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 hisEquilibrium of Heterogeneous Substances, equation 133.”

The very impressive mention of "

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

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 ofSamuelson'smany 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 opusFoundations 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. |

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

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

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

“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 athermodynamic equilibriumsystem 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) |

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 ‘

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

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

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

“Little has been done to develop the principle [of entropy] as afoundationfor 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 possiblevariationsof 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. |

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

“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

At the 1989

“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. |

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,Quotes | ByPaul Samuelson.”— William Barnett (2007) [16]

The following are other quotes:

“The formalmathematical analogybetween classicalthermodynamics and mathematical economic systems has nowbeen explored. This does not warrant the commonly metattempt to find moreexact analogiesof 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).

(b) Samuelson, P. A. (1983).

(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).

(b) Samuelson, Paul A. (1970). "Maximum Principles in Analytical Economics",

4. Samuelson, Paul. (1972).

5. Samuelson, Paul. (1989). “Gibbs in Economics”, in:

6. Samuelson, Paul A. (1980).

7. Poundstone, William. (2006).

8. Hokikian, Jack. (2002).

9. Mirowski, Philip. (1988).

10. Liossatos, Panagis, S. (2004). "Statistical Entropy in General Equilibrium Theory."

11. (a) Samuelson, Paul A. (1960). “Structure of a minimum equilibrium system”. In: Pfouts, R.W. (Ed.),

(b) Smith, Eric and Foley, Duncan. (2008). "Classical Thermodynamics and Economic General Equilibrium Theory",

12. Joyner, James. (2009). “Paul Samuelson, Revolutionary Economist, Dead at 94.”

13. Szenberg, Michael, Gottesman, Aron A. and Ramrattan, Lall. (2005).

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).

17. (a) Samuelson, Paul A. (1970). “Maximum Principles in Analytical Economics” (pgs. 67-68), Nobel Prize Lecture; in:

(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”,

(b) Thims, Libb. (2008).

(c) Bailey, Kenneth D. (1994).

19. Crowther-Heyck, Hunter. (2005).

20. Mooslechner, Peter, Schumerth, Helene, and Schurz, Martin. (2004).

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”,

● Samuelson, Paul A. (1990). “Gibbs in Economics (subsection: How thermodynamics impacts economics, pg. 263-)” (pgs. 255-68); in

External links

● Paul Samuelson – Wikipedia.