## Austrian Economics and Math

I respond to that blog post I had earlier brought to your attention. An excerpt:

I can’t think of a single prominent Austrian who ever said anything remotely like, “I hate math.”…So you can see why Albrecht’s whole premise seems foreign to me, and serves only to reassure outside critics that Austrians are a bunch of Know Nothing rubes.

To be sure, in Internet discussions you can often see rank-and-file fans of the Austrian School blasting the “mathturbation” of mainstream economists. But their point isn’t, “Math is stupid and a waste of time.” No, their point is that the elegance and majesty of mathematical truth is being illegitimately smuggled over to endorse the conclusions of the economic models in question, when such moves (they claim) are unwarranted. Since Albrecht doesn’t challenge that notion–and actually seems to agree with it–it really makes me wonder who his target audience is for his blog post.

Indeed, we really have no idea who Albrecht is tut-tutting in his post, since he provides not a single link to anyone guilty of the error he is chiding. I would encourage Albrecht to go find, say, three good examples of what he means, so we can be clear on whether there is really a problem in the School.

Then I quote from Mises (and link to Rothbard talking about the mathematical field of chaos theory) to show that these giants of Austrian economics were quite well versed in math.

Hmm. Perhaps Albrecht is speaking to people like me.

I casually will make fun of keynesian economists as being obsessed with math and relying on math instead of logic and so on and so forth. Now, like other Austrians, I don’t literally mean that math is useless or that I don’t like it or anything like that.

But at the same time, when I make these comments, I don’t usually go into that full explanation. So to the layman who overhears me, he might very well mistake that Austrians are just anti-math (in fact, I get this criticism from keynesians I argue with frequently).

So perhaps I’m unintentionally engaging in bad PR. I say things like “As an Austrian, I don’t care about your fancy mathematical models,” and I don’t mean that 100% literally, but perhaps others don’t pick up on the implication…

Logic is math.

No, math is applied logic. Logic is not a subset of math, if anything it’s the other way around.

What is boolean algebra if not a special case of other types of algebra?

Math uses logic, but logic exists without math. If there were no math, there would still be logic.

It may be down to how math is taught in the US. Schools in Czech are on average just as bad as gov’t schools in the US, but still I remember I spent the first month as a high school freshman discussing with our math teacher what it means when I say “if it rains, mushrooms grow” and what the exact opposite of this sentence is (it’s not anything containing “if” btw). In other words, we did formal logic as the cornerstone of math.

Then three years later, as an exchange student and a high school senior inLas Vegas, we did some quite advanced calculus, but it wasn’t about understanding the subject but rather memorizing the procedures, the derivatives of certain functions. You had to fit a given question into one of the memorized patterns and the marks were given according to your ability not to make a trivial counting error along the way. Nobody understood the big picture, including the teacher.

This is not to criticize US vs European schooling, both is bad and I just got lucky with my teacher. But rather that math is more than summing up the right numbets. Math is not accounting, it’s logic. And Rothbard certainly is all for math when understood like that. I think he even had a bachelor degree in math.

Speaking of Accounting. Surprisingly few economists have studied it, nor been involved in any sort of day to day transaction processing. Maybe Mises Institute should team up with some online Accounting & Bookkeeping courses.

Basics of computerised accounting could also be a good background, spreadsheets, databases, statistics.

People don’t come to the Austrian school looking for those things though, plenty of other places teach it, probably better than the Mises Institute can do… division of labour is helpful. I would suggest there must be a collaboration opportunity available somewhere.

By the way, based on boolean logic, the exact opposite of the sentence “if it rains, mushrooms grow”, would be “it did rain and mushrooms are not growing”.

¬( R → M )

¬( ¬R ∨ M )

R ∧ ¬M

However, having said that, boolean logic has the limitation it cannot model uncertainty, and many people when commonly using “if” are conveying an element of meta-knowledge about unknowns. Then you get to three value logic which is a whole new ballpark.

http://en.wikipedia.org/wiki/Three-valued_logic

This leads to some arguable simplifications, for example, in 3VL what is the value of (R ∧ ¬R) when R is UNKNOWN? The answer should be FALSE but you can’t get there by applying the operators. Then you go down the weirdness of N-value logic algebra (for amusement purposes only).

“By the way, based on boolean logic, the exact opposite of the sentence “if it rains, mushrooms grow”, would be “it did rain and mushrooms are not growing”.”

As I understand it, the second proposition is the negation, not the opposite of the first. The first is a statement that identifies a cause-effect relationship, one of sufficiency, between two events. The second describes a particular instance where event 1 (the supposed cause) happened but event 2 (the predicted effect) did not follow. It disputes the sufficiency of event 1 for the occurrence of event 2, thus questioning the veracity of the first proposition. It demonstrates it to be a false statement of the relationship between events 1 and 2.

It may be a minor quibble, but I just thought I’d point it out all the same.

Actually, Albrecht himself points out (inadvertently) a danger of math-heavy thinking. He mentions that one of his fellow students showed him that he needs to assume finite goods to show preferences are discontinuous. If there are infinite goods, then you can have continuous preferences. This is technically correct, but it’s nonsense. There is no such thing, and can be no such thing in our world, as infinite goods. Keep in mind, you don’t need “lots and lots” of goods, you need “infinite” goods. These are completely different things..

This is the danger of overuse of math. You lose the economics for the math. I have found in the reading I’ve done that good economics are often sacrificed for mathematical complexity.

“But their point isn’t, “Math is stupid and a waste of time.”

You play with words. Most austrians think “Math is stupid and a waste of time in Economics”. I think it is a mistake to have such a radical view on mathematics applied in economics. Math is useful to some extent in the social sciences.

Too bad some Austrians still do not want to admit. I agree with most of the austrian ideas in economics except on the issue of Math.

I think you are the one playing with words. The premise of the original post is as you state. Bob is refuting that premise, and gave very specific reasons. Since Albrecht provided no support for the premise, do you have an examples?

*any examples

Bob, don’t you think he was just engaged in hyperbole, and meant “hate math” as “disdain the use of math and economics quote?

Well he writes this at one point Gene:

Careful readers will have noticed something by now. I’m not urging Austrian economists to study mathematical economics. No. My central point is smaller. Study math, The Real Thing.Which Austrian would disagree with that? Not Mises. Not Rothbard. Not Murphy.

He even, in the very beginning, said his statement was a broad brush stroke but that he stands behind it. So it certainly sounds like he meant it, and not a much weaker claim.

Well, people do “stand behind” hyperbolic claims, so long as the reader interprets them as hyperbolic!

OK, so what is the claim he is standing behind Gene? It can’t be, “Austrians hate using math in their economics, and I think that’s wrong,” because later on he explicitly says that’s *not* what he’s arguing.

He’s says he wants Austrians to study mathematics on its own, because this will make them better Austrian economists. I want to know a single famous Austrian who would disagree with that.

I give a sketch of a proof of the Pythagorean theorem in my principles book as an example of deductive reasoning from axioms. Do you think any Austrian would get mad at me for bringing hated mathematics into a discussion of economic theory?

Dictating! Was supposed to read “disdain the use of math in economics.”

Speaking of Austrian economists with famous mathematician relatives, there’s also Carl Menger’s son Karl Menger.

It would probably have come as a surprise to him to hear it suggested that the disciples of his father “hate mathematics.”

I myself am quite fond of mathematics, it being my area of study apart from all my other interests I spend my free time on. What I am not terribly impressed by (nor for that matter was the Mathematician turned Economist John von Neumann) are attempts to reduce the whole of economics to linear algebra. But I rather think of economics as a particular application of formal logic.

Slightly off topic, but Krugman has come up with yet another definition of “austerity”:

http://krugman.blogs.nytimes.com/2015/01/06/the-record-of-austerity/

It would seem that now “austerity” means change in government spending. Forget about debt, forget deficits, forget about interest rates, forget about QE (totally irrelevant), forget about tax, those are no longer important (not what Krugman used to say but who is surprised). Strangely since government spending is directly fed into the GDP equation, there’s also an immediate correlation in the first derivatives… this is deep, must mean something.

Keynesian economists hate math. That’s a broad brushstroke, but I stand by it.

😉

By way of explanation, the first (perhaps only??) rule of math is be Konsistent, and don’t Kontradict yourself.