• James B. Kadtke
  • Yurii A. Kravtsov
Part of the Springer Series in Synergetics book series (SSSYN, volume 69)


As recently as 50 years ago, there was a firm conviction among many scientists that the universe was fundamentally mechanistic, and that at some level mathematical prediction of physical events could be exact. This view was of course rooted in the “romantic” period of the history of science (the 19th and beginning of the 20th centuries) when the overwhelming advances in science and technology often obscured the possibility that fundamental limitations to the power of science could exist. The situation has changed rather dramatically in recent decades. Most scientists will agree now (as did the most acute minds long ago) that long-term mathematical prediction of complicated physical systems is in practice unachievable. What is remarkable is that this realization has evolved from the “precise” science of classical mechanics, which has long upheld the principles of Laplacian determinism. This is due, ironically, to the development in the last twenty years of a consistent framework for “chaotic” dynamical systems, often generalized now to “nonlinear dynamics”. These ideas have required an essential revision of the concepts of dynamical behavior and classical predictability.


Radial Basis Function Nonlinear Correlation Chaotic Time Series Predictability Time Mathematical Prediction 
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© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • James B. Kadtke
  • Yurii A. Kravtsov

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