Chaos Theory

A name given to recent wide-ranging attempts to uncover the statistical regularity hidden in processes that otherwise appear random, such as turbulence in fluids, weather patterns, predator-prey cycles, the spread of disease, and even the onset of war. Systems described as "chaotic" are extremely susceptible to changes in initial conditions. As a result, small uncertainties in measurement are magnified over time, making chaotic systems predictable in principle but unpredictable in practice.

Over the past three decades, the study of chaotic systems has dramatically expanded from physics to include all the natural and even social sciences. Chaotic phenomena now include such physical and biological systems as the weather, water dripping from a faucet, bands in the rings of Saturn, oscillations in the populations of organisms, and the fluctuations of populations in complex ecosystems. In physics, though, chaotic systems are ‘classical’ in scale and thus subsumable in principle under classical mechanics with its deterministic laws of motion. Still even for the simplest systems, minute uncertainties in the initial conditions and the effect of countless interactions with other systems in nature, together with unusual characteristics in the underlying mathematics (e.g., ‘strange attractors’) make complete predictability impossible even in principle. Surprisingly, then, chaos breaks the long-standing philosophical link between determinism and predictability. Still since it is describable by deterministic equations, chaos theory supports a strictly deterministic philosophy of nature, although within subtle epistemic limits.

It is possible, however, as Polkinghorne suggests, that chaotic systems may one day be more accurately described by more complex theories, sometimes referred to as ‘holistic chaos’. The current deterministic laws would then be seen as simple approximations to holistic chaos through what Polkinghorne calls ‘downward emergence.” Finally, the new theories of holistic chaos would, hopefully, suggest an indeterministic interpretation. It is also possible that a satisfying connection will be found between chaos at the present, classical level, and quantum mechanics (sometimes referred to as ‘quantum chaology’), suggesting that the uncertainty in the initial conditions that, together with coupling to the environment, drive chaotic behavior is at least partially due to quantum indeterminism.

Contributed by: Dr. Robert Russell / Dr. Christopher Southgate