How Machines and Magnets Taught Science a New Way to Explain the World

A new study published in AI & Society argues that two of the twentieth century’s most transformative scientific traditions—cognitive science and statistical physics—arrived, independently and almost simultaneously, at the same profound methodological discovery: that some phenomena can only be understood by building artificial models of them and watching what those models do. Francesco Gagliardi, an independent scholar based in Rome, reconstructs the history of what the late Italian historian of science Roberto Cordeschi called the “Discovery of the Artificial” and extends it into a sweeping claim about the unity of modern science. In Gagliardi’s account, the early twentieth century witnessed not one but two parallel epistemological revolutions, both driven by the same inescapable problem: complexity.

The story begins with Cordeschi’s original insight, which Gagliardi revisits and reinterprets. In the 1930s and 1940s, researchers in the emerging behavioral sciences began constructing machines—mechanical and, later, electronic artifacts—that could reproduce intelligent and adaptive behavior. These were not merely engineering curiosities. They functioned as scientific models: ways of testing hypotheses about how minds and nervous systems might work. Kenneth Craik’s 1943 proposal that organisms carry internal models of external reality, Warren McCulloch and Walter Pitts’s 1943 logical calculus of neural activity, and the later cybernetic machines of Norbert Wiener’s circle all exemplified what came to be known as the “Synthetic Method.” Rather than analyzing a natural system into its components and deriving its behavior from first principles, the synthetic method proceeds in the opposite direction: it assembles an artifact from simple parts and observes whether the target behavior emerges.

Gagliardi’s central move is to pair this familiar narrative with a less obvious one from physics. In 1920, Wilhelm Lenz proposed a radically simplified model of ferromagnetism, and his student Ernst Ising worked out its properties in 1925. The Lenz–Ising model represents a magnetic material as a lattice of spins, each of which can point up or down and interacts only with its nearest neighbors. Nothing about the model resembles a real magnet in its fine detail. Yet this deliberately crude artifact turned out to capture something essential about how collective phenomena—phase transitions, critical points, cooperative behavior—arise from local interactions. Gagliardi argues that the introduction of the Ising model in the 1920s represents a methodological turning point in the physical sciences directly analogous to the one occurring at the same time in the behavioral sciences: the embrace of artificial, simulative models as legitimate instruments of scientific understanding.

Why did both fields converge on this strategy? Gagliardi’s answer lies in the mathematics of complexity. In the kinetic theory of gases, the nineteenth-century triumph of Ludwig Boltzmann and James Clerk Maxwell, it was possible to move analytically from the microscopic behavior of particles to macroscopic laws: the model could be solved in closed form, yielding the ideal gas law. But the Ising model resists such treatment. It has been formally proven, in work by Sorin Istrail published in 2000, that computing the ground state of the Ising model is computationally intractable—an NP-hard problem. Assuming the widely held conjecture that P does not equal NP, no closed-form analytical solution exists except in trivial cases. The same wall of intractability confronts cognitive modelers: Paul Thagard and Kevin Verbeurgt showed in 1998 that a connectionist model of coherence as constraint satisfaction is equivalent to the NP-complete Max-Cut problem. When exact analysis is impossible, the only route to understanding is simulation—running the model and observing its behavior.

This is where the concept of computational irreducibility enters. For complex systems, whether biological or material, there is often no shortcut from the model’s specification to its outcomes; one must simply let the dynamics unfold. Gagliardi contends that this epistemic necessity, rather than any mere fashion or convenience, explains why both cognitive science and statistical physics became what he calls “complexity sciences.” Both disciplines, in his phrase, “discovered the artificial”: they came to accept that understanding a system may require building an internal model of it whose behavior can be observed, even when no analytic derivation of that behavior is available. The artificial model becomes not a substitute for explanation but the very medium of explanation.

The philosophical stakes of this claim are considerable. Traditional accounts of scientific explanation, descending from Galileo’s famous declaration that the book of nature is written in mathematical language, privilege derivation: to explain is to deduce consequences from mathematical first principles. Gagliardi argues that the synthetic method extends rather than abandons this Galilean language. The new language of models and simulations adds to mathematical description the capacity to create and run artificial systems whose behavior can be studied. He points to Ernst Mach’s nineteenth-century observation that all science seeks to replace or economize experience through the mental reproduction of facts—reproductions that are easier to handle than experience itself and can stand in for it. Simulation, on this view, is the modern technological fulfillment of Mach’s epistemology of thought-economies, closer in spirit to a gedankenexperiment than to a laboratory measurement.

The article also engages a live debate in the philosophy of science about the epistemic status of computer simulations. Are simulations experiments, or are they theory? Gagliardi notes that observing the physical system under study belongs to the empirical verification phase of the scientific method, whereas observing a simulation pertains to theory and to the deduction of a model’s properties. He acknowledges that this distinction is contested: philosophers such as Anouk Barberousse, Cyrille Imbert and Sara Franceschelli, Claus Beisbart, and Judith Jebeile have argued for a genuine affinity between experiments and simulations, while others, including Julian McClelland and Darrell Rowbottom, treat simulations as instruments rather than faithful recreations of phenomena. Gagliardi’s historical framing gives this debate new context: the question of what simulations are is inseparable from the century-long process by which both physics and the mind sciences learned to trust artificial models.

Perhaps the most provocative element of the paper is its appeal to weak emergence, a concept developed by Mark Bedau, to characterize the new kind of scientific understanding that the synthetic method affords. In systems like the Ising model, there is no causal reductionism linking the internal model to macroscopic phenomena in the way that the kinetic theory analytically links molecular motion to the gas laws. Instead, macroscopic patterns depend on, but are not derivable from, the micro-dynamics—a dependence that must be exhibited through simulation rather than demonstrated through derivation. Gagliardi suggests that explanation centered on the internal functional organization of systems, in the tradition of Robert Cummins’s functional analysis, offers a shared explanatory idiom for both disciplines. Understanding becomes a matter of seeing how a system’s organization produces its capacities, a form of comprehension that simulation makes possible and that pure mathematics alone cannot deliver.

The convergence Gagliardi describes has contemporary resonance. The 2024 Nobel Prize in Physics, awarded for foundational work on artificial neural networks, underscored how deeply the physics of collective phenomena and the science of mind have become intertwined: John Hopfield’s 1982 neural networks drew explicitly on statistical-mechanical ideas, and Boltzmann machines, developed by David Ackley, Geoffrey Hinton and Terrence Sejnowski in 1985, carry the name of the great statistical physicist. Recent work by Iris van Rooij and colleagues has argued for reclaiming artificial intelligence, with its computational models and simulation techniques, as a theoretical foundation for cognitive science, with computational complexity theory playing a central role. Gagliardi’s historical analysis provides the deep background for these developments: they are not accidents of interdisciplinary fashion but expressions of a shared “Culture of the Artificial” that has been consolidating for a hundred years.

The paper, dedicated to the memory of Roberto Cordeschi, ultimately offers a vision of scientific unity that is neither reductionist nor pluralist in the usual senses. Cognitive science and statistical physics remain distinct disciplines with distinct subject matters, yet they are aligned at a deeper epistemic level: both have learned that the road to understanding complex, adaptive, collective phenomena runs through the construction of artificial models and the observation of their simulated behavior. In extending the Galilean language of mathematics into a language of model-building and simulation, twentieth-century science did not abandon rigor; it redefined what counts as explanation for a world whose systems are too complex to be solved, and rich enough to be understood only from the inside out.

Subject of Research: The historical convergence of the synthetic method and artificial modeling in cognitive science and statistical physics

Article Title: The discovery of the artificial and the use of the synthetic method in cognitive and physical sciences

Article References: Gagliardi, F. (2026). The discovery of the artificial and the use of the synthetic method in cognitive and physical sciences. AI & SOCIETY. https://doi.org/10.1007/s00146-026-03291-4

Image Credits: AI Generated

DOI: 10.1007/s00146-026-03291-4

Keywords: synthetic method, discovery of the artificial, cognitive science, statistical physics, Ising model, cybernetics, computer simulation, computational irreducibility, weak emergence, complexity science, Roberto Cordeschi, history of science