in organisms.
Ray Dougherty presents a number of saltation examples, and asks if such an event may have been the cause of the development of communication capabilities in animals. There is evidence in this direction, for example in the development of the lizard cochlea. Other examples are inversion or duplication of organs.
Saltation events in the development of the brain and cochlea may well have been the source of the evolution of the information processing capabilities in humans. The evolution tree of the cochlea and the current distribution of its sizes offers support for this hypothesis.
The animal with the largest cochlea is the guinea pig -- its cochlea was developed in a feedback system with the lizard cochlea: lizards predate guinea pig young, but can't hear sounds in a high frequency, creating evolutionary pressure for the guinea pigs to communicate at a higher frequency level.
Ray shows some Mathematica code to map the space of possible cochlea spaces. He then moves into possible approaches to analyzing the shape of the cochlea using mathematical methods. One approach that is bound to fail is trying to map the cochlea into 2D planar surfaces -- that's geometrically impossible.
NKS offers a possible approach to the problem, because its discrete systems offer a good model for "discontinuities". Ray suggests writing a generative grammar defining a mathematical function for each signal complexity for any shape cochlea. The grammar would generate what Ray calls Poincare complexity strings, combining sinusoidal functions in a nested way.
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