Saturday, November 7, 2009

Inventing your mother-in-law or More is Different II

P. W. Anderson, “Emergence, Reductionism and the Seamless Web: When and Why Is Science Right,” Current Science 78:6 (2000), 1. [Based on the Pagels lecture, Aspen, 1999].

Anderson suggests that emergence is the mechanism for consilience (the unifying of disparate pieces of knowledge) and reduction is the evidence for it. Theories may be under-determined, i.e., there may be many possible theories that can explain what is actually known. Hence, a successful theory may not actually correspond to what is happening. If there are only a few constraints (hypotheses, observations) that a theory must satisfy it has sometimes been the case that more than one theory can satisfy the constraints. However, as the number of constraints increases, acceptance of a theory is more likely and it becomes hard to conceive of alternative theories that could satisfy these constraints. Reduction can greatly increase the number of conditions that a theory must satisfy. For example, any alternative to quantum theory must be able to explain all known principles of atomic physics and of chemistry. Anderson concludes ``it is as impossible to `socially construct’ science as it is to invent A. Abrikosov or your mother-in-law.’’

Anderson mentions work of Kirkpatrick concerning the problem of satisfying many constraints. An example is this Science paper.

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