junho 18, 2015

Its from Bits

A distinction is often made between theories based upon explicit mechanisms of causation versus theories based upon statistical or other seemingly non-mechanistic assumptions. Evolution is a mechanistic theory in which the mechanism is selection and hereditability of traits acting in concert. In a nutshell, stressful forces upon organisms that differ genetically select those individuals possessing genes that confer on the individual and its offspring the greatest capacity to reproduce under those stresses. 

Consider next a statistical explanation of the observation that the heights of a large group of children in an age cohort are well described by a Gaussian (aka normal) distribution. Invocation of the central limit theorem (CLT) provides a statistical explanation; but the question remains as to why that theorem applies to this particular situation. The applicability of the theorem hinges on the assumption that each child’s height is an outcome of a sum of random influences on growth. So are we not also dealing here with a mechanistic explanation, with the mechanism being the collection of additive influences on growth that allow the applicability of the CLT? If the influences on growth were multiplicative rather than additive, we might witness a lognormal distribution. Is it possible that all scientific explanation is ultimately mechanistic? Let us look more carefully at the concept of mechanism in scientific explanation, for it is not straightforward.

In everyday usage, we say that phenomenon A is explained by a mechanism when we have identified some other phenomenon, B, that causes, and therefore explains, A. The causal influence of B upon A is a mechanism. However, what is accepted by one investigator as an explanatory mechanism might not be accepted as such by another. [...] Does the search for mechanism inevitably propel us into an infinite regress of explanations? Or can mechanism be a solid foundation for the ultimate goal of scientific theory-building? Consider two of the best established theories in science: quantum mechanics and statistical mechanics. Surprisingly, and despite their names, these theories are not actually based on mechanisms in the usual sense of that term. Physicists have attempted over past decades to find a mechanism that explains the quantum nature of things. This attempt has taken bizarre forms, such as assuming there is a background “aether” comprised of tiny things that bump into the electrons and other particles of matter, jostling them and creating indeterminancy. While an aether can be rigged in such a way as to simulate in matter the behavior predicted by Heisenberg’s uncertainty principle, and some other features of the quantum world, all of these efforts have ultimately failed to produce a consistent mechanistic foundation for quantum mechanics. Similarly, thermodynamics and statistical mechanics are mechanism-less. Statistical arguments readily explain why the second law of thermodynamics works so well. In fact, it has been shown that information theory in the form of Maximum Entropy provides a fundamental theoretical foundation for thermodynamics.

If we pull the rug of mechanism out from under the feet of theory, what are we left with? The physicist John Archibald Wheeler posited the radical answer “its from bits,” by which he meant that information (bits)—and not conventional mechanisms in the form of interacting things moving around in space and time—is the foundation of the physical world (its). There is a strong form of “its from bits,” which in effect states that only bits exist, not its. More reasonable is a weaker form, which asserts that our knowledge of “its” derives from a theory of “bits.”

[...] Mechanistic explanations either lead to an infinite regress of mechanism within mechanism, or to mechanism-less theory, or perhaps to Wheeler’s world with its information-theoretic foundation. What is evident is that as we plunge deeply into the physical sciences, we see mechanism disappear. Yet equally problematic issues arise with statistical theories; we cannot avoid asking about the nature of the processes governing the system that allow a particular statistical theory to be applicable. In fact, when a statistical theory does reliably predict observed patterns, it is natural to seek an underlying set of mechanisms that made the theory work. And when the predictions fail, it is equally natural to examine the pattern of failure and ask whether some mechanism can be invoked to explain the failure. -- John Harte, Maximum Entropy and Ecology, pp.8--11

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