Reason: Dimensions, Reification, and Cognitive Entrapment
On Space, Time, and the Map Mistaken for the Territory
Author’s Preface
This essay is part of the Reason Series. The aim is not to dazzle with technical language but to return to first principles. It is about how human beings come to accept abstractions—like “dimensions”—as if they were real objects in the world. Such acceptance is not innocent. It shapes how people think about space, time, physics, mathematics, and even daily experience.
Two mistakes will appear again and again. The first is reification: treating an idea as if it were a concrete thing. The second is the map–territory error: confusing our ways of describing the world with the world itself. Both mistakes are common, even among brilliant scholars. In fact, the smarter the thinker, the more elaborate the trap can become. This essay works through examples of space, time, and dimensional thinking to show how these errors play out, and why common sense, though often dismissed, remains essential.
Introduction
Everyone experiences the world as extended in space and unfolding in time. But people do not immediately think of these as “dimensions.” That word belongs to mathematics and science, not to lived experience. Dimensions are abstractions: useful ways of speaking about extension, distance, and orientation. Yet over time, they have come to be treated as if they were part of the very fabric of reality.
Today, most people casually say that the world has “three dimensions.” If they have read about physics, they may even say “four dimensions” to include time. Some, under the influence of science fiction or modern theoretical physics, may speak of ten or eleven dimensions. These statements have passed into cultural common sense. But they are the result of centuries of abstraction, not simple observation.
This essay traces that development. It begins with bodily orientation, moves through the emergence of spatial language, examines the invention of orthogonal axes and coordinate systems, and ends with cultural reification of “dimensions.” Along the way, it considers how scholars get trapped inside their frameworks, mistaking their abstractions for the real world.
Discussion
Space and Time as Dimensions
Space is experienced directly: one can walk across a room, climb a tree, or see the distance between two houses. Time is experienced differently: as succession, change, and memory. The difference is obvious in daily life. One can return to a place but never return to a moment.
When mathematics speaks of space as “three dimensions” and time as a “fourth dimension,” this is not a discovery about reality but a way of fitting experience into a formal scheme. Einstein’s theory of relativity famously treats space and time together as “spacetime.” This works beautifully for calculation—predicting how planets move or how light bends near the sun—but it should not be mistaken for an exact picture of how space and time appear in life. In the world of experience, space and time are not the same.
The confusion arises when people hear that physics describes the world as “four-dimensional” and assume this means reality itself has four literal dimensions. This is reification: mistaking a description for the thing described.
Bodily Orientation and Its Unequal Salience
Human orientation begins with the body. Gravity makes “up” and “down” unavoidable: babies learn quickly which way is up. “Forward” and “backward” are tied to motion and perception: the eyes face forward, legs move forward more easily than backward. “Front” and “back,” “top” and “bottom” are similarly anchored.
“Left” and “right,” however, lack such anchors. The body is bilaterally symmetrical. Gravity does not help, nor does motion. As a result, left–right distinctions are cognitively weaker. People confuse them constantly. Drivers miss turns. Pilots have famously confused left and right with disastrous results. A familiar joke captures the problem: “No, your other left.”
The point is that orientation begins with strong experiential contrasts, not with abstract “dimensions.” Dimensions came later, long after humans were already moving, pointing, and naming directions.
The Origins of Spatial Language
If one accepts evolutionary accounts, early humans navigated without words. They saw, remembered, and acted, but language had not yet evolved. At some point, words were invented for the most salient contrasts: up/down, near/far, inside/outside. These words allowed coordination: “Up the hill,” “Behind the tree,” “Come closer.”
The step to “dimensions” was much later. Only with organized building, surveying, and astronomy did humans begin to formalize space. Ancient Egyptians stretched ropes with knots to mark right angles for land measurement after the Nile floods. Greek geometry built on such practices, defining points, lines, and planes. But even then, “dimension” was not a feature of reality—it was a way of making sense of measurement. Quantitative dimensions—numbers assigned to directions—came only with arithmetic joined to geometry.
Orthogonality and the Right Angle
The hallmark of dimensions in mathematics is orthogonality. In plain words: independence. Two lines at right angles measure different things. Moving along one does not change your position along the other. This makes calculation possible.
Right angles were a practical discovery before they became a mathematical one. Builders used plumb lines to ensure walls were vertical. Farmers used stakes and ropes to square fields. Carpenters set beams at right angles to stabilize structures. These practices were mathematized later, formalized into geometry.
But there is nothing necessary about right angles in nature. Rivers bend, mountains slope, and paths curve. Orthogonality is a human convention. It works because it simplifies problems. That does not mean the world itself is built from right angles.
Coordinate Systems and Rotation
Children often learn coordinates as fixed: an x-axis and a y-axis on paper, or “north and east” on a map. It is not obvious that these axes can be rotated without changing the figure. To understand that requires formal geometry and algebra. Descartes’ La Géométrie (1637) brought these ideas together, allowing lines and curves to be described by equations.
The insight is profound: coordinates are arbitrary. One can rotate the system, or even bend it, and the geometry remains. In advanced physics, different coordinate systems describe the same reality, chosen only for convenience. The arbitrariness shows that “dimensions” are conventions of representation, not parts of the world itself.
Cultural Belief in Three or Four Dimensions
Despite all this, cultural teaching has fixed the idea of three dimensions of space and one of time. School diagrams show cubes labeled with three axes. Textbooks call time a fourth dimension. Popular science adds more: ten in string theory, eleven in M-theory.
These numbers are not observations but conventions. Yet many accept them as if they were direct truths. Science fiction compounds the belief, speaking of “slipping into the fifth dimension” or “travelling through hyperspace.” The result is a widespread reification: dimensions treated as literal parts of reality rather than as mathematical scaffolding.
The Map and the Territory
Alfred Korzybski’s famous dictum, “The map is not the territory,” captures the heart of the problem. A map is a representation. It helps, but it is not the land itself. Directions on a road map are useful, but no one confuses them with the terrain.
The same is true of equations and dimensions. They are maps of a kind. They guide us through experience and allow predictions. But they are not reality itself. Mistaking them for reality is the map–territory error, closely allied with reification.
Layers of the World and of Language
It is useful to distinguish layers.
The outer world: rocks, rivers, mountains, trees. Things that exist whether or not anyone describes them.
The inner world: memory, perception, attention. The way the world is experienced from within.
The world of language: words, symbols, mathematics. Constructions that begin in the mind and become external when spoken, written, or calculated.
Mathematics belongs to the third layer. It is a kind of language. It may describe patterns in the outer world, but it cannot reveal the “thing in itself.”
Physicists and Mathematical Abstractions
Some physicists treat mathematics pragmatically. Richard Feynman, for instance, emphasized that equations work but are not reality. Others lean toward Platonism, believing mathematics reveals the actual structure of the universe. Max Tegmark goes further, claiming the universe is mathematics.
Even among pragmatists, language often slips. When a physicist says “spacetime curvature tells matter how to move,” it sounds as though equations are agents. Such language blurs the line between description and ontology. Listeners can easily come to believe that the mathematics is the world.
Cognitive Entrapment and Scholarly Habits
This is not limited to mathematics or physics. Scholars in every field are prone to what I call cognitive entrapment: the habit of thinking within a framework so rigidly that its assumptions are never questioned.
Medieval theology became trapped in debates such as how many angels could dance on the head of a pin—an apocryphal but fitting image. Modern philosophy debates free will versus determinism without agreeing on what “will” or “cause” mean. Moral philosophers argue about deserts and fairness without noticing the assumptions built into the terms.
From the outside, these debates can look absurd. From the inside, they seem serious. This is the nature of cognitive entrapment: thinking inside a metaphorical box until the box becomes invisible.
Summary
Dimensions are not part of reality but part of language. They are ways of speaking about orientation and extent. Up/down, front/back, left/right are grounded in experience. “Three dimensions” and “four dimensions” are mathematical conventions, useful for calculation but not truths about the world.
The deeper lesson is to keep abstractions in their place. Reification and the map–territory error lead people to confuse tools for reality. Scholars of theology, philosophy, and physics alike have fallen into this trap. Common sense, though imperfect, reminds us that abstractions are maps, not the terrain itself.
Reading List
Korzybski, A. (1933). Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. Lakeville, CT: International Non-Aristotelian Library.
Korzybski is central for understanding the map–territory distinction, which lies at the heart of this essay’s argument. He shows how people mistake words, models, and abstractions for the world itself. The essay’s discussion of “dimensions” as conventions rather than realities echoes his point that language and symbols inevitably leave things out and cannot be confused with the territory they represent.
Hayakawa, S. I. (1949). Language in Thought and Action. New York: Harcourt, Brace & Company.
Hayakawa builds on Korzybski but in a more accessible style. He demonstrates how ordinary speech can trap people into errors of thought when metaphors and abstractions are taken literally. His warnings about misusing words relate directly to the essay’s concern with reification—treating dimensions and equations as if they were part of reality rather than descriptions.
Descartes, R. (1637/1954). La Géométrie. New York: Dover Publications.
Descartes’ work is crucial for understanding how coordinate systems were first mathematized. His merging of algebra with geometry marks the point when orientation and direction—once tied to the body and experience—became abstract axes that could be rotated at will. The essay’s section on rotating coordinate systems draws directly on this shift, showing that dimensions are conventions of representation rather than features of the world.
Euclid. (c. 300 BCE/1956). The Thirteen Books of Euclid’s Elements (T. L. Heath, Trans.). New York: Dover.
Euclid laid the groundwork for geometry as a formal system. His definitions of lines, planes, and right angles illustrate how everyday practices like building walls and squaring fields were turned into abstract concepts. The essay’s discussion of orthogonality and the cultural emphasis on right angles reflects Euclid’s lasting influence on how people conceptualize space.
Tegmark, M. (2014). Our Mathematical Universe. New York: Knopf.
Tegmark argues for a radical form of mathematical Platonism: the claim that the universe is itself mathematics. This provides a contemporary example of reification in physics, where abstractions are treated as ontological truths. The essay positions Tegmark’s view as an instance of scholars mistaking the map for the territory, illustrating how even modern science is vulnerable to cognitive entrapment.
Cartwright, N. (1999). The Dappled World: A Study of the Boundaries of Science. Cambridge: Cambridge University Press.
Cartwright emphasizes that scientific laws and models are local tools that work under certain conditions, not universal descriptions of reality. Her position supports the essay’s argument that mathematics and models are epistemological devices, not ontological facts. By insisting on limits and context, Cartwright provides a counterpoint to views like Tegmark’s and illustrates how one can avoid reification by treating models as maps with boundaries.