Monday, June 18, 2012

Reduction as Idealization

I cannot remember who tipped me to this 1972 article in Science by physicist Philip W. Anderson called "More is Different".  It is an exploration of the notions of reduction and emergence.  The main thrust of Anderson's argument is familiar:

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and construct the universe.  In fact, the more the elementary particle physicists tell us about the nature of the fundamental physical laws, the less relevance they seem to have to the very real problems in the rest of science, much less to those of society
The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity.  The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles.  Instead, at each level of complexity entirely new properties appear...(p.393)

The article is worthwhile for a number of very nice briefly described examples of symmetry breaking and properties which emerge with scale.

There is a absurdly simple insight lurking in these sorts of discussions which I now belated appreciate.  We all realize that coarse-grained descriptions of phenomena which neglect fine details will be limited in their accuracy by definition.  But while reductive analysis of natural systems is extremely fruitful, it is also always an idealization.  Experimenters work hard to break down and isolate some phenomenon, and models and theories are constructed to best capture it.  The environment needs to be screened out  -- it is "noise" which we abstract from.  But what is lost in this idealization is not trivial.  In nature, there are no isolated systems, no ceteris paribus conditions (in fact, there is absolutely no reason to think the universe as a whole is some sharply bounded closed system).

When this is considered, emergent properties at higher levels of scale lose the sense of being especially surprising or mysterious.

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