The theory of nonlinear complex systems has become a successful and widely used problem-solving approach in the natural sciences - from laser physics, quantum chaos and meteorology to molecular modeling in chemistry and computer simulations of cell growth in biology. In recent times it has been recognized that many of the social, ecological and political problems of mankind are also of a global, complex and nonlinear nature. And one of the most exciting topics of present scientific and public interest is (...) the idea that even the human mind is governed largely by the nonlinear dynamics of complex systems. In this wide-ranging but concise treatment Prof. Mainzer discusses, in nontechnical language, the common framework behind these endeavours. Special emphasis is given to the evolution of new structures in natural and cultural systems and it is seen clearly how the new integrative approach of complexity theory can give new insights that were not available using traditional reductionistic methods. (shrink)

Even beginners and young graduate students will have something to learn from this book." (Andre Hautot, Physicalia, Vol. 57 (3), 2005)"All-in-all, this highly ...

Klaus Mainzer legt in diesem essential dar, dass die Zukunft von KI und Digitalisierung eine nüchterne Analyse erfordert, die Grundlagenforschung mit Anwendung verbindet. Berechenbarkeits- und Beweistheorie können dazu beitragen, Big Data und Machine Learning sicherer zu bewältigen. Dabei zeigt sich, dass die komplexen Herausforderungen der digitalen und analogen Welt in Grundlagenfragen der Mathematik, Informatik und Philosophie tief verwurzelt sind.

Modern cognitive science cannot be understood without recent developments in computer science, artificial intelligence, robotics, neuroscience, biology, linguistics, and psychology. Classic analytic philosophy as well as traditional AI assumed that all kinds of knowledge must eplicitly be represented by formal or programming languages. This assumption is in contradiction to recent insights into the biology of evolution and developmental psychology of the human organism. Most of our knowledge is implicit and unconscious. It is not formally represented, but embodied knowledge which is (...) learnt by doing and understood by bodily interacting with ecological niches and social environments. That is true not only for low-level skills, but even for high-level domains of categorization, language, and abstract thinking. Embodied cognitive science, AI, and robotics try to build the embodied mind in an artificial evolution. From a philosophical point of view, it is amazing that the new ideas of embodied mind and robotics have deep roots in 20th-century philosophy. (shrink)

Die moderne Kognitionswissenschaft kann nicht verstanden werden ohne Einbeziehung der neuesten Errungenschaften aus der Computerwissenschaft, künstlichen Intelligenz , Robotik, Neurowissenschaft, Biologie, Linguistik und Psychologie. Die klassische analytische Philosophie, wie auch die traditionelle AI, setzten voraus, dass alle Arten des Wissens explizit durch formale oder Programmsprachen dargestellt werden müssen. Diese Annahme steht im Widerspruch zu den rezenten Einsichten in die Evolutionsbiologie und Entwicklungspsychologie des menschlichen Organismus. Der größte Teil unseres Wissens ist implizit und unbewusst. Es ist kein formal repräsentiertes, sondern ein (...) verkörpertes Wissen, das durch Handeln gelernt und durch körperliche Interaktion mit ökologischen Nischen und gesellschaftlichen Umgebungen verstanden wird. Dies gilt nicht nur für niedere Fertigkeiten, sondern auch für höher gestellte Domänen: Kategorisierung, Sprache und abstraktes Denken. Die verkörperte Erkenntniswissenschaft, AI und Robotik versuchen, den verkörperten Geist in einer artifiziellen Evolution zu bilden. Vom philosophischen Standpunkt gesehen ist es erstaunlich, wie tief die neuen Ideen des verkörperten Geistes und der Robotik in der Philosophie des 20. Jahrhunderts verankert sind. (shrink)

Molecules have more or less symmetric and complex structures which can be defined in the mathematical framework of topology, group theory, dynamical systems theory, and quantum mechanics. But symmetry and complexity are by no means only theoretical concepts of research. Modern computer aided visualizations show real forms of matter which nevertheless depend on the technical standards of observation, computation, and representation. Furthermore, symmetry and complexity are fundamental interdisciplinary concepts of research inspiring the natural sciences since the antiquity.

In the age of digitization, the world seems to be reducible to a digital computer. However, mathematically, modern quantum field theories do not only depend on discrete, but also continuous concepts. Ancient debates in natural philosophy on atomism versus the continuum are deeply involved in modern research on digital and computational physics. This example underlines that modern physics, in the tradition of Newton’s Principia Mathematica Philosophiae Naturalis, is a further development of natural philosophy with the rigorous methods of mathematics, measuring, (...) and computing. We consider fundamental concepts of natural philosophy with mathematical and computational methods and ask for their ontological and epistemic status. The following article refers to the author’s book, “The Digital and the Real World. Computational Foundations of Mathematics, Science, Technology, and Philosophy.”. (shrink)

Proceedings of the NATO Advanced Study Institute on Proof and Computation, held in Marktoberdorf, Germany, July 20 - August 1, 1993.

Suvremenu kognitivnu znanost ne možemo razumjeti bez najnovijeg razvoja računalne znanosti, umjetne inteligencije , robotike, neuroznanosti, biologije, lingvistike i psihologije. Kako klasična analitička filozofija, tako i tradicionalna AI pretpostavile su da sve vrste znanja moramo prikazati formalnim ili programskim jezicima. Ova je pretpostavka u proturječju s nedavnim uvidima u biologiju evolucije i razvojnu psihologiju ljudskog organizma. Većina je našega znanja implicitna i nesvjesna. To nije formalno prikazano, nego utjelovljeno znanje koje učimo radeći, a razumijevamo tjelesnim suodnosom s ekološkim nišama i (...) društvenim okolišima. To vrijedi ne samo za vještine na niskoj razini nego i za visokorazinska područja kategorizacije, jezika i apstraktnog mišljenja. Utjelovljena kognitivna znanost, AI, kao i robotika pokušavaju umjetnom evolucijom stvoriti utjelovljeni um. S filozofskoga gledišta, zapanjuje da tradicionalni pojmovi kognitivne znanosti i AI s formalnim predodžbama znanja pripadaju tradicionalnoj liniji filozofije.Modern cognitive science cannot be understood without recent developments in computer science,Artificial Intelligence , robotics, neuroscience, biology, linguistics, and psychology. Classic analyticphilosophy as well as traditional AI assumed that all kinds of knowledge must explicitly be representedby formal or programming languages. This assumption is in contradiction to recent insightsinto the biology of evolution and developmental psychology of the human organism. Most ofour knowledge is implicit and unconscious. It is not formally represented, but embodied knowledgewhich is learnt by doing and understood by bodily interacting with ecological niches and social environments.That is true not only for low-level skills, but even for high-level domains of categorization,language, and abstract thinking. Embodied cognitive science, AI, and robotics try to build theembodied mind in an artificial evolution. From a philosophical point of view, it is amazing that thenew ideas of embodied mind and robotics have deep roots in the history of philosophy. (shrink)

La science cognitive moderne ne peut être comprise sans les progrès récents en informatique, intelligence artificielle, robotique, neuroscience, biologie, linguistique et psychologie. La philosophie analytique classique et l’intelligence artificielle traditionnelle présumaient que toutes les sortes de savoir devaient être représentées explicitement par des langages formels ou programmatiques. Cette thèse est en contradiction avec les découvertes récentes en biologie de l’évolution et en psychologie évolutive de l’organisme humain. La majeure partie de notre savoir est implicite et inconsciente. Elle n’est pas représentée (...) formellement, mais constitue un savoir incarné, qui s’acquiert par l’action et se comprend en interaction corporelle avec nos niches écologiques et nos environnements sociaux. Cela n’est pas seulement vrai pour nos aptitudes élémentaires, mais aussi pour nos facultés supérieures de catégorisation, de langage et de pensée abstraite. Science cognitive incarnée, l’intelligence artificielle, ainsi que la robotique, tentent de construire un intellect incarné en évolution artificielle. Du point de vue philosophique, il est admirable de voir à quel point les nouvelles idées d’intellect incarné et de robotique sont ancrées dans la philosophie du XXe siècle. (shrink)

No kind of technology has had such a profound effect upon our lives and society as the new knowledge-based systems which start to overcome the traditional computer technology. Few areas of science raise such high expectations and meet with so much sceptical resistance as Artificial Intelligence (AI). So it is the task of philosophy of science and technology to analyze the factual methodological possibilities of AI-technology. After a historical sketch of AI-development (Chapter 2), the technological foundations of expert systems are (...) described (Chapter 3). It is a surprising result of analysis that expert systems are technical realizations of well-known philosophical methodologies. In this very sense, AI is not only technology, but philosophy too (Chapter 4). On the other hand the question arises if knowledge-based systems can support the work of philosophers of science who want to explain the process of scientific research, inventions, and discoveries. This application of AI for the philosophical professionals is discussed in the 5th chapter. In the 6th chapter some scenarios of AI-technology are described which are expected in the nineties. Then, besides philosophy of science and technology, we have to consider the ethical questions which arise in evaluating the factual impact of AI-technology on our lives and society. (shrink)

Molecular models are typical topics of chemical research depending on the technical standards of observation, computation, and representation. Mathematically, molecular structures have been represented by means of graph theory, topology, differential equations, and numerical procedures. With the increasing capabilities of computer networks, computational models and computer-assisted visualization become an essential part of chemical research. Object-oriented programming languages create a virtual reality of chemical structures opening new avenues of exploration and collaboration in chemistry. From an epistemic point of view, virtual reality (...) is a new computer-assisted tool of human imagination and recognition. (shrink)

Die platonische Naturphilosophie erklärte die Symmetrie der Welt durch statische reguläre Körper, deren Konstruktion in der Euklidischen Geometrie gerschtfertigt wurde. Demgegenüber sucht die neuzeitliche Naturwissenschaft die Symmetrien der Welt in ihren dynamischen Makro- und Mikrogesstzen, die invariant bleiben gegen physikalische Automorphismen. Dabei fällt der mathematischen Gruppentheorie eine Schlüsselrolle zu. Invarianten zur Beschreibung von Symmetrien werden nicht nur in der Relativitätstheorie, Quantenmechankik und Kristallogie entdeckt, sondern neurdings such in Biologie, Chemie und Madizin.

Mit P. Bernays geht S. Körner in der Nachfolge von I . Kant und J.F. Fries davon aus, "daß eine gewisse Art rein-anschaulicher Erkenntnis als Ausgangspunkt der Mathematik genommen werden muß." Andererseits betont Körner einen Wechsel z.B. der geometrischen Anschauung in den nicht-euklidischen Geometrien, der durch die Unabhängigkeitsbeweise für geometrische Axiome (z.B. Parallelenaxiom) möglich wurde. Analog könnte man von einem Wechsel der mengentheoretischen Anschauung in nicht-cantorschen Mengenlehren sprechen, der durch Unabhängigkeitsbeweise mengentheoretischer Axiome (z.B. Auswahlaxiom, Kontinuumshypothese) eingeleitet wurde. In der Algebra (...) werden Axiomensysteme untersucht, in denen nicht mehr alle anschaulichen Rechengesetze der (reellen) Zahlen (z.B. Kommutativgesetz bei Quaternionen, Assoziativgesetz bei Oktaven) gelten. Für die Analysis lassen sich nonstandard Modelle (A. Robinson) angeben. Angesichts dieses Pluralismus der Modelle und Axiomensysteme kann man nicht mehr von der einen anschaulichen Mathematik sprechen — wie in den Tagen von Euklid, Piaton, Leibniz und Kant. Es stellt sich daher die Aufgabe einer Erkenntnistheorie der Mathematik, deren Kategorien den modernen Problementwicklungen Rechnung tragen, aber auch ihre anschaulich-konstruktiven Grundlagen aufzeigen. (shrink)

In the age of globalization, economic growth and the welfare of nations decisively depend on basic innovations. Therefore, education and knowledge is an important advantage of competition in highly developed countries with high standards of salaries, but raw material shortage. In the twenty-first century, innovations will arise from problem-oriented research, crossing over traditional faculties and disciplines. Therefore, we need platforms of interdisciplinary dialogue to choose transdisciplinary problems and to cluster new portfolios of technologies. The clusters of research during the excellence (...) initiative at German universities are examples of converging sciences. The integration of natural and engineering sciences as well as medicine can only be realized if the research training programs generate a considerable added value in terms of multidisciplinary experience, international networking, scientific and entrepreneurial know-how, and personality development. The Carl von Linde-Academy is presented as an example of an interdisciplinary center of research and teaching at the Technical University of Munich. (shrink)

In spite of their growing specialization, modern natural sciences intend to reduce their theories to some fundamental structures: Physics tries to unify the different physical forces in one fundamental force. Chemistry tries to explain the structure of chemical substances by the quantum mechanics of molecules. Biology tries to reduce the processes of life to biochemical and biophysical laws. Mathematically, the unification of natural science can be described by structures of symmetry, the specialization of science, the variety, and emergence of new (...) phenomena by symmetry breaking. In the following, the successes and lacks of the reductionistic program are shown in recent developments of physics, chemistry, and biology. Philosophical discussions on holism, reductionism, and unification of science can be clarified by structures of symmetry and symmetry breaking. Alternative non-reductionistic view-points are not only possible, but desirable for the lacks in the reductionistic program. Nevertheless, the categorical framework of symmetry and symmetry breaking supports interdisciplinary work and gives new insight in a common structure and theory of natural science. (shrink)

A SUMMARY IN ENGLISH [by Editor] Since Brouwer, Weyl, and, more recently, Lorenzen, KANT as an authority [in the philosophy of mathematics in general] has often been called in against some “uncritical” Formalism and Structuralism. The core of the present paper is to show, in the main, that the Denkmuster (patterns of thinking) of Kant is still very much alive in mathematics today to be in harmony with Formalism. The study is carried out in three parts, in the light of (...) the “concept of construction” of (i) Kant himself, (ii) Lorenzen's Operationalism, and (iii) Formalism in general. (shrink)