## June 17, 2004

### Why social scientists need to throw away their classical paradigms

Posted by shonk at 09:55 PM in Economics, Geek Talk | TrackBackBrian Doss has responded to my response to my initial response to his critique of Steven Strogatz’ book *Sync* (whew! Have I broken the record for hyperlinks in a single sentence yet?). There’s a lot to cover here, but I’ll try to do what I can with it.

First, he rightly points out that much of his original point is uncontroversial:

My small beef with the concept that there was any sort of ‘the emerging’ science of spontaneous order was in the (I thought) uncontroversial point that the fields of Biology (macro, micro, and molecular) and Economics both concern themselves with spontaneous order and have done so for centuries (more or less) prior to the publication of ‘Sync’. As that was the case, I further noted that since we have 2 sciences studying specific kinds of spontaneous order and that neither science requires mathematics to either understand the subject matter or to gain knowledge in the first place, that perhaps the author of ‘Sync’ should take some hints and possible insights.

This is all true, but at the same time misleading. While biology has generally done a good job describing the spontaneous order processes that come into play in evolution, the “pure” biological approach is not well-suited to, for example, explaining the tertiary structure of proteins. The tertiary structure of a protein is the general shape of the protein, which is determined by the sequence of amino acids of which the protein is made, but which can be surprisingly complex and three-dimensional. One of the big revelations to come since proteins were first understood as sequences of amino acids is that knowing the higher-order structure of a protein is crucial to understanding what it does and how. And scores of mathematicians are intimately involved in trying to understand exactly how these higher-order structures arise.

In fact, mathematical biology is one of the hottest fields in mathematics today, and much of the research in that area stems from attempts to understand the structures of both proteins and of nucleic acids (i.e. DNA and RNA). And, perhaps surprisingly, advances in that field have had bidirectional influences on supposedly “abstract” areas like knot and braid theory.

Also, to borrow the definitive example from Strogatz’ book, biology did a very poor job of explaining the spontaneous order evident in the simultaneous flashing of Thai fireflies. It took some very hard-core mathematics (and some extreme simplifying assumptions) to even begin to explain how millions of fireflies could all flash in unison without having some “master” firefly. Even verifying those explanations (or discrediting them, for that matter) is something that should be experimentally possible, but such an experiment would be very difficult and has not, as yet, been carried out. This fact, along with the fact that the explanation required significant assumptions, is what led me to say in my previous post that “the mathematics of spontaneous order is both several steps ahead of and well behind the real world.”

The point of this digression is simply to suggest that the classical approaches are reaching their limiting points even in biology and that the days where one didn’t need to know mathematics to do chemistry are swiftly fading. Which isn’t to say that mathematics might not benefit from incorporating the techniques of biology and economics as they relate to spontaneous order, but, based on my admittedly very limited understanding of those two subjects, I have my doubts as to how much fruit such an attempt would bear.

Why do I have doubts? Quite simply, because biology and economics have generally done a good job noting that spontaneous order *does arise* in the relevant areas, but have not done a particularly good job by themselves of explaining *why*. Which is not to say that the why is not understood, but the best explanations I’ve seen (here I would cite, for example, Dawkins’ *The Selfish Gene*or pretty much any microeconomics course) derive, ultimately, from game theory, which is itself a distinguished mathematical discipline, dating back to at least [Fermat].

Back to Doss’ post: he rightfully points out that I unfairly posed the following parenthetical question:

(as a side note, both Doss and Swanson, in the original Catallarchy post linked above, seem to reject mathematics because it conflicts with the principles of Austrian economics and the Austrians’ rejection of empirical economics is well-known; so my question is this: if Austrians reject empiricism as well as mathematics (i.e. deduction), how, exactly, do they advocate gaining knowledge? (Of course, I know the answer, but the Austrian-sympathizers would do well, in my opinion, to keep this question in mind)).

Of course, mathematics does not conflict with the principles of Austrian economics/praxeology (although some of the more zealous and narrow-minded Austrian sycophants seem to think it does); rather, it is the application of mathematical methods to economics in parallel to the classical application of mathematics to physics that conflicts with Austrianism. Or, as Doss puts it, the classical “methods appropriate for studying the physical sciences are inappropriate for studying thinking, acting, subjective humans.”

However, I do think that many Austrians have a fairly poor grasp of exactly what mathematics is, which is why I added the disclaimer that they would do well to keep the above question in mind. I grant that this strikes of pedantry, but I think it’s an important point, and Doss seems to be one of those Austrians who doesn’t seem to understand mathematics very well:

Mathematical methods work in the physical sciences (and to a lesser extent in life sciences) because (a) there is an objective, unchanging reality to the physical laws of the universe and therefore it is (b) possible to design experiments where aspects of reality can be held constant, and thus strict, formal, mathematical relationships can be inferred from the data.

The key misunderstanding, I think, derives from a conflation of the terms “mathematical” and “computational”. Not that this is an uncommon confusion: my non-math friends occasionally ask me what it is, exactly, that I do, occasionally jesting that I must be adding some really big numbers. In fact, mathematics is, ultimately, the discipline devoted to determining the abstract structure that logically follows from a particular axiom set. Mathematicians aren’t, generally speaking, taking a particular equation and plugging a bunch of different values into it to see what results.

In this sense, in fact, mathematics is remarkably similar to Austrian economics itself. Doss links to a Mises article which explicitly compares economists to mathematicians, a comparison I’ve made myself many times before. In fact, in my view, the Austrian school is the most mathematical of all schools of economics by a wide margin. As Doss points out, though, “[t]he difference, of course, is that Austrian scholars have followed a verbal logical formalism instead of a mathematical one.” Which is something I have never well understood. I simply cannot understand why the Austrians consistently reject symbolic logic (which I would call “formal logic”, though obviously an Austrian would contend that my definition is incomplete). Which isn’t to say I haven’t seen the arguments, it’s just that I don’t understand them. For example, here’s what Rothbard has to say on the matter in “Toward a Reconstruction of Utility and Welfare Economics” (which parallels his argument in *Man, Economy and State*):

The suggestion has been made that praxeology is not really scientific, because its logical procedures are verbal ( literary ) rather than mathematical and symbolic. But mathematical logic is uniquely appropriate to physics, where the various logical steps along the way are not in themselves meaningful; for the axioms and therefore the deductions of physics are in themselves meaningless, and only take on meaning operationally, insofar as they can explain and predict given facts. In praxeology, on the contrary, the axioms themselves are known as true and are therefore meaningful. As a result, each step-by-step deduction is meaningful and true. Meanings are far better expressed verbally than in meaningless formal symbols. Moreover, simply to translate economic analysis from words into symbols, and then to retranslate them so as to explain the conclusions, makes little sense, and violates the great scientific principle of Occam s Razor that there should be no unnecessary multiplication of entities.

In a sense, Rothbard is correct to point out that the Austrians’ deduction is slightly different from standard formal logic, because, in formal logic, you are free to use valid propositions in the deduction even though those propositions may not make any sense when translated into natural language, whereas the Austrians want to use propositions that are both valid and meaningful at every step along the way. However, I disagree with his suggestion that, as such, translating into a formal language is a pointless and superfluous step. If Austrian deductions are, in fact, valid, then they should be translatable into formal language and still hold as valid deductions; the fact that many other deductions might be possible in that formal language that would be invalid to the Austrian would be irrelevant. Rothbard’s objection serves, it seems to me, as a valid rationale as to why an Austrian wouldn’t want to deduce *in* the formal language itself, but I don’t think it at all justifies the apparent disdain the Austrians have for *confirming* the deductions they’ve already made in this rigorous way (such confirmation being something I’ve asked for before).

Now, Rothbard is quite right that meaning is better expressed in words than in symbols, which is why it would, presumably, be difficult to translate Austrian axioms/deductions into formal language, but difficulty, in and of itself, shouldn’t serve as justification for not attempting the task. I also find it curious that Rothbard employs Occam’s Razor as a scientific principle, as the Austrians seem to be so disdainful of scientific methodology in economics. Besides the fact that Occam’s Razor is totally inapplicable in this realm, anyway, as the notion that “the simplest explanation is usually the best” says nothing about how to go about *confirming* conclusions that one has reached.

Having digressed again, I want to make the point Doss (and many other Austrians, for that matter) may be closing his mind to mathematical insights that actually buttress his position because he views mathematics through a classical lens. As a matter of fact, modern mathematics, with its investigations into chaos and complexity, is actually making the case that predictive determinism is essentially impossible. As commenter buck40 points out:

One of the main insights [of modern mathematics] is that prediction and control are in most cases false hopes. Those who apply the insights of complex adaptive systems to social sciences do not seek control, do not counsel control. Quite the opposite, they help policy makers understand why efforts to control will surely fail. You might find that they are your allies in a way, that they are all Hayekians in a manner of speaking.

In that light, consider, for instance, the recent *No Treason* post “Butterflies and Sweatshops,” where John T. Kennedy suggests that not only is the effect of an individual purchase on third world working conditions too small to predict, but that the effect of that purchase simply *cannot* be predicted to any level of certainty. I think we would all agree that the world economy is more complicated than the three body problem, yet even the three-body problem cannot, in general, be solved explicitly. Hayek and Mises argued that central planners suffered from a knowledge problem, that someone trying to direct the economy could not, practically speaking, acquire enough knowledge to accurately predict how their interventions would affect the economy. Chaos theorists have extended that further, essentially demonstrating that this is not merely a practical problem, but that, in fact, such a prediction is manifestly impossible, even in the abstract. So, chaos/complexity theorists are “all Hayekians in a manner of speaking”.

Similarly, insights in network theory are helping to explain, for example, both the scale-free aspects of internet hyperlinks and the resiliency of the power grid. One can only imagine that a solid grounding in network theory coupled with an understanding of economics might well yield new insights into economic phenomena.

And, finally, it should be pointed out that the work being done by Strogatz and others is demystifying spontaneous order, demonstrating that there’s nothing supernatural about markets or evolution, but rather that the fruits of spontaneous order are all around us and that the mechanisms that underlie this order are often very simple. To return to the fireflies, the simultaneous flashing that is almost certainly a result of the interaction of coupled oscillators is more extensive than could ever be coordinated by some master firefly keeping time.

Dude, awesome.

Definitely a lot to think about between this and back40's post. I'm definitely a mathophobe so your observation that I'm unnecessarily conflating computation and mathematics is probably on the mark. My initial take is that I'm going to have to do a mea culpa on this one and concede. ^_^ But we'll see.

Posted by: Brian W. Doss at June 17, 2004 10:19 PMDude, awesome.

Definitely a lot to think about between this and back40's post. I'm definitely a mathophobe so your observation that I'm unnecessarily conflating computation and mathematics is probably on the mark. My initial take is that I'm going to have to do a mea culpa on this one and concede. ^_^ But we'll see.

Posted by: Brian W. Doss at June 17, 2004 10:19 PM**Shonk:** *The key misunderstanding, I think, derives from a conflation of the terms “mathematical” and “computational”. Not that this is an uncommon confusion: my non-math friends occasionally ask me what it is, exactly, that I do, occasionally jesting that I must be adding some really big numbers. In fact, mathematics is, ultimately, the discipline devoted to determining the abstract structure that logically follows from a particular axiom set.*

I agree with your definition, and I agree with your assessment that most individuals do not have a clear concept of what “Mathematics” actually is/are.

**Shonk:** *In this sense, in fact, mathematics is remarkably similar to Austrian economics itself. Doss links to a Mises article which explicitly compares economists to mathematicians, a comparison I’ve made myself many times before. In fact, in my view, the Austrian school is the most mathematical of all schools of economics by a wide margin. As Doss points out, though, “[t]he difference, of course, is that Austrian scholars have followed a verbal logical formalism instead of a mathematical one.” Which is something I have never well understood. I simply cannot understand why the Austrians consistently reject symbolic logic (which I would call “formal logic”, though obviously an Austrian would contend that my definition is incomplete). Which isn’t to say I haven’t seen the arguments, it’s just that I don’t understand them.*

And the reason that you do not understand them is because they reject *formal logic* in preference for *Mysticism*, and mysticism is incomprehensible by its nature.

**Shonk:** *I disagree with his suggestion that, as such, translating into a formal language is a pointless and superfluous step. If Austrian deductions are, in fact, valid, then they should be translatable into formal language and still hold as valid deductions; the fact that many other deductions might be possible in that formal language that would be invalid to the Austrian would be irrelevant. Rothbard’s objection serves, it seems to me, as a valid rationale as to why an Austrian wouldn’t want to deduce in the formal language itself, but I don’t think it at all justifies the apparent disdain the Austrians have for confirming the deductions they’ve already made in this rigorous way (such confirmation being something I’ve asked for before).*

Shonk, people like Rothbard and Rand are divinely inerrant geniuses. Who are you to question them?

Obviously the Emperor’s New Clothes are the most exquisite in the land.

**Shonk:** *As a matter of fact, modern mathematics, with its investigations into chaos and complexity, is actually making the case that predictive determinism is essentially impossible.*

hehehe ...

Posted by: The Serpent at June 21, 2004 11:51 AM*Shonk: As a matter of fact, modern mathematics, with its investigations into chaos and complexity, is actually making the case that predictive determinism is essentially impossible.*

hehehe …

Just to be clear, the point I was making was that complexity theory suggests that we are incapable of predicting the future even in a deterministic system with any degree of accuracy.

Posted by: shonk at June 21, 2004 09:00 PMYeah, I had a feeling you were gonna say that. ;)

I don't think you will survive as a *red* blood cell Mr. Shonk. I think you were born and bred to be a *white* blood cell.

Ahhh, but who knows ... right? Perhaps you are destined to be a germ or a virus?

Posted by: The Serpent at June 22, 2004 10:52 AM*I don’t think you will survive as a red blood cell Mr. Shonk. I think you were born and bred to be a white blood cell.*

Yeah, I've always been a better critic than an idealogue.

Posted by: shonk at June 22, 2004 04:00 PM**Ideologue** = A student of or expert in ideology

**Ideology** = the study of ideas, their nature and source

Ergo …

**Ideologue** = A student or expert in the study of ideas, the nature of ideas, and the source of ideas.

**Critic** = A person who forms and expresses judgments of people or things according to certain standards or values (i.e. “Ideas” (or memes) … see above).

You aren’t trying to play the pessimist on me, are you shonk?

So what are the “standards and values” that you based your criticism on? Let me guess … its something similar to Rothbard’s mystical ramblings?

Ohhh wait, you had a problem with Rothbard’s mystical ramblings too – didn’t you?

Are Rothbard and Rand “Ideologues”, or fellow “Critics”?

Posted by: The Serpent at June 23, 2004 11:39 AMPowered by Movable Type 2.661

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