Pro Elegance – a vote of confidence

Noah has a blog entry called The End of Elegance. In it, he’s hoping that “elegance” will go away as a desideratum of Linguistic theory. Or, maybe not go away, but be relegated to lesser importance. Or … actually, it’s a little hard to tell exactly what he means – which is always the case when you’re essentially arguing for a re-weighting of things, but won’t specify what weighting you’re after.

His jumping off point is a line in the introduction to Understanding Minimalism – which is something like a textbook on The Minimalist Program in syntax, though not exactly an introductory one. It is the book that cleared up for me just what Minimalism was about, and how one goes about applying it, and I highly recommend it to Linguists who want to know what the methods and issues are.

Here’s the line:

As in any other domain of scientific inquiry, proposals in linguistics are evaluated along several dimensions: naturalness, parsimony, simplicity, elegance, explanitoriness, etc.

I’d have to agree that it’s a problematic line. First, there’s the jokey “explanitoriness.” Then there’s the fact that “explanitoriness,” while clearly more important than the others, comes late in the list and is presented as merely one among equals. Finally, it isn’t clear that these things are dimensions of evaluation – especially since they don’t share units of measurement. We can’t talk about a relationship between “elegance” and “explanitoriness” in any but the vaguest of terms. (Actually, to get nit-picky about it, I suspect that everything in the list are actually just ways of emphasizing aspects of “explanatoriness,” but that’s a discussion for another day.)

Then again, this is an introduction to a book about Minimalism, and it’s doubtful that the authors mean to go into any great depth about their theory of scientific meaning. The introduction just sets out some basic assumptions – and I, for one, don’t see any problem with prefering elegant theories to inelegant ones, all other things equal.

Noah is apparently concerned that other things won’t be equal:

The order is certainly not determined by each dimension’s relative epistemological importance. The next sentence in the paragraph makes this clear, but even without that next sentence, a little careful thought suffices to show none other than explanitoriness (or, perhaps more, erm, elegantly, explanatory scope) even have any epistemological importance.

Which would be fair enough if the authors had claimed that these things shared epistemological importance, but I don’t see anything in that introduction to indicate that they did. Quite the contrary, they spend that and the next page arguing that data collection and organization has to come first. First you make a theory like Principles and Parameters (and/or its most famous implementation: Government and Binding Theory) that covers the data, and then you go about reworking that theory so that it’s more natural, parsimonious and elegant. Furthermore, it’s only within the context of having accepted that theory that these other measures gain in importance. In the authors’ words:

In other words, once explanatory adequacy is bracketed, as happens when only accounts that have P-and-P-architectures are considered, an opening is created for simplicity, elegance, and naturalness to emerge from the long shadow cast by Plato’s Problem and to become the critical measures of theoretical adequacy.

That sounds to me like a solid two-stage approach. First you look at the data and come up with a theory that explains the facts. Once you’re broadly satisfied with your theory, you refine it and hope that the process of refinement increases your understanding. “Explanatoriness” – which Noah correctly asserts is epistemologically prior to the others – must be satisfied before you get to the other criteria, which are really criteria for refining a theory. Elegance, parsimony, etc. are parasitic on having first explained something. I really don’t see any ground for objection: that seems to me to be exactly the right way to look at these things.

Noah is also concerned that while we understand what “explanatoriness” is, we don’t really know what we mean by the others.

My problem with elegance is more or less the same as my problem with simplicity, with maybe a dash of my problem with naturalness thrown in for good measure. Even if we can come up with an acceptable definition of elegance (which I’m not at all sure we can, and I don’t think the “I know it when I see it” criterion will work here), I don’t doubt that a more elegant theory is more aesthetically pleasing than a less elegant theory. But I don’t see how elegance can possibly matter when evaluating a theory’s claim to constitute knowledge.

My first bone to pick here is that I don’t think we have any better idea what “explanatoriness” is than we do for “elegance.” I suspect Noah’s confusing “predictive power” with “explanatoriness,” so let’s go ahead and clear that up: “predictive power” is NOT what the authors are talking about here. (NOTE: I’m deliberately chosing “power” over “accuracy” here to try to collapse two desiderata: scope and accuracy. A good theory is one that gets a wide range of things right.) In Physics, there’s no harm in conflating the two, because there are almost always clear tests (even though they may be prohibitively expensive, or difficult to the point of impossible to run at our current level of technology) that one can devise to test one’s hypothesis. In Linguistics, unfortunately, we can’t directly test the things we’re hypothesizing, at least not at the current level of technology – and this is especially true for Syntax. This is a common problem among social sciences, in fact, and the basis of their Physics Envy in the first place. Since there’s only so far you can go in directly verifying what you believe, it sort of comes down to the gut feelings of the people who are well versed in the data and the literature at some level. This is the source of the much-lamented claim that no Economist has ever changed his mind on the basis of data. Russ Roberts bangs that drum as though he wants Economists to change – but the problem is probably not with Economists, or Economics as an academic field, but with Economics as a subject. The kinds of things under study don’t lend themselves to tests that force acquiesence to opposing points of view, and asking an economist to change his view on the basis of data means asing him to give up a lot of honestly-acquired assumptions about the way the world works on the basis of data that is by nature correlative rather than experimental, and therefore ultimately inconclusive. “Explanatoriness” isn’t coterminous with “predictive power” in some fields, and Syntax is one such field. This isn’t to say there isn’t overlap: nothing is more convincing than coming up with a theory in Syntax and realizing later that something that seems a priori unrelated turns out to fall in line with it. But neither are they exactly the same thing.

So what’s “explanitoriness?” Well, that’s the point, isn’t it? We don’t know to any degree of precision. Just like we don’t know what “naturalness” and “elegance” are to any degree of precision either. “Explanatoriness” is just the feeling that things have been explained. Sorry, I would like to be able to say more, but that’s just sort of how it is. Ultimately, we’re human beings, not gods, and at the end of the day our conviction that we’ve arrived at the truth is merely that: a conviction determined by our innate emotional makeup. In social sciences, we can usually say with certainty what the wrong answers are. But among the answers that we haven’t eliminated as clearly wrong, it can be really hard to say which are better. The only approach I’m aware of is to cultivate expertise and try to hold researchers to a sense of personal integrity that requires them to give up the fight when a competing approach seems to explain more. As long as researchers fight fair, “explanatoriness” is the measure of which theories win the public debate and attract followers. Researchers don’t always fight fair, but what can you do?

Let’s look at the second part of that quotation again:

Even if we can come up with an acceptable definition of elegance (which I’m not at all sure we can, and I don’t think the “I know it when I see it” criterion will work here), I don’t doubt that a more elegant theory is more aesthetically pleasing than a less elegant theory. But I don’t see how elegance can possibly matter when evaluating a theory’s claim to constitute knowledge.

Actually, I’d like to take a stab. I see people use “elegant” mostly in situations where two/multiple things which there is no reason to believe are connected can be made to seem or shown to be connected in a convincing way. Call it the “two birds with one stone” principle. So, an “elegant” move in Chess is usually when someone is facing two unconnected lines of attack, and to the casual observer it looks like dealing with one will expose a weakness in dealing with the other, and the player nevertheless manages to make a single move that puts him in a position of strength to deal with both lines simultaneously. An “elegant” solution to a math problem is similar. We’re faced with something that looks complicated, and it looks like we’ll have to go through many steps to simplify one part of the problem before dealing with another. An “elegant” solution in that case manages to simplify both parts of the problem simultaneously. An elegant solution to a crime novel is when a series of events which seem unrelated and are in any case confusing are shown not only to be connected, but in a simple way. “Elegance” usually plays on the unexpected, seeing things that are not immediately obvious, and in a way that connects things that did not seem connected before.

To the extent people share that impression of what “elegance” is, it is obvious what it has to do with “a theory’s claim to constitute knowledge.” In fact, it is central to explanation. If two (or more) things which seem to be unrelated and lack explanations can be shown to be related in a convincing way, then knowledge has been advanced. Of course, this is, as mentioned above, parasitic on “explanatoriness.” If the theory is elegant but fails to correspond to reality, then it’s worthless. “Elegance” does nothing to make a useless theory useful. But this is why the authors insisted that different desiderata acquire different levels of importance at different stages of theory development. You must absolutely start with a theory that explains things, and elegance, parsimony, simplicity and naturalness be damned. Once you have a basic explanation, you refine that explanation by trying to make it more elegant, parsimonious, simple and natural. To the extent that elegance finds unexpected connections between parts of the theory, it cannot fail to advance knowledge.

I think if there is a complaint about the quoted line that makes sense it’s that “elegant” is really a catch-all term that covers the rest. So, the authors could (and should) have just said “As in any other domain of scientific inquiry, proposals in linguistics are evaluated according to how elegant and explanatory they are.” And then they should have added that the relative importance of the two depends on the stage of the theory – that elegance takes over as a theory gets mature. And they should have gone on to say that “explanatoriness” is prior to “elegance,” and that “elegance” is composed of “simplicity, parsimony and naturalness.”

By the way, the reason for the ordering in the original sentence, the reader will have surmised by now, is that the authors believe that the Principles and Parameters Theory is in a stage of development where things have been more or less adequately explained, and we’re now ready to expand our understanding of the explanation by paring down the theory. Interestingly, I don’t agree with that assessment. I think Minimalism is actually the approach that should have been taken from the get-go, and that in addition to being a better theory across the latter-day criteria, it’s also much more explanatory than Government and Binding ever was. Government and Binding made the wrong generalizations, and precisely because in those days people were simply stating observations gussied up in theoretical jargon. Social sciences should start with Minimalist-style approaches, actually. And in any case, the empirical coverage of Government and Binding Theory was actually pretty poor, and there is no reason to believe that we were in a stage where the existing theory was ready for wholesale refinement on that basis. The reason to refine Government and Binding Theory was actually more to do with explanatoriness, actually – it noted trends but didn’t account for them! But that is neither here nor there. The overall points are that (1) yes, “elegance” is related to a theory’s claim to knowledge and is an appropriate criterion for evaluating a theory’s worth, but (2) only provided the theories being compared are more or less equal in terms of explanatory power, and (3) the authors did, in fact, make that second point clear in their introduction, just not in the sentence that was taken as Noah’s jumping off point.

Conclusion: I do not want an End to Elegance, least of all in the social sciences.

One thought on “Pro Elegance – a vote of confidence

  1. Pingback: Breaking: Elegance still dead » Source-Filter

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