Robert J. Russell's Chaos & Complexity: Scientific Perspectives On Divine Action PDF

By Robert J. Russell

ISBN-10: 0268008124

ISBN-13: 9780268008123

This choice of fifteen study papers explores the results of chaos and complexity in actual, chemical, and organic structures for philosophical and theological matters relating to God's motion on the earth. It resulted from the second one of 5 foreign study meetings being co-sponsored through the Vatican Observatory, Rome, and the heart for Theology and the average Sciences, Berkeley. The overarching objective is to give a contribution to positive theology because it engages present examine within the ordinary sciences and to enquire the philosophical and theological components in ongoing theoretical study within the typical sciences.

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Example text

Although orbits diverge and follow increasingly different paths, they eventually must pass close to one another again. The orbits on a chaotic attractor are shuffled by this process, much as a deck of cards is shuffled by a dealer. The randomness of the chaotic orbits is the result of the shuffling process. The process of stretching and folding happens repeatedly, creating folds within folds ad infinitum. A chaotic attractor is, in other words, a fractal: an object that reveals more detail as it is increasingly magnified [see Figure 2].

In the state space such a motion corresponds to a cycle, or periodic orbit. No matter how the pendulum is set swinging, the cycle approached in the long-term limit is the same. Such attractors are therefore called limit cycles. Another familiar system with a limit-cycle attractor is the heart. A system may have several attractors. If that is the case, different initial conditions may evolve to different attractors. The set of points that evolve to an attractor is called its basin of attraction.

The state is thus a point in a plane, whose coordinates are position and velocity. Newton's laws provide a rule, expressed mathematically as a differential equation, that describes how the state evolves. As the pendulum swings back and forth the state moves along an "orbit," or path, in the plane. In the ideal case of a frictionless pendulum the orbit is a loop; failing that, the orbit spirals to a point as the pendulum comes to rest. A dynamical system's temporal evolution may happen in either continuous time or in discrete time.

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Chaos & Complexity: Scientific Perspectives On Divine Action (Scientific Perspectives on Divine Action, Vol 2) by Robert J. Russell


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