By Klaus Mainzer
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Extra info for Thinking in Complexity: The Complex Dynamics of Matter, Mind, and Mankind
The hinge at the top is perfect1y frictionless. The weight at the lower end is heavy, but very smalI. The force of gravity always pulls it straight down. In Fig. 7a, the pendulum is drawn in a two-dimensional Euclidean plane with the angle a of elevation, the force F of gravity, the pull F cos a along the rod, and the force F sin a turning it. In order to visualize the dynamical behavior of the pendulum we have to develop a dynamical model with astate space and a phase portrait. The state of the pendulum is fully determined by the angular variable a (with a = and a = 2][ denoting the same angle) and the angular velocity v.
This continuum is the Stoics' pneuma, whose tensions and vibrations are said to determine the various states of nature. The multifarious forms of nature are only transistory patterns that are formed by varied tensions of the pneuma. Modern thinking leaps, of course, to the patterns of standing water waves or sound waves or the patterns of magnetic fields. Nevertheless, neither the Stoic nor the Taoist heuristic background led to the development of a physical theory of acoustic or magnetic fields comparable to Galilean mechanics with its background of an atomistic philosophy of nature.
In general, we summarize the modeling process as follows. A dynamical model is prepared for some experimental situation. We may imagine the laboratory devices of physicists like Galileo and Newton or biologists observing some organisms or even sociologists working on some social groups. \. / .......... 4a-c. Geometrie representation ofa dynamical system: (a) Instantaneous veloeity as tangent veetor, (b) veloeity vector field, (c) phase portrait The dynamical model consists of the state space and a vector field.