Local Entanglements in the History of Mathematical Economics

Abstract

The purpose of this special issue is to illustrate the importance that local aspects—issues concerning, for example, attitudes, styles, institutions, groups of individuals, specific needs in terms of public policies, or tools shared at specific places—have played in the history of the mathematization of economics. This might sound counterintuitive, since mathematical economics is usually regarded as predominantly placeless. More than any other kinds of ways of doing economics, mathematical economics, because of its connections with mathematics, is regularly considered as the embodiment of placelessness and atemporality. However, this placelessness of mathematics strongly contrasts with the claims of many contemporary historians and philosophers of mathematics who, in the last few decades, by working on different interpretative frameworks found in the history of science, have convincingly shown that the standards and practices of mathematics, including pure mathematics, are not universally fixed. On the contrary, the standards and practices of mathematics tend to change over place and time as mathematics interacts with other fields and other spheres of human activity. Despite their eternal character, even certain elements of mathematics such as particular proofs or lemmas also tend to change over time and place, as the ways these objects are used, reproduced, and mobilized depend on the evolving dynamics of mathematicians’ communities who know or who choose to ignore them at a particular time or in a particular place. In brief, mathematics has been localized.¹ Is it then historically pertinent to localize mathematical economics? We believe so.

The articles in this special issue were first presented in a series of four online conferences in 2021 and 2022, during which each one of them was collectively discussed. Participants circulated their work among the other contributors and presented a first version of it, followed by a second one six months later, expanded and improved thanks to the comments and criticisms of the other participants. The four conferences made it possible to discuss the specific contents of each paper and their connections with the “local entanglements” theme. As a basis for these discussions, we sent to the participants a brief text that broadly pictured a historiographical context of ongoing discussions on the history of mathematical economics and that also surveyed the meanings and relevance of the local entanglements as a historiographical category in different attempts in the history and philosophy of science to localize past scientists’ practices and ideas.

Let us briefly discuss some of these historiographical elements as they have developed in recent decades in the history of economics literature, before attempting to illustrate how the local entanglements perspective might be implemented.

Historiographical Background

The transformation of economics from a literary/verbal discipline to a mathematical one has been the focus of significant contributions to the history of economics literature. Of central relevance are the approaches that have studied this transformation from the perspectives of economics as modeling and of economics as an exact science.

In the economics-as-modeling approach, contributions over the last three decades by Mary Morgan, Marcel Boumans, and others have been of tremendous importance in showing how this transformation can insightfully be understood as resulting from a long historical process that made economics a modeling-qua-engineering science (Morgan and Morrison 1999; Morgan 2012; Boumans 2005). By exploring the idea that the history of scientific knowledge can be regarded as the history of different practical reasoning styles, and by regarding modeling in economics as one or several particular styles of reasoning, this approach has been successful in placing the actual working practices of past economists at the forefront of historical analysis. In this approach, emphasis is put on past economists’ models displaying experimental-like characteristics that are treated as the epistemic equivalent of a material instrument or device helping economists to better observe and measure economic phenomena. By making observation and measurement more reliable, these instruments help economists in their daily practice to decide how evidence and inference should be weighted for the purpose of producing reliable scientific knowledge. Over time, as new devices are created, new inferential instruments are available and new observational criteria are established, and what counts as reliable knowledge evolves concomitantly. In this way, in this economics-as-modeling and instrumentalist approach, experiment-like models are distinguished from purely axiomatic models, presented as truth-making objects uniquely relevant within the close and purely immaterial mathematical world of the models themselves (Boumans 2012; Morgan 2012). Axiomatic models are regarded as being concerned only with logical consistency, which is in fact a key feature in mathematics, as it rests at the basis of mathematical practices of rigor. From this perspective of a history of economics that has successfully and mainly focused on the applied and its interconnections with the histories of technocracy and policymaking, immaterial mathematical rigor does not automatically imply reliable economic knowledge useful for thinking about as well as shaping or reforming the economy. From this modeling instrumental approach perspective, sound economic knowledge was legitimately produced and circulated through working practices that were not rigorous in the way a mathematician defines rigorous.

This yields the historiographical remark that certain cognitive practices such as axiomatic theorizing in economics and in statistics, which eventually had some direct or indirect relevance in the development of modeling practices such as those in econometrics, have not been fully considered by the economics-as-modeling approach.

In the alternative approach that has focused on economics as an exact science, historians, including over the last three decades Giorgio Israel, E. Roy Weintraub, Philip Mirowski, Robert Leonard, and Nicola Giocoli, among others, have advanced our understanding of the integration of science, in particular of physics, as well as of axiomatic and nonaxiomatic mathematics, into economics during the first half of the twentieth century.² Their key idea is that mathematics is not a monolith; rather its images have continuously evolved over time and space. Weintraub in particular has shown that even mathematical rigor has its own historical intelligibility and contingency. He has also brought an awareness to the history of economics of the varying hierarchies of the images of mathematics. Rather than regarding the mathematical community as uniform, he disaggregates it into specific local groups to show that the ways economics was mathematized historically depended on the specific mathematical practices of those individuals and communities mathematizing economics. While the approach that focuses on the mathematization of economics as an exact science notes the boundaries between mathematicians’ and economists’ worlds and practices, its practitioners have emphasized the evolving images of mathematics held by communities of mathematicians and mathematical economists trained as mathematicians. They have concentrated on the theoretical, with, for example, significant efforts put into reconstructing the history of general equilibrium analysis, economic dynamics, expected utility theory, and the theory of games, to name a few.

Although there was an important influence of mathematics on economics during the twentieth century through the active participation and contributions of trained mathematicians, the diffusion and developments of mathematical economics in many places and spaces took form through the active role of scholars, mainly economists, who were not trained in mathematics and whose images of mathematics were consequently not framed within the professional practices of mathematics. As a result, the importance of other contingent and cognitive aspects of the local entanglements of particular cases in the history of mathematical economics has not been fully considered.

Economics became a modeling science as it was mathematized, and at the same time it became a mathematical discipline as it adopted modeling practices. The historiographical categories of economics as modeling and of economics as an exact science briefly sketched above have enlightened us in significant ways about how economics transitioned from a literary/verbal discipline to a mathematical/statistical one, by explaining for example how modeling practices came to be durably adopted by economists and how specific economic theories came to be stabilized. They nonetheless have tended to exclude from their historical scope particular cases, particular practices, and particular contingent and cognitive aspects that in fact contributed in ways yet to be studied to the emergence and development of mathematical economics in specific places as well as to the circulation from one place to another of mathematical economics.

And yet, many economists and noneconomists as well contributed to the development of theoretical economics as well as applied economics, sometimes even being simultaneously involved with policy activities. The historiographical separation between the theoretical and the applied makes it hard to consider their entanglements. More generally, this historiographical separation tends to overlook the fact that, while mathematical practices were increasingly adopted to theorize economics, they were also concomitantly and progressively embraced to theorize econometrics, statistics, engineering, and computing—the fields that shaped in manifold different ways the applied in economics of the twentieth century. The overlapping practices within and outside academia of economists, social scientists, statisticians, engineers, computer scientists, and policymakers at best reached local consensuses on the balance between the applied and the theoretical in economics and were never completely stabilized globally (Biddle and Boumans 2021; Backhouse and Cherrier 2017; Backhouse and Biddle 2000).

In what follows, we will show how the local entanglements can start fitting in and completing the historical picture of the development and diffusion of mathematical economics.

The Local Entanglements

Recent contributions in the history of economics have evoked a local entanglements dimension in a similar sense that we intend to explore in this special issue. For instance, the historiographical categories of schools of thought and intellectual circles partially overlap with ours (Forget and Goodwin 2011). Similarly, the concept of creative community or collaborative circle displays the importance of the local dimension (Charles and Théré 2011). Here, however, we intend to apply the category of local entanglement to the history of mathematical economics. At the same time, accounts emphasizing embodied practices in the history of macroeconometric modeling have also taken into account the situatedness of economists’ activities (Stapleford 2017; Boumans and Duarte 2019). Local entanglements in our perspective broaden the category of practice to include (seemingly) disembodied or cognitive activities, such as theorizing with abstract mathematics or axiomatization, as well as embodied forms of activities related to empirical and policy work.³ Scholars studying the nexus between economics and engineering have similarly stressed the relevance of locality (Duarte and Giraud 2020). In our take on the local, we consider a variety of disciplinary and nondisciplinary entanglements to address the complex of circuits and the relationships involved in the emergence, development, and diffusion of mathematical economics. This might even include entanglements between mathematical economics and the social sciences more broadly (Backhouse and Fontaine 2010) as well as the humanities.

Our take on the local entanglements in the history of mathematical economics is inspired by recent discussions in the history of science. As a category in the historiography of science, one finds that the local does not refer to one single concept or a unique understanding of “place,” but to a manifold of “places.” This manifold has been used by historians of science to interpret geographically embodied scientific discourses, to localize scientific cultures, to situate scientific rationalities, and to look at scientists’ practices and identities in their proper settings. These places have been explored to address the history of interdisciplinarity in specific parts of the world and have given rise to concepts such as “trading zones,” with which one might regard interactions between scientists of different disciplinary provenance as a quasi-anthropological concrete experience of exchange (Galison 1997, 1998). Some of these ways of using the local have in common the fact that they focus on the situatedness of scientific knowledge circulation/production, that is, on how locality conditions the practices of knowing, of securing credibility, and of producing meaning.

For instance, our article in this issue on Edwin Wilson and Harold Hotelling displays the centrality of the Harvard School of Public Health for Wilson and of the Food Research Institute at Stanford University for Hotelling in shaping their attitude, practices, and work in statistics during the 1920s and 1930s. Wilson came to consider statistics as necessarily linked to the disciplinary subject to which it was applied, whereas Hotelling eventually treated statistics as a transversal discipline, destined to serve all the social sciences indiscriminately, that is, as a universal language.

In a similar vein, Gianluca Damiani offers the sometimes parallel, sometimes overlapping stories of two institutional figures, William Riker and Lionel McKenzie, and the departments of economics and political science they headed at the University of Rochester. McKenzie and Riker shared an interest in the quantitative and mathematized approaches to their respective disciplines. They worked side by side therefore in several senses: they shared a common space, with their disciplinary departments located in the same building; they shared the geographical reality of long, cold winters; and they also shared a cognitive, intellectual personal and political space, with converging interests, similar life troubles, and many more. In this sense, Damiani proposes a true interweaving of different ways of understanding the local. The local is a point of view that thus privileges a place rather than an author or a concept; yet, a “place” is a multifaceted and polyvalent concept; the physical, cognitive, geographical, political, and social spaces overlap in his narrative.

Other ways of using the category of local entanglements emphasize more malleable characteristics of scientific knowledge such as credibility and meaningfulness. When knowledge migrates and thus changes the local context in which it is embedded, its credibility and meaningfulness are often exposed to criticism. However, the migration process also involves the development of new ideas and practices. The interdependence between the circulation of knowledge and the production of new ideas is central to Matheus Assaf's account of the history of the Institute of Pure and Applied Mathematics (Instituto de Matemática Pura e Aplicada, or IMPA) in Rio de Janeiro. Writing almost an “intellectual biography” of the institute, Assaf shows how, initially influenced by Bourbaki mathematicians visiting from France in the 1950s, the institute developed by establishing strong ties with American universities, such as the University of California at Berkeley. Berkeley's influence overlapped, however, with needs related to political and social contexts inherent in Brazilian society and academia, with some important IMPA scholars being associated with other economics departments in Brazil and other IMPA figures holding important economic leadership roles in the Brazilian government. What characterized IMPA economists was their positioning somewhere between mathematics and economics: for mathematicians, mathematical economics was “applied,” while for economists, the development of the general equilibrium models typically studied by IMPA doctoral students was about as theoretical as it got. In short, it was a hybrid form of knowledge, located at the intersection of different but locally overlapping disciplines, a way of theorizing economics and applying mathematics, with both national and international dimensions.

The history of IMPA recalls that knowledge can be held by individuals, but contemporary scientific knowledge is often held by institutions and groups rather than by stand-alone individuals. Kuukkanen (2012) argues for instance that groups and communities of individuals may be taken as epistemic subjects: a group of individuals can thus both possess a given scientific knowledge (without any further reduction to individual knowledge) and decide what to do with that scientific knowledge. Groups of individuals that share a certain scientific knowledge usually also share a “place,” either a physical or institutional place. If we identify those places with the group that they host, we may in some sense say that knowledge may be held by “places.” Thus, focusing on places rather than on individuals may allow for the study of specific kinds of place-related knowledge.

Yann Giraud provides a case study in which visual practices and their connected thought style supported and sustained the production and diffusion of place-related knowledge. By focusing on the London School of Economics (LSE) educational and research spaces during the 1930s, Giraud argues that the visual approach of diagrammatic economics developed there as a legitimate and appropriate stylistic way of exposing, formulating, and clarifying economic theoretical ideas. Giraud's way of addressing visualization situates the work developed by the generation of LSE-trained economists in that intermediate space between “theory” and “applied,” which by its hybrid nature escaped categorization both in terms of “economics as an exact science” and of “economics as modeling.” Visualization was a way of theorizing that the members of the young community of LSE economists like John Hicks and Abba Lerner appropriated in their own particular ways and adjusted to their own research programs. As an expression of a shared thought style and a common experience, LSE diagrammatic economics of the 1930s, Giraud argues, helps make sense of these different research programs.

Importantly, knowledge that is tied to places and communities of individuals makes the distinction between rational and social particularly intricate.

Ivan Boldyrev displays this intricacy of rational and social aspects. Boldyrev provides a narrative of the first international topological conference in Moscow in 1935 and its enduring effects on economics. The conference proved an unrepeatable and unrepeated meeting point between mathematicians and scientists who would never meet again. It was a transnational encounter between different scientific cultures and political ideologies that were nevertheless united by the powerful heuristics provided by topology. The conference proved the starting point for long-lasting ideas that would later apply the new topological heuristic to many economic fields. The Moscow conference illustrates the intricate overlapping of social and rational aspects in a specific place. And yet, the distinction between the rational and the social breaks down in Boldyrev's narrative. For instance, one may argue that the interest in mathematics—beyond its rational dimension—acted as a social platform for networking at the Moscow conference, while certain political aspects, such as the difficulty of speaking freely to each other, had obvious repercussions on the intellectual dimension of the debate. The local perspective allows Boldyrev to dodge the dichotomous categorization between the rational and social in favor of a different kind of narrative that we may call, following David Livingstone, situated rationality (see Livingstone 2003: 184; see also Kuukkanen 2012). Situated rationality considers that what counts as rational depends on the place where rationality is evaluated, thus implying that a social component is ultimately embedded into every situated rationality.

Livingstone, who has perhaps offered the most systematic historiographical analysis of the local embeddedness of science, suggests that all these ways of using the local in the history of science tend to agree on the idea that, like space and the social, the places of science and the places of social, political, and cultural practices are dynamically entangled as they are mutually constituted. This reciprocal dependency between all these kinds of practices lies at the very heart of Livingstone's take on the local entanglement in the history of science. It allows him to concentrate on the local practices of science to show how scientific knowledge is embodied in social, political, and cultural practices. His approach consists therefore of looking at science as a set of particular spatial practices. In this way, willing to unpack the implications that material and metaphorical spaces of scientific and nonscientific activities of scientists of the past had on the history of science, he has focused on spaces that represented concrete sites or specific regions or nations but also bestowed an even broader metaphorical meaning to the local. Applying Livingstone's proposed approach to the question of the rational/social dichotomy, we could say that—locally considered—the dichotomy ceases to be relevant. In fact, in a local setting, scientific work is not thought of and structured in terms that clearly decouple the rational and the social, but rather within a continuum, where social interactions have cognitive and rational implications, when the pace of rational reflection and analysis is often and willingly dictated by sociocultural factors. This profound overlap and entanglement often make a discourse aimed at separating the two aspects sterile.

Willing to provide new standpoints, Livingstone considered the evolving and overlapping spaces in which historical actors moved. In each one of these spaces, historical actors found a particular “range of possible, permissible and intelligible utterances and actions” (Livingstone 2003: 7) that justified and restricted the set of behaviors they adopted, the repertoire of inferences they made, and the collection of meanings that they gave to the world and that at the same time eased (or not) communication with their peers. All this led him to suggestively specify what are the spaces of science. In his words,

In its most determinate aspect, the local is a manifold of multiple spaces of practice within which scientific communities pursue their disciplinary and nondisciplinary commitments that influence the scientific knowledge they create. This may take place in geographically located sites as well as through communities spread out around geographical space that nevertheless share a common attitude, or a concern, or a method or tool. These communities may be formally institutionalized or informally organized. The local is also a manifold of multiple spaces of communication practices that frame the ways individuals and scientific communities learn about, interpret, and reappropriate scientific knowledge coming from somewhere else. In its most malleable aspect, the local might refer to places that can be spaces of controlled experimentation like laboratories where the world is manipulated.

The local could also be spaces of consumption and reception of scientific knowledge where particular individuals and communities who occupy concrete material or metaphorical spaces interpret and appropriate in locally distinctive ways the scientific knowledge that has been produced somewhere else. The local could be a shared ethos or a national, regional, or professional identity, and more often than not could be several of those things at the same time.

All this implies that the driving forces fostering changes in the practices of economics that justified mathematical economics might have arisen from outside the communities of those who developed mathematical economics. Sometimes, this might have resulted from needs, expectations, and troubles of the surrounding and evolving society, and other times as a consequence of the encounter and amalgamation of scientific and nonscientific practices within scientific and nonscientific contexts in the daily work of our historical actors. The role that economic knowledge played in society, and the influence that that society exercised over the development of economics, might have been locally contingent: a historiographical stress on the local entanglements may therefore downplay or reinforce the distinction between the theoretical and the applied, between models and mathematics.

To this extent, Erwin Dekker shows us the articulated and complex interaction between the role of economic knowledge in society and its theoretical counterpart, embedded within a local context. The work of Jan Tinbergen and the political context of the Netherlands, in particular the tension between theory and economic policy, are deeply entangled in the work of the future Nobel Prize winner. To that purpose Dekker describes Tinbergen's work as neither theoretical nor applied economics; it was rather a policy science, answering to the needs of a local and institutional context that motivated it. Tinbergen's development of analytical and econometric tools must be understood—Dekker tells us—contextually with the needs of the Dutch state in terms of policymaking. Tinbergen's theoretical advances were in sum the result not of efforts to produce or understand the structure or foundations of economics, but rather of efforts to respond to pragmatic needs that Tinbergen was confronted with in his daily work at the Dutch Central Bureau of Statistics. Yet, this reading of Tinbergen becomes possible, or at least much easier, once we focus on the place where he produced that knowledge, which also means that we focus on how that specific place valued knowledge, and how he used it.

The entanglement of rational and social aspects, of scientific and nonscientific practices, derives—in Dekker's narrative—from Tinbergen's working place—a context that structures and guides Tinbergen's economic thinking. Yet, this local overlapping of scientific and nonscientific practices may hardly be split into distinct sets of influences, one being “scientific” and the other not. The “multilayered mosaic” of scientific and nonscientific practices, locally scrutinized, is irreducible to smaller scientific and nonscientific components, and the entanglement of rational and social aspects cannot be disentangled.

A similar entanglement between scientific and nonscientific practices can be found in Roger Backhouse's account of the encounter between Paul Samuelson, the Sloan School, and the MIT economics department. Samuelson at MIT—along with several colleagues—will develop an interest in finance, and in particular in trying to “beat the market.” This interest, shared by several members of the department, will come to coincide and mingle with the propensity for problem-solving and the taste for the use of mathematics typical of MIT culture. Backhouse thus illustrates how a place can overlap and join social and rational aspects in the development of new ideas. At the same time, the local approach proposed by his article makes it possible to treat “a community as an epistemic subject” where “the social can be seen as something that enables rationality” (Kuukkanen 2012: 309), through the overlapping of scientific and nonscientific practices, again a case of Livingstone's situated rationality. Indeed, it is the communities of researchers of which Samuelson was a member that held at once the sociocultural interest for financial assets, revealing the MIT engineering ethos and its willingness to beat the market. Backhouse shows how this ethos was crucial for the emergence of a set of ideas designed to describe the behavior of financial assets. Although Samuelson is clearly the central figure in this historical episode, he belonged to different and overlapping scientific communities: the sociocultural interest derives from the specific work group in which Samuelson is placed, and the interest to beat the market is an economist's dream, while the engineering ethos derives directly from MIT as an institution.

In short, it is the local entanglement between Samuelson, his research team, his institutions, and his social acquaintances that creates the blending that enables the birth of a new branch of economics, and it is through a local gaze that it is possible to better understand this specific contribution to intellectual history. The local approach thus makes it possible to treat the whole community, rather than a single individual, as capable of developing specific knowledge, as well as the tastes and interests of this community as an engine of development for new economic ideas. The “social” and “rational” aspects of the place that Samuelson occupies simply coincide, and the scientific and nonscientific aspects of his narrative overlap, creating a case of situated rationality.

Legitimacy, authenticity, credibility, and reliability aspects in the history of knowledge production locally considered might also be key for clarifying the historical track of the circulation of mathematical economics. The local category suggests that as past scientific practices and ideas moved from one place to another, they were varyingly perceived as legitimate, authentic, credible, and reliable, reflecting thus that what passes as (scientific) knowledge is contingent on place and time. This might suggest that as mathematical economics moved across different spheres of activities, sites, research centers, universities, cities, countries, or continents, its practices and its content did not necessarily remain invariant. This would imply that as it moved, it was translated, adapted, or transformed in some places, but also ignored, contested, or rejected in others. In both cases, the legitimacy/illegitimacy of mathematical economics would have been justified at the local level where in addition to disciplinary aspects, social, political, ethical, and cultural practices had their say in the implicit negotiations within specific spaces that eventually granted or did not grant such legitimacy to mathematical economics.

During the twentieth century, mathematical economics developed in particular communities, based in particular places, grounded in particular ideas and practices. These local particularities gained social and scientific legitimacy and came to be regarded locally as the authentic practices of economics, informing scientific economics and influencing economic policymaking. Now that historians of science are currently scrutinizing the histories of science and capitalism, and historians of economics are studying the history of economic knowledge in socialism, from the locally entangled perspectives, it seems even more appealing to zoom in on the overlapping spaces where those economists and noneconomists who prompted the development of mathematical economics acted (Rieppel, Lean, and Deringer 2018; Düppe and Boldyrev 2019).

Paul Erickson focuses on questions of choice during the process of building knowledge. For this, he delves into the category of local cultures of theory, which arise when groups of scholars or disciplinary communities, bound by a shared discourse and common practices, enforce in their practices, and work their preference for, certain notational and computational approaches or deliberately adapt existing methods to align with their particular objectives. On this basis, Erickson contextualizes Elinor Ostrom's theoretical choices in the process that led her to publish Governing the Commons. He shows how, after her encounter with Reinhard Selten in Germany in the early 1980s, game theory would serve as a key theoretical inspiration for her. Not primarily concerned with mathematical rigor, she selectively used some parts of game theory and changed them to suit her purposes, which amounted to finding ways of making sense of the very local problems of “the commons” as related to the large diversity of empirical cases that she was considering. Borrowing from strategic games, she developed her own institutional framework for locally managing “common pool resources,” characterized by an original interdisciplinary positioning straddling political science, economics, and sociology. In this sense, game theory proved to be a tool of great versatility for Ostrom, more a descriptive than a deductive system, capable of bending to her specific local needs.

All in all, the local entanglement perspective has—we believe—the potential to reveal new and neglected aspects of the history of the mathematization of economics. Our main claim is that it is an attempt to look at the history of mathematical economics, and hence of modern economics, from a different perspective that somehow downplays some aspects of the history of mathematization and reinforces others; while this by no means diminishes the value of other approaches, it allows for a different understanding and focuses attention on potentially neglected topics. In brief, it allows for taking the diversity of varying local contexts within which economics developed as a mathematical and statistical discipline directly connected or undirectedly connected with economic policy concerns.

A local perspective allows us to, paraphrasing Livingstone, put rationality in its place, thus treating the legitimacy and credibility of scientific knowledge as contingent on a place and a community; places of scientific practice are a mosaic, an entanglement of social, political, cognitive, epistemic, and cultural practices, and the same practice is often all those things simultaneously. A local perspective thus downplays the distinction between theoretical and applied, between analytical and contextual, or between epistemic and nonepistemic. From a local perspective, places, rather than being “containers” of social life, are “an active ingredient in social and cultural life” (Finnegan 2008: 371).

These local perspectives propose different narratives and thus argumentative and explanatory logics of knowledge production that go beyond the traditional dichotomies (theoretical/applied, analytical/contextual, rational/social), reflecting rather the ways of living and working peculiar to specific places, which often escape these dichotomies and respond to needs and interactions whose primary explanation lies in the places and institutions that generated them. The local perspective thus offers a new and different way of looking at the history of the mathematization of economics.

Notes

References