a mechanistic, mathematical world

From a modern vantage point, it can be hard to imagine a world not conceived in mathematical terms. That nature operates by fixed laws; that the universe, at its most basic, is a vast and orderly system of forces and particles—these are assumptions so deeply ingrained in the modern mind that they feel self-evident. But the view that the cosmos is fundamentally mechanical and describable in the language of mathematics is only a few centuries old and part of a radical transformation in how people came to understand reality.

The earliest seeds of this transformation were philosophical and symbolic. In the sixth century BCE, Pythagoras proposed that numbers lay at the root of all things. He argued that the harmony of the universe was not a metaphor but a literal property: music, geometry, the orbits of heavenly bodies—these were all reflections of a deeper, mathematical order. Plato would later refine this view, positing a realm of ideal forms more real than the material world, with mathematics as the key to accessing it. To know the world, one had to look beyond appearances, to grasp the unchanging structures that gave rise to them.

Yet for all their metaphysical ambition, these early thinkers stopped short of mechanizing the cosmos. While some strands of ancient thought—especially Stoicism and certain mystical traditions—suggested a rational order underlying the universe, others emphasized divine will, animism, or participatory relationships between human and cosmos. Aristotle, whose worldview would come to dominate medieval thought, saw nature as goal-directed. Everything had a final cause—an inherent end or purpose. The stone fell not because of gravity, but because its natural place was the Earth. The heart beat not because of mechanics, but because it was the seat of vital heat, the source of life.

It was not until the scientific ferment of the early modern period that a different conception began to take hold. In the sixteenth and seventeenth centuries, European thinkers confronted a cosmos that was growing larger and stranger by the year. The discovery of new worlds, new stars, and new instruments made the old Aristotelian certainties increasingly difficult to defend. Telescopes revealed imperfections in the heavenly spheres; careful measurements undermined the idea of a stationary Earth. The universe no longer obeyed ancient categories. It called out for a new language.

That language was mathematics. Galileo Galilei, often credited with founding modern science, argued in his 1623 work Il Saggiatore that nature was a book written in mathematical characters: triangles, circles, and other geometrical figures. Without understanding this language, one could not hope to read its meaning. Galileo, Il Saggiatore (1623), trans. Stillman Drake, in Discoveries and Opinions of Galileo (New York: Anchor Books, 1957). He was not content with describing motion in everyday terms; he sought to express it in equations. In doing so, Galileo rejected the qualitative explanations of Aristotle and replaced them with a physics of measurable properties—speed, mass, acceleration.

René Descartes took this further. In his Meditations on First Philosophy and Principles of Philosophy, he argued that reality consisted of two distinct substances: res extensa (extended substance—matter) and res cogitans (thinking substance—mind). This Cartesian split allowed matter to be fully mechanized. The body was a machine. Animals, lacking minds, were automata. The natural world, too, was a vast clockwork—its motions determined by universal laws that, in principle, could be written down and solved. It was a vision of stunning clarity and terrifying simplicity.

Isaac Newton provided the machinery. His Philosophiæ Naturalis Principia Mathematica, published in 1687, described a universe bound by gravity and governed by three laws of motion. For the first time, the movements of planets and falling apples were unified under a single mathematical framework. Isaac Newton, Philosophiæ Naturalis Principia Mathematica (1687), Book I and III. Newtonian physics offered predictive power, conceptual elegance, and empirical confirmation. With it, the mechanistic worldview achieved dominance.

The impact of this vision cannot be overstated. It offered not only understanding but control. Nature could now be tamed, modeled, manipulated. The Industrial Revolution was as much a triumph of this worldview as it was of steam and iron. Machines proliferated not just in factories, but in metaphors. The body became a machine. The brain, a kind of hydraulic device or later, a computer. Society, an assembly of gears and incentives. Each new domain of inquiry—economics, physiology, psychology—adopted the mechanical model and reaped its fruits.

But somewhere along the way, the metaphor hardened into metaphysics. Mathematics, once a tool, became an ontology. The world was not like a machine—it was one. And that which could not be quantified came to be seen as vague, subjective, or unreal. Poetic language, moral insight, religious intuition—these were relegated to the margins. In their place stood the clarity of equations.

The shift was subtle but consequential. Galileo had used mathematics to describe motion; Newton to model force; Pierre-Simon Laplace, a century later, imagined in his Philosophical Essay on Probabilities a mind that, knowing the position and momentum of every particle, could predict the entire future. Pierre-Simon Laplace, A Philosophical Essay on Probabilities (1814), trans. Frederick Truscott and Frederick Emory (New York: Dover, 1951), p. 4. This was determinism in its purest form. The future was already written—in mathematics.

This view also absorbed, or at least repelled, its alternatives. Older frameworks that included purpose or meaning were cast as pre-scientific. Even when evolutionary biology introduced apparent directionality into the story of life, it was framed not as final cause but as the outcome of natural selection. Teleology was smuggled in but denied citizenship.

Yet cracks were already appearing. Quantum mechanics, developed in the early twentieth century, challenged the determinism and objectivity that had defined classical physics. The behavior of subatomic particles could only be described in terms of probabilities. Observation changed the system observed. Figures like Niels Bohr, Werner Heisenberg, and Wolfgang Pauli suggested that classical conceptions of reality were insufficient. Pauli in particular, through correspondence with Carl Jung, explored the possibility of a psycho-physical reality that might reconnect psyche and matter. On Pauli and Jung: See Arthur I. Miller, Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung (W. W. Norton, 2009), esp. Chapters 6–8.

The Newtonian clockwork had not been dismantled, but it was no longer the whole story.

Meanwhile, the rise of systems thinking and complexity theory exposed further limitations. In biology, for example, the whole is often more than the sum of its parts. Emergent properties—such as consciousness, metabolism, or social behavior—could not be fully explained by analyzing components in isolation. The mathematical models grew more sophisticated, but the metaphor of mechanism began to strain.

These conceptual shifts echoed in neuroscience and the study of mind. While great strides have been made in mapping neural correlates of mental states, the subjective character of experience—the “what it is like”—has remained elusive. This problem, known as the hard problem of consciousness, was explicitly framed by philosopher David Chalmers in the 1990s. David Chalmers, “Facing Up to the Problem of Consciousness,” Journal of Consciousness Studies 2, no. 3 (1995): 200–219. His formulation spurred renewed interest in alternative models: panpsychism, which sees mind as a fundamental aspect of matter; dual-aspect monism, which posits an underlying reality expressing itself as both mind and matter; and other non-reductive philosophies.

These views challenge the mechanistic assumption that subjectivity is secondary or derivative. They argue instead that any account of reality that excludes consciousness is, by definition, incomplete.

Underlying many of these critiques is a deeper recognition: that our metaphors shape what we see. The machine was a powerful metaphor—it brought order, clarity, and progress. But it also constrained thought. It framed nature as inert, life as computation, and mind as epiphenomenon. As philosopher Mary Midgley noted in Science and Poetry, we are “haunted by the machine metaphor” long after it has ceased to serve us well. Mary Midgley, Science and Poetry (Routledge, 2001), p. 1.

New metaphors are emerging. The world as network, as field, as organism, as unfolding process. These offer different insights—not necessarily truer, but broader. They suggest a cosmos that is dynamic, participatory, even alive in some sense. A world not merely observed but engaged.

Yet the mechanistic, mathematical worldview persists, and not without reason. Its predictive power and practical success remain immense. It is not wrong, but partial. Like all frameworks, it highlights certain features and obscures others. Its story is still being told—but perhaps no longer alone.

What lies beyond the machine? If consciousness is not merely a byproduct of computation, if matter itself resists total mathematization, how might our scientific and philosophical frameworks evolve? The next pieces in this series will explore these questions—examining both the cracks in the old edifice and the shapes of the emerging paradigms.