Wednesday, July 28, 2010

Models, laws and the limits of reductionism

I am currently reading Stuart Kauffman's "Reinventing the Sacred" and it's turning out to be one of the most thought-provoking books I have read in a long time, full of mind-bending ideas. Kauffman who was originally trained as a doctor was for many years a member of the famous Institute for Complexity in Santa Fe, which is a bastion of interdisciplinary research.

Kauffman is a kind of polymath who draws upon physics, chemistry, biology, computer science and economics to essentially argue the limitations of reductionism and the existence of emergent phenomena. He makes some fascinating arguments for instance about biology not being reducible to specific physics. One of the main reasons this cannot be done is because the evolution of complex biological systems is contingent and can follow any number of virtually infinite courses depending on slightly different conditions; according to Kauffman, this infinity is not just a ‘countable infinity’ but an ‘uncountable one’ (more on this mind-boggling distinction later). Biological systems are also highly non-linear and full of feedback and 'surprises' and these qualities make their prediction not just very difficult in practice but even in principle.

I am sure I will have much more to say about Kauffman’s book later, but for now I want to focus on his argument against reductionism based on what is called the ‘multiple platform’ framework. Kauffman’s basic thesis draws on an argument made by the Nobel laureate Philip Anderson. Anderson wrote a groundbreaking article in Science in 1972 extolling the limits of reductionism. To illustrate the multiple platform principle, he talked about computers processing 1s and 0s and manipulating them to give a myriad number of results. The question is: is the processing of 1s and 0s in a computer uniquely dependent upon the specific physics involved (which in this case would be quantum mechanics)? The answer may seem obvious but Anderson says that it’s hard to make this argument, since one can also get the same results from manipulating buckets that are either empty (0s) or filled with water (1s). Thus, the binary operations of a computer cannot be reduced to specific physics since they can be modeled by ‘multiple platforms’.

Another example that Kauffman cites is of the Navier-Stokes equations, the basic equations of fluid dynamics. The equations are classical and are derived from Newton’s laws. One would think that they would be ultimately reducible to the movements of individual particles of fluid and thus to quantum mechanics. Yet as of today, nobody has found a way to derive the Navier-Stokes equations from those of quantum mechanics. However, the physicist Leo Kadanoff has actually ‘derived’ these equations by using a rather simple ‘toy world’ of beads on a lattice. The movement of fluids and therefore the equations can be modeled by moving the beads around. Thus, we again have an example of multiple platforms leading to the same phenomenon, precluding the unique dependence of the phenomenon on a particular set of laws.

All this is extremely interesting, but I am not sure I follow Kauffman here. The toy world or the bucket brigades that Kadanoff and Anderson talk about are models. Models are very different from physical laws. Sure, there can be multiple models (or platforms) for deriving a given set of phenomena, but the existence of multiple models does not preclude dependence on a unique set of laws. A close analogy which I often think of is from molecular mechanics. A molecular mechanics model of a molecule assumes the molecule to be a classical set of balls and springs, with the electrons neglected. It is supposed to reproduce the properties of molecules like their geometry and energy. By any definition this is a ludicrously simple model that completely ignores quantum effects (or at least takes them into consideration implicitly by getting parameters from experiment). Yet, with the right parametrization, it works well-enough to be useful. There could conceivably be many other models which could give the same results. Yet nobody would make the argument that the behavior of molecules modeled in molecular mechanics is not reducible to quantum mechanics.

Kauffman’s argument that the explanatory arrows don’t always point downwards because one cannot always extrapolate upwards from lower-level phenomena is very well-taken. Emergent properties are surely real. But at least in the specific cases he considers, I am not sure that one can make an argument about phenomena not being reducible to specific physics simply because they can be derived from multiple platforms. The multiple platforms are models. The specific physics constitutes a set of laws, which is quite different.

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