## Economists — math-heavy astrologers

from **Lars Syll**

Ultimately, the problem isn’t with worshipping models of the stars, but rather with uncritical worship of the language used to model them, and nowhere is this more prevalent than in economics. The economist Paul Romer at New York University has recently begun calling attention to an issue he dubs ‘mathiness’ – first in the paper ‘Mathiness in the Theory of Economic Growth’ (2015) and then in a series of blog posts. Romer believes that macroeconomics, plagued by mathiness, is failing to progress as a true science should, and compares debates among economists to those between 16th-century advocates of heliocentrism and geocentrism. Mathematics, he acknowledges, can help economists to clarify their thinking and reasoning. 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.

‘I’ve come to the position that there should be a stronger bias against the use of math,’ Romer explained to me. ‘If somebody came and said: “Look, I have this Earth-changing insight about economics, but the only way I can express it is by making use of the quirks of the Latin language”, we’d say go to hell, unless they could convince us it was really essential. The burden of proof is on them.’

Right now, however, there is widespread bias in favour of using mathematics. The success of math-heavy disciplines such as physics and chemistry has granted mathematical formulas with decisive authoritative force. Lord Kelvin, the 19th-century mathematical physicist, expressed this quantitative obsession:

“When you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it… in numbers, your knowledge is of a meagre and unsatisfactory kind.”

The trouble with Kelvin’s statement is that measurement and mathematics do not guarantee the status of science – they guarantee only the semblance of science. When the presumptions or conclusions of a scientific theory are absurd or simply false, the theory ought to be questioned and, eventually, rejected. The discipline of economics, however, is presently so blinkered by the talismanic authority of mathematics that theories go overvalued and unchecked.

One might note that Romer’s actual argument is dubious even if one can select useful quotes from him. The AER argument concerns who has the best model for growth theory… it is a purposive critique of other’s maths to prioritise models and principles that are no better… its concept of science is also untenable

Mathiness certainly has its attractions; models, no matter how complex, are still easier to deal with than real human beings.

This is nothing new. Aristotle wrote in the Nicomachean Ethics that ” our discussion will be adequate if it has as much clearness as the subject matter admits, for precision is not to be sought for alike in all discussions,… for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits… “

Mathiness is NOT the problem — scientific incompetence is

Comment on Lars Syll on ‘Economists — math-heavy astrologers’

“The economist Paul Romer at New York University has recently begun calling attention to an issue he dubs ‘mathiness’ …” (see intro). This is somewhat beside the point. First of all, Paul Romer rediscovered a phenomenon that is as old as neoclassical economics: “Mr. Stanley Jevons, and M. Walras, of Lausanne, without communication, and almost simultaneously, have worked out a ‘mathematical’ theory of Political Economy; — and anyone who thinks what is ordinarily taught in England objectionable, because it is too little concrete in its method, and looks too unlike life and business, had better try the new doctrine, which he will find to be much worse on these points than the old.” (Bagehot, 1885, PE. 27)

Secondly, Paul Romer messes the whole issue up with a false analogy: “Romer believes that macroeconomics, plagued by mathiness, is failing to progress as a true science should, and compares debates among economists to those between 16th-century advocates of heliocentrism and geocentrism.” (See intro)

As a matter of fact, the debates of the advocates of heliocentrism and geocentrism were strictly PHYSICAL, i.e. about whether the earth stands still and the sun moves or just the other way round, and mathematics/geometry was only insofar an issue as it has been assumed since Plato that planetary orbits must be perfect circles.

So, if the current macroeconomic debates resemble anything medieval then the debates about how many angels can dance on a pinpoint. This debate was indeed vacuous because angels are NONENTITIES. In contradistinction, the debate about heliocentrism and geocentrism had REAL content. Likewise, the question whether planetary orbits are circles or ellipses had REAL content. And this is why the measurements of Brahe became decisive. Physicists NEVER had a mathiness problem, only economists have.

As an economist, Romer does not understand what science is all about. This is not a big problem, though, because his fellow economists have no idea either.

Non-science or pseudo-science is easily recognizable. It is much harder with what Feynman called cargo cult science: “So I call these things cargo cult science, because they follow all the apparent precepts and forms of scientific investigation, but they’re missing something essential, …”*

What is missing? Clearly, macroeconomic theory lacks content. The fatal defect is the vacuousness of fundamental concepts like utility, optimization, equilibrium, production function, capital, perfect competition, demand function, etcetera. All these concepts are NONENTITIES like angels or the Easter Bunny. It is NOT formalization that has to be criticized in the first place, it is the all pervasive green cheese assumptionism which has become the hallmark of current macro.

Ultimately, nonentities cannot be formalized. With superficial and faulty formalization economists abuse mathematics: “When very sound and proper mathematics is misused and misapplied to fairyland problems without any basis in the real world, that fact that the mathematics itself is impeccable makes the whole obnoxious game just that more offensive.” (Blatt, 1983, p. 173)

But things are even worse. Mathematical economists do not really understand the math that they apply. This, too, is not news: “The so-called ‘mathematical’ economists in the narrower sense — Walras, Pareto, Fisher, Cassel, and hosts of other later ones — especially, have completely failed even to see the task that was before them. Professor Hicks has to be added to this list, which is regrettable because he wrote several years after decisive work had been done — in principle — by J. von Neumann and A. Wald. (Morgenstern, 1941, p. 369)

The project of the proper formalization of economics, though, had one fatal drawback: von Neumann left the underlying theory untouched: “But this [establishing the analytic mother-structure] required one very crucial maneuver that was nowhere stated explicitly: namely, that the model of Walrasian general equilibrium was the root structure from which all further work in economics would eventuate.” (Weintraub, 2002, p. 121)

This means that von Neumann swallowed all the vacuous concepts of Walrasianism from utility to equilibrium: “In any event, it seems that Morgenstern finally convinced von Neumann that they must proceed tactically by means of the conciliatory move of phrasing the payoffs in terms of an entity called ‘utility’, but one that von Neumann would demonstrate was cardinal — in other words, for all practical purposes indistinguishable from money …” (Mirowski, 2002, p. 127)

So, we arrive at the proper definition of mathiness as FORMALIZATION OF NONENTITIES. As genuine cargo cult scientists economists habitually apply mathematics without deeper understanding: “The mathematical language used to formulate a theory is usually taken for granted. However, it should be recognized that most of mathematics used in physics was developed to meet the theoretical needs of physics. … The moral is that the symbolic calculus employed by a scientific theory should be tailored to the theory, not the other way round.” (Wittgenstein, quoted in Schmiechen, 2009, p. 368)

From calculus to set theory, economists did it always the other way round.

With mathiness, Paul Romer sloganized a pseudo-problem. For a mathematician’s assessment of the ingrained mathematical incompetence of economists see Jonathan Barzilai’s Open Letter to the President of the American Economic Association.**

Egmont Kakarot-Handtke

References

Bagehot, W. (1885). The Postulates of English Political Economy. Library of Economics and Liberty. URL http://www.econlib.org/library/Bagehot/bagPE1.html.

Blatt, J. (1983). How Economists Misuse Mathematics. In A. S. Eichner (Ed.), Why

Economics is Not Yet a Science, pages 166–186. Armonk, NY: M.E. Sharpe.

Mirowski, P. (2002). Machine Dreams. Cambridge: Cambridge University Press.

Morgenstern, O. (1941). Professor Hicks on Value and Capital. Journal of Political

Economy, 49(3): 361–393. URL http://www.jstor.org/stable/1824735.

Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited, volume 1. Norderstedt: Books on Demand, 2nd edition.

Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, NC, London: Duke University Press.

* Wikipedia https://en.wikipedia.org/wiki/Cargo_cult_science

** Scientific Metrics, Open Letters and papers http://scientificmetrics.com/publications.html

Just a bit off I think. In “The Mathematical Experience” Davis and Hersh comment that “The imposition of mathematics is by fiat, but once established it carries with it many social consequences.” In simpler terms by the imposition of mathematics, in economics or any other aspect of life winners and losers are identified and given the mathematical “seal of approval” or “finger of disgust.” Some who “use mathematics” assert it is the antithesis of rhetoric. In fact, that is not the case. Mathematics is rhetorical. It is used often for persuasive purposes. Mostly by latching onto mathematics’ supposed “absolute knowledge” capability. Problem being no such capability exists or ever has. Most mathematicians understand this. It is this false connection by economists and many other social scientists that makes the use of mathematics by social scientists (including most particularly economists) very frightening. A lot of destructive things can result when one firmly believes what one writes and proposes is certified with absolute knowledge. Professional mathematicians are very uncomfortable with “behavioral-science mathematics,” believing strongly behavioral scientists neither understand well the basics of the philosophy of mathematics or the very real limits of applying mathematics “in the world.” Mathematicians seldom speak about such issues publicly. One who has is Neal Koblitz. His “Mathematics as Propaganda” is golden. Take a look. It’s an amusing send up of “behavioral” mathematics. He in particular shows how tempting it is for behavioral scientists to “use” mathematics to claim the prestige and “take seriousness” that goes with it.

As the comments suggest the issue here is mathematics, apart from or with economics. Historically, mathematics was for the larger part of human history for the last 4,000 years viewed as the paradigm of infallibly secure knowledge. It is not and was not. Mathematics is a collective creation. And thus subject to the same limitations and application issues as all other collective creations. But the loss of the fairy tale of “absolute certainty” does not mean either that mathematics is useless or that the search for knowledge is doomed. In fact, just the opposite. Heisenberg’s Uncertainty Principle first and later relativity physics and Quantum Theory show the fallacy of mathematical absolutism. But they also vastly expand our knowledge and understanding. The economics profession and economists are still holding onto absolutist mathematics. By doing so they place an impediment in the way of expanding knowledge of economic actions and actors. Along with economists’ adoration for and use of 19th century physics as their model of science and their complete failure to explore, let alone apply relativity theory and mathematics, evolutionary theory, or the 50 years of social constructionist work that has provided so much new knowledge of science, mathematics, and just about every other aspect of our collective lives. Mainstream economics and economists are anachronistic in the extreme. That hurts them, the science of economics, and all of us who have to suffer as a result of the kinds of conclusions economic research comes up to “help” us.

Paul Romer gives the example of Robert Solow:

“WHO WAS ENGAGED IN SCIENCE when he developed his mathematical theory of growth”

and of Joan Robinson:

“WHO WAS ENGAGED IN ACADEMIC POLITICS when she waged her campaign against capital and the aggregated production function” (Romer P. 2015);.