How Physics Lost Its Language
@sam Modern physics began with a rejection of language. When Bohr and Heisenberg declared that what cannot be expressed mathematically is not physics, they severed the discipline from its natural retroductive roots and placed it within a new metaphysics of formalism—a belief that equations, not causes, define reality. The physics of Newton, Maxwell, and Faraday had been an engineering art, a language of forces and fields tied to the tangible world, but with Einstein and the quantum revolution, that language gave way to statistics, probabilities, and abstract spaces. The pursuit of why was replaced by the calculation of what. Yet without the retroductive imagination of natural philosophy, the mathematical mastery of nature risks becoming mute without meaning. Carl Friedrich von Weizsäcker noted in 1971 that “Philosophy as a university discipline commands no authority today… mainly because the task of philosophy is so difficult. Philosophy can be defined as continued questioning. Socrates practiced it thus, in an exemplary manner.”
The Bohr–Heisenberg Dictum
In the early 20th century, Niels Bohr and Werner Heisenberg drew a decisive line that would redefine the nature of physics: if an idea could not be expressed mathematically, it was not physics. This statement was not merely a methodological guideline—it was a declaration of philosophical territory. Physics, once a branch of natural philosophy concerned with understanding why the world behaves as it does, was redefined as the quantitative science of predicting what will happen under given conditions. Explanation, in the classical sense, was replaced by formalism.
By making mathematics the sole arbiter of physical truth, Bohr and Heisenberg inadvertently transformed physics into a new kind of metaphysics—not the retroductive reasoning of causes and essences, but a formal metaphysics of equations. In this view, the mathematical structure of a theory is reality, and anything that cannot be represented within that structure is declared meaningless. Where earlier metaphysics asked “What is being?” the new formalism asked “What can be calculated?” The metaphysical commitment did not disappear; it merely migrated from ontology to formalism.
This shift, born in the quantum revolution, established a new orthodoxy: mathematics became the only legitimate language of physical truth. Words could illustrate, but not explain. Any concept not reducible to equations—“wave,” “cause,” “substance”—was dismissed as unscientific speculation. What had once been a conversation between nature and reason was now a monologue of symbols.
The Age of Engineering Mathematics
The irony, however, is that the mathematics of earlier centuries—from Galileo through Maxwell—was not metaphysical at all. It was engineering mathematics: mathematics in the service of building, modeling, and manipulating the physical world. Newton’s Principia was a handbook of celestial mechanics; its equations described real forces acting on real bodies. Maxwell’s field equations governed motors, telegraphs, and generators. Even Faraday, who lacked formal mathematical training, developed visual and experimental analogies that guided the engineers of the industrial age.
In that era, mathematics was a tool—a compressed way of representing observable relationships. It did not replace physical understanding; it embodied it. The “field” was a calculational model for stress and strain in an invisible ether, not an ontological claim. The “force” was something an engineer could measure with pulleys and weights. Classical physics was an applied art, rooted in mechanism and visualization.
Einstein and the Detachment from Mechanism
Einstein’s work in relativity was the first great rupture. His equations of spacetime curvature described motion and gravitation with some accuracy—but they offered no mechanical picture of how curvature itself arose. Space and time ceased to be measurable backdrops and became flexible coordinates in a mathematical geometry. Engineers today still use Newton, but the theoretical physicist now inhabited a world of tensors, not forces.
The mainstream adoption of relativity ushered in a new aesthetic: simplicity of equation replaced intelligibility of cause. To “explain” a phenomenon now meant to encode it mathematically, not to describe the underlying mechanism in natural language. The ancient question “why”—so central to natural philosophy—was set aside in favor of “how much” and “how fast.”
From Determinism to Probability
Quantum mechanics completed the transformation. Heisenberg’s matrix mechanics and Schrödinger’s wave functions introduced a fundamentally statistical worldview. The deterministic trajectory of a particle gave way to probability amplitudes—not descriptions of things in motion, but of likelihoods for measurement outcomes. Einstein, who famously resisted this, insisted that “God does not play dice.” Yet by mid-century, physics had accepted that it does—and that the dice are the equations.
This statistical formalism is perhaps the most profound philosophical break in the history of science. The equations of quantum mechanics are predictive, but they are not descriptive in any ordinary sense. They say nothing about what an electron is or why it behaves as it does—only what numbers will appear on a detector screen. The universe became, in effect, a black box: its inner workings were not only unknown but declared unknowable.
Formalism Without Mechanism
By the mid-20th century, the mathematical formalism of physics had evolved beyond engineering entirely. Quantum field theory described interactions not as forces but as exchanges of abstract operators. General relativity replaced the gravitational “force” with spacetime curvature. String theory would later postulate ten or eleven dimensions, not as testable mechanisms but as mathematical necessities of a model. The discipline’s center of gravity had shifted from empirical intelligibility to formal coherence.
Meanwhile, engineers—the practical heirs of Galileo and Newton—continued to build the modern world using 19th-century physics. The electronics that run quantum computers rely on Maxwell’s equations; the rockets that escape Earth’s gravity depend on Newton’s mechanics, not Einstein’s curvature. Our civilization remains classical in its functioning, even as our cosmology drifts ever deeper into abstraction.
The Exile of Natural Philosophy
The exile of language from physics was not inevitable. It was a cultural decision—one that equated linguistic explanation with unscientific speculation. But the cost of this decision is profound: physics lost its interpretive power. The ability to articulate why a system behaves as it does in conceptual terms—the hallmark of retroduction, reasoning from observed effects to the most plausible causes—was dismissed as unscientific.
Yet retroduction is precisely how discovery works. Faraday’s conception of lines of force, Kepler’s search for harmony, Maxwell’s analogies with fluid flow—all were retroductive insights, expressed first in language, only later in mathematics. The explanatory imagination precedes the equation.
Retroduction as Physics
To restore natural philosophy is not to abandon mathematics; it is to reassert that mathematics expresses, but does not replace, understanding. Retroduction—the disciplined use of language to infer underlying mechanisms—complements engineering mathematics rather than competing with it. Language gives meaning to the symbols; it tells us what we are manipulating and why.
In this view, physics and engineering form a continuous spectrum. Engineering mathematics allows us to act upon phenomena. Natural philosophy allows us to understand their origin and nature.
One without the other is incomplete. Without mathematics, philosophy drifts into speculation; without language, physics degenerates into calculation without comprehension.
Toward a Reunification of Knowing and Doing
The Bohr–Heisenberg dictum sought rigor but achieved silence. By forbidding non-mathematical explanation, physics severed itself from the intuitive and retroductive modes of thought that once guided discovery. The task now is not to reject mathematics but to rehumanize it—to bring back the language of “why” alongside the equations of “how.”
Natural philosophy, expressed in clear conceptual language, is not an unscientific relic. It is the missing half of physics—the part that lets us not just compute the world, but comprehend it.