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Showing posts sorted by relevance for query physics envy. Sort by date Show all posts
Showing posts sorted by relevance for query physics envy. Sort by date Show all posts

Sunday, December 16, 2012

Physics Envy


Yes, I suffer, badly. Not only that, but I distrust those that don’t. A good dose of Physics Envy is the sign of good theoretical taste.  That’s why I prize fMRI snaps of frontal lobes awash in green whenever ‘CERN,’ ‘Higgs boson,’ ‘renormalizable,’ ‘Standard Theory,’ ‘SU-3 symmetry,’ etc. are flashed to visual and auditory fields.  It is beyond dispute: Physics is THE science. It provides THE models for explanation.  Its methodological precepts should be stolen and copied at every opportunity. What physics has is what every right-minded science should aspire to. The fact that we are likely to fall short (maybe very short) is no excuse.

I mention this because I had an acute spike in my physics-enviometer recently as I read some old essays by Steven Weinberg (collected here).  Here are four observations he made with suggestions of how these may be relevant to linguistics.

1. Weinberg, aficionados of Chomsky’s philosophical writings might recall, is a strong proponent of the Galilean style (GS), which consists in ”making abstract models of the universe to which the physicists, at least, give a higher degree of reality than they accord the ordinary world of sensations.” GS values a theory’s explanatory reach as well as its empirical coverage. Indeed, at some times, explanatory power outweighs (and should outweigh) empirical coverage and empirical anomalies and (apparently) contradictory evidence is (and should be) set aside for the sake of further theoretical development.   

The relevance of this methodological attitude to linguistics is pretty evident. Linguistics is very data rich. Experiments (acceptability judgments) are cheap and easy. The problem is not finding another “fact” that resists explanation, but putting together a theory that has even a hint of non-trivial deductive explanatory structure. GS values this enterprise and reminds us that theories can be worth pursuing (and discarding) for reasons other than how many data points they (appear) to cover (or miss).

2. Weinberg remarks on what we want from our theories:

…there are explanations and explanations.  We should not be satisfied with a theory that explains the Standard Model in terms of something complicated an arbitrary…To qualify as an explanation, a fundamental theory has to be simple- not necessarily a few short equations, but equations that are based on a simple physical principle…And the theory has to be compelling- it has to give us the feeling that it could scarcely be different from what it is (ch 1).

These desiderata are reminiscent of those endorsed by the Minimalist Program, which, as Chomsky has repeatedly observed, are the in tune with the standard methodological tenets widespread in the successful sciences, viz. physics. Note Weinberg’s gloss on “simple” and “compelling.” Simple theories are based on natural principles, ones that make sense. This is also what makes them compelling. Within linguistics, the Minimalist Program endorses a similar mindset.  What makes for a simple and compelling theory of FL?  What are natural principles of UG?  These are very abstract very hard questions. But, as Weinberg observes for physical theories, they are the questions that any science with explanatory ambitions must confront.  Indeed, we might do worse than evaluate the success of a research program with how well it manages to operationalize these very important concerns.  For what it’s worth, I believe that one of the successes of the Minimalist Program is that it has tried (somewhat successfully in my view) to grapple with these issues. The central motif is that FL/UG is a computational system. We should explore its computational design features and look for natural ones.  Principles like Extension/No-tampering, Inclusiveness, Minimality, and Locality make computational sense. The program is to explore exactly how such notions operate and exactly what computational virtues they reflect.  Natural, simple principles, with great explanatory potential, that’s what we ought to be looking for!

3. Weinberg notes that what basic theory finds is likely to be irrelevant for many concerns:

The discovery of a final theory is not going to help us cure cancer or understand consciousness…We probably already know all the fundamental physics we need for these tasks (Ch 1).

There are many questions within linguistics where the results of minimalist theorizing will likely be irrelevant.  So far as I can tell, if you are interested in how kids acquire their grammatical competence in real time or how people parse sentences in real time or in how exotic language ‘E’ forms questions or relative clauses or how it expresses anaphoric dependencies then GB (and for many questions the Aspects Standard Model) is more than adequate to your task.  This is especially the case if, as I believe, a desirable boundary condition on adequate Minimalist theory (note: theory, not program) is that it preserve the generalizations embodied in these earlier descriptions of FL/UG. At any rate, much of what minimalism aims to accomplish will likely be of little relevance to these other investigations for roughly the same reasons that Weinberg notes above.

4. Weinberg describes the explananda of physics as follows:

…physicists are interested in the explanation of regularities, of physical principles, rather than individual events…Biologists, meteorologists, historians and so on are concerned with the causes of individual events…while a physicist only becomes interested in an event…when the event reveals a regularity of nature…(Ch2).

Another way of putting this is that physicists aren’t interested in what happens but in what could happen.  Linguists, at least those interested in competence, are very similar.  They are not interested in performances (what so and so said at this and this time) but the capacity that underlies these performances (which, to confess, I for one believe we will never be able to explain).  But more than this, linguists of the generative variety are interested in regularities, and high level ones at that. We often describe these as “effects,” island effects, principle C effects, Weak Cross Over effects etc.  These are highly stylized regularities and work in syntax aims to discover such effects and explain why they hold. Gathering linguistic data is worthwhile to the degree that these sorts of effects/generalizations are discovered.  Why? Because understanding the etiology of these effects is the key to unraveling the general properties of FL.  Linguists tend to underappreciate this point.  Effects (and anomalies, which are systematic counter-examples to effects) are what drive theory in the serious sciences.[1] They should do so in linguistics as well. Moreover, just as in physics, the aim should be to deduce these regularities from more and more general principles. As Weinberg puts it:

…we explain a physical principle when we show how it can be deduced from a more fundamental physical principle.

Weinberg has a very interesting discussion of what ‘fundamental,’ ‘deduced,’ and ‘principle,’ mean in the context of physics, which I urge you to look at.[2] In the context of contemporary linguistics, it is equally important to get a bead on the interpretation of these terms, especially given minimalist aspirations.  I have discussed my views of this elsewhere (here) (and I have some papers discussing this that are on the way out that I will link to when they come out) but for now, let’s just note that the ambitions are partially reductive, the aim being to deduce the laws of GB from more general principles.  Reduction does not imply elimination, rather the converse. And finding general accounts for the structure of FL need not imply that the principles of UG are domain general rather than domain specific (see here).  However, looking to deduce principles of UG from more general considerations, most likely of a computational sort, is what physics enviers should be aspiring to and Weinebrg’s examples illustrate the subtleties of this enterprise in a domain far more successful than our own.


There is a lot more in these Weinberg’s essays that I found thought provoking. Physics envy is a great motivator.  If you want to fuel your methodological mirror neurons, Weinberg’s popular writings are not a bad place to go.






[1] I will discuss effects and anomalies and their role in linguistics in a future post.
[2] Weinberg notes that “physicists try to explain just those things that are not dependent on accidents, but in the real world most of what we try to understand does depend on accidents.” Compare this to Norvig’s conception of scientific understanding (discussed here).

Thursday, September 28, 2017

Physics envy and the dream of an interpretable theory

I have long believed that physics envy is an excellent foundation for linguistic inquiry (see here). Why? Because physics is the paradigmatic science. Hence, if it is ok to do something there it’s ok to do it anywhere else in the sciences (e.g. including in the cog-neuro (CN) sciences, including linguistics) and if a suggested methodological precept fails for physics, then others (including CNers) have every right to treat it with disdain. Here’s a useful prophylactic against methodological sadists: Try your methodological dicta out on physics before you encumber the rest of us with them. Down with methodological dualism!

However, my envy goes further: I have often looked to (popular) discussions about hot topics in physical theory to fuel my own speculations. And recently I ran across a stimulating suggestive piece about how some are trying to rebuild quantum theory from the ground up using simple physical principles (QTFSPP) (here). The discussion is interesting for me in that it leads to a plausible suggestion for how to enrich minimalist practice. Let me elaborate.

The consensus opinion among physicists is that nobody really understands quantum mechanics (QM). Feynman is alleged to have said that anyone who claims to understand it, doesn’t. And though he appears not to have said exactly this (see here section 9), it's a widely shared sentiment. Nonetheless, QM (or the Standard Theory) is, apparently, the most empirically successful theory ever devised. So, we have a theory that works yet we have no real clarity as to why it works. Some (IMO, rightly) find this a challenge. In response they have decided to reconstitute QM on new foundations. Interestingly, what is described are efforts to recapture the main effects of QM within theories with more natural starting points/axioms. The aim, in other words, is reminiscent of the Minimalist Program (MP): construct theories that have the characteristic signature properties of QM but are grounded in more interpretable axioms. What’s this mean? First let’s take a peak at a couple of examples from the article and then return to MP.

A prominent contrast within physics is between QM and Relativity. The latter (the piece mentions special relativity) is based on two fundamental principles that are easy to understand and from which all the weird and wonderful effects of relativity follow. The two principles are: (1) the speed of light is constant and (2) the laws of physics are the same for two observers moving at constant speed relative to one another (or, no frame of reference is privileged when it comes to doing physics). Grant these two principles and the rest follows. As QTFSPP outs it: “Not only are the axioms simple, but we can see at once what they mean in physical terms” (my emphasis, NH) (5).

Standard theories of QM fail to be physically perspicuous and the aim of reconstructionists is to remedy this by finding principles to ground QM as natural and physically transparent as those that Einstein found for special relativity.  The proposals are fascinating. Here are a couple:

One theorist, Lucien Hardy, proposed focusing on “the probabilities that relate the possible states of a system with the chance of observing each state in a measurement” (6). The proposal consists of a set of probabilistic rules about “how systems can carry information and how they can be combined and interconverted” (7). The claim was that “the simplest possible theory to describe such systems is quantum mechanics, with all its characteristic phenomena such as wavelike interference and entanglement…” (8). Can any MPer fail to reverberate to the phrase “the simplest possible theory”? At any rate, on this approach, QMs is fundamentally probabilistic and how probabilities mediate the conversion between states of the system are taken as the basic of the theory.  I cannot say that I understand what this entails, but I think I get the general idea and how if this were to work it would serve to explain why QM has some of the odd properties it does.

Another reconstruction takes three basic principles to generate a theory of QM. Here’s QTFSPP quoting a physicist named Jacques Pienaar: “Loosely speaking, their principles state that information should be localized in space and time, that systems should be able to encode information about each other, and that every process should be in principle reversible, so that information is conserved.” Apparently, given these assumptions, suitably formalized, leads to theories with “all the familiar quantum behaviors, such as superposition and entanglement.” Pienaar identifies what makes these axioms reasonable/interpretable: “They all pertain directly to the elements of human experience, namely what real experimenters ought to be able to do with systems in their laboratories…” So, specifying conditions on what experimenters can do in their labs leads to systems of data that look QMish. Again, the principles, if correct, rationalize the standard QM effects that we see. Good.

QTFSPP goes over other attempts to ground QM in interpretable axioms. Frankly, I can only follow this, if at all, impressionistically as the details are all quite above my capacities. However, I like the idea. I like the idea of looking for basic axioms that are interpretable (i.e. whose (physical) meaning we can immediately grasp) not merely compact. I want my starting points to make sense too. I want axioms that make sense computationally, whose meaning I can immediately grasp in computational terms. Why? Because, I think that our best theories have what Steven Weinberg described as a kind of inevitability and they have this in virtue of having interpretable foundations. Here’s a quote (see here and links provided there):

…there are explanations and explanations.  We should not be satisfied with a theory that explains the Standard Model in terms of something complicated an arbitrary…To qualify as an explanation, a fundamental theory has to be simple- not necessarily a few short equations, but equations that are based on a simple physical principle…And the theory has to be compelling- it has to give us the feeling that it could scarcely be different from what it is. 

Sensible interpretable axioms are the source of this compulsion. We want first principles that meet the Wheeler T-shirt criteria (after John Wheeler): they make sense and are simple enough to be stated “in one simple sentences that the non sophisticate could understand,” (or, more likely, a few simple sentences). So, with this in mind, what about fundamental starting points for MP accounts. What might these look like?

Well, first, they will not look like the principles of GB. IMO, these principles (more or less) “work,” but they are just too complicated and complex to be fundamental. That’s why GB lacks Weinberg’s inevitability. In fact, it takes little imagination to imagine how GB could “be different.” The central problem with GB principles is that they are ad hoc and have the shape they do precisely because the data happens to have the shape it does. Put differently, were the facts different we could rejigger the principles so that they would come to mirror those facts and not be in any other way the worse off for that. In this regard, GB shares the problem QTFSPP identifies with current QM: “It’s a complex framework, but it’s also an ad hoc patchwork, lacking any obvious physical interpretation or justification” (5).

So, GB can’t be fundamental because it is too much of a hodgepodge. But, as I noted, it works pretty well (IMO, very well actually, though no doubt others would disagree). This is precisely what makes the MP project to develop a simple natural theory with a specified kind of output (viz. a theory with the properties that GB describes) worthwhile.

Ok, given this kind of GB reconstruction project, what kinds of starting points would fit?  I am about to go out on a limb here (fortunately, the fall, when it happens, will not be from a great height!) and suggest a few that I find congenial.

First, the fundamental principle of grammar (FPG)[1]: There is no grammatical action at a distance. What this means is that for two expressions A and B to grammatically interact, they must form a unit. You can see where this is going, I bet: for A and B to G interact, they must Merge.[2]

Second, Merge is the simplest possible operation that unitizes expressions. One way of thinking of this is that all Merge does is make A and B, which are heretofore separate, into a unit. Negatively, this implies that it in no way changes A and B in making them a unit, and does nothing more than make them a unit (e.g. negatively, it imposes no order on A and B as this would be doing more than unitizing them). One can represent this formally as saying that Merge takes A,B and forms the set {A,B}, but this is not because Merge is a set forming operation, but because sets are the kinds of objects that do nothing more than unitize the objects that form the set. They don’t order the elements or change them in any way. Treating Merge (A,B) as creating leaves of a Calder Mobile would have the same effect and so we can say that Merge forms C-mobiles just as well as we can say that it forms sets. At any rate, it is plausible that Merge so conceived is indeed as simple a unitizing operation as can be imagined.

Third, Merge is closed in the domain of its application (i.e. its domain and range are the same). Note that this implies that the outputs of Merge must be analogous to lexical atoms in some sense given the ineluctable assumption that all Merges begin with lexical atoms. The problem is that unitized lexical atoms (the “set”-likeoutputs of Merge) are not themselves lexical atoms and so unless we say something more, Merge is not closed. So, how to close it? By mapping the Merged unit back to one of the elements Merged in composing it. So if we map {A,B} back to A or to B we will have closed the operation in the domain of the primitive atoms. Note that by doing this, we will, in effect, have formed an equivalence class of expressions with the modulus being the lexical atoms. Note, that this, in effect, gives us labels (oh nooooo!), or labeled units (aka, constituents) and endorses an endocentric view of labels. Indeed, closing Merge via labeling in effect creates equivalence classes of expressions centered on the lexical atoms (and more abstract classes if the atoms themselves form higher order classes). Interestingly (at least to me) so closing Merge allows for labeled objects of unbounded hierarchical complexity.[3]

These three principles seem computationally natural. The first imposes a kind of strict locality condition on G interactions. E and I merge adhere to it (and do so strictly given labels). Merge is a simple, very simple, combination operation and closure is a nice natural property for formal systems of (arbitrarily complex) “equations” to have. That they combine to yield unbounded hierarchically structured objects of the right kind (I’ve discussed this before, see here and here) is good as this is what we have been aiming for. Are the principles natural and simple? I think so (at least form a kind of natural computation point of view), but I would wouldn’t I?  At any rate, here’s a stab at what interpretable axioms might look like. I doubt that they are unique, but I don’t really care if they aren’t. The goal is to add interpretatbility to the demands we make on theory, not to insist that there is only one way to understand things.

Nor do we have to stop here. Other simple computational principles include things like the following: (i) shorter dependencies are preferred to longer dependencies (minimality?), (ii) bounded computation is preferred to unbounded computation (phases?), (iii) All features are created equal (the way you discharge/check one is the way you discharge/check all). The idea is then to see how much you get starting from these simple and transparent and computationally natural first principles. If one could derive GBish FLs from this then it would, IMO, go some way towards providing a sense that the way FL is constructed and its myriad apparent complexities are not complexities at all but the unfolding of a simple system adhering to natural computational strictures (snowflakes anyone?). That, at least, is the dream.

I will end here. I am still in the middle of pleasant reverie, having mesmerized myself by this picture. I doubt that others will be as enthralled, but that is not the real point. I think that looking for general interpretable principles on which to found grammatical theory makes sense and that it should be part of any theoretical project. I think that trying to derive the “laws” of GB is the right kind of empirical target. Physics envy prompts this kind of search. Another good reason, IMO, to cultivate it.



[1] I could have said, the central dogma of syntax, but refrained. I have used FPG in talks to great (and hilarious) effect.
[2] Note, that this has the pleasant effect of making AGREE (and probe-goal architectures in general) illicit G operations. Good!
[3] This is not the place to go into this, but the analogy to clock arithmetic is useful. Here too via the notion of equivalence classes it is possible to extend operations defined for some finite base of expressions (1-12) to any number. I would love to be able to say that this is the only feasible way of closing a finite domain, but I doubt that this is so. The other suspects however are clearly linguistically untenable (e.g. mapping any unit to a constant, mapping any unit randomly to some other atom). Maybe there is a nice principle (statable on one simple sentence) that would rule these out.

Wednesday, April 17, 2013

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.

Tuesday, January 6, 2015

For SM (scientific method) fans

Here's a couple of things that I ran across lately that tackles SM issues.  I know that many of you are into this sort of thing (and my view is that this is ok so long as it is among consenting adults). So here is a piece by Noah Smith where I first ran across the discussion and here is a piece that he links to. The discussion was prompted by a piece in Nature (here) by two important physicists complaining yet again about string theory's lack of visible empirical support and a reply by Brian Greene and a tweet by Sean Carroll defending the virtues of "elegance" and "explanatory" power  as good arbiters of scientific worthiness.

This is all very interesting and good fun, especially when viewed from the linguistic sidelines. However, I find the whole discussion of more sociological than scientific or philosophical interest.

First note how the piece in Nature pulls out the whole Popper falsification card to poop on what it doesn't like. I think I've noted before (here) that this maneuver is generally used as a rhetorical slap in the face and that the people who use it have a none too subtle view of what Popper had in mind. At any rate, I agree with Carroll that falsification is a pretty blunt critical tool and that it cannot carry the weight that its wielders seem to believe that it has. So, whether Popper meant falsification in this way or not, that's its current usage as the Nature piece demonstrates yet again.

Second, nobody is suggesting relying exclusively on elegance or explanatory power as a metric for theory evaluation.  Everyone agrees that it would be nice were there some novel data as well. What's at stake is what to make of theories that seem to have little chance of being empirically tested, where facing the tribunal of experiment seems like a far fetched hope.  The answer obviously is that there will be lots of disagreement and that nothing profound can be concluded.  Elegance and explanatoriness do matter and among extant theoretical options some are better or worse along these dimensions and that is a good thing to know. But, nobody thinks that this is enough. The question then is what to do when one is in such a bind and what I mean here is that the question is what research should be funded. Physics is not cheap and so it is reasonable to ask whether elegance and explanatoriness are sufficient to keep pumping the big bucks into the field.  I can imagine different people concluding differently. And, IMO, I believe that this is what most of the fight is about, at least sotto voce. It's one thing to pour tons of cash into a field with obvious empirical pizzaz (think Hubel pix) and technological benefits. It's another to support elegance and explanatoriness. Scientists have staked their prestige on not being theologians. They are publicly the hard core realists: just the facts m'am sorts of people. This is science's special virtue (at least public relations wise) and what lends it its prestige. The debate about SM in the pieces here touches the core of this conceit. And that is a good thing, for whatever SM is (and it is not one thing at all) it's not that. SO the prestige gained by citing it endlessly is attained under false premises. Not a good thing for real scientists to do.

Third, linguists would benefit from thinking about the issues raised here in physics. That's not because linguistics is like physics. It isn't. Physics is the most successful scientific domain (recall I have lots of physics envy, as should you) and linguistics is still a very young field with modest accomplishments (though there are some of a non-trivial nature as I've argued endlessly). But that's why the debate is worth our while. Because to its supreme success, physics is where large methodological issues should be hashed out, not in underdeveloped domains like ours. Of course, once hashed out there, there may be take home messages, but don't count on it.

So take a look. The pieces are short and combative. They all make reasonable points. The debate is also inconclusive. There is no one size fits all SM. There are techniques that have proved useful in some places at some times. If we are lucky they may prove to be useful again. We  muddle through and do our best. SM is the injunction to use your smarts creatively. Sadly, there is no recipe for that.