Friday, November 14, 2008

Post-blogging the PSA: Gauge Freedom and Drift

It's taken me a few days to recover from the excellent PSA. I talked to many people who had a great time and who thought this year's program was exceptionally well-balanced to reflect both old classics and new debates in philosophy of science.

On the first day I was happy to attend two sessions which reflect the interpretative difficulties arising from the central role of some mathematics. In the first session, Richard Healey summarized his paper "Perfect Symmetries", followed by Hilary Greaves' and David Wallace's attempts to critically reconstruct Healey's central argument. Very roughly, Healey aims to distinguish cases where a symmetry in the models of a theory explains observed empirical symmetries in physical systems from cases where there are theoretical symmetries with no analogous explanatory power. In the latter case, the theoretical symmetries may just amount to 'mathematical fluff' or 'surplus structure' that lack physical significance.

Then it was time for some biology and the symposium "(Mis)representing Mathematical Models in Biology". The session began with biologist Joan Roughgarden's summary of different kinds of models in biology, followed by Griesemer, Bouchard and Millstein talking about different issues in their interpretation. Both Griesemer and Millstein emphasized the importance of a biologically grounded understanding of the components of a biological model, and argued that a merely mathematical definition of such components would block our understanding of biological systems. Millstein was especially emphatic (to quote from a handout from a previous presentation of hers) "Selection and drift are physical, biological phenomena; neither is a mathematical construct." That is, when we look at the changes in some biological system over time, we cannot think of the changes as resulting from a genuine process of selection with some additionally mathematically represented divergence from some ideal that we label as "drift". Instead, drift itself must be countenanced as a genuine process that makes its own positive contribution to what we observe in nature.

While it is a bit of a stretch, there is at least a suggestive analogy between these debates in physics and biology: in both cases, we have a useful and perhaps indispensable mathematically identified feature of our theories whose physical and biological status can remain in doubt, even for our best, current scientific theories. Here, it seems to me, we see some of the costs of deploying mathematics.

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