Tuesday, May 12, 2015

Leeches, a rant

Editor's note: I didn't post this at the time ... but I was going through my backlog of unfinished posts and random ideas over my lunch break and found this to be pretty entertaining on a re-read. It's a bit unfair to macroeconomists, but if any of you out there are interested in my views on macroeconomics in one of my more bitter moods, this is a good one .... it's for entertainment purposes only. I generally think academic macroeconomists do a good job given the limited data -- it's a tough field!


Prescribing leeches. From Wikimedia commons.
A working macroeconomist reading [Keynesian proponents] Krugman and DeLong feels as a doctor would if the Surgeon General got up and said that the way to cure cancer was to draw blood using leeches.
That is David Levine, cited approvingly by John Cochrane.

I apologize in advance for what is basically a rant.

From my experience slowly learning the subject of macroeconomics, looking through the imported mathematical machinery, I would actually say that the current state of the art in macro is not just leeches, but abstract mathematical models of idealized leeches.

I have some advice that should apply all around -- to Krugman, DeLong, Levine, Cochrane, Samuelson, Sumner and every other macroeconomist: you do not understand your field very well. Sure, you understand it much better than I do or some random person off the street. But the sum total of macroeconomic knowledge seems to be effectively zero [the random person's knowledge seems to be negative on average]. I have been through a first year graduate textbook on macroeconomics. There is quite literally nothing in it on the subject of figuring out how an economy works. There are models of things that have results that may or may not reflect real economic behavior. There are collections of potential effects. Are they real? Who knows? Who cares? There are a couple of plots of data -- mostly to illustrate that the real world actually irrefutably violates the assumptions of the models. In the end, it is a math book that sets about solving different simplifications of a problem it made up.

It feels like studying Galois theory -- a topic from mathematics that seems to just exist to solve a single problem (why is there no quintic equation) for which there is no real-world application. Macro differs from string theory, about which many physicists have a similar opinion, in that string theory seems to be mildly concerned that it is supposed to be a physical theory of things that exist.

Keynes is like the application of leeches, huh? My own opinion is that the era of Fisher through Keynes and Samuelson is the era where the language of mathematics was introduced to economics. The study of the Great Depression is akin to the Cholera outbreak of the mid 1800's in London and its effect on epidemiology. That would put economics about 100 years behind medicine (not because it is backward, but because good data wasn't available). With that analogy, it should have felt to Levine as if the Surgeon General got up and said the way to cure cancer is to collect population data and do statistical analysis. Leeches would be more like going back to Hume.

One issue when you are immersed in a subject is that you tend to think of the current state of the art being comparable to the current state of the art in other fields. In general these things cannot be compared except by analogies ... and the problem there is that you are making analogies between things that are not understood.

But I'm going to do it anyway.

In the following, the word "know" is used in the sense that not only do all mainstream macroeconomists agree on the details, but that the formulation of the problem and its solution is effectively the same across textbooks. In physics, the details of the mechanism behind the Lamb shift are taught pretty much identically in every textbook and all physicists agree that it is a real effect with an uncontroversial empirical value. In that sense, physicists "know" the Lamb shift.

Macroeconomics does not currently know what money is or does

There are various theories out there about how money acquires value -- some involving the fact that fiat money can be used to pay taxes, others involving more social mechanisms, still others based on expectations of agents. There are current arguments in the literature about whether monetary policy has a strong effect on most economies (or just some economies) or not.

In medicine this is a bit like not understanding the function of food. I'm not talking about details like what kind of diet is best, but rather broad things like how (or whether) food provides energy.

An equivalent unresolved problem in physics is dark energy in cosmology. Dark energy behaves in a particular way in General Relativity (that's where it gets its name), but its microscopic origin is unknown. There are theories involving cancellation in the quantum fluctuations of elementary particles or that it results from properties of the string theory vacuum based on the so-called anthropic principle. It's basically a complete mystery that I'd say is on the level of money in macroeconomics. You'd hear a different story from different economists about the value of money much like you'd hear a different story from different physicists about the nature of dark energy.

Macroeconomics does not currently know what causes recessions or what they are

Some economists think that recessions a normal function of an economy. Some believe that they can be mitigated by government policy to great advantage.

If this were medicine, it would represent a state of the art that did not agree as to whether someone was actually sick or not. Is the illness doing what needs to be done to the body to eliminate inefficiency? Or should we give the patient a fever reducer?

I had a hard time coming up with a good physics analogy here. Should I use the hypothetical Unruh effect? Gamma ray bursts? Baryon asymmetry? The stong CP problem? High temperature superconductivitySonoluminescence?

But I've settled on the arrow of time. Some physicists think this is solved by entropy. However it doesn't make sense that the initial state of the universe (i.e. nearly uniform energy in the big bang) should be low entropy compared to today. In a sense, we have no real reason for time to flow in any particular direction and some fun results -- like quantizing the Wheeler-deWitt equation resulting in time dropping out of the model completely -- end up with a confused mess (or radical simplification, depending on your viewpoint).

...

Considering the unsolved problems in economics, leeches would actually represent a step forward from not understanding what food is or whether the patient is sick!

16 comments:

  1. Preach it, brother! Could not agree more.

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  2. Preach it, brother! Could not agree more.

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  3. Rcessions are caused by a demand or supply shock. Everyone knows that!

    But don't ask me what a demand/supply shock is because I don't know.

    You can use Galois Theory to prove that squaring the circle is impossible, but I admit that this is not a very real-worldish application.

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    1. Except in the case where they are caused by changes in productivity (i.e. RBC) ...

      I think the constructibility proofs came much later ... when people were trying desperately to figure out other uses for it :)

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  4. It feels like studying Galois theory -- a topic from mathematics that seems to just exist to solve a single problem (why is there no quintic equation) for which there is no real-world application.

    Hard to think of a worse example than Galois Theory.
    Hermann Weyl, Symmetry, ρ 138.
    "Galois' ideas, which for several decades remained a book with seven seals but later exerted a more and more profound influence upon the whole development of mathematics, are contained in a farewell letter written to a friend on the eve of his death, which he met in a silly duel at the age of twenty-one. This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind."

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    1. Galois life was pretty epic, and his idea to look at the connections between field and group theory were a good example of great mathematical works. But contra Weyl, the results themselves have little application and many mathematicians go through undergraduate (and even graduate) education without ever studying it. It has no application in physics or any other science.

      I studied it as part of my math degree. It's a great example of doing mathematics, but the results themselves have no real world application -- exactly the point I was trying to make about economics! It's some really nice theory with some fun math, but no (apparent) real world application!

      What specifically is Weyl basing his claims on?

      Here's a modern math professor asking whether Galois theory is necessary:

      http://mathoverflow.net/questions/34125/is-galois-theory-necessary-in-a-basic-graduate-algebra-course

      Galois is super cool, though!

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    2. Weyl thinks Galois theory is a good example of math, not an end in and of itself:


      Turning from physics to mathematics, [Weyl] gives an extraordinarily concise epitome of Galois theory, leading up to the statement of his guiding principle: "Whenever you have to do with a structure-endowed entity, try to determine its group of automorphisms".


      http://www-history.mcs.st-andrews.ac.uk/history/Biographies/Weyl.html

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  5. Aaargh. Frankly, I find such anti-historicism horrifying. It is like criticizing Aristotle & Shakespeare for being full of platitudes and cliches, or worse not noticing that your mom bought the cliches you are speaking in from A & S. Galois Theory is the first and most easily graspable instance of enormously important concepts in mathematics and physics - giving birth to group theory, field theory (not applying one to another) and abstract algebra and in turn being founded on high-school algebra as a treatment by Arnol'd or Abhyankar might give. Weyl was talking about basically all the mathematics of the rest of the 19th century and the Galoisian spirit of the 20th (Hilbert/Noether/ Van der Waerden/Bourbaki). And both in the abstract as above and the concrete, the conscious way that Galois's theory inspired Riemann Surfaces/Complex Analysis/Function fields and through that the development of the fundamental group by Poincare on the one hand, (people more knowledgeable than me have said that some of this seems to be in Galois already) and the continuous world of Lie theory to which Weyl made so many contributions. Weil, Grothendieck etc of course made it clear that the algebraic topological fundamental group was not merely analogous to Galois theory, e.g. of function fields/ riemann surfaces which it had descended from, but unified, subsumed both in general theories. Klein's solution of the quintic, a quintic formula, in his classic The Icosahedron IIRC was another return to the roots / further development, as was all of his & Poincare's work in modular forms / discrete subgroups of Lie Groups to be anachronistic. Elliptic curve cryptography, the elliptic curves stemming from the RS / galois theory stream of Galois, over the Galois (Finite) Fields stemming from another, are used in everyone's cell phones.

    It has no application in physics or any other science. No, everything is an application of it. Weyl's gauge theory, sheaf / fibre bundle theory (generalized from the discrete, galois case) is inconceivable without it.

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    1. I think we have different definitions of "Galois theory" -- your definition seems to be the mathematics used by Evariste Galois while my definition is the mathematics of Galois groups.

      Galois theory ≠ group theory

      Also Ruffini and Lagrange came up with the ideas about permutation groups that Galois extended. I guess he came up with the name "group", but if you've ever had a class on group theory you know that there are lots of theorems due to Lagrange.

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  6. Entertaining rant Jason. I've encountered a Galois field in error correction (and I'm familiar w/ Galois' brief life story, and his role with proving no guarantee of closed form solution to quintics and above), but after reading the comments here I can see that Galois fields probably have little or nothing to do with Galois theory. I certainly have no idea! It's always fun to encounter vast new regions of my ignorance.

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    1. The relationship appears to be that they call finite fields Galois fields, but the results in error correction have more to do with Sylow theorems ... but maybe there is more to it than that ...

      https://en.wikipedia.org/wiki/Sylow_theorems

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    2. To clarify:

      Galois theory has to do with the automorphism groups of field extensions (Galois groups), whereas Galois fields are just another name for finite fields -- one that I don't remember using, but maybe we did -- which you can talk about independently of Galois theory.

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    3. Thanks. I'd never heard of Sylow theorems before.

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    4. It just seems like this would lead to confusion.

      Wikipedia just re-directs Galois field to finite field:

      https://en.wikipedia.org/w/index.php?title=Galois_field&redirect=no

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    5. Ha!... well, I encountered them again this month when asked to size a Reed-Solomon encoder/decoder in terms of computational requirements (I looked at FPGAs). I've seen Galois fields discussed in processor instruction set documentation. Here's an example. I wonder why they latched onto that name?

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