On the methods of physical and social sciences

Shonk, over at Selling Waves, has revisited a post of mine from way back in September where I lauded and also gently chided the book "Sync", a work about the 'emerging science of spontaneous order'.

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.

It was not clear from my original post that I made my point somewhat lightheartedly; while I am an admitted mathophobe, I don't deny that mathematics qua mathematics is a useful, indeed essential part of modern civilization. I know that I don't want to be the first one to try out a suspension bridge built by an engineer who rejects the use of math in favor of an 'intuitive' approach...

However, Shonk (and to a lesser extent Andrew David Chamberlain) took exception to my invocation of Marshall's "Burn the Mathematics" dictum, going into an extended general defense of mathematics in science and the pursuit of knowledge. All well and good, and similarly so in his follow-up. The problem arises when he throws a barbed aside at both myself and Tim Swanson (both Austrian economists):

(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)).

As Shonk seems to suggest himself, the point is unfair and slightly dishonest. In my original post, I never suggested (as Shonk implies) that mathematics qua mathematics should be rejected because it "disagrees with the principles of Austrian Economics." The point was that, ala Physics Envy, methods appropriate for studying the physical sciences are inappropriate for studying thinking, acting, subjective humans.

Further, the idea that Austrians reject deduction is ludicrous. What is "extreme a priorism" than deduction? The difference, of course, is that Austrian scholars have followed a verbal logical formalism instead of a mathematical one[1].

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. So long as a physical theory is not refuted by the data of experience, it works, and due to the nature of physical reality, it always works given a certain scale[2].

None of this holds or obtains in the social sciences. There are no constant relations such that a mathematical formula could be deduced to predict future behavior. Borrowing again from "Physics Envy, Indeed" and Lukelea, the fundamental particle of social study is a human being, no two of which are identical (including genetically identical twins). If there is no constant, underlying reality to social interaction (i.e. no social equivalent of C, Pi, Planck?s constant, etc), then empirical research methods are doomed to failure (or, at least, never deliver on their promised truth claims) in trying to develop useful theory and understanding of social/human phenomena.

A reason that physical scientists must study physical phenomena the way they do is in part because they have no knowledge of what it is like to be a molecule or a particle, and thus have to observe their behavior to understand it. Social scientists, who are of the same category of existence as their targets of study, have personal insight into what it is to be human. Mises recognized this and, extrapolating from some a priori true axioms (?man acts?, etc) that are known by virtue of being human, human action could be studied and understood. The advantage of such a methodological starting point is that you don?t have to make ultimately unsupportable claims to absolute predictive ability (which have to be made by empirical economists as a consequence of their positivism) to understand and comment on economic phenomena. Giving up the claim of predictive certitude means never having to say you?re sorry. ^_^[3]

Acting as though we don't have this information (that is, using the methods of the physical sciences to study social/human phenomena) is in error.

This critique goes both ways, of course. Just as it is wrong to use the methods of physical science on social science questions, it is wrong to use social science methods on physical phenomena. After all, despite all the meditation of eastern mystics, none of them deduced a physical constant of the universe. ("Oh! 3.14159... of course!", says the Yogi after a vigorous post-meal burp atop the desolate mountain.) The idea is that you use the methods that are appropriate for what you intend to study, and that there are different methods.

Ultimately, though, this may be much ado about nothing, in that Mises himself likens economic thought to the theoretical thinking of a mathematician. So long as the mathematics is used as a formalism to guide questions and give structure to theoretical thinking, its not really that bad of a problem. It is when people start believing their formalistic equations about the economy[4] actually apply to reality that we get into trouble?


fn1. A point brought up by ADC in the comments to Physics Envy that I slightly disagree with was that while Neoclassical formalism is bad, "[T]he Austrian response of no formalism is bad also." The context of his comment suggests that to ADC, formalism requires math. Does it? I don't think so, but I could be wrong. I think Austrian verbal formalism isn't recognized by mainstream economists precisely because of their bad mathematical formalism.

fn2. Of course, when we're able to notice scales where the old theory starts to part ways with reality, new theories come into play based on new data. This pursuit of ever-perfect physical theory is only possible, again, because there is an unchanging physical reality that is being studied. If, for example, C, Pi, and Planck's constant were variable, physics as we know it would not be possible. Of course, neither would life as we know it, either.

fn3. I kid, I kid. Joudan desu yo.

fn4. I?m thinking specifically of the National Income equation. It makes sense on an accounting level, but too many doofi (doofuses?) of the statist economic bent talk, write about, and act as if that equation was algebraically true, and thus you can ?solve? for one variable by targeting another (and holding the rest constant, I imagine). That is not only asinine, ignorant, and false, but also profoundly dangerous to liberty and prosperity when in the hands of policymakers who might believe it.

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"Mathematical methods work

"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."

hmmm, I think this is a rather antique and untutored understanding of both maths and physics. You might find yourself less antagonistic if you investigated a bit more deeply.

What the hell is with that

What the hell is with that long, rather disturbing email exchange that "rufus" posted? Was it pasted into the wrong window by mistake, maybe?

As for back40's article, it doesn't really seem applicable to the discussion at hand. Just because it has happened in the past that different disciplines have cross-pollinated, that doesn't mean that economics is or will ever be a math-based discipline...

p.s. Brian, as a fellow mathophobe, it's reassuring that hear an aversion to the more abstruse realms of mathematics need not preclude a real understanding of economics. ^_^

"Can absolute, unchanging

"Can absolute, unchanging human relations be represented in an equation, ala Boyle?s Law (for a simple example; feel free to subsitute any arcane supralong equation, for the point is the same regardless)?"

This goes to the heart of the confusion in that it is both antique and seemingly unaware of the practice of modern physics and math. Old style "Newtonian" physics and the maths that support it deal with the seemingly determinate world of large objects. When the scale shrinks to atomic level and below then nothing is determinate, it is probabilistic, and a whole new math evolved to do this physics. What physicists, mathematicians and social scientists, including economists, have discovered is that tools and insights from each discipline have applicability in others.

It isn't cybernetic, machine like precision and control, it is much richer and not particularly useful for prediction. One of the main insights 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.

Alex, I think Rufus made a

Alex, I think Rufus made a mistake in posting that into the comments, so I fixed the error. Though, if *I* was in error, I apologize...

Very interesting post. I've

Very interesting post. I've responded, somewhat incoherently, but hopefully instructively. I don't think we're actually disagreeing very much; rather, I think that we're sort of arguing past each other because we're using different vocabularies.

Do you have any insights to

Do you have any insights to offer on why human action can somehow be mathematically modeled in a way that give predictive value? Can absolute, unchanging human relations be represented in an equation, ala Boyle's Law (for a simple example; feel free to subsitute any arcane supralong equation, for the point is the same regardless)?

Just curious. My question here goes to the meat of my thesis. Is your position that your aesthetic judgement of my viewpoint (being antique) negates my thesis?

Dude, awesome. Definitely a

Dude, awesome.

Definitely a lot to think about between your response and back40's comment. As I said, 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.

You may be right about the

You may be right about the differences between the physical and social sciences vis-a-vis mathematics, but there is another difference as well. As someone many years ago (I forget who, but he was a science fiction writer) said "During the Manhattan project, the scientists said there were about four methods which might work in refining the needed uranium, and they all turned out to work. During the War On Poverty, the scientists said there were about 10 schemes which could work on reducing poverty, and NONE of them worked."

I have taken, over the years, to reading the phrase "social science" as though the words were in German, since the phrase makes no sense using the commonly understood meaning of the words in English.