Chaos Theory and Dependent Origination
For many systems in nature, such as the weather, no future or past state can be predicted scientifically from knowing the system's initial conditions -- even with the right equations. This results from the lack of infinite accuracy in measuring the initial conditions. And I do mean infinite; nothing less will suffice.
Such systems are said to be examples of "dynamical instability," or "chaos." To the dismay of determinists such as Amy who put all their faith in systems, this means that it can never be possible to predict the long-term outcome of such a system by knowing its initial conditions.
Chaos Theory, employing fractal geometry, is the study of complex, non-linear systems. It does not suggest that the outcomes of such systems are random. Everything has causes -- in these cases, too many different causes to yield predictions better than by chance. Thus many aspects of the physical universe must remain forever mysterious, even to the people of the future. However, there is an underlying order in the apparent randomness of such irreversible systems. Order sometimes emerges from chaos spontaneously, seemingly violating entropy. See on-line course on Chaos Theory by Dr. Matthew Trump, Prigogine Center for Studies in Statistical Mechanics, U. of Texas http://order.ph.utexas.edu/chaos/.
Another theory of causality also qualifies determinism: the Buddhist doctrine of "dependent origination" or "dependent co-arising." To scientists, it seems formally the same as Chaos Theory, but more inclusive. Where Chaos Theory only explains the interdependence of physical causality, dependent co-arising also includes mental factors in the web of mutual causal interaction. In contrast to our simplistic notion of causation whereby A causes B, which causes C, which causes D, the Buddhist theory recognizes the true complexity of causation. Everything is involved causally with everything else. According to the Buddha, causality is a function of relationship, of mutual factors that cannot be isolated, including "feedback" interactions -- the mutual influence of dependent and independent variables. As Joanna Macy explains, "No effect arises without cause, yet no effect is predetermined, for its causes are multiple and mutually affecting. Hence there can be novelty as well as order. Thus, Buddhist teachings presented a middle way between the positions of determinism and indeterminacy that had polarized the discussion of causality." (Joanna Macy, Mutual Causality in Buddhism and General Systems Theory: The Dharma of Natural Systems. Albany: State University of New York Press, 1991, pp. 18-19.)