April 16, 2016

Mathiness is NOT the problem — scientific incompetence is

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

Blog-Reference and Blog-Reference and Blog-Reference on May 3, 2017, adapted to context

“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 of 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, ...”#1

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 that has become the hallmark of current macroeconomics.

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. This is the fatal methodological blunder with regard to formalization.

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.#2

Egmont Kakarot-Handtke

Bagehot, W. (1885). The Postulates of English Political Economy. Library of Economics and Liberty. URL
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
Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited, volume 1. Norderstedt: Books on Demand, 2nd edition. URL
Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, London: Duke University Press.

#1 Wikipedia
#2 Jonathan Barzilai, Scientific Metrics, Open Letters and papers

For a detailed overview see cross-references Mathiness. See also cross-references Paradigm Shift and Axiomatization. Immediately preceding Mathiness and the Ur-blunder.

Related '#DrainTheScientificSwamp' and 'Hooray! The formalization issue is finally settled' and 'Wikipedia, economics, scientific knowledge, or political agenda pushing?'.

REPLY to Brian Romanchuk on May 4, 2017

You say “Mainstream: MMT has no math!”

When you drive a car you have velocity and acceleration/deceleration. The latter is the first derivative of the former. So, by driving a car you have the NATURAL math of calculus. It is just there, whether you have ever heard of calculus or not is irrelevant. Whether you actually measure the velocity is irrelevant. The math is just there.

The same holds for economics. The NATURAL math of economics is the elementary math of accounting. Whether you can do the math or whether you actually measure flows or stocks is irrelevant. The math is just there.

The problem with economists is (i) that they do not know what the NATURAL math of a given economic phenomenon is, (ii) that they grab a piece of math from the math department, and apply it without a deeper understanding. A familiar example is the application of calculus to utility maximization, which is downright idiotic because utility is a NONENTITY. And here you have it in a nutshell: “Walras approached Poincaré for his approval. ... But Poincaré was devoutly committed to applied mathematics and did not fail to notice that utility is a nonmeasurable magnitude.” (Porter)

Neither Walras nor the rest understood this and because they were not immediately fired for their manifest scientific incompetence, they simply carried on.

The proper definition of mathiness is (i) not to understand what the natural math of an economic phenomenon is, and (ii), the formalization of NONENTITIES (demand functions, production functions, IS functions, equilibrium, etcetera). Economists got it wrong on both counts from Jevons/Walras/Menger via Keynes to DSGE. With Jason Smith’s information economics mathematical incompetence has actually reached a maximum.#1

The natural math of macroeconomics is the elementary math of national accounting. The fact of the matter is that Keynes, Post Keynesians, and MMT got it provable wrong.#2

Keynes’ two-liner is simply false: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (GT, p. 63)

Neither pro- nor anti-Keynesians have realized in 80+ years that the two-liner is false according to the natural mathematics of accounting.#3 The snag is that stupid people do not understand the unassailable mathematical proof of their stupidity and this is why IS-LM and MMT and Post Keynesianism and Krugman and Jason Smith and all the other half-wits are still around.

Scientific self-governance or what has been reintroduced by Paul Romer as Feynman integrity simply does not work in economics. Economics is for 150+ years a cargo cult science and orthodox mathiness and heterodox anti-math is only the most conspicuous symptom.

#1 IS-LM ― a crash course for EconoPhysicists
#2 Where MMT got macro wrong
#3 The Common Error of Common Sense: An Essential Rectification of the Accounting Approach

REPLY to Brian Romanchuk on May 4, 2017

So, we agree on these concrete results:
  • The statement ‘MMT has no math’ is false.
  • Every economic phenomenon has its natural math.
  • The natural math of macro/MMT is accounting.
  • MMT got the elementary math of accounting provably wrong.
  • The error/mistake/blunder is the same as with Keynes.#1
  • The problem of MMT is NOT mathiness but insufficient math competence.
  • Because the formal foundations of MMT are false the whole analytical superstructure of MMT is false.#2
  • MMT is refuted according to the scientific criteria of formal/material consistency.
  • The further propagation of MMT violates scientific standards.
#1 How Keynes got macro wrong and Allais got it right
#2 The final implosion of MMT

REPLY to Brian Romanchuk on May 5, 2015

Thank you for the clarification. All others are invited to proceed to the future of economics. See True macrofoundations: the reset of economics or here.