More on Samuelson and the damage he has done to economic theory

I received a note from a friend and colleague on the note I did on the most damaging graph in the history of the sciences. He wrote:

Thanks for your blog on Samuelson. Only about twelve months ago did it dawn on me just how much damage Samuelson has done. I was thinking then of the Foundations, but of course you are right: his introductory textbook has been much more influential. Because his first degree was in physics, I don’t suppose he ever encountered a course in the History of Economic Thought in his life.

Samuelson’s first degree was in physics! This was news to me. So I did a bit of hunting, and now I am not sure that my colleague wasn’t right, and that Samuelson’s Foundations may have done as much harm as his introductory text and the Keynesian-cross. None of the standard online biographies mention physics, but there was then this on Paul Samuelson which is an entry in the online Encyclopedia of Human Thermodynamics, a link I shall certainly preserve. This is part of what it says about Samuelson:

In hmolscience, Paul Samuelson (1915-2009) (CR:89|#52) was an American economist noted, in economic thermodynamics, notable for his circa 1940 to 1970s efforts to derive economics via what he refers to a “mathematical isomorphisms” of the thermodynamics of Willard Gibbs, as communicated to him via his mentor Edwin Wilson and the so-called Harvard Pareto circle.

Economic stability | Equation 133
In 1938, Edwin Wilson, amid various letter communicates on his steam engine/physical chemistry based “mathematical economics” course, he was teaching at Harvard, wrote the following to Samuelson with critical comments on a paper by Samuelson:

“Moreover, general as the treatment is I think that there is the possibility that it is not so general in some respects as Willard Gibbs would have desired. [In] discussing equilibrium and displacements from one position of equilibrium to another position [Gibbs] laid great stress on the fact that one had to remain within the limits of stability. Now if one wishes to postulate the derivatives including the second derivatives in an absolutely definite quadratic form one doesn’t need to talk about the limits of stability because the definiteness of the quadratic form means that one has stability. I wonder whether you can’t make it clearer or can’t come nearer following the general line of ideas [that] Gibbs has given in his Equilibrium of Heterogeneous Substances, equation 133.”

The very impressive mention of “equation 133”, from Gibbs’ subsection “Internal Stability of Homogeneous Fluids as indicated by Fundamental Equations”, is the following:

U – TS + PV – M_1 m_1 – M_2 m_2 … – M_n m_n \,

Wilson, in other words, is suggesting, as it seems to be, to Samuelson that he use the Gibbs fundamental equation to formulate a theory of economic stability. Very hilarious indeed. Even the best of the best top dozen of the three dozen or so known human free energy theorists have been barely able to get a handle on this very intricate problem. No wonder Samuelson, into the 1970s, would become so irritated when people queried him about entropy and or sent him entropy-based economic papers to look at.

And where does all this lead:

Samuelson’s general economic model, in particular, was influenced by Gibbsian equilibrium criterion. His 1947 book Foundations of Economic Analysis, from his doctoral dissertation, is based, in theme, on Gibbs’ 1876 On the Equilibrium of Heterogeneous Substances. [1] Samuelson was the sole protegé of the polymath Edwin Wilson, who had himself been the sole protegé of Yale’s great physicist Willard Gibbs. During these formative years, Gibbs’ theories on equilibrium and chemical thermodynamics influenced them both in their ideas on the equilibrium of economic systems. In his seminal Foundations, Samuelson suggested, for example, that variation of the demand for a factor with a change in its price was analytically similar to thermodynamic variation in the pressure, volume, and temperature of an ideal gas. [9] All of this is pure Gibbsian. In fact, one may argue that the terms “foundation” and “variation” were plucked directly from the first page of the abstract to Equilibrium, wherein Gibbs states:

“Little has been done to develop the principle [of entropy] as a foundation for the general theory of thermodynamic equilibrium, which may be reformulated as follows: for the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy, the variation [δ] of its entropy shall either vanish or be negative.”

In short, Samuelson seemed to have adopted the variational logic of differential equations employed in thermodynamics, where variation goes by the mathematical name of “derivative”, to be applied in economics. Samuelson, however, maintains that his borrowing of thermodynamics to application in theoretical economics is only as “mathematical isomorphisms” between the maximum-minimum structures of thermodynamics and the cost-profit-utility systems of economics.

A very interesting idea in 1947, certainly worth pursuing. That we now can see it is a dead end is neither here nor there to all of world’s economists who have taken the trouble to learn maths rather than looking at the way an economy works.

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