Notes

Chapter 7: Mechanisms in Programs and Nature

Section 2: Three Mechanisms for Randomness


History [of randomness]

In antiquity, it was often assumed that all events must be governed by deterministic fate—with any apparent randomness being the result of arbitrariness on the part of the gods. Around 330 BC Aristotle mentioned that instead randomness might just be associated with coincidences outside whatever system one is looking at, while around 300 BC Epicurus suggested that there might be randomness continually injected into the motion of all atoms. The rise of emphasis on human free will (see page 1135) eroded belief in determinism, but did not especially address issues of randomness. By the 1700s the success of Newtonian physics seemed again to establish a form of determinism, and led to the assumption that whatever randomness was actually seen must reflect lack of knowledge on the part of the observer—or particularly in astronomy some form of error of measurement. The presence of apparent randomness in digit sequences of square roots, logarithms, numbers like π, and other mathematical constructs was presumably noticed by the 1600s (see page 911), and by the late 1800s it was being taken for granted. But the significance of this for randomness in nature was never recognized. In the late 1800s and early 1900s attempts to justify both statistical mechanics and probability theory led to ideas that perfect microscopic randomness might somehow be a fundamental feature of the physical world. And particularly with the rise of quantum mechanics it came to be thought that meaningful calculations could be done only on probabilities, not on individual random sequences. Indeed, in almost every area where quantitative methods were used, if randomness was observed, then either a different system was studied, or efforts were made to remove the randomness by averaging or some other statistical method. One case where there was occasional discussion of origins of randomness from at least the early 1900s was fluid turbulence (see page 997). Early theories tended to concentrate on superpositions of repetitive motions, but by the 1970s ideas of chaos theory began to dominate. And in fact the widespread assumption emerged that between randomness in the environment, quantum randomness and chaos theory almost any observed randomness in nature could be accounted for. Traditional mathematical models of natural systems are often expressed in terms of probabilities, but do not normally involve anything one can explicitly consider as randomness. Models used in computer simulations, however, do very often use explicit randomness. For not knowing about the phenomenon of intrinsic randomness generation, it has normally been assumed that with the kinds of discrete elements and fairly simple rules common in such models, realistically complicated behavior can only ever be obtained if explicit randomness is continually introduced.


From Stephen Wolfram: A New Kind of Science [citation]