How Influential Was Mechanics in the Development of Neoclassical Economics? A Small Example of a Large Question

Grattan‐Guinness, I.

doi:10.1017/s1053837210000489

Cited by 12 publications

(5 citation statements)

References 109 publications

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“…Analogies with rational mechanics played a pivotal role in the search for formal models in economics (Grattan-Guinness 2010). This approach, which was pursued by Pareto and his followers, did have great success in the case of static equilibrium.…”

Section: Discussionmentioning

confidence: 99%

Economic Dynamics and the Calculus of Variations in the Interwar Period

Pomini

2018

J Hist Econ Thought

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Analogies with rational mechanics played a pivotal role in the search for formal models in economics. In the period between the two world wars, a small group of mathematical economists tried to extend this view from statics to dynamics. The main result was the extensive application of calculus of variations to obtain a dynamic representation of economic variables. This approach began with the contributions put forward by Griffith C. Evans, a mathematician who, in the first phase of his scientific career, published widely in economics. Evans’s research was further developed by his student Charles Roos. At the international level, this dynamic approach found its main followers in Italy, within the Paretian tradition. During the 1930s, Luigi Amoroso, the leading exponent of the Paretian School, made major contributions, along with his student Giulio La Volpe, that anticipated the concept of temporary equilibrium. The analysis of the application of the calculus of variations to economic dynamics in the interwar period raises a set of questions on the application of mathematics designed to study mechanics and physics to economics.

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Section: Discussionmentioning

confidence: 99%

Economic Dynamics and the Calculus of Variations in the Interwar Period

Pomini

2018

J Hist Econ Thought

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“…Adapting the concept of constrained dynamics from Lagrangian mechanics (Flannery, 2011;Lagrange, 1788), it carries on an "unfinished business" (Leijonhufvud, 2006, pp. 26-30) of the early neoclassicals such as Irving Fisher (1892) or Vilfredo Pareto (1897): Inspired by the description of stationary states in classical mechanics, they derived an economic theory of static equilibrium (Glötzl et al, 2019;Grattan-Guinness, 2010;Mirowski, 1989;Pikler, 1955). Despite some efforts, they were unable to describe analogously the adaptive processes that were thought to converge to the states analyzed in static theory (Donzelli, 1997;Leijonhufvud, 2006;McLure and Samuels, 2001).…”

Section: Modeling Dynamics Subject To Constraints In Different School...mentioning

confidence: 99%

Modeling the out-of-equilibrium dynamics of bounded rationality and economic constraints

Richters

2021

Preprint

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The analogies between economics and classical mechanics can be extended from constrained optimization to constrained dynamics by formalizing economic (constraint) forces and economic power in analogy to physical (constraint) forces in Lagrangian mechanics. In the differential-algebraic equation framework of General Constrained Dynamics (GCD), households, firms, banks, and the government employ forces to change economic variables according to their desire and their power to assert their interest. These ex-ante forces are completed by constraint forces from unanticipated system constraints to yield the ex-post dynamics. The flexible out-of-equilibrium model can combine Keynesian concepts such as the balance sheet approach and slow adaptation of prices and quantities with bounded rationality (gradient climbing) and interacting agents discussed in behavioral economics and agent-based models. The framework integrates some elements of different schools of thought and overcomes some restrictions inherent to optimization approaches, such as the assumption of markets operating in or close to equilibrium. Depending on the parameter choice for power relations and adaptation speeds, the model nevertheless can converge to a neoclassical equilibrium, and reacts to an austerity shock in a neoclassical or post-Keynesian way.

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“…Most mathematics was devised for use in the physical sciences, especially physics, astronomy and engineering; students of these other sciences habitually chose and maybe adapted mathematical topics already in place, but this practise may not be so effective in other sciences. For example, Walras's ideas belong to a period when mechanics was deployed in some detail as a source for theories in economics; but few useful consequences followed from it [88]. Indeed, a fresh emulation of mechanics occurred in economics from the 1950s onwards, drawing upon the new kinds of dynamic equilibrium that had been introduced from the late 1880s by Poincaré and Lyapunov [141]; but the emulation content was very modest.…”

Section: Limitations Of Broadness: Different Mathematics For Differenmentioning

confidence: 99%

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

Grattan‐Guinness

2011

Log. Univers.

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A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: 'omnipresent' and 'multipresent' theories, and 'ubiquitous' notions that form dependent parts, or moments, of theories. The category of 'facets' is also introduced, primarily to assess the roles of diagrams and notations in these two disciplines. Various consequences are explored, starting with means of developing applied mathematics, and then reconsidering several established ways of elaborating or appraising theories, such as analogising, revolutions, abstraction, unification, reduction and axiomatisation. The influence of theories already in place upon theory-building is emphasised. The roles in both mathematics and logics of set theory, abstract algebras, metamathematics, and model theory are assessed, along with the different relationships between the two disciplines adopted in algebraic logic and in mathematical logic. Finally, the issue of monism versus pluralism in these two disciplines is rehearsed, and some suggestions are made about the special character of mathematical and logical knowledge, and also the differences between them. Since the article is basically an exercise in historiography, historical examples and case studies are described or noted throughout. Mathematics Subject Classification (2000). Primary 00A30, 01A55, 01A60, 01A85, 03-03, 03-99; Secondary 00A35, 00A69, 00A71, 00A79, 03B10, 03C55, 03G05, 30-03, 31-03.Keywords. History and philosophy of pure and applied mathematics, history and philosophy of symbolic logics, parts and moments, generality of theories, theory change, monism and pluralism, sets and multisets, abstract algebras, metamathematics, model theory.

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How Influential Was Mechanics in the Development of Neoclassical Economics? A Small Example of a Large Question

Cited by 12 publications

References 109 publications

Economic Dynamics and the Calculus of Variations in the Interwar Period

Economic Dynamics and the Calculus of Variations in the Interwar Period

Modeling the out-of-equilibrium dynamics of bounded rationality and economic constraints

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

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