Thursday, August 7, 2014

Math Anxiety: Sandwichman's father was a carpenter

As that famous non-meteorologist, Bob Dylan, once sang, "You don't need a weatherman To know which way the wind blows."

Some background on the Gödel caper: about a week and a half ago, John Quiggin posted at Crooked Timber on "Austrian economics and Flat Earth geography." There was a bit of discussion there of Gödel incompleteness, mathematical formalism and economics, by John, Lee Arnold and Scott Martens.

Sandwichman posted several comments having to do with Henry Hazlitt's indignant response to Keynes's statement in the General Theory that classical economists resemble Euclidean geometers in a non-Euclidean world and, more extensively, on John Maurice Clark's 1921 essay "Soundings on non-Euclidean economics."

That essay is central to episode 12 of SCIOD, "Euclidean Rhapsodies" which is scheduled for publication on EconoSpeak on September 2. There were several allusions to "non-Euclidean economics" before Keynes's analogy -- by Pigou, Wesley Mitchell and Clark. The important things to keep in mind is, first, that "non-Euclidean economics" is a self-conscious metaphor but, more importantly, it is also a critique of a stealth metaphor.

Economists are not "simply doing math" when they use math in their arguments. They are also making claims about the relationship between their models and the world. You don't need to be a mathematician (or a mathematician's son) to question the validity -- even the coherence -- of those claims. Here is how Clark framed the issue:
It is fairly obvious, if one stops to think of it, that there are systems of economics with axioms fully as far removed from each other as the geometrics of Euclid and the non-Euclideans; perhaps as far apart as the conventional physics and Einstein. Probably the foremost non-Euclidean economist is Professor Veblen, and his theory of invidious prestige might be called a theory of economic relativity. 
Orthodox economics undertakes to interpret equilibrium: Veblen undertakes to interpret progressive change. And in the social world this is much the same as saying that orthodox economics studies the assumptions of contentment and Veblen the assumptions of discontent, both of which are undeniable facts. Since undeniable facts are difficult to ignore, the net result is very largely to call them by different names. 
What do I mean by non-Euclidean economics in the present instance? The question can best be answered by taking six axioms which represent in a general way what might be called the orthodox position on a number of important points, and inverting them. …
It might be objected, pedantically, that Clark's axioms were somewhat arbitrary -- in a 1924 revision, he expanded them to eight -- and that his "inversions" were not, strictly speaking, inversions. Here are the axioms, the two added ones are in italics:
Proposition 1. Economics is the science of wealth, and wealth consists of things (a) useful, (b) limited in supply, (c) exchangeable, (d) appropriable. 
Proposition 2. Consumption is the end of economic activity and production is a means to that end. 
Proposition 3. The standard of economic service is the gratification of human wants through the increase of marketable goods and services. 
Proposition 4. A bargain between two persons concerns primarily those two persons, and only incidentally, under special conditions, becomes ‘affected with a public interest.’ 
Proposition 5. As a general rule, cost varies in proportion to output: “overhead costs” which are independent of output are the exception and arise in connection with large fixed capital only. 
Proposition 6. Private enterprise is necessary and efficient because people will work and sacrifice for their individual ends where they reap the fruits themselves and will not work as well for a collective end. 
Proposition 7. The rational foresight of individuals is at the basis of individualistic economics. 
Proposition 8. Capital, including machinery, consists of instruments of production utilized by human beings for the production of wealth.
Clark's father, by the way, was John Bates Clark, pioneer of marginal productivity theory.

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