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 (e.g., environment, energy, information, health, welfare) 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 (e.g., graduate schools) 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)
Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. (...) In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time. (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)
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.
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)
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)