[.ca] Information and Self-Organization: A Macroscopic ... (ISBN 3540330216)

physics approach:
Self-Organization is not the function given to a neural net (although they have taken it) used for pattern recognition, nor is it a cult somewhere in Germany. After following Haken's work for 6-8 years it is good to see a summary of sorts. Haken was working with self-organizing similarities in the 80's when unification ideas were rampant. Haken uses this same analogy by equating the basic form to stochastic differential equations. It is somewhat easier to approach the differential equation as a dynamical system driven by random vector fields of which the Ito form (stuff Kalman filters are made of) is a special case. Without going into martingales Brownian motion ergodic theorems of Markovian processes Haken does give a convincing argument for what he terms MIP (max. information principle) and information gain in the system. Linguistically converted this means that the process may be likened to a diffusion process with thermodynamic stuff. This paves the way for the transfer of information from one organization structure diffusion (in the wave) front to another. It seems to me, however, that a much simpler proof would be; show the parallel between Haken's basic form and the Lax form of an evolution equation. Establish relationship to Hirota's derivatives. Usually represented and manifested as the Korteweg-deVrie equations the polynomials groups describing the equation easily convert to Hiroto derivatives. Show fundamental relationship to n-solitons and vertex operators, establish relationship to Heisenberg and Clifford algebras, show Fock representation of Bosons using Maya diagrams, show Boson-Fermion correspondence. Complex variables, infinite dimensional algebras, Fermions, and Bosons; The principle of superposition does not apply to non-linear waves, despite that there exists exact solutions containing an arbitrary number of parameters suggesting an infinite dimensional transformation group acting on spaces of solutions of integrable systems (Reaction-diffusion as one type shock waves as another). Because of this self-symmetry in scales of complex polynomials, transformational methods work well. If waves are information densities and an increase in entropy is an increase of information Hiroto's derivatives would give the mathematical link showing the degrees of information transfer between types of diffusion front (waves) and another. The similarity of scales, the repeating nature, then transfer of one wave front (diffusion) through another without annihilation.