Abstract
The real world presents the worst-case scenario to the Law of Diminishing Information: Physical information is indestructible. This could at least be a consequence of the symmetry of the physical laws. As an example, we take the pattern ORDER in Figure 6.7 built of real particles, e.g. gas molecules. They will diffuse in the course of time, until the initial pattern has completely disappeared. The physical world is, however, time-reversible: if all the velocities of the particles were reversed, the initial pattern ORDER would reappear. All the information was still there!
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Reference
Instead of ‘stability’, the terms ‘order’ and ‘antichaos’ have been used to name the opposite to ‘chaos’ Kauffmann, 1991, p.64.
Both x and y may be points in multidimensional spaces (Section 9.10). The entropy is invariant to changes of the metrics Royden,1968, p. 127 of the spaces.
Like Cauchy’s convergence principle for series applied to a comparison with a geometric series Kreyszig, 1993, p.786.
The pioneering paper by Edward Lorenz, published before the name chaos was coined, had the title Deterministic nonperiodic flow in The Journal of Atmospheric Sciences, 20, 1963 p. 130–141 Peitgen&Jürgens&Saupe, 1992, p.657.
i.e. can be expressed in the form of a quotient a/b (b≠0) of integers a and b Iyanaga&Kawada, 1980, p.919.
Technically, such transformations are called homeomorphisms Kauffinann, 1991, p.54, and can be defined on the basis of a neighbourhood concept satisfying e.g. the four Hausdorff axioms Alexandroff, 1961, p.23.
The Nature of the Physical World, here quoted from Dawkins, 1998, p. 135.
‘Physics and Reality’, here quoted from French,1979, p.53.
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© 2002 Springer Science+Business Media New York
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Kåhre, J. (2002). Deterministic Dynamics. In: The Mathematical Theory of Information. The Springer International Series in Engineering and Computer Science, vol 684. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0975-2_11
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DOI: https://doi.org/10.1007/978-1-4615-0975-2_11
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