Complex Systems and the Evolution of Matter

  • Klaus Mainzer


How can order arise from complex, irregular, and chaotic states of matter? In classical antiquity philosophers tried to take the complexity of natural phenomena back to first principles. Astronomers suggested mathematical models in order to reduce the irregular and complex planetary orbits as they are experienced to regular and simple movements of spheres. Simplicity was understood, still for Copernicus, as a feature of truth (Sect. 2.1). With Newton and Leibniz something new was added to the theory of kinetic models. The calculus allows scientists to compute the instaneous velocity of a body and to visualize it as the tangent vector of the body’s trajectory. The velocity vector field has become one of the basic concepts in dynamical systems theory. The cosmic theories of Newton and Einstein have been described by dynamical models which are completely deterministic (Sect. 2.2).


Hamiltonian System Phase Portrait Dissipative System Vortex Point Velocity Vector Field 
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© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Klaus Mainzer
    • 1
  1. 1.Lehrstuhl für Philosophie und WissenschaftstheorieUniversität AugsburgAugsburgGermany

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