Jürgen Klüver

A mathematical theory of communication: Meaning, information, and topology

This article proposes a new mathematical theory of communication. The basic concepts of meaning and information are defined in terms of complex systems theory. Meaning of a message is defined as the attractor it generates in the receiving system; information is defined as the difference between a vector of expectation and one of perception. It can be sown that both concepts are determined by the topology of the receiving system.

Self-organized learning by self-enforcing networks

We describe a new type of self-organized learning neural networks, namely the Self-Enforcing Network SEN. After introducing our theoretical and methodical frame, basically orientated to the theory of Piaget, we show the logical principles of SEN, including a new activation function, a new learning rule, and a specific visualization algorithm. The operations of SEN are demonstrated with the examples of assimilating new perceptions of animals, the application of a SEN to direct marketing, and the usage of a SEN as consulting system for pupils and beginners at the university. Apparently SEN can be used in many different contexts.

Topology, computational models, and social‐cognitive complexity

The topology or topological structure S, respectively, of a complex system can be defined in a graph theoretical way, i.e., S ⊆ ((V × V), E), V being a set of vertices and E a set of edges. Therefore, a topological structure in this sense can be represented as a directed graph. A relation e(v1, v2), e ∈ E, v1, v2 ∈ V may represent, e.g., a social relation in a social group between group members, a cognitive (semantical or logical) relation between concepts or an economical relation between economical actors. By defining a certain topology and by adding certain rules of interaction between elements vi and vj ∈ V, one obtains a literally universal modeling schema for arbitrarily complex problems (6). This modeling schema will be applied in this article to several different problems, i.e., predictions of social group dynamical processes, the diagnosis of certain diseases via a medical diagnosis system constructed this way, and the solving of a murder case in a detective story. The schema will in some cases be extended to two levels, i.e., one element of a first level will consist of different elements itself.

The evolution of social geometry

O ne of the main scientific enterprises in the last decades was and is the search for general principles of complex systems, i.e., laws or mathematical regularities that are valid for such different phenomena such as chemical reactions, life, economy, social interactions, and human thinking. The most remarkable event for these investigations was without doubt the founding of the Santa Fe Institute (SFI), where researchers from different scientific fields should gather and combine their studies for the common goal. Because the research of the SFI was dominated mainly by natural scientists, it seemed inevitably to look for “laws of complexity” the same way physicists or biologists are used to. Therefore scholars such as Kauffman [1, 2] or Gell-Mann [3] investigated “power laws” or principles of “organized criticality,” which they hoped to find in physical, biological, and social complexity likewise. In other words, the basic assumption was that there must be some laws, which guide the observable behavior of complex systems, regardless, which domains of reality they belong to. The SFI and related research groups have demonstrated a lot of results that are of interest to scholars in rather different fields of scientific enterprise. In particular Kauffman [1, 2] and Holland [4, 5] have successfully extended their research from natural and computer sciences to problems of the social and the cognitive sciences. Therefore the hope for general principles of complexity is far from refuted. Above all, the formal tools that were developed during these studies such as, e.g., cellular automata, Boolean nets, genetic algorithms, and artificial neural nets, have demonstrated their fruitfulness also in the social and cognitive sciences (cf. Klüver [6]). Yet despite a lot of interesting results, the impact of complexity research to the social sciences is still rather small, and not many social theorists believe that it is useful to look for parallels between natural and social systems. The main reason for this is probably that often there are no identical laws that govern the behavior of complex systems belonging to different levels of emergence. Therefore the search for principles of complexity must be extended into additional regions: one also has to shift the focus of research to principles that underlie the dynamics and evolution of complex systems in general, but are no laws of complexity in the usual sense. This essay takes that path, i.e., looking for general principles that determine the laws of specific complex systems. The reason for this is the belief that in most cases there are no laws that describe and explain physical, biological, and social complexity in the literal same way. Social, biological, and physical systems must all be studied in their own right and with regard to their peculiarities. But there may be principles in a rather abstract sense that show that all the different laws, which determine the dynamics and evolution of different types of complex systems, are all variations to the same air. I believe that, e.g., by analyzing some aspects of sociocultural evolution, JÜRGEN KLÜVER

The regulatory algorithm (RGA): a two-dimensional extension of evolutionary algorithms

In orientation to new developments in evolutionary biology we propose an extension of evolutionary algorithms in two dimensions, the regulatory algorithm (RGA). It consists of two levels of vectors, the regulatory vector and the structural vector. Each element of the regulatory vector is connected with one or several elements of the structural vector, but not vice versa. The connections can be interpreted as steering connections, the switching on or off of the structural elements and/or as switching orders for the structural elements. An RGA that operates with the usual genetic operators of mutation and crossover can be used for avoiding rules like penalty or default operators, it is in certain problems significantly faster than a standard genetic algorithm, and it is very suited when modeling and optimizing systems that consist themselves of different levels. Examples of RGA usage are shown, namely, the optimal dividing of socially deviant youths in a hostel, the optimal introduction of communication standards in information systems, and the allocation of employees to superiors by taking into regard the different personality types.

The socio-cultural evolution of our species. The history and possible future of human societies and civilizations.

Many biologists and social scientists have noted that with the development of human culture, the biological evolution of Homo sapiens was usurped by socio‐cultural evolution. The construction of artificial environments and social structures created new criteria for selection, and biological fitness was replaced by ‘cultural fitness’, which is often different for different cultures and is generally not measured by the number of offspring. Moreover, the mechanism of socio‐cultural evolution is different from the model of biological evolution that was proposed by Charles Darwin (1809–1882), and refined by many others. In essence, socio‐cultural evolution is ‘Lamarckian’ in nature—it is an example of acquired inheritance, as described by the French naturalist Jean‐Baptiste Lamarck (1744–1829)—because humans are able to pass on cultural achievements to the next generation. Yet, the idea that cultural fitness has replaced biological fitness does not fully take into account the thousands of years of human biological evolution that occurred long before socio‐cultural evolution, in its strictest sense, took its course. Modern Homo sapiens first appeared about 200,000 years ago; however, socio‐cultural evolution only began about 10,000 years ago, when early hunter–gatherer societies began to change their simple forms of segmentary social differentiation during the so‐called Neolithic revolution, which was mainly caused by the invention of agriculture and cattle breeding. In mathematical terms, one could say that human biological evolution created an attractor: a stable state impervious to change. Various mathematical models of biological evolution, namely the genetic algorithm (Holland, 1975), show that the generation of such an attractor is the usual result of evolutionary processes (Kluver, 2000). Nevertheless, socio‐cultural evolution did not end biological evolution; in fact, for most of the time that Homo sapiens has existed, socio‐cultural evolution has been so slow that it could not have affected biological evolution. Here, I attempt to explain why modern humans …

Interacting neural networks and the emergence of social structure

The article describes a computational model for the simulation of the emergence of social structure or social order, respectively. The model is theoretically based on the theory of social typifying by Berger and Luckmann. It consists of interacting artificial actors (agents), which are represented by two neural networks, an action net, and a perception net. By mutually adjusting of their actions, the agents are able to constitute a self-organized social order in dependency of their personal characteristics and certain features of their environment. A fictitious example demonstrates the applicability of the model to problems of extra-terrestrial robotics.

Sociocultural Evolution and Cognitive Ontogenesis: A Sociocultural-Cognitive Algorithm

Sociocultural evolution is defined as the permanent interplay between the evolution of social order, cultural achievements and cognitive ontogenetic development. The key concept is that of social roles that are defined as a set of social rules and role specific knowledge. Sociocultural evolution accordingly is defined as the enlargement and variation of roles and in their social and cognitive dimension and as the variation of the relations between roles. The main theoretical thesis is the hypothesis of heterogeneity: sociocultural evolution is possible only if the degree of role autonomy in a particular society is large enough.A computational model, the sociocultural-cognitive algorithm is described that captures the main features of the evolution of societies. In particular it can be shown via the model why the hypothesis of heterogeneity is so important: it explains the special way of Western culture that was able totranscendcultural thresholds that limited the evolution of comparable societies.

Social differentiation as the unfolding of dimensions of social systems

We argue that by the use of geometrical concepts it is possible to construct a mathematical model of social evolution, that is a mode] of the theory of social differentiation developed particularly by Habermas and Luhmann. To capture this theory it is necessary to define the concept of dimensions of social spaces. The model is implemented into a hybrid computer program which consists of a stochastic cellular automaton (CA) and a genetic algorithm (GA); the latter changes the rules of the CA. The most important results show that the model behaves in ways very similar to the social systems known from human history. So there may be mathematical reasons for the course human history has taken.

A self-enforcing neural network as decision support system for air traffic control based on probabilistic weather forecasts

We demonstrate the application of a new self-organized learning neural network, the Self-Enforcing Network SEN, to the problem of selecting the right direction of operation for runways at the airport of Frankfurt/M. The SEN is given real data on different days for the forecasted wind situations and generates a recommendation for the selection of a suited direction of operation. The results demonstrate that the recommendations of SEN are sound ones insofar that they are very compatible with the factual decisions of air traffic control at Frankfurt Airport. In some cases air traffic control could have planned earlier with the results of SEN. Hence this SEN system demonstrates that it could be a helpful decision support system for this problem.