Introduction

The center of gravity of macroeconomics shifted toward the United States (US) with the Second World War, as some European economists immigrated to the US (Hagemann 2011, Backhouse 2017) and a new generation of American economists took up tools introduced by early econometricians (Assous and Carret 2022). Paul Samuelson’s late 1930s discussion of the accelerator-multiplier interaction was key to that transformation. His 1939 multiplier-accelerator (MA) model quickly became a base camp for a new generation of economists, serving as the foundational tool from which various theoretical expeditions were launched. Many of them, who were closely associated with Alvin Hansen, who had joined Harvard in 1937, used the model to address a variety of new macroeconomic issues. Interestingly, that model was initially used by economists such as Thomas Schelling, Alexander and others for accounting for growth rather than for business cycles (Assous, Boianovsky and Dávila-Fernández 2024).

My aim in this article is to understand how Richard Goodwin used the MA model and transformed it for accounting for economic irregularities and innovations. Also at Harvard, Goodwin was connected to Hansen; his relationship with Joseph Schumpeter, however, was perhaps more profound. While Hansen embraced the modeling strategies of his contemporaries, Schumpeter, in contrast, consistently challenged them, particularly those developed by economists like Ragnar Frisch, Samuelson, and eventually Goodwin (Velardo 2025; Louçã 2001, 2015; Vieira and Assous 2025).

Goodwin was perhaps the most inclined of his fellow econometricians to develop small models rather than a vast, all-encompassing theory. The price to pay was ending up with fragmented pieces, leaving the question of their unification open. He was optimistic enough, however, that such a strategy would allow him to map new territories and to eventually find ways to connect them. Within six years (1946-1951), he developed no fewer than six models. Historians and economists examining this period primarily focus on Goodwin’s contribution to nonlinear macrodynamics.¹ The introduction of non-linearities into the MA model in 1951 proved to be particularly successful, as it was responsible for generating self-sustaining cycles. It influenced later modelers to build upon this foundation (Sasakura 1996; Matsumoto 2009; Matsumoto and Suzuki 2016; Zhao and Zhang 2024). Interestingly, Goodwin began by developing linear MA models (1946, 1948), which are usually interpreted as stepping stones toward his more complete 1951 framework (Velupillai 1990, Sordi & Vercelli 2006). Within this interpretation, Goodwin’s main achievement was viewed as a way to depart from Frisch’s impulse-propagation approach and a way to avoid reliance on exogenous shocks.

This article intends to offer a different view by arguing that Goodwin’s main motivation was to explore various ways of accounting for the effects of such shocks. Fundamentally, using linear and nonlinear MA models, Goodwin sought to provide new insights into the effects of exogenous shocks, which he viewed as a critical means to account for irregularities and move beyond a mechanical representation of economic movements. In sum, a study of Goodwin’s modeling of technical progress provides a better understanding of his ambitious intellectual project to formalize capitalist dynamics.²

Duarte and Hoover’s (2012) historical account of shock modeling traces the shifting epistemic status of shocks from Frisch’s impulse–propagation framework through Haavelmo’s probabilistic turn to Klein’s macroeconometric models. We contend that our study adds a new dimension to that reflection in highlighting a singular way to account for shocks, especially those related to technical progress and innovations.

Several models will be examined with the aim to highlight how Goodwin incorporated in various ways technical progress and discussed its impact on the dynamics. Section 1 provides an overview of his formative years and the development of his methodological toolkit. This context is essential to grasp the research lines followed by Goodwin. Section 2 places Goodwin within the Frisch-Schumpeter debate on innovation. In 1946, he devised a first way to derive irregular movements from the multiplier-accelerator. More precisely, this model superimposed a sinusoidal curve onto a linear model assumed to generate damped cycles, thereby showing how irregular movements could emerge (Section 3). Two years later (Goodwin 1948), in a contribution that sought to solve an empirical puzzle echoing Hansen’s reflections on the multiplier-accelerator, he proceeded differently. From then on, he integrated innovations directly into an “accelerator” showing how erratic innovations may distort the amplitude and periodicity of the cycle (section 4). In a continued effort to better account for investment decisions related to surplus capital, Goodwin (1951) ultimately revised his view on nonlinearities. The inclusion of non-linearity allowed him to show how this time continuous technical progress may generate complex, irregular cyclical dynamics.³ The model acts as a veritable “frequency converter”, a feature we suggest discussing on the basis of simulation (section 5).

1. Goodwin’s Formative Years and the Development of a Methodological Toolkit

Goodwin’s intellectual path was shaped by the Great Depression and his early Marxist leanings. A student at Harvard in the early 1930s, he became an active member of a Marxist association. He realized that his convictions created a significant obstacle, as he “knew that as a Marxist I would be unemployable in an American university.” This led him to pursue monetary economics for his dissertation while studying at Oxford—a field technical enough to “conceal his ideological leanings” (Goodwin 1985, 4).

Goodwin found this diversion from his true interests deeply frustrating, stating that he “found it unbearable to devote [his] life to a study totally unrelated to [his] own interests” (Goodwin 1985, 4). Upon his return to Harvard in 1937, his career took a decisive turn when he reconnected with Schumpeter. His initial skepticism toward Schumpeter gave way to admiration, as he came to appreciate the economist’s deep understanding of Marx. Goodwin described Schumpeter as an “intelligent reactionary, fully cognizant of the contribution of Marx” (Goodwin 1985, 4).⁴

This new intellectual alliance with Schumpeter was pivotal. Goodwin saw them as forming a unique “club” dedicated to the ambitious project of understanding the historical evolution of capitalism. His personal ambition became to extend their intellectual project by providing a mathematical formalization of their theories (Vieira and Assous 2025).

This intellectual quest was supported by a blend of economic and physical science expertise. Alongside his economic studies, Goodwin taught physics at Harvard during World War II, an experience he took advantage of “to better practice the art” of applied mathematics (Goodwin 1985, 7). This background, combined with his exposure to cybernetics seminars in the mid-1940s (Velupillai 1998a), made him intimately familiar with dynamical systems and concepts like frequency and resonance.

In the mid-1940s, Goodwin found a perfect starting point for his project in the MA model, a framework pioneered by figures like Samuelson and influential in the intellectual circles around Hansen at Harvard. This model’s ability to account for turning points offered a powerful foundation for Goodwin’s own explorations.⁵

2. The Dialogue on Shocks as Innovation: Frisch, Schumpeter, and Goodwin

Goodwin recognized an opportunity to use the MA model to better understand the effects of shocks. His discussions of shocks primarily refer to Frisch and Schumpeter. Specifically, in both 1946 and 1951, these were his exclusive citations on the topic. Notably, his 1948 work on this subject did not draw upon the contributions of his contemporaries. This selection, seemingly at the expense of incorporating insights from the probabilistic revolution or the work of public policy modelers like Jan Tinbergen, was arguably motivated by Goodwin’s explicit interest in innovation shocks, as articulated by Frisch and Schumpeter. He thus engaged with a pivotal debate that sought to reconcile the visions of two prominent economists. Louçã’s (2001, 2015) meticulous correspondence analysis between them reveals the intensity of these exchanges and the issues that underpinned them.

Frisch’s contribution (1933) is well known. He favors a propagation approach, in which shocks are merely punctuating disturbances, random hits with a club that disrupt the regular motion of an economic “rocking horse”. He sees macroeconomics as a deterministic mathematical system, in which propagation represents the intrinsic properties of the system. These properties determine the system’s tendency to oscillate, characterized by intrinsic damped cycles. The impulse, or shock, is therefore the crucial force that maintains the system in a state of permanent movement. He uses the metaphor of a rocking horse hit by a stick to illustrate this idea: the shock provides the initial energy that sets the system in motion, while the deterministic structure of the system (the rocking horse) determines the periodicity and damping of oscillations. The shocks are considered to be errors in relation to the deterministic system (Duarte and Hoover 2012).

Schumpeter, disagreeing with Frisch, insists on the central role of endogenous innovations, stemming from entrepreneurial activity. He sees innovations not simply as exogenous shocks, but as internal driving forces that fundamentally transform the economy.⁶ He criticizes the mechanical analogy, as it fails to capture the irreversible, historical nature of innovations. He prefers the analogy of biological mutations,⁷ and opposes the classification of innovations as mere impulses.⁸

Frisch sought to reconcile the two points of view by proposing a new mechanical analogy, a pendulum with a self-sustaining mechanism powered by a flow of innovations.⁹ However, despite this attempt at reconciliation, the fundamental divergence persists. Schumpeter acknowledges that Frisch’s analogy represents progress but insists on the need to consider the “irregularities, deformation and shifts in the body of economic relations throughout the cycle” (Louçã 2015).

This is when Goodwin comes in. A decade after Frisch’s first attempts, he embarked on the ambitious project of modeling the business cycle by integrating technical progress. Goodwin, much like Frisch, sought to convince Schumpeter of the relevance of his own modeling, aiming to align his theoretical constructs with Schumpeterian intuitions. Goodwin himself later clarified the nature of this relationship in a June 22, 1991, email to Paolo Sylos Labini, stating that regarding their conceptions of innovation, “[t]here was no disagreement between me and Schumpeter on this point, only a matter of methodology.”¹⁰

As we will discuss in more detail, Goodwin’s proximity to Schumpeter created a key divergence between his approach and that of Frisch. While Frisch regarded shocks as errors—exogenous disturbances disrupting a deterministic system—Goodwin attributed to them a central, driving role in economic dynamics. This initial disagreement is a specific instance of a broader trend. Goodwin’s emphasis on the role of shocks sets his contributions apart from many of those of his contemporaries. As he may have recognized, much like Tinbergen would decades later, what most interested economists “was not the shocks but the mechanism generating endogenous cycles”, and that the role of this mechanism “might very well be…overestimated” (Tinbergen 1987, 125, quoted by Louçã, 232). We summarize this information in Table 1.

3. Innovation as Excitation: Goodwin’s Transposition of Physical Resonance to Economic Dynamics (1946)

Building on his experience teaching physics at Harvard during World War II (see section 1), Goodwin imported the concept of resonance from that discipline into economics, applying it in his 1946 article. This provided him with his first opportunity to formalize Schumpeterian ideas. The model studies the impact of sinusoidal shocks (essentially technical progress) on an (oscillating) MA model. To clarify what it does, I offer a mechanical analogy: Frisch (1933) envisions a damped rocking horse being hit with sticks whereas Goodwin (1946) depicts the business cycle in terms of coupled pendulums.¹¹

Although Goodwin himself did not use this metaphor, in physics it is a classic example of the concept of resonance that he imported into his work. This paper employs this metaphor to explain his 1946 article for two reasons. First, it aids intelligibility: Goodwin’s concepts come from another discipline and are not intuitive. Second, the metaphor reveals an epistemic dimension. The analysis of dispositions (in this case: his background as a physics teacher)¹² must be complemented by the exploration of what sociologists call categories or schemes of perception (Bourdieu 2013, Bourdieu and Delsaut 1981) or mental structures (Goldmann 1970).

A first pendulum acts as a resonator (or “passive oscillator”). It represents the MA model. A second pendulum is the exciter (or “active oscillator”), which is technical progress. This sustains the cycle because “so long as capitalism is not stationary” then “the oscillations…will not tend to die out” even though “the mechanism itself has damping” (Goodwin 1946, 103). These two pendulums are connected by a rigid rod that allows them to be coupled.

The rod connects to a second rod mounted on a ball bearing, which supports both pendulums. Through this arrangement, an interdependence is established between the two, illustrating the relationship between the MA model and technical progress. The second pendulum is moved away from its equilibrium point, triggering its oscillations. These have a certain frequency, which in turn depends on the length of the wire (a general property of pendulums). We observe the reaction of the first pendulum. If its natural frequency is the same as that of the second pendulum (in other words, if its wire is of similar length), then they enter into resonance. There is a maximum transfer of energy between the two pendulums (or between the MA model and technical progress), i.e. the resonator (the first pendulum or multiplier-accelerator) exhibits a considerable amplitude increase. This is the case when we have a MA (oscillating) model with technical progress in sinusoidal form (see Figure 1).

Figure 1

L(t) as “innovational expenditure”, referred to in the text as “technical progress.”

Source: Goodwin (1946).

However, Goodwin himself acknowledged that “[i]t is undoubtedly not true that the time shape of l(t) is sinusoidal” (1946, 99), and he thus proceeded to break down technical progress into a multitude of components—a sum of sinusoids. The response of the mechanism to each component is calculated by defining its system response units. Regarding this series of impulses, Goodwin argues that “[t]his is essentially the same method as that proposed by Frisch to handle the problem of random disturbances” (1946, 104). This is one of the few quotations in the article that shows the importance of Frisch’s work for Goodwin. Thus, the innovation (pendulum 2) is less regular than before. Then, by adding up these responses, the resulting shape of the system exhibits irregular cycles (see Figure 2).

Figure 2

Application of the non-periodic “innovational expenditures” L(t), as an external excitation to the system.

Source: Goodwin (1946).

Unlike the technical progress function in model 2, the exciter does not have a well-defined frequency; it is irregular. It is therefore slightly misleading to invoke the concept of resonance. Resonance occurs when an oscillating system is excited by an external force at a frequency close to its natural frequency. To transpose this case into our previous analogy, we must imagine that pendulum 2 (technical progress) now receives small projectiles randomly, which make its oscillations irregular. The exaggerated nature of this import of concepts suggests that Goodwin is looking at business cycles through the lens of mathematical physics.

The approach consisted in introducing into the MA model innovations conceived in sinusoidal form, i.e. innovations that were intrinsically fluctuating. The strategic approach favored at the time appeared crystal clear: to give substantial economic significance to a concept derived from classical mechanics. The idea was to import a formalization in accordance with the laws of motion and oscillation to shed light on the dynamics specific to economic activity, postulating a structural analogy between physical systems and economic systems in their capacity to generate undulatory movements. Admittedly, as Frisch (1933) put it, innovations guarantee the persistence of the cycle. But the real novelty of this model lies in the ability of innovations to amplify the cycle itself—in line with Schumpeter’s intuitions—and, more fundamentally, to distort it, removing it from the regularity of expected patterns. Goodwin demonstrates that the impulse’s form can actively engage with the system’s structure via resonance or interference, thus subtly blurring Frisch’s sharp distinction between propagation and impulse.

4. Stepping from the Base Camp: The Flexible Accelerator as a Bridge to Innovation (1948)

In 1948, Goodwin published the chapter “Secular and Cyclical Aspects of the Multiplier and the Accelerator” in the collective work “Income, employment and public policy: essays in honor of Alvin Hansen.” Goodwin’s chapter aims to reconcile seemingly contradictory empirical data on both the short-term economic cycle and long-term growth. He once again invokes the MA model for this purpose, but its classical form proved insufficient to resolve this empirical puzzle, prompting him to amend it.

Between 1946 and 1948, the form of the accelerator in Goodwin’s work changed considerably, evolving from the model discussed in the previous section to the flexible accelerator. While Sordi and Vercelli (2006) have clearly demonstrated this transformation, our analysis will place a particular emphasis on the integration of innovations within this new version. Initially, Goodwin adopted Samuelson’s (1939) proposal fairly strictly with the following investment function (in 1946):

$I = \kappa \{C(t) – C(t – \theta )\}$       (1)

where κ is the coefficient determining the amount of investment when there is a change in consumption between C(t) and C(t – θ). Investment is then endogenous, determined by the need to adjust the capital stock to consumption variations (and, therefore, indirectly to production growth). It is to such a mechanism, as I outlined in the previous section, that Goodwin applied the force of technical progress, clearly obtaining the emergence of irregularities within the economic dynamic.

However, this overly mechanical relationship left him unsatisfied. Consequently, in 1948, Goodwin set about refining his 1946 MA model, equipping income formation with a linear but flexible accelerator. This development was accompanied by the abandonment of the sinusoidal conception of technical progress. The hypothesis that this new accelerator was a way of generating economic irregularities without resorting to the ad hoc artifice of sinusoidal technical progress cannot be considered irrelevant. The approach begins from a situation where the ratio between capital stock and production is not respected, but targeted, and observes how the system evolves. Henceforth, the investment equation

$\stackrel{\cdot }{k} = 1 / \xi (\kappa y + \varphi – k)$¹³       (2)

governs the model, with “ξ as the dimensions of time, and may be interpreted as meaning that any excess or deficiency of capital is removed at a rate which would abolish it in ξ years, if nothing else changed” (Goodwin 1948, 120). Thus, investment is proportional to the gap between desired capital (always relative to the capital-production ratio, which is now explicit in the form κy, i.e., a constant multiplied by production) and actual capital (k). This accelerator alone still does not produce a self-sustaining cycle (i.e., endogeneity). To keep it going, Goodwin reintroduces technical progress. The novelty is that this time he does so directly via the accelerator! When technical progress is absent or constant, the marginal efficiency of capital (via κ) determines the equilibrium target, and the dynamics converge. But as soon as technical progress (ϕ) intervenes, it displaces this target, preventing convergence to a fixed equilibrium and making capital and investment dynamics dependent on both income and innovations. Let’s use a simple numerical example to clarify this model. Assume we want to achieve a capital stock level (k) equal to 1.5 times production (thus κ = 1.5). With initial production (y) and capital stock both equal to 20, our capital stock target is 30. The velocity is such that we would reach this target in two periods (ξ = 2). This means that we will have an investment of 5 in period 1, and 5 in period 2, to reach a capital stock of 30, which is our target. Now, if we add innovations, the dynamics change. For example, with an innovation (ϕ) that increases investment by 4 in period 2, the capital stock rises to 34. This is a simplified example that isolates the amount of production from the impact of investment. However, the core of the reasoning is clear: for each level of production—for a given state of technique—there is an optimal level of capital (k/y ratio). This ratio is not automatically achieved, but the logic of investment tends toward it, at which point the cycle would end. However, innovations prevent this target from being reached, causing fluctuations around it.

Similar to his 1946 model, this framework departs from Frisch’s propagation-centric view, as Goodwin permits innovations (conceived as “impulses”) to distort the cycle’s intensity and periodicity (a result that brings him closer to Schumpeter). Notably, the model redefines the propagation/impulse boundary by embedding impulses directly within the investment mechanism, a core component of the propagation system itself. Effectively, he began to blur the line between exogenous and endogenous impulses, which had previously separated Frisch and Schumpeter. He then took this even further by introducing non-linearity into the accelerator, a development we will analyze in the next section.

5. Beyond the Dichotomy: Integrating Shocks and the self-sustaining Cycle

A few months later, again in his quest to better account for investment decisions relating to surplus capital, Goodwin shifts gears and focuses on non-linearities. Commentators have clearly shown that Goodwin’s introduction of nonlinearities was sparked by his discovery of nonlinear oscillators, a concept he learned from his physicist colleague, Philippe Le Corbeiller, at Harvard. Initially developed to model self-sustaining oscillations in electronic circuits, these oscillators were later applied to biological phenomena such as heartbeats (Velupillai 1998a, 1998b; Assous and Carret 2022). This once again demonstrates the significant influence of Goodwin’s background as a physics professor on his economic modeling.

In late 1948, he attended the Econometric Society meeting in Cleveland to present the core concepts of his upcoming 1951 paper, which he had already developed (Goodwin 1949). In refining the model presented in 1948 by segmenting the investment function into three distinct values, each depending on the gap between desired and actual capital, he managed to get a first model generating self-sustained cycles. When the desired capital is greater than the capital actually present in the economy, the investment function takes on its highest possible value. In contrast, when the desired capital is less than the actual capital, then the investment function takes on its lowest possible value so that surplus capital is reduced at the rate of its depreciation. Finally, when desired and actual capital coincide, net investment is equal to zero and equilibrium is reached. The equilibrium is unstable, meaning that any small deviation from it leads to a self-reinforcing process. This dynamic behavior, described in detail by Gandolfo (2010), results in the formation of a limit cycle. Most commentators have emphasized this feature of Goodwin’s model (e.g., Matsumoto 2009; Matsumoto and Suzuki 2016; Sasakura 1996; Zhao and Zhang 2024; Mignon 2010; Velupillai 1990, 1998a, 1998b; Sordi and Vercelli 2006). A less discussed but equally important aspect of Goodwin’s work is his deeper motivation. With hindsight, his ultimate goal was to build a more comprehensive model that incorporated exogenous shocks he associated with technical progress. His intention was to articulate self-sustained oscillations with these shocks, whether at the aggregative or disaggregate level—a preoccupation he maintained forty years later: “At the moment my only task remains to try to make some progress in analyzing […] evolution of innovative change in the economic structure” (Goodwin 1991).¹⁴

This becomes clear when examining Goodwin’s second model in which technical progress is assumed to exert a constant force on desired capital. Desired capital is therefore no longer simply a fixed ratio of total production; instead, a trend is now added to it via technical progress. Nevertheless, in perfect continuity with previous modelling architectures, technical progress once again plays a role in distorting the business cycle. Although Goodwin alludes to this subject, he is very brief. To corroborate this assertion, we therefore conducted a high-fidelity simulation of the model, followed by a spectral analysis that proved conclusive (Figure 3). Higher spectral width (on the y-axis) indicates that the cycle exhibits a wider range of frequencies, signifying greater irregularity. The x-axis represents the magnitude of the shock (technical progress). Because each simulation corresponds to a unique combination of model parameters, a multiplicity of graphs is presented. In other words, for each parameter combination, we can observe whether the introduction of technical progress (the shock) makes the cycle more irregular.

Figure 3

Effect of constant shock amplitude on cycle regularity.

Source: The Author.

The dense information represented in these graphs can be summarized in a statistical table (Table 2).

For each value of a (constant shock resulting in a permanent change in the trend value), we can observe the percentage of cases in which irregularity increases or decreases. For example, for a = 0.7, there is an increase in irregularity in 77.8% of parameter combinations, and a decrease in 7.41% of cases. This reveals a large majority of destabilizing influence from technical progress, with a small proportion of neutral shock influence (14.79%). For every value of a, a majority of combinations result in the model being destabilized. On average, across these six values, there are 72.87% of cases in which the cycle is more irregular than without a shock.¹⁵

This is a far-reaching change compared to previous models. This model represents a profound and innovative departure from Goodwin’s earlier work. Previous models introduced irregular technical progress to generate economic irregularities, but this new approach reveals that such irregularities can emerge from the interaction of smooth technical progress with a limit cycle. In other words, the integration of non-linearity into the model’s architecture has generated a true frequency converter (as Goodwin himself remarked), metamorphosing a stable input into a fluctuating, complex output.

It should be recognized that, in contrast to Frisch’s original view, the inherent structure of the system permits the intensity of the impulse to influence the periodicity of the cycle. More fundamentally, a clear paradigm shift has occurred away from Frisch’s impulse/propagation dichotomy. The validity of the “impulse” notion itself is challenged if it presupposes a constant exogenous force. Until now, mathematical tools had inclined modelers to apply external impulses to a deterministic system. It is clear that, in this model, even more so than in his previous ones, Goodwin manages to break free from this dichotomy. He himself claims compatibility with Schumpeterian theory (which may seem surprising at first glance, given that Schumpeter talks about innovations in swarms): “The mode of action of this progress has considerable affinity with the Schumpeterian theory of innovations. New ideas requiring investment occur regularly, but nonetheless investment goes by spurts” (Goodwin 1951, 8).

Conclusion

Richard Goodwin’s early works, between 1946 and 1951, offer a fascinating insight into his ambition to formally represent capitalist dynamics. While scholars have conventionally highlighted Goodwin’s pursuit of self-perpetuating cycles, our analysis reveals a crucial, yet overlooked, dimension of his intellectual project. We argue that he was persistently striving to account for economic irregularities by incorporating a specific treatment of shocks, thereby seeking to move beyond a purely mechanical representation of economic movements.

We have shown how Goodwin explored several approaches to integrating technical progress and the analysis of its impact on economic dynamics. His evolution is evident in his models, from his 1946 work, which ultimately incorporated irregularities into the MA model by superimposing an irregular innovation curve on it, to his 1948 contributions, where erratic innovations destabilized cycles through the investment function. Eventually, his embrace of non-linearity in his 1951 model allowed him to demonstrate how stable technical progress could generate complex, irregular cyclical dynamics, acting as a “frequency converter”, a feature confirmed by our simulations.

Goodwin’s intellectual journey was characterized by the use of tools from mathematical physics to shed light on economic processes. Consequently, he was able to explain economic phenomena, particularly cyclical irregularities, using relatively simple and concise hypotheses.

He established novel research directions, bridging the theoretical landscapes of Frisch and Schumpeter. His analytical approach frequently blurred the conventional distinctions between endogenous and exogenous forces, or between propagation and impulse, even as his chosen modeling instruments often necessitated the formal use of exogenous shocks. Crucially, the outcomes of his models consistently resonated with Schumpeterian intuitions, revealing economic irregularities, a degree of irreversibility stemming from innovations, and the capacity to embed a historical dimension within the concept of innovation itself. Ultimately, Goodwin’s methodological choice to focus on developing specific models rather than constructing a comprehensive general theory has undoubtedly opened up promising avenues of research. Nevertheless, this approach reveals the intrinsic difficulties of articulating theoretical approaches with potentially contradictory assumptions.

Acknowledgments

I am deeply grateful to all those who generously contributed to this article through their insightful reviews and helpful comments, including my colleagues at the Triangle Laboratory. Special thanks are due to Gary Mongiovi for graciously serving as my mentor for the RHETM Students’ Work-in-Progress Competition. My sincere appreciation also goes to my PhD advisors, Michaël Assous and Roberto Lampa, for their continuous support, and to Paolo Paesani for his valuable guidance during the 2025 ESHET Summer School. Finally, I extend my deep appreciation to the Archives Department at the University of Siena for granting crucial access to the Goodwin papers, which made this research possible.

Competing Interests

The author has no competing interests to declare.