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By Jürgen Klüver

When i began with this booklet numerous years in the past I initially meant to write down an advent to mathematical structures idea for social scientists. but the extra i assumed approximately platforms thought at the one facet and theoretical sociology at the different the extra I turned confident that the classical mathematical instruments are usually not rather well fitted to the issues of sociology. Then I grew to become accustomed to the researches on advanced platforms by way of the Santa Fe Institute and specifically with mobile automata, Boolean networks and genetic algorithms. those mathematically extremely simple yet super effective instruments are, in my view, rather well applicable for modeling social dynamics. as a result i attempted to reformulate numerous classical difficulties of theoretical sociology when it comes to those formal structures and description new probabilities for a mathematical sociology which will sign up for instantly at the nice traditions of theoretical sociology. the result's this e-book; no matter if I succeeded with it's in fact as much as the readers. because the readers will understand, the booklet couldn't were written via me on my own yet in basic terms by means of the joint labors of the pc team on the Interdisciplinary heart of study in greater schooling on the collage of Essen. The participants of the gang, Christina Stoica, Jom Schmidt and Ralph Kier, are named in different subchapters as co-authors. but much more very important than their contributions to this ebook have been the everlasting discussions with them and their endurance with my new and intensely speculative rules. Many thanks.

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Example text

Accordingly, states that are reached again after k other states are attractors of the period k+ I. Since the important point in the above definition is the number of different states between the reaching of an attractor, I will use the above definition here. g. ff(Z) = f(Z) + f(Y), then F obviously constructs a straight line in the state space. In this case, there is of course no attractor, because the (linear) trajectory constantly proceeds in the same direction. However, this can only happen iff itself is linear, which means that we are dealing with a linear system.

Selforganization means that the systems realize their interactions on the basis of intrasystemic rules; adaptation means that the rules of interaction can be varied because of particular environmental requirements until the system reaches sequences of states that are adequate for the system with regard to the environmental requirements. Before we look at the relations between self-organization and adaptation more systematically, I would like to illustrate these remarks with the example of a computer program, which Jorn Schmidt and I have developed; it is a combination of a cellular automaton (CA) with a genetic algorithm, of which a detailed description will be given in chapters three and four.

Remains the same. However, the important parameters of the rule, namely the link weights, do change. e. the number of neurons that have an effect on the neuron j, does not change. When a network has learned something, it can "remember" it on specific conditions: if a system has learned to solve a problem after learning to solve a previous one, and it is confronted with the first problem again, it will solve it immediately - it has changed its behavior in the learning process. Obviously, this is what Bateson called learning I.

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