Comment on Lars Syll on ‘Debunking the use of mathematics in economics’

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What Velupillai criticizes is the application of topology in equilibrium theory. The persistent abuse of mathematics is a rather obvious fact that has been observed by many — notably heterodox economists: “It is difficult to contemplate the evolution of the economic science over the last hundred years without reaching the conclusion that its mathematization was a rather hurried job.” (Georgescu-Roegen, 1979, p. 271)

That economists misapply mathematics is what Velupillai said on numerous occasions. He concluded:

“Somewhere between the Political Arithmetician, alias the National Income Accountant, and the Financial Analyst, alias the Accountant, lies the task of the quantitative economist’s analytical role, and none of the theoretical or applied tasks of these two pragmatic and paradigmatic figures requires anything more than arithmetic, statistics and the rules of compound interest.” (Velupillai, 2005, p. 866)

The fact of the matter is that economists even messed up the elementary mathematics of accounting (2012).

What economists have attempted again and again is to take a mathematical tool and then to reformulate the economic problem so that it fitted the tool. Calculus, for example, required the introduction of a well-behaved production function and decreasing returns. This led to some funny cognitive dissonances.

“’So, Brian, what are you working on these days?’ Arthur had given him the two-word answer just to get started: ‘Increasing returns.’ And the economics department chairman, ..., had stared at him with a kind of deadpan look. ‘But — we know increasing returns don't exist.’ ‘Besides,’ jumped in Rothenberg with a grin, ‘if they did, we'd have to outlaw them!’ And then they'd laughed.” (Waldrop, 1993, p. 18)

This is how reality vanished from economics.

The same funny logical headstands happened with topology. “Surely it would be considered absurd, bordering on the insane, if a surgical procedure was implemented because a tool for its implementation was devised by a medical doctor who knew and believed in topological fixed-point theorems?” (See intro and Nadal, 2004, p. 36)

From the fact that Orthodoxy always holds the sharp mathematical knife at the blade with terrible/ridiculous results does not follow that knives have to be abandoned but only that Orthodoxy has to be abandoned.

By the way, the appropriate mathematical tool for the solution of the ‘age-old problem of the equality between supply and demand’ is not a set of equations but a simulation (2015, Sec. 4).

Egmont Kakarot-Handtke

References

Georgescu-Roegen, N. (1979). Energy and Economic Myths, chapter Measure, Quality, and Optimum Scale, pages 271–296. New York, NY, Toronto, etc.: Pergamon.

Kakarot-Handtke, E. (2012). The Common Error of Common Sense: An Essential Rectification of the Accounting Approach. SSRN Working Paper Series, 2124415: 1–23. URL

Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: The Market. SSRN Working Paper Series, 2547098: 1–10. URL

Nadal, A. (2004). Behind the Building Blocks. Commodities and Individuals in General Equilibrium Theory. In F. Ackerman, and A. Nadal (Eds.), The Flawed Foundations of General Equilibrium, pages 33–47. London, New York, NY: Routledge.

Velupillai, K. (2005). The Unreasonable Ineffectiveness of Mathematics in Economics. Cambridge Journal of Economics, 29: 849–872.

Waldrop, M. M. (1993). Complexity. London: Viking.