From: Dave Zachariah (davez@kth.se)
Date: Sun Apr 27 2008 - 10:20:24 EDT
on 2008-04-26 18:50 Jurriaan Bendien wrote: > It is difficult to understand how a chaotic system can be a > "system", how a chaos can be determinate, how a chaos can be in > equilibrium, or what the equilibrium in a chaos would consist of, > beyond the constancy of chaos. > > Seems to me to be the task of theory to specify to what extent (in > what sense) a system is determinate and to what extent it features > indeterminacy. A minimal condition for a scientific theory is that it > permits us to predict that some states of affairs are more likely than > others, and that some states of affairs cannot happen. Random > variability in a distribution would therefore exist only within > certain specifiable limits. > > If the phenomenon being studied is truly a chaos, it does not permit > of a scientific theory about it. In reality, price movements are > rarely chaotic, though if I relate price movements of completely > different commodities I might find that there is no statistical > correlation between them at all, and that their relationship do > not follows any general pattern. But all that says is that from a > certain point of view a phenomenon is chaos - from another point of > view it is determinate. Actually, strictly speaking "chaotic systems" are deterministic. They are completely determined by their laws of motion and boundary conditions. What makes them "chaotic" is that their future states are practically impossible to predict given current information. That is because an infinitesimally small perturbation of the initial conditions can drastically alter their path in the state-space. But this does not preclude the scientific study of temporally unpredictable systems. C.f. evolutionary biology or geology. //Dave Z _______________________________________________ ope mailing list ope@lists.csuchico.edu https://lists.csuchico.edu/mailman/listinfo/ope
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