# Complexity and Self-Organisation

# Complexity and Self-Organisation

So far, our discussion has mainly been concerned with inanimate matter. Only in Chapter 3 did we notice what is missing in “information” if “meaning” is excluded. A phenomenological theory of the generation of “meaningful information” is given in Chapter 4 and this chapter. If we are dealing with genetic sequences, making use of four classes of symbols (referring to the four nucleotides used in nucleic acids), a sequence including n positions has 4^{n} different possibilities. The sequence space is then a point space including 4n points, one for each possible sequence. The distances between any two sequences of this length corresponds to the number of positions occupied by different symbols. A value parameter is introduced which finally determines the population structure. The mutant spectrum appears in the form of a rather dissipated “cloud” that has one or several value maxima, a fact that is due mainly to the presence of “neutral sequences” (i.e. sequences of equal fitness value). The theory confirms formally Darwin’s result. However, the interpretation is completely different from the one generally encountered. Under normal conditions there is no fittest single individual. Rather, fitness is a property of a population, expressed by an eigenvalue of a matrix to which contribution is made by all the individuals present. Since we are dealing with coupled differential equations, the linear case can be expressed by the matrix of rate coefficients. However, according to a mathematical theorem by Perron and Frobenius, only the largest eigenvalue of the matrix is stable. To this we can assign the term “fittest”. The theory uncovers many surprising details. It also unifies the mechanisms of origin and evolutionary adaptation, both referring to different regions in the solutions of the same system of coupled differential equations. Some mathematical details can be found in the Appendices, including contributions from Peter Richter and Peter Schuster.

*Keywords:*
natural selection, Darwin, autocatalysis, instruction, fitness, chaos theory, evolution machines, adaptation, origins, universe

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