Tuesday, September 2, 2014

SCIOD 12: Euclidean Rhapsodies

"It is fairly obvious," John Maurice Clark, explained to Irving Fisher, Frank Knight and other participants in a 1920 American Economic Association seminar, "that there are systems of economics with axioms fully as far removed from each other as the geometries of Euclid and the non-Euclideans..."

Non-Euclidean geometry was topical in 1920. On May 29, 1919, a total eclipse of the sun could be viewed from Brazil and Africa and provided the opportunity to test a prediction of Einstein's theory of general relativity about the displacement of light from a star as it passes the sun. The conclusions from those observations were hailed as "the most important result obtained in connection with the theory of gravitation since Newton's day."

Clark's paper, "Soundings in non-Euclidean Economics," was not the first foray into this particular metaphor, nor would it be the last. In his inaugural lecture as Professor of Political Economy at Cambridge, "Economic science in relation to practice," Arthur Cecil Pigou quoted extensively from Bertrand Russell's Principles of Mathematics regarding the relationship between the Euclidean and non-Euclidean geometries, which "are equally true," and realistic science, which can only be decided, "so far as any decision is possible, by experiment and observation." 

In 1920, Pigou recycled his 1908 non-Euclidean ruminations -- and the Russell quote -- in The Economics of Welfare, arguing that Russell's distinction was "applicable to the field of economic investigation. It is open to us to construct an Economic Science either of the pure type represented by pure mathematics or of the realistic type represented by experimental physics."

In The General Theory of Employment, Interest and Money Keynes also employed the geometrical metaphor, comparing classical theorists (Professor Pigou among them!) to:
Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring.
Of course it was not literally the axioms of Euclidean geometry that classical economic theorists clung to but rather the doctrine, taught by them "from the time of Say and Ricardo..." that "supply creates its own demand..."
-- meaning by this in some significant, but not clearly defined, sense that the whole of the costs of production must necessarily be spent in the aggregate, directly or indirectly, on purchasing the product.
As it informs a theory of employment --"practically without discussion" -- that doctrine suggests what Keynes described as "two fundamental postulates," that: "1. The wage is equal to the marginal product of labour" and "2. The utility of the wage when a given volume of labour is employed is equal to the marginal disutility of that amount of labour."

Clark was more prolific in cataloging the axioms of the "Euclidean" economic orthodoxy. Originally, he listed six propositions and expanded that to eight in a revised version published in 1924. In both versions, it was the final proposition that Clark dwelt on: "Capital, including machinery, consists of instruments of production utilized by human beings for the production of wealth."

In contrast to this standard assumption, Clark suggested "the alternative proposition that human beings are instruments of production utilized by machines for the machines' increase and biological development." Instead of the operationally pointless speculation about whether machines might development consciousness and enslave humans, Clark offered the more realistic question, "how many and how important and far-reaching are the things the machines have done to us which we did not intend nor foresee, compared to the things we specifically employed them to do?" I have condensed Clark's own answer to his question, while indicating ... the ellipses:
Machines may be conceived as making bargains with man in which they offer him things he very much desires, and in exchange bind him to serve and maintain them, to eliminate the unfit among them and promote their racial progress, and to alter his own social and political arrangements in whatever ways may be necessary in keeping pace with the increasingly complex social organization of the machines themselves, and in keeping the children of man faithful to the service the machines require.… By such methods they have succeeded in imposing on man many things he never bargained for, some of which he finds extremely unwelcome.… 
They are responsible for the "industrial cycle," and as long as their own overhead costs are covered in periods of depression, they have not assumed full responsibility for the corresponding overhead costs of human beings.... 
As for their methods of maintaining control: some classes they bribe with large rewards, other classes, largely technicians, and technical-scientists, do not need to be bribed: their minds are captured by the material they work in.… 
What I have called Euclidean Economics, in general, serves the interests of the machines. It directs attention to the bribe they offer, and away from the conditions they exact. It has countenanced the machines in neglecting to assume the burden of human overhead costs, and in this, as in other matters, by insisting on putting man on a higher level than machines in respect to freedom, it has sometimes put him on a lower level in respect to care for his material needs.… 
The machines tend to confine discretion in industry to the few whom they take into their confidence, while the bulk of labor has largely lost the power to make any constructive contribution to the technique of industry. The job belongs to the machine, and labor feels little responsibility for it. Labor's state of mind and conduct shows the consequences of this, and many laborers appear to alternate between the slave-morality of getting as much as possible and giving as little, and the spasmodic need of exerting power of some sort. 
Two points are worth emphasizing. First, Clark's brief mention of overhead costs obliquely alludes to his monumental forthcoming work on the economics of overhead costs. Second, the complicity of what Clark called Euclidean Economics with the interests of the machines implicates that economics as one of the machines to the extent that it "grinds out" conclusions from premises. 

Clark did indeed use the language of machinery to describe economic theory in a 1948 note to Wesley Mitchell:
"In dealing with the evolutionary character of the mechanisms, I sometimes think 'theory' of the abstract sort is a device for converting usefully enlightening ideas about behavior and motivation into paper mechanisms whereby armchair theorists can grind out misleading results."
By this time, however, he was not only referring to the "Euclidean" ideas of classical economists but equally to the "more orthodox than the master" school that had grown up around Keynes. In a 1941 letter to Keynes, Clark had also referred to a "mechanism," in this case, "the 'income flow analysis' of which yours is the most noted presentation..." Clark was concerned that this Keynesian school risked succumbing "to the dangers of too-undiscriminating application from which classical economics suffered." In his reply, Keynes concurred with this view.

Reviewing a 1949 essay by Paul Samuelson on the mathematics of income determination,  Clark again reiterated his concerns about "what happens to the Keynesian theory when it is simplified by isolating the central mathematical formula and its corollaries from the context of factors that do not lend themselves to this treatment, and which Keynes handled in 'literary' fashion." Clark summed up his misgivings about Samuelson's approach in the following terms:
The upshot seems to be that investment cannot be treated as a simple rising function of current income alone, without doing violence to the essential facts; and that a more realistic (and dynamic) treatment inevitably introduces instability. Even without allowing for this, equilibrium comes to depend on the intersection of two lines which are so nearly parallel that the determinateness of the outcome becomes dubious (current graphic representations sometimes grossly exaggerate the angle of intersection). Samuelson saves himself by a concluding sentence, emphasizing "the violence done to complex reality by the simplified statistical abstractions of this paper." But is such a vague and general last-moment caveat sufficient? (emphasis added)
In noting "the intersection of two lines which are so nearly parallel," the "simple mathematical device" Clark criticized was Samuelson's graphic exposition of investment and consumption. He could as easily have been talking about matters having to do with a distinction between Euclidean and non-Euclidean geometries, which, after all, "are equally true" (and equally non-realistic).

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