Causality Principle, Deterministic Laws and Chaos
  • Heinz-Otto Peitgen
  • Hartmut Jürgens
  • Dietmar Saupe


For many, chaos theory already belongs to the greatest achievements in the natural sciences in this century. Indeed, it can be claimed that very few developments in natural science have awakened so much public interest. Here and there, we even hear of changing images of reality or of a revolution in the natural sciences.


Natural Science Weather Forecast Chaos Theory Catastrophe Theory Causality Principle 
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  1. 2.
    Pièrre Simon de Laplace (1749–1829), a Parisian mathematician and astronomer.Google Scholar
  2. 3.
    This is also called the indeterminacy principle and states that the position and velocity of an object cannot, even in theory, be exactly measured simultaneously. In fact, the very concept of a concurrence of exact position and exact velocity have no meaning in nature. Ordinary experience, however, provides no evidence of the truth of this principle. It would appear to be easy, for example, to simultaneously measure the position and the velocity of a car; but this is because for objects of ordinary size, the uncertainties implied by this principle are too small to be observable. But the principle becomes really significant for subatomic particles such as electrons.Google Scholar
  3. 4.
    Dover Publications, New York, 1965. First published by Cambridge University Press, London, 1922. This book is still considered one of the most important works on numerical weather forecasting.Google Scholar
  4. 5.
    Richardson uses the word computer here to mean a person who computes.Google Scholar
  5. 6.
    See Peitgen, H.-O., Jürgens, H., Saupe, D., and Zahlten, C., Fractals — An Animated Discussion. Video film, Freeman 1990. Also appeared in German as Fraktale in Filmen und Gesprächen, Spektrum der Wissenschaften Videothek, Heidelberg, 1990.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Heinz-Otto Peitgen
    • 1
    • 2
  • Hartmut Jürgens
    • 3
  • Dietmar Saupe
    • 4
  1. 1.CeVis and MeVisUniversität BremenBremenGermany
  2. 2.Department of MathematicsFlorida Atlantic UniversityBoca RatonUSA
  3. 3.CeVis and MeVisUniversität BremenBremenGermany
  4. 4.Department of Computer ScienceUniversität FreiburgFreiburgGermany

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