This Festschrift volume in honour of Prof. E R Caianiello contains invited papers of eminent scientists who have worked in the several areas to which Prof. Caianiello has given seminal contributions: quantum field theory, foundations of quantum mechanics and maximal acceleration (Vol. 1); neural nets, general systems theory and various topics of cybernetics (Vol. 2). The wide range of topics covered shows the fruitfulness of a higher unifying perspective on seemingly diverse subjects.

This book is an introduction to the simple math patterns used to describe fundamental, stable spectral-orbital physical systems (represented as discrete hyperbolic shapes), the containment set has many-dimensions, and these dimensions possess macroscopic geometric properties (which are also discrete hyperbolic shapes). Thus, it is a description which transcends the idea of materialism (ie it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy, and which has a natural structure for memory, where this construct is made in relation to the main property of the description being, in fact, the spectral properties of both material systems and of the metric-spaces which contain the material systems, where material is simply a lower dimension metric-space, and where both material-components and metric-spaces are in resonance with the containing space. Partial differential equations are defined on the many metric-spaces of this description, but their main function is to act on either the, usually, unimportant free-material components (to most often cause non-linear dynamics) or to perturb the orbits of the, quite often condensed, material trapped by (or within) the stable orbits of a very stable hyperbolic metric-space shape.

The classic book on a major modern theory

Physics at the beginning of the twenty-first century has reached new levels of accomplishment and impact in a society and nation that are changing rapidly. Accomplishments have led us into the information age and fueled broad technological and economic development. The pace of discovery is quickening and stronger links with other fields such as the biological sciences are being developed. The intellectual reach has never been greater, and the questions being asked are more ambitious than ever before. Physics in a New Era is the final report of the NRC's six-volume decadal physics survey. The book reviews the frontiers of physics research, examines the role of physics in our society, and makes recommendations designed to strengthen physics and its ability to serve important needs such as national security, the economy, information technology, and education.

The book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker. Some original chapters and sections have been deleted, and a new chapter about further insights and results of ur-theoretic research of the late 1980’s and 1990’s has been included. Carl Friedrich von Weizsäcker combines the perspectives of science, philosophy, religion and politics with a view towards the challenges as well as the responsibilities of our time.

As suggested by the title of this book, I will present a collection of coherently related applications and a theoretical development of a general systems theory. Hopefully, this book will invite all readers to sample an exciting and challenging (even fun!) piece of interdisciplinary research, that has characterized the scientific and technological achievements of the twentieth century. And, I hope that many of them will be motivated to do additional reading and to contribute to topics along the lines described in the following pages. Since the applications in this volume range through many scientific disciplines, from sociology to atomic physics, from Einstein’s relativity theory to Dirac’s quan tum mechanics, from optimization theory to unreasonable effectiveness of mathe matics to foundations of mathematical modeling, from general systems theory to Schwartz’s distributions, special care has been given to write each application in a language appropriate to that field. That is, mathematical symbols and abstractions are used at different levels so that readers in various fields will find it possible to read. Also, because of the wide range of applications, each chapter has been written so that, in general, there is no need to reference a different chapter in order to understand a specific application. At the same time, if a reader has the desire to go through the entire book without skipping any chapter, it is strongly suggested to refer back to Chapters 2 and 3 as often as possible.

The subject “Systems sciences and cybernetics” is the outcome of the convergence of a number of trends in a larger current of thought devoted to the growing complexity of (primarily social) objects and arising in response to the need for globalized treatment of such objects. This has been magnified by the proliferation and publication of all manner of quantitative scientific data on such objects, advances in the theories on their inter-relations, the enormous computational capacity provided by IT hardware and software and the critical revisiting of subject-object interaction, not to mention the urgent need to control the efficiency of complex systems, where “efficiency” is understood to mean the ability to find a solution to many social problems, including those posed on a planetary scale. The result has been the forging of a new, academically consolidated scientific trend going by the name of Systems Theory and Cybernetics, with a comprehensive, multi-disciplinary focus and therefore apt for understanding realities still regarded to be inescapably chaotic. This subject entry is subdivided into four sections. The first, an introduction to systemic theories, addresses the historic development of the most commonly used systemic approaches, from new concepts such as the so-called “geometry of thinking” or the systemic treatment of “non-systemic identities” to the taxonomic, entropic, axiological and ethical problems deriving from a general “systemic-cybernetic” conceit. Hence, the focus in this section is on the historic and philosophical aspects of the subject. Moreover, it may be asserted today that, beyond a shadow of a doubt, problems, in particular problems deriving from human interaction but in general any problem regardless of its nature, must be posed from a systemic perspective, for otherwise the obstacles to their solution are insurmountable. Reaching such a perspective requires taking at least the following well-known steps: a) statement of the problem from the determinant variables or phenomena; b) adoption of theoretical models showing the interrelationships among such variables; c) use of the maximum amount of – wherever possible quantitative – information available on each; d) placement of the set of variables in an environment that inevitably pre-determines the problem. That epistemology would explain the substantial development of the systemic-cybernetic approach in recent decades. The articles in the second section deal in particular with the different methodological approaches developed when confronting real problems, from issues that affect humanity as a whole to minor but specific questions arising in human organizations. Certain sub-themes are discussed by the various authors – always from a didactic vantage –, including: problem discovery and diagnosis and development of the respective critical theory; the design of ad hoc strategies and methodologies; the implementation of both qualitative (soft system methodologies) and formal and quantitative (such as the “General System Problem Solver” or the “axiological-operational” perspective) approaches; cross-disciplinary integration; and suitable methods for broaching psychological, cultural and socio-political dynamisms. The third section is devoted to cybernetics in the present dual meaning of the term: on the one hand, control of the effectiveness of communication and actions, and on the other, the processes of self-production of knowledge through reflection and the relationship between the observing subject and the observed object when the latter is also observer and the former observed. Known as “second order cybernetics”, this provides an avenue for rethinking the validity of knowledge, such as for instance when viewed through what is known as “bipolar feedback”: processes through which interactions create novelty, complexity and diversity. Finally, the fourth section centres around artificial and computational intelligence, addressing sub-themes such as “neural networks”, the “simulated annealing” that ranges from statistical thermodynamics to combinatory problem-solving, such as in the explanation of the role of adaptive systems, or when discussing the relationship between biological and computational intelligence.