Zwischen Berechenbarkeit und Nichtberechenbarkeit. Die Thematisierung der Berechenbarkeit in der aktuellen Physik komplexer Systeme |
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Authors: | Jan C Schmidt |
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Institution: | 1. TU Darmstadt, Schlo?, Institut für Philosophie, D-64283, Darmstadt
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Abstract: | Between Calculability and Non-Calculability. Issues of Calculability and Predictability in the Physics of Complex Systems. The ability to predict has been a very important qualifier of what constitutes scientific knowledge, ever since the successes
of Babylonian and Greek astronomy. More recent is the general appreciation of the fact that in the presence of deterministic
chaos, predictability is severely limited (the so-called ‘butterfly effect’): Nearby trajectories diverge during time evolution;
small errors typically grow exponentially with time. The system obeys deterministic laws and still is unpredictable, seemingly
a paradox for the traditional viewpoint of Laplacian determinisms. With the concept of deterministic chaos the epistemological
issue about an adequate understanding of predictability is no longer just a mere philosophical topic. Physicists on the one
hand recognize the limits of (long term) predictability, computability and even of scientific knowledge, on the other hand
they work on concepts for extending the horizon of predictability. It is shown in this paper that physics of complex systems
is useful to clarify the jungle of different meanings of the terms ‘predictability’ and ‘computability’ — also with philosophical
implications for understanding science and nature. Today, from the physical point of view, the relevance of the concepts of
predictability seems to be underestimated by philosophers as a mere methodological topic. In the paper I analyse the importance
of predictability and computability in physics of complex systems. I show a way how to cope with problems of unpredictability
and noncomputability. Nine different concepts of predictability and computability (i.e. open solution, sensitivity/chaos,
redundancy/chance) are presented, compared and evaluated.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | chaos theory complex systems computability methodology nonlinearity predictability |
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