In existographies, Paul Samuelson (1915-2009) (GEcE:#) [CR:132] was an American physics-trained 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.

Overview
Samuelson, a student of Edwin Wilson, the sole protege of Willard Gibbs, and from hims he learned that the variational calculus of chemical thermodynamics could be used as a general model to reformulate utility. Samuelson, in short, in some ways, was a precipitate of the Harvard Pareto circle, noted for his use of analogy concepts from chemistry (e.g. Le Chatelier's principle), physics (equilibrium), thermodynamics (entropy) in various economic theories; for being a second generation student, so to speak, of Willard Gibbs; and for his post-1970s strong vocal skepticism of the use of thermodynamics, particularly entropy, in economic models. The following is an snippet from Samuelson’s collected works abstract: (Ѻ)

“One of Samuelson's many novel contributions was that he generalized and applied mathematical methods developed for the study of thermodynamics to the field of economics. His inspiration for doing so came, in part, from his mentor, polymath Edwin Wilson who was a former Yale student of the founder of chemical thermodynamics, Willard Gibbs. Samuelson, therefore, is a successful example of interdisciplinarity, and he combined these ideas in his magnum opus Foundations of Economic Analysis (1947).”

Samuelson won the 1970 Nobel Prize in economics for his theories, the second year of the prize. [3]

Education | Pareto-Henderson-Gibbs
In 1925, Samuelson, age 20, completed his BS in physics (Ѻ)(Ѻ)(Ѻ) from the University of Chicago, after which he completed his MS in 1936 at Harvard. From 1937 to 1940, Samuelson entered the Harvard’s Society of Fellows (1937-40), an alternative program, founded by Abbott Lawrence and Lawrence Henderson (1878-1942), where students could spend three years pursuing any research that interested them, but were prohibited from working on their PhD dissertations.


Samuelson learned about Gibbs-Pareto based economic equilibrium models, in the 1930s at Harvard from either Lawrence Henderson, whose program he was in, and or Edwin Wilson, one of his dissertation mentors, from whose lectures he learned Le Chatelier's principle.

Samuelson learned about Gibbs-Pareto based economic equilibrium models, in the 1930s at Harvard from either Lawrence Henderson, whose program he was in, and or Edwin Wilson, one of his dissertation mentors, from whose lectures he learned Le Chatelier's principle.

Henderson, of note, had in 1928 published an equilibrium theory of blood, during which time he assumedly began to learn about Gibbs, in followup to this, published his 1935 Pareto’s General Sociology: a Physiologists Interpretation, in which he explains French-Italian engineer Vilfredo Pareto’s 1916 four-volume Treatise on General Sociology, and Pareto’s view of society as a system of “human molecules”, via the logic of Gibbsian thermodynamics, using what Henderson calls Gibbsian "analogies", where a social system is said to contains individuals roughly analogous to "Gibbs’ components". [18]

Direct connections between Henderson and Samuelson, if they exist, in regards Henderson specifically mentoring Samuelson about Gibbs and Pareto and sociology/economics, remain to be ferreted out.

American science historian Hunter Crowther-Heyck (2005) seems to stitch out some semblance of a Henderson-Samuelson-Pareto connection, stating that Samuelson used Pareto’s ophelimity model of utility, which in turn was being popularized, at Harvard, in the 1930s, in the enthusiastic seminars on Pareto that Henderson was giving. [19]

Education | Pareto-Wilson-Gibbs
In any event, at some point along the line, during this period at Harvard, Samuelson studied under American mathematician Edwin Wilson, who was interested in Pareto economics theories, possibly via Henderson influence, and who himself had been the sole protégé of American engineer Willard Gibbs. In 1970, in his famous two-cultures ambivalent Nobel Laureate speech “Maximum Principles in Analytical Economics”, in reflection on this Wilson influence, Samuelson stated the following: [17]

“I was struck by a remark made by an old teacher of mine at Harvard, Edwin Bidwell Wilson. Wilson was the last student of J. Willard Gibbs' at Yale and had worked creatively in many fields of mathematics and physics; his advanced calculus was a standard text for decades; his was the definitive write-up of Gibbs' lectures on vectors; he wrote one of the earliest texts on aerodynamics; he was a friend of R. A. Fisher and an expert on mathematical statistics and demography; finally, he had become interested early in the work of Pareto and gave lectures in mathematical economics at Harvard. My earlier formulation of the inequality in Eq. 4:

owed much to Wilson's lectures on thermodynamics. In particular, I was struck by his statement that the fact that an increase in pressure is accompanied by a decrease in volume is not so much a theorem about a thermodynamic equilibrium system as it is a mathematical theorem about surfaces that are concave from below or about negative definite quadratic forms. Armed with this clue, I set out to make sense of the Le Chatelier principle.”

This, to note, is a "social ideal gas law" like formulation. In lecture, Wilson had taught Samuelson Le Chatelier’s principle, which explained to Samuelson that in a system (chemical or economic) the changes in the equilibrium is a constrained maximization problem when one of the constraints is marginally tightened or relaxed and thus solved by the “variation principle”.

At some point therein, in this 1930s period, Wilson taught a seminar on mathematical economics which Samuelson and a few others attended. [20] This seminar may be "Wilson's lectures on thermodynamics" to which Samuelson is referring (1970) to above?


A photo of Samuelson, in his later years, in his office, in an article discussing how in 1938 he remaindered “utility” theory as obsolete. (Ѻ)

A photo of Samuelson, in his later years, in his office, in an article discussing how in 1938 he remaindered “utility” theory as obsolete. (Ѻ)

Dissertation
Samuelson, following his Harvard’s Society of Fellows intellectual sojourn, quickly wrote up his PhD dissertation, after which, as the story goes, when he completed his defense of his doctoral dissertation, one member of the committee turned to another and said, “did we pass?”. Specifically, as William Barnett, in co-editor association with Samuelson (2007), summarizes: [16]

“It is widely reported that at the end of Samuelson’s dissertation defense at Harvard, the great economist Joseph Schumpeter turned to Nobel Laureate, Wassily Leontief, and asked, ‘Well, Wassily, have we passed?’”

The exact date of this defense needs to be tracked down, but whatever the case, most sources report that Samuelson received his PhD in 1941 from Harvard —though, to note, somehow, he had moved to MIT before finalizing his PhD (see below) (check).

Samuelson’s thesis, according to Andrew W. Lo, modeled each person as an economic agent, and assumed that each individual acted so as to maximize a quantity called ‘expected utility’, a model with which he assumed should be able to predict their behavior in much the same way that physicists predict the behavior of physical objects.

The thesis soon won international acclaim as well as the David A. Wells Prize (1941) for best publishable thesis, and was eventually published in 1947 under the title Foundations of Economic Analysis, the first run 750 copies selling out and soon thereafter was selling at nearly 50,000 copies a year, and would soon become one of the highest selling college textbooks of all time, and as Samuelson latter put it, the work done in his Foundations, won him the 1970 Nobel Prize. [13]

Harvard → MIT | Newton's third law of motion
In Dec 1939, Samuelson received a letter of recruitment from Harold Freeman, a former co-student with Samuelson from 1936-68, who was now an associate professor at MIT. In Oct 1940, Samuelson departed from Harvard, owing to a number of argumentative circumstances, to MIT where he became professor of economics. [14] In this transition, period, sometime one or after October 10, when MIT president Karl Compton offered Samuelson an assistant professorship, Rupert Maclaurin—an economics professor and son of former MIT president Richard Maclaurin—phoned him daily, dangling before him the prospect research funds, including money offered by businessman Roger Babson (1875-1967) to support the study of the “implications for economics of Isaac Newton’s law of action and reaction” (see: third law of motion), as English economist and Samuelson biographer Roger Backhouse summarizes things. [15]


A signed copy of Samuelson’s 1947 Foundations of Economic Analysis, with its opening Willard Gibbs quote: “mathematics is a language”, from which he supposedly borrowed the minima and maxima differential methods for use in economic analysis. (Ѻ)

A signed copy of Samuelson’s 1947 Foundations of Economic Analysis, with its opening Willard Gibbs quote: “mathematics is a language”, from which he supposedly borrowed the minima and maxima differential methods for use in economic analysis. (Ѻ)

Foundations | 1947
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. [2] 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. [10]

Samuelson | 1960-70s
Into the late 1950s going into the 1960s, Samuelson seems to have gone on the defensive in regards to his physical chemistry stylized economics models, in particular in regards to whether or not his analogies or thermodynamics conceptualized "mathematical isomorphisms" are real or just fictional contrivances. In 1960, to exemplify, Samuelson commented the following: [11]

“The formal mathematical analogy between classical thermodynamics and mathematic economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes – such as entropy or energy – in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should ‘utility’ be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?”

At this point, one can begin to see Samuelson's mind begin to fall apart on this issue. His statement: "why should there be laws like the first or second laws of thermodynamics holding in the economic realm?", is clearly indicative of this. The reversal of this statement is that the first and second laws hold in all systems of the universe, as such the question becomes: "what are the economic determinants involved in the quantification of the governance of the first and second laws in economic terms?"


Samuelson in Washington in 1962, with an angry look.

Samuelson in Washington in 1962, with an angry look.

Curiously, although Samuelson used and discussed thermodynamics in his own work, he seemed to become more and more pessimistic of the use of entropy and thermodynamics in general by others, especially in his later years, particularly after his 1970 Nobel prize win. In 1972, for instance, in a dismissal of the idea of a sociological thermodynamics, Samuelson concluded: [4]

“The sign of a half-baked speculator in the social sciences is his search for something in the social system that corresponds to the physicist's notion of entropy.”

Yet, in 1974, Samuelson wrote that a high-PQ trader “is in effect possessed of a ‘Maxwell’s demon’ who tells him how to make capital gains from effective peek into tomorrow’s financial page reports.” [7] Again, in the 1980 edition of his famous Economics textbook, he outlines a discussion on “entropy economics”. In the same work, he outlines how, in his view, energy and entropy are consequential for economics: [6]

“You can’t make a perpetual motion machine that will run by dropping a ball’s bouncing back to higher than its point of release. That’s a consequence of the first law of thermodynamics—which guarantees conservation (or constancy of the total energy). More subtle, but no less consequential for economics, is the second law of thermodynamics: it requires that the total entropy (or ‘disorder’) irreversibly increases, while the total of energy is remained constant.”

So, on one hand (1972), he states that people who use entropy in the social sciences are half-baked, yet he advises its use in economics on the other hand (1980); a point of inconsistency in his mind? A turning point in the mind of Samuelson occurred following the publication of the eleventh edition (1980) of his Economics. In subsequent editions (after the eleventh), noted Egyptian-born American physicist Jack Hokikian, all mentions of entropy and the laws of thermodynamics had been removed? [8]

At the 1989 Gibbs Symposium, organized to honor the memory of the theoretical physicist Willard Gibbs on the 150th anniversary of his birth, Samuelson had become even more pessimistic on the use of thermodynamics in economics:

“As will become apparent, I have limited tolerance for the perpetual attempts to fabricate for economics concepts of ‘entropy’ imported from the physical sciences or constructed by analogy to Clausius-Boltzmann magnitudes.”


Volumes 1-5 of Samuelson's Collected Scientific Papers (Ѻ); see hmolscience power center genealogy.

Collected Scientific Papers (Paul Samuelson)

Volumes 1-5 of Samuelson's Collected Scientific Papers (Ѻ); see hmolscience power center genealogy.

He continues: [5]

“The monthly mail still brings grandiose schemes to replace the dollar as a unit of value by energy or entropy units. Superficial knowledge of thermodynamics, brought into contact with ignorance of economics, cannot even in the presence of the catalyst of noble intentions beget stable equilibrium of useful of useful products. This is not a tautology, merely a finding of fifty-five years of reading the morning mail.”

Whatever the reason, it is very curious that a student of Gibbs would find such irritation at the use of energy and entropy in the study of economic systems?

Quotes | On
The following are noted tributes:

“Samuelson won the Nobel Prize in economics in 1970, while a professor at MIT. I was an undergraduate engineering student at MIT from 1959 to 1963. To all students at MIT in all fields, there were to ‘gods’ who loomed over the rest of the faculty: the great mathematician, Norbert Wiener, and the economist, Paul Samuelson.”
— William Barnett (2007) [16]

Quotes | By
The following are other quotes:

“The formal mathematical analogy between classicalthermodynamics and mathematical economic systems has nowbeen explored. This does not warrant the commonly metattempt to find more exact analogies of physical magnitudes—such as entropy or energy—in the economic realm. Whyshould there be laws like the first or second laws ofthermodynamics holding in the economic realm? Why should "utility'' be literally identified with entropy, energy, or anythingelse? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematicalisomorphism that does exist between minimum systems thatarise in different disciplines?”
— Paul Samuelson (1960), "Publication"; cited by Jason Smith [21]

“As will become apparent, I have limited tolerance for the perpetual attempts to fabricate for economics concepts of ‘entropy’ imported from the physical sciences or constructed by analogy to Clausius-Boltzmann magnitudes. The monthly mail still brings grandiose schemes to replace the dollar as a unit of value by energy or entropy units. Superficial knowledge of thermodynamics, brought into contact with ignorance of economics, cannot even in the presence of the catalyst of noble intentions beget stable equilibrium of useful of useful products. This is not a tautology, merely a finding of fifty-five years of reading the morning mail.”
— Paul Samuelson (1989), “Gibbs in Economics” (pg. 256) [5]

References
1. (a) Caldi, D. G. and Mostow, George D. (1989). Proceedings of the Gibbs Symposium, May 15-17, (section: Gibbs in economics, by Paul Samuelson, pgs. 255-68). American Mathematical Society.
(b) Samuelson, P. A. (1983). Foundations of Economic Analysis (extended edition). Holiday House.
(c) Jolls, K. R. (1990). Gibbs and the art of thermodynamics, Gibbs in economics, Proceedings of the Gibbs Symposium (Providence, R.I.), 293-321.
2. Samuelson, Paul (2003). "How I Became an Economist", 1970 Laureate in Economics, 5 September, Nobel Prize Organization.
3. (a) Mirowski, Philip (1989). More Heat than Light: Economics as Social Physics, Physics as Nature's Economics. Cambridge Univ. Press.
(b) Samuelson, Paul A. (1970). "Maximum Principles in Analytical Economics", Nobel Prize Lecture.
4. Samuelson, Paul. (1972). The Collected Scientific Papers (pg. 450). Vol. 3, ed. R. Merton. Cambridge, Mass.: MIT Press.
5. Samuelson, Paul. (1989). “Gibbs in Economics”, in: Proceedings of the Gibbs Symposium, Yale University, May 15-17, 1989 (editors: Daniel Caldi and George Mostow) (pgs. 255-). American Mathematical Society.
6. Samuelson, Paul A. (1980). Economics, 11th ed. (pg. 747). McGraw-Hill.
7. Poundstone, William. (2006). Fortune’s Formula (pgs. 207, 346). MacMillan.
8. Hokikian, Jack. (2002). The Science of Disorder: Understanding the Complexity, Uncertainty, and Pollution in Our World (pg. 235). Los Feliz Publishing.
9. Mirowski, Philip. (1988). Against Mechanism: How to Protect Economics from Science (pg. 94). Rowman & Littlefield.
10. Liossatos, Panagis, S. (2004). "Statistical Entropy in General Equilibrium Theory." Department of Economics, Florida International University.
11. (a) Samuelson, Paul A. (1960). “Structure of a minimum equilibrium system”. In: Pfouts, R.W. (Ed.), Essays in Economics and Econometrics: A Volume in Honor of Harold Hotelling. University of North Carolina Press. Reprinted in Stiglitz, J.E. (Ed.), 1966. The Collected Scientific Papers of Paul A. Samuelson, MIT Press, Cambridge, MA, pp. 651–686.
(b) Smith, Eric and Foley, Duncan. (2008). "Classical Thermodynamics and Economic General Equilibrium Theory", Journal of Economic Dynamics and Control, 32:7-65, Department of Economics Graduate Faculty, New School University, 2005 manuscript.
12. Joyner, James. (2009). “Paul Samuelson, Revolutionary Economist, Dead at 94.” OutsideTheBeltway.com, Dec. 14.
13. Szenberg, Michael, Gottesman, Aron A. and Ramrattan, Lall. (2005). Paul A. Samuelson: on Being an Economist (Samuelson’s 1940 dissertation, pgs. 20-22). Jorge Pinto Books.
14. Backhouse, Roger E. (2013). “Paul A. Samuelson’s Departure from Harvard to MIT” (pdf), Department of Economics, University of Birmingham, Jan.
15. (a) Samuelson, Paul A. (1940-41). The Hurwicz 1940-41 year when MIT launched its graduate degree racket, PASP Box 39 (Hurwicz).
(b) Backhouse, Roger E. (2013). “Paul A. Samuelson’s Departure from Harvard to MIT” (pdf), Department of Economics, University of Birmingham, Jan.
(c) Roger Babson – Wikipedia.
16. Samuelson, Paul and Barnett, William A. (2007). Inside the Economist’s Mind: Conversations with Eminent Economists (§:Coeditor’s Preface: an Overview of the Objectives and Contents of the Volume, pgs. xi-). Wiley.
17. (a) Samuelson, Paul A. (1970). “Maximum Principles in Analytical Economics” (pgs. 67-68), Nobel Prize Lecture; in: Science, 173(1971):993-94.
(b) Hunsaker, Jerome and Mac Lane, Saunders. (1973). “Edwin Bidwell Wilson (1879-1964)” (pdf) (pgs. 297-98), 38-pages. National Academy of Sciences.
18. (a) Cannon, Walter B. (1943). “Biographical Memoir of Lawrence Joseph Henderson 1878-1942”, US National Academy of Science, Vol XXIII, Second Memoir.
(b) Thims, Libb. (2008). The Human Molecule, (preview) (pg. 20). Morrisville, NC: LuLu.
(c) Bailey, Kenneth D. (1994). Sociology and the New Systems Theory: Toward a Theoretical Synthesis (pg. 104). SUNY Press.
19. Crowther-Heyck, Hunter. (2005). Herbert A. Simon: the Bounds in Modern America (pg. 68-69). JHU Press.
20. Mooslechner, Peter, Schumerth, Helene, and Schurz, Martin. (2004). Economic Policy Under Certainty (pg. 146). Edward Elgar Publishing.
21. Smith, Jason. (2013). “Economics for Fun and Profit” (Ѻ), Information Transfer Economics, BlogSpot, Apr 1.

Further reading
● Samuelson, Paul A. (1985). “Thermodynamic Theory as Mathematical Economics Could have Discovered It”, Mathematical Social Sciences, 10(3): 281.
● Samuelson, Paul A. (1990). “Gibbs in Economics (subsection: How thermodynamics impacts economics, pg. 263-)” (pgs. 255-68); in Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989 by D.G. Caldi, George D. Mostow, American Mathematical Society, 1990.

External links
● Paul Samuelson – Wikipedia.