Monday, January 09, 2012

Power Law Spectra a Fundamental Law of the Universe

According to Hector Sabelli,
Power spectrum analysis related energy with time. Power is the statistical frequency of action quanta; temporal frequency is 1 over time. As a rule, physical energy is a function of frequency; the higher the frequency, the greater the energy. In 1/f patterns, the greater the frequency, the lesser the energy (power). (Bios, 151)
Action = energy x time. Energy is work. Thus, action = work x time. Further, Power = work/time, meaning if work = energy, then energy = power x time. Thus, Action = power x time x time (time squared).

The theory of entropy says everything is seeking the lowest energy state. Thus, high frequencies are more stable in 1/f patterns.

This relation among action, energy, entropy, power, and time results in power law spectra, which are necessary (if not sufficient) for self-organization. This implies that self-organization is a fundamental feature of the universe. Entropy drives self-organization, which results in greater complexity.

Human action = human work x time. Thus, the natural pattern one should see in human inter-actions is once created by power laws. We should see power law spectra in sizes of firms, longevity of firms, city sizes, wealth distribution -- anything that is the result of human action. If and when we do, we are seeing a natural process at work; if and when we do not, we are either seeing an equilibrium state caused by low density, or an equilibrium state caused by unnatural interventions into the process (by "unnatural" I mean rules or values from one spontaneous order being introduced into another, foreign, order). Self-organization takes place in the far-from-equilibrium, or critical, realm -- not in states of equilibrium. Thus, equilibrium theories of the economy -- or of any spontaneous order -- in which there is sufficient density for self-organization to occur are wrong. Perhaps, not even wrong.
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