Minimalist Physics?

I was recently rereading some essays by Steven Weinberg (here) and was reminded why it is that I have a severe case of physics envy. It is not only the depth of the results, both theoretical and empirical, and not only the fact that when it comes to explanation, what you find in physics is the gold standard, but my envy is also grounded in a respect for the disciplined way that physicists talk about even the most obscure methodological matters. Weinberg, in discussing his reductionist urges, makes three points that should resonate with those who have a minimalist pulse.  He discusses these on pages 37-40.  Here’s “lessons” he draws from “the history of science in the last three hundred years” (btw, I am pretty sure that the last quoted passage is said/written with tongue firmly in cheek).

1.     The aim of fundamental physics is to “explain why everything is the way it is. This is Newton’s dream, and it is our dream.”

2.     “The importance of phenomena in everyday life is, for us, a very bad guide to their importance in the final answer.”

3.     Indeed, whether something is ubiquitous or common is a very unreliable guide to its interest or importance: “We do not know about muons in our everyday life. But as far as we know, muons play just as fundamental a role (which may or may not be very fundamental) as electrons  [which is “ubiquitous in ordinary matter” –NH] in the ultimate scheme of things.”

4.     “We are not particularly interested in our electrons or our muons. We are interested in the final principles that we hope we will learn about by studying these particles. So the lesson is that the ordinary world is not a very good guide to what is important.”

5.     “…if we are talking about very fundamental phenomena, then ideas of beauty are important in a way that they wouldn’t be if we were talking about mere accidents…[P]lanetary orbits don’t have to be beautiful curves like circles because planets are not very important on any fundamental level. On the other hand, when we formulate the equations of quantum field theories or string theories we demand a great deal of mathematical elegance, because we believe that the mathematical elegance that must exist at the root of things in nature has to be mirrored at the level where we are working.  If the particles and fields were working on were mere accidents…then the use of beauty as a criterion in formulating our theories would not be so fruitful.”

6.     “…in the theories we are trying to formulate, we are looking for a sense of uniqueness, for a sense that when we understand the final answer, we will see that it could not have been any other way. My colleague John Wheeler has formulated this as the prediction that when we learn the ultimate laws of nature we will wonder why they were not obvious from the beginning.”

These have more than a passing resemblance to oft quoted minimalist dicta.  (1) is the familiar minimalist credo: the aim is not only to know what is the case but to know why it is the case.

(2) sums up why it is that looking at large collections of surface data are very likely to be irrelevant.  Real explanations lay hidden beneath the surface of things, just as much in the study of FL as in the study of basic physics.

(3) reinforces the point in (2) and also suggests the hazards of concentrating on the common, a feature not unknown to the statistically inclined. Common/frequent does not imply theoretically important unless one has a pretty surfacy/empiricist conception of theory.

(4) is a favorite of mine: think of the distinction between linguistics and languistics. But it goes deeper.  We study languages because we believe that studying these will tell us something about the nature of human cognition and biology.  They are instruments for probing minds/brains, the latter (not languages) being the ultimate objects of inquiry.  In this sense linguistics is not about language any more than physics in Weinberg’s conception, is about electrons or muons. 

(5) starts moving onto very subtle but important territory. Weinberg and Chomsky share the idea that at fundamental levels reality is simple and elegant. The converse of this is that complexity is the result of interacting systems. As fundamental theory describes single (i.e. non-interacting) there is no place within fundamental theories for interaction effects. Thus we expect (and find) simplicity and elegance. So here’s a regulative ideal: simplicity holds at fundamental levels and complexity arises from the interaction of simple systems. Thus, when looking for the fundamental look for the simple and when it eludes you assume that the complexity is a sign of two or more interacting simple systems.  This is, admittedly, murky advice.  However, at times, murky methodological advice can be important and consequential. Weinberg and Chomsky identify two projects where this is likely to be the case.

And last we have (6): it provides a kind of ex post conception of a notion Chomsky has been fond of: “virtual conceptual necessity (VCN)” Ex post, VCN cannot guide research: it simply describes what we are looking for: a theory that when stated will seem both obviously true and inevitable.  We can, however, get an inkling about what kinds of notions such a theory will contain.  For example, FL will have to contain a rule that puts elements together (merge) and it would be very surprising given what we know if its operations were not regulated by natural computational considerations like cyclicity and locality.  These are candidate basic notions for a theory that has VCN. As Weinberg puts it:

That [Wheeler’s conception above -NH] may very well be true. If it is, I suspect it will be because by the time we learn the ultimate laws of nature, we will have been so much changed by the learning process that it will become difficult to imagine that the truth could be anything else…

Note the historical gloss Weinberg gives to Wheeler’s dictum. This is why I added “given what we know” above. Given minimalism’s roots in Generative Grammar research over the last 60 years operations like merge and notions like cyclicity and locality and economy must be part of any reasonable account. That’s Weinberg’s version of VCN, and as we can see, it’s not limited to the dreams of linguists.  All good science, at least all good basic science, appears to share the dream.