Thursday, April 7, 2016

The mathematics is not the issue here, Dude

Wishy thinking.

I had a conversation on Twitter with Mike Sankowski, who thought I might have misread an essay at Aeon about how economics was a pseudoscience obscured by math, and perhaps I did.

I had linked to an earlier post I had written about using math. My point was that pseudoscience can happen with or without math. Therefore it's not the math that's the problem -- it's the wishy thinking, ideology, or unquestioned assumptions.

But after my conversation with Mike and a re-read of the article I realize there was a thread that I missed -- because I don't see math that way. Here are some quotes from the author as well as quotes from economists selected by the author:
But the ubiquity of mathematical theory in economics also has serious downsides: it creates a high barrier to entry for those who want to participate in the professional dialogue, and makes checking someone’s work excessively laborious. Worst of all, it imbues economic theory with unearned empirical authority. 
... mathematics in economic theory serves, in McCloskey’s words, primarily to deliver the message ‘Look at how very scientific I am.’ 
Krugman named economists’ ‘desire ... to show off their mathematical prowess’ 
When mathematical theory is the ultimate arbiter of truth, it becomes difficult to see the difference between science and pseudoscience

I take it you've read through those quotes. Now change math to something challenging to learn but that you've conquered in your own field and re-read them. Try putting French, oil painting, or drafting in the place of math. 'Look how very artistic I am.' 'desire ... to show off their French prowess'. English probably creates a higher barrier to entry for much of the world to participate in the economic dialog than math.

The thing is that if you know math, none of these things are true. If you know math, it doesn't imbue things with empirical authority. If you know math, checking work isn't excessively laborious. If you know math, it isn't difficult to tell the difference between science and pseudoscience.

If you know math, the people you might want to impress with your mathematical knowledge probably also have that mathematical knowledge. I can assure you that impressing a high school student with my math skills doesn't give me a sense of pride. Teaching one how to use math does. No one who knows economics-level math is going to be impressed with your economics-level math. I have never been impressed by math [1], but I have been impressed the insight math communicates. If you have an insight into human nature, I am impressed with the insight, not the vocabulary you express it with. Anyway, any time hear people say economists try to impress people with their math skills it makes me chuckle. Those skills could only be impressive to people who don't have them.

The insight here is that math is seen by the mathless as 1) a barrier to entry, 2) a pure signalling strategy, 3) difficult, and 4) a veneer of respectability, empirical accuracy, etc. It's not seen as legitimate or necessary. This is belied by this quote:
Fortunately, non-experts also participate in the market for economic theory.
Imagine the variants:
Fortunately, non-experts also participate in nuclear reactor design. 
Fortunately, non-experts also participate in commercial aircraft design.
The difference is that the educational and experience barriers to entry in the latter two are seen as legitimate. Why the difference?

I came up with an a good analogy ...
When technology is applied to cell phones, it's seen as a gee whiz factor (even if they monitor your GPS location), but when technology is applied to voting (e.g. the Diebold voting machine controversy in the US) it's seen as a barrier to transparency.
There are two factors here. First, we intuitively understand how voting works (or at least think we do). Second, we see the inner workings of voting as more important than the inner workings of a cell phone.

Because we feel we should understand how voting works [2], and it's important to us, technology is a obfuscating barrier. Because no one cares how a cell phone works [3], technology is seen as a wonder.

I think this is what is happening with math. Everyone thinks they should intuitively understand economics, and money is important to them. Therefore the math is an obfuscating barrier. No one thinks they should understand quantum field theory, and it's results don't impact our day to day lives much, so math is just seen as part of the wonder. I think that's why physics blogs are different from economics blogs.

The technology and the math are not the issue here. It's the gulf between the desire to understand and the capacity to understand something important.

The thing is that mathematics is behind some of the greatest advances in understanding in physics. And sometimes the math came before the intuition. Newton left some of the calculus out of his book because he felt more people would understand what he was talking about if he just used trigonometry. But Newton understood it in terms of calculus. Heisenberg confused everyone with his matrix mechanics, but it got the answers right. Quantum mechanics became more broadly accepted when Schrodinger showed how it works with differential equations that were more commonly used in physics at the time. However, most modern physicists understand quantum mechanics in terms of matrix elements (Dirac showed how the two fit together). Einstein's work led to tensor fields and differential geometry becoming a bigger part of physics. [Update: see comments below. Einstein's insight into general relativity came from Minkowski's mathematical representation of special relativity as a 4D space-time.]

In these cases, it was the lack of understanding of math that was the barrier to initial understanding. Later on, when things became well understood, quantum physics became the subject of popular books. I imagine that if some quantum device was to be used to encrypt your bank account information in the 1930s, people would have been up in arms about physics being just a veneer of respectability over some kind of Ponzi scheme. And that's the crux: economics isn't well understood, so it's not yet amenable to transparent talk and clear diagrams. But it deals with employment and money, so it's important to people.

It's completely understandable that people are angry and want to forego the math to see what's really going on.


PS I have a solution: nihilism. Macroeconomic policy doesn't seem to be that important to actual outcomes according to the information equilibrium framework, and most of the macroeconomics coming from the pros seems to be wrong. If you find the math to be obfuscating, just realize that if you were to get through it, there's not much you're missing out on in terms of policy-relevant knowledge. If you find the math to be obfuscating, just realize you can ignore macroeconomics and expect zero impact on your life.



A response that gets into Wittgenstein and Plato from Tom Hickey.

Also, I think I should have kept to solely The Big Lebowski references instead of combining them with ones from The IT Crowd.


Update 12 April 2016

Noah Smith has weighed in favorably on the Aeon article, so you might be interested in an different take. While I agree with the points made by Pfleiderer and about Lucas, neither have anything to do with math (Pfleiderer's point about chameleon models is Holbo's two step of terrific triviality and Lucas tried to evade empirical discipline, respectively). And my opinion of Paul Romer's mathiness claim has been made known here. Put simply economists do not understand limits in the context of extant reality.

The subtitle of the article reads:
By fetishising mathematical models, economists turned economics into a highly paid pseudoscience

However it has nothing to do with math, but rather politics and uninformative data.


[1] At least in the service of real world applications. People who are good at pure math still amaze me. Take Terry Tao for instance. My math skills, meager as they are compared to the likes of most theoretical physicists (part of the reason I didn't go the postdoc route), nearly entirely derive from my intuition about the physical systems the math represents. If I understand the system, the math follows. If I don't, the math is hard. It's really like any other language. If I know what I'm talking about, the words flow easily. If I don't, then they don't.

[2] I say feel because many of us don't actually know how it works. In presidential elections there's the whole elector business. But even in Washington state, there were people who were going to mail in their ballot for the primary for the Democratic nominee and not attend the caucus. The primary doesn't count for Democratic delegates in Washington.

[3] One of my favorite facts is that the GPS in your cell phone depends on Einstein's theory of general relativity to work, which is behind the accurate predictions of the big bang theory. Couple that with the knowledge that I'm sure there are young Earth creationists who use the GPS on their cell phone.


  1. Economic insight gives understanding.

    Maths does not give economic insight.

    Maths gives results.

    1. "Economic insight gives understanding."

      Insight and understanding are synonyms. ... so you are saying "economic understanding gives understanding".

      "Maths does not give economic insight."

      How do you know this? Are there economic insights (i.e correct economic theories)? Have all mathematical approached been tried?

      Is there some logical proof that math is incapable of representing economics? Ironically, that would be math giving an insight into economics!

      It's fuzzy thinking and fuzzy language like this that warrants a mathematical approach to economics. I have no idea what you mean or how you arrived at it.

    2. Playing semantic games will keep you from having insights.

      Einstein's insightful imagining that mass distorts space-time came before his application of tensor mathematics to the problem.

      Mathematics is a tool. It is not the insight/understanding itself.

    3. You are wrong about general relativity. Let's ask Einstein himself:

      "I mused incessantly over the problem [gravitation]. ... Of importance here proved to be Hermann Minkowski's analysis of the formal basis of the special theory of relativity"

      Tensor formulation (Minkowski) comes first, then insight into general relativity. I assume you just made that up on the fly. Your error should have been obvious from what you typed. How do you have a concept of "space-time" that can be distorted without the 4-vector representation?


      "Playing semantic games will keep you from having insights."

      To which I reply

      "Non-judgment inspires the doorway to boundaries"

    4. More Einstein [ibid.]

      "I am now occupied exclusively with the gravitational problem, and believe that I can overcome all difficulties with the help of a local mathematician friend. But one thing is certain, never before in my life have I troubled myself over anything so much, and that I have gained great respect for mathematics, whose more subtle parts I considered until now, in my ignorance, as pure luxury! Compared with this problem, the original theory of relativity is childish."

    5. If you look more closely at the development of Einstein's thinking on general relativity you will see that there was considerable conceptual development before 1912, at which time his collaboration with Grossman began, and even before 1910. Your quotes above relate to the period after 1910. Einstein first realized that matter distorts space-time then went about looking for the mathematics with which he could formalize his theory. He had predicted the gravitational bending of light in 1907. The insights and conceptual development came first. The mathematics later.

      "Non-judgment inspires the doorway to boundaries"

      How silly and inappropriate a quote. Chopra is talking about pathways to ultimate consciousness not intellectual insights.

    6. Einstein first realized that matter distorts space-time then went about looking for the mathematics with which he could formalize his theory.


      There is no such thing as "space-time" (a 4D manifold) before Minkowski invented it. Minkowski died in 1909 and he published his 4D formulation in 1907. He was Einstein's former teacher. It's called Minkowski space-time for chrissake.

      Since there was no such thing as space-time without Minkowski, Einstein could not have imagined gravity as distortions of something that didn't exist and that he did not invent.

      Additionally, Einstein's 1908 publication of bending light had nothing to do with space-time curvature, but rather was a simple scattering calculation [pdf]. It is incorrect (the correct approach shown in the pdf). And the simple scattering approach is incorrect precisely because it misses the curvature of space-time.

    7. Minkowski's space-time applies to non-accelerated frames of reference and special relativity. It was Einstein who conceived of curved space-time applicable to accelerated frames of reference which developed into general relativity.

    8. "...nearly entirely derive from my intuition about the physical systems the math represents. If I understand the system, the math follows."

      Hoist by your own petard.

    9. It was Einstein who conceived of curved space-time applicable to accelerated frames of reference which developed into general relativity.

      I'm not sure you quite understand this subject. Let me rewrite this sentence for you in a way that may help you realize that spacetime (curved or not) does not exist without Minkowski's math.

      It was Einstein who conceived of locally Minkowski space-time applicable to accelerated frames of reference which developed into general relativity.

      If you mention space time again without mentioning Minkowski you obviously don't grasp general relativity.


      And you left off the first part of my sentence:

      "My math skills, meager as they are compared to the likes of most theoretical physicists ..., nearly entirely derive from my intuition about the physical systems the math represents."

      You caught me. I'm not Einstein. I'm not as good at seeing how pure mathematical structures can have physical applications.

      I wasn't talking about Einsteins math, but my own.

      Apparently you know better than Einstein himself does about the influence Einstein's teacher Minkowski had on Einstein!


    10. "I'm not sure you quite understand this subject. Let me rewrite this sentence for you in a way that may help you realize that spacetime (curved or not) does not exist without Minkowski's math."

      So what?

      It was Einstein that conceived the next step. It was his insight that made the next step possible.

      You just cannot admit that you have it wrong.

      "I wasn't talking about Einsteins math, but my own."

      Again, so what?

      Your admission supports my argument.

      Einstein may have considered how Minkowski's formulations might have been adapted to accelerated frames of reference, but it was Einstein that made the conceptual leap to curved space. Then he had to find a mathematics to formally describe it.

    11. "I'm not Einstein. I'm not as good at seeing how pure mathematical structures can have physical applications."

      I'm not so sure Einstein was that good either. That's why he had to enlist the help of Grossman. In other the words the mathematics did not inform his conceptualization of the application of relativity to gravity.

    12. "In other the words the mathematics did not inform [Einstein's] conceptualization of the application of relativity to gravity."

      Even though Einstein said it did.

      Have you seen Annie Hall?

  2. It's fuzzy thinking and fuzzy language like this that warrants a mathematical approach to economics. I have no idea what you mean or how you arrived at it.

    I couldn't possibly agree more. That comment is composed of three attempted aphorisms: they are supposed to convey deep general self-evident truths in a terse manner, but in reality they just beg the questions. The end result is vacuous pomposity.

    Apply that to the much longer Hickey reply and see what you get. Good luck!

    B.L. Zebub

    1. " The end result is vacuous pomposity."

      Yeah, but so what?

  3. Jason, thanks for that link to Terry's Tao's blog. I read through... interesting, but I found it to be riddled with errors, so I did him the favor of setting him straight. (@_@)

    1. I'm not entirely sure what he is saying most of the time either.

  4. Jason,

    Let me first say that I sympathize with your position. I do believe maths is necessary in economics. By itself it doesn't make economics "scientific", but it does help clarifying ideas. This advantage, however, comes at a cost: to understand economics, now it's necessary to understand maths.

    With that out of the way: this subject of maths in economics is rather complex and full of nuances. To make things worse, often the critics of maths in economics choose unclear language.

    The Aeon article -- in my opinion -- contains only a mild criticism of maths in economics. Granted, comparing economics with astrology (Chinese or otherwise) was provocative and this may suggest Alan Jay Levinovitz is too radical. In my reading, however, that perception is not accurate. I might be mistaken, but Levinovitz is not calling to abandon maths altogether.

    Maybe the best way to understand that is by comparing Levinovitz's article to a paper entitled "Mathematical Modelling and Ideology in the Economics Academy", by Tony Lawson (the link is below). Lawson is a professor of economics and philosophy at Cambridge University and a mathematician, by training.

    To give you some context on Lawson's paper: it was part of a debate between him and a group of heterodox economists on the issue of ideology vs maths as the reason why neoclassical economics is a failure. The paper, in other words, is targeted to those other heterodox economists.

    I don't want to frame your own perception of the paper, so I'll leave you to judge it by yourself. My only suggestion is to ask yourself what is Lawson's main conclusion?

    (There are other things you could think of, like when compared to the Levinovitz article, what kind of evidence Lawson presents? If you are familiar with the history of economic thought, when did the mathematization of economics first begin? Are all contemporary schools of economic thought equally mathematized, and do all of them disagree in their basic policy prescriptions? But all this is optional and not needed to get the gist of his argument, only to evaluate it)

    Good hunting.

    B.L. Zebub

    1. I had to take some time to unscramble exactly what was being said in that paper. In the introduction, (almost) every new concept is given a new term that doesn't have its usual definition.

      The specific conditions required for the sorts of mathematical methods that economists continually wield to be generally applicable, I have shown, are a ubiquity of (deterministic or stochastic) closed systems. A closed system is simply one in which an event regularity occurs. ...

      Employing the term deductivism to denote the thesis that closed systems are essential to social scientific explanation (whether the event regularities, correlations, uniformities, laws, etc., are either a prior constructions or a posterior observations), I conclude that the fundamental source of the discipline’s numerous, widespread and long lived problems and failings is precisely the emphasis placed upon forms of mathematical deductivist reasoning.

      Deductivism (here) = systems with event regularities are essential to social scientific explanation
      Deductivism (elsewhere) = inference from true premises does not lead to false conclusions

      Closed system (here) = system where an event regularity occurs
      Closed system (elsewhere) = a system that does not allow transfers in or out of the system

      In reality, "closed system" is closer to Hume's idea of the uniformity of nature (I have no idea because "event regularity" is never defined), which is something you have to accept if you want to employ any kind of scientific inductive reasoning from a few observations.

      But after reading and re-reading the introduction, I gathered Lawson's thesis is that the fundamental source of economics' problems is its emphasis on using math to describe things that regularly happen.

      The possible solutions to this seem to be that economists should either 1) tackle things that never happen the same way (how could you possibly do this?) or 2) not use math for things that regularly happen (even though it was invented precisely for this purpose).

      Later on, Lawson says:

      ... doctrine that all serious economics must take the form of mathematical modelling [pervades economics].

      The thing is, everything we observe as an economic fact is a number. Interest rates, unemployment rates, prices, inflation, recessions (changes in numbers). What are you going to talk about in economics if you're not going to refer to these numbers? Who does this? And why shouldn't you, as a general rule, use mathematics to talk about numbers?

    2. On comparing economics to astrology

      I have reluctantly come to the view that economics is roughly at the stage of premodern science, or scholasticism. It has its Brahes but no Keplers yet, no Galileos, no Newtons. That does not mean that it is unscientific, but it is only weakly empirical. And, from what I hear, it has become less empirical since the mid 20th century, and at the same time has become more mathematical. Whether the math is a cover for the lack of empirical rigor I don't know.

      In the pre-modern period European university students studied astrology. Even Newton did not renounce it, and he pursued alchemy, probably to the point that it impaired both his physical and mental health. Astrology was not regarded as it is today, nor was it simply fortune telling. It was used to organize a good bit of knowledge, not just astronomy but medicine, biology, psychology, and social and political knowledge, adn probably other fields besides. So to compare economics to astrology in historical context, as the article does, is not as demeaning as it might seem.

    3. BTW, I mean that inhaling poisonous gases probably impaired Newton's health, not that belief in alchemy did so. :)

    4. @Jason (April 9, 2016 at 8:53 PM)

      I don't want to put my ideas in your head, but I suspect by now this will not surprise you: to me, Lawson's position is utterly nihilistic.

      In other words, his criticism of maths in economics is way more radical than Levinovitz's. That's the comparison one needs to put Levinovitz in perspective.

      B.L. Zebub

    5. Incidentally, whether that is good or bad is for you to decide.

      B.L. Zebub

    6. "On comparing economics to astrology"

      At least astrologers were able to accurately time the movements of the heavenly bodies.

    7. "At least astrologers were able to accurately time the movements of the heavenly bodies."

      And of course this highlights the fundamental difference between the natural sciences and the social sciences - natural phenomena can be understood and predicted by the application of unchanging laws (well more or less) while social phenomena are ephemeral. Physicists and mathematicians and most modern economists fail to understand this.

    8. "while social phenomena are ephemeral"

      Ha! I dare you to support that with evidence.

      People always say that kind of stuff to sound "very serious". But there are a lot of very well established regularities in economics. For example Okun's law. And here's some evidence that you're mistaken:

      Ephemeral = 60+ years?

      How about 200+ years?

    9. "Ephemeral = 60+ years?

      How about 200+ years?"

      Let's not quibble - let's call it an eon - by then we will all have been fated to heat death.

  5. I like Kenneth Boulding's quip:

    "Mathematics brought rigor to economics. Unfortunately it also brought mortis."


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