This book presents a novel approach to neural nets and thus offers a genuine alternative to the hitherto known neuro-computers. The new edition includes a section on transformation properties of the equations of the synergetic computer and on the invariance properties of the order parameter equations. Further additions are a new section on stereopsis and recent developments in the use of pulse-coupled neural nets for pattern recognition.

It is increasingly being recognized that the experimental and theoretical study of the complex system brain requires the cooperation of many disciplines, in cluding biology, medicine, physics, chemistry, mathematics, computer science, linguistics, and others. In this way brain research has become a truly interdis ciplinary endeavor. Indeed, the most important progress is quite often made when different disciplines cooperate. Thus it becomes necessary for scientists to look across the fence surrounding their disciplines. The present book is written precisely in this spirit. It addresses graduate students, professors and scientists in a variety of fields, such as biology, medicine and physics. Be yond its mathematical representation the book gives ample space to verbal and pictorial descriptions of the main and, as I believe, fundamental new insights, so that it will be of interest to a general readership, too. I use this opportunity to thank my former students, some of whom are my present co-workers, for their cooperation over many years. Among them I wish to mention in particular M. Bestehorn, L. Borland, H. Bunz, A. Daf fertshofer, T. Ditzinger, E. Fischer, A. Fuchs, R. Haas, R. Honlinger, V. Jirsa, M. Neufeld, M. Ossig, D. Reimann, M. Schanz, G. Schoner, P. Tass, C. Uhl. My particular thanks go to R. Friedrich and A. Wunderlin for their constant help in many respects. Stimulating discussions with a number of colleagues from a variety of fields are also highly appreciated.

This book presents the invited lectures given at the International Symposium on Synergetics of Cognition held at SchloB Elmau, Bavaria (Fed. Rep. of Germany), June 4-8, 1989. The understanding of the processes underlying cognition is certainly one of the most challenging and difficult problems confronting the human mind. It is an enterprise that requires the cooperation of scientists from fields ranging from the neurosciences and psychology through biology to the computer sciences, physics and mathematics. The papers included in this volume reflect this joint effort. As will be evident, there is a remarkable convergence of ideas stemming from various fields, for instance, the earlier ideas on Gestalt theory celebrate a come back and remarkable analogies are being established with modem concepts of self-organization as dealt with in the interdisciplinary field of synergetics. The individual topics range from the "microscopic level", where new exciting results on specific oscillations of neural activity are reported, to computer simulations of perception, and finally psychological experiments at the "macroscopic level". We hope that this book will convey to its readers the same enthusiasm that was felt by the participants of the symposium. We wish to thank Mrs. U. Funke for the excellent organisation of the sym posium, and the Volkswagen-Stiftung, Hannover, for its financial support. We are furthermore grateful to Christoph Stadler and Zora Franko for their help in com piling the name and subject indexes. Finally we wish to thank Springer-Verlag, in particular Dr. Angela Lahee, for the excellent cooperation.

Synergetics may be considered as an interdisciplinary effort dealing with the gene ral problem of how science can cope with complex systems. The preceding symposia on synergetics were devoted to systems of physics, chemistry and partly also biolo gy and sociology. It was possible to develop adequate concepts to describe and even to calculate evolving macroscopic spatial, temporal, and functional structures which emerge through self-organization of the individual parts of the systems under con sideration. This book contains the invited papers presented at the Symposium on the Synerge tics of the brain, Schloss Elmau, Bavaria, May 2 to 7, 1983. The inclusion of this topic in the synergetics enterprise represents a big step towards a treatment of complex systems. Most probably the human brain is the most complex system we know of. As the organizers believe, this symposium provides the reader with a good cross section of experimental results and theoretical approaches to cope with the complex problems of structure and function of the brain. It was generally felt that such a joint meeting between experimentalists and theoreticians is of great importance for future development of this field. Modern experimental methods, e. g. multielectrode derivations allow or will allow us, in short, to collect huge amounts of data. Simi larly high-speed computers will flood us with an enormous number of outputs once the basic model equations have been chosen.

and processes which are exclusive to humans in their encoding, storing, decoding and retrieving spatial knowledge for various tasks. The authors present and discuss connectionist models of cognitive maps which are based on local representation, versus models which are based on distributed representation, as well as connectionist models concerning language and spatial relations. As is well known, Gibson's (1979) ecological approach suggests a view on cognition which is diametrically different from the classical main stream view: perception (and thus cognition) is direct, immediate and needs no internal information processing, and is thus essentially an external process of interaction between an organism and its external environment. The chapter by Harry Heft introduces J. J. Gibson's ecological approach and its implication to the construction of cognitive maps in general and to the issue of wayfinding in particular. According to Heft, main stream cognitive sciences are essentially Cartesian in nature and have not as yet internalized the implications of Darwin's theory of evolution. Gibson, in his ecological approach, has tried to do exactly this. The author introduces the basic terminology of the ecological approach and relates its various notions, in particular optic flow, nested hierarchy and affordances, to navigation and the way routes and places in the environment are learned.

The shared platform of the articles collected in this volume is usedto advocate a dynamical systems approach to cognition. It is arguedthat recent developments in cognitive science towards an account ofembodiment, together with the general approach of complexity theoryand dynamics, have a major impact on behavioral and cognitivescience.

Neuroscience is ripe for a paradigm change as Freeman and Mountcastle describe. Brain Oscillations provide an important key to this change. In this book the functional importance of the brain's multiple oscillations is treated with an integrative scope. According to the author, neurophysiology and cognition demand integrative approaches similar to those of Galilei and Newton in physics and of Darwin in biology. Not only the human brain but also lower brains and ganglia of invertebrates are treated with electrophysical methods. Experiments on sensory registration, perception, movement, and cognitive processes related to attention, learning, and memory are described. A synopsis on brain functions leads to a new neuron assemblies doctrine, extending the concept of Sherrington, and new trends in this field. The book will appeal to scientists and graduate students.

The spontaneous formation of well organized structures out of germs or even out of chaos is one of the most fascinating phenomena and most challenging problems scientists are confronted with. Such phenomena are an experience of our daily life when we observe the growth of plants and animals. Thinking of much larger time scales, scientists are led into the problems of evolution, and, ultimately, of the origin of living matter. When we try to explain or understand in some sense these extremely complex biological phenomena it is a natural question, whether pro cesses of self-organization may be found in much simpler systems of the un animated world. In recent years it has become more and more evident that there exist numerous examples in physical and chemical systems where well organized spatial, temporal, or spatio-temporal structures arise out of chaotic states. Furthermore, as in living of these systems can be maintained only by a flux of organisms, the functioning energy (and matter) through them. In contrast to man-made machines, which are to exhibit special structures and functionings, these structures develop spon devised It came as a surprise to many scientists that taneously-they are self-organizing. numerous such systems show striking similarities in their behavior when passing from the disordered to the ordered state. This strongly indicates that the function of such systems obeys the same basic principles. In our book we wish to explain ing such basic principles and underlying conceptions and to present the mathematical tools to cope with them.

Complexity, Cognition and the City aims at a deeper understanding of urbanism, while invoking, on an equal footing, the contributions both the hard and soft sciences have made, and are still making, when grappling with the many issues and facets of regional planning and dynamics. In this work, the author goes beyond merely seeing the city as a self-organized, emerging pattern of some collective interaction between many stylized urban "agents" – he makes the crucial step of attributing cognition to his agents and thus raises, for the first time, the question on how to deal with a complex system composed of many interacting complex agents in clearly defined settings. Accordingly, the author eventually addresses issues of practical relevance for urban planners and decision makers. The book unfolds its message in a largely nontechnical manner, so as to provide a broad interdisciplinary readership with insights, ideas, and other stimuli to encourage further research – with the twofold aim of further pushing back the boundaries of complexity science and emphasizing the all-important interrelation of hard and soft sciences in recognizing the cognitive sciences as another necessary ingredient for meaningful urban studies.

This edited volume is scientifically based, but readable for a larger audience, covering the concept of "embodied cognition" and its implications from a transdisciplinary angle. The contributions are from the fields of psychology, computer science, biology, philosophy, and psychiatry. First, the roots of embodiment are described with historical, computer-science, and phenomenological viewpoints. It is argued that embodied cognition is relevant for the discussion of intentionality, with a particular focus on underlying neural processes as well as the context of synergetics and self-organization theory. As cognition is socially embedded, a large section of this book concentrates on "embodied communication": How does embodiment influence the way to approach others, what role do body movements play in social interaction, what is the function of nonverbal synchrony in interpersonal relationships and psychotherapy? Embodied cognitive agents are further embedded in particular cultural and environmental contexts. This book thus addresses the active role that cultural and environmental aspects play in driving cognition. Some applications of embodiment, e.g. to psychotherapy and aesthetics are also presented.