The Problem of Space from Plato to The Matrix

Perhaps the most insidious problem in the history of philosophy is the problem of space. Because the average person, when looking around, does not even question the existence of space. Everything is simply there. You might ask: How can something so obvious be a problem? That is precisely why the problem of space is insidious. It has become a problem precisely because not only ordinary people but also extraordinary individuals have lived in this world. These extraordinary individuals asked: Is space a body? If it is not a body or object, then what is it? Does it exist prior to objects or did it emerge alongside them? Is there really such a thing as space, and if so, where is it? Of course, the absence of kunefe back then may have had some influence. When I start thinking, I find myself in kunefe. Anyway.

One of these extraordinary individuals was Plato. His contemplation of the problem of space arose somewhat out of necessity. As is well known, he posited two worlds: an ideal world (the world of Forms) and the real world. In the world of Forms, every thing has its original essence—unchanging, perfect, and eternal. The world we see, hear, and live in, however, is transient and imperfect. Using his own examples, a carpenter’s bed is a copy of the Form of the bed in the world of Forms; the painter’s depiction of a bed is a copy of a copy. Similarly, concepts such as goodness, justice, and beauty originate from the world of Forms. Here the problem of space begins. Because the world of Forms is not concrete, does not occupy space, and exists as something known only through reason or as what we call heaven. It exists elsewhere. But how can something from the world of Forms become visible? This question initiates the problem of space. To resolve it, Plato creates a new intermediary realm between the two worlds and calls it Khora. It is the field in which Forms enter and become concrete. Khora, in his own words, resembles clay used for making dough. Clay takes on every shape but has no shape of its own. It is like a mirror: it accepts every reflection but is itself no reflection. You cannot comprehend it through reason or through the senses. Plato himself recognized this problem but could not explain it, leaving it as a puzzle for future generations.

The first to take up this problem directly was Aristotle, Plato’s student. Unlike Plato, Aristotle was a naturalist, concerned with concrete things, and he found his teacher’s abstract concept of space illogical. Since his work on physics focused on motion, he encountered the question: When a moving object travels from one place to another, where is that place? He was thus compelled to define space. He declared that space is the inner surface of the boundary that directly surrounds a body. In other words, if there is a container, its interior is what we call space or place. Objects perform their natural motions within this container. But for rational beings, Aristotle’s definition remains inadequate because it leaves unanswered the question: Where is this container? Aristotle himself was aware of the issue but had no answer. He only stated that the exterior of what he called space is immobile and infinite. In summary, for Aristotle space is fixed and finite.

Aristotle’s somewhat unintuitive conception of space and the universe, with no viable alternative emerging, remained largely accepted until Descartes. Of course, Descartes did not wake up one morning and say: Today I will think about what space or the universe is. Descartes’s primary concern was matter. Long before saying I think therefore I am, he had already separated thinking from matter. Having stripped himself of everything, he still found he could think. Even if an evil demon showed him objects and bodies in a dream, he could still think after removing those bodies—thus he existed. After establishing his existence, he asked: What is matter? What makes something matter? Is it its color, hardness, or weight? He realized that all these properties are changeable. If I melt a candle, its color and shape change, yet it remains matter. Therefore, he concluded, the only unchanging feature is that it occupies space. From this he reached the following conclusion: Anything that is matter occupies space, and anything that occupies space is matter. Having reached this conclusion, the rest followed as easily as taking off a sock. Since matter occupies space and nothing that does not occupy space can be matter, there can be no such thing as empty space. If space is matter itself, then space without matter—emptiness—is meaningless. There is no empty space; space cannot exist independently of matter. In summary, while for Aristotle space is the outer boundary of a body, for Descartes space or the universe is matter itself. Space is no longer outside but within—the definition of matter now includes space. The universe is now completely full, with no void. Naturally, this view also changed the prevailing notion of motion since antiquity. The idea that motion occurs through bodies pushing one another now came to the fore. When a body moves, the empty space it leaves is immediately filled by another body, creating a vortex.

Descartes was not as fortunate as Aristotle, and his views did not hold sway as long. Soon after, two geniuses emerged: Newton and Leibniz. These two geniuses, regarding time, motion, and space, communicated constantly through Newton’s friend Clarke, since Newton preferred not to engage Leibniz directly. Newton was driven to think about the problem of space by a purely technical question: How can absolute motion be distinguished from relative motion? Without being able to distinguish whether a body is truly accelerating or merely accelerating relative to another, he could not formulate the laws of motion. He therefore divided the concept of space into two. The first is observable space, in which distances between bodies can be measured. The second is space that has no relation to anything external, always existing in the same unchanging form. Bodies exist within it, but it is independent of them; even if all bodies ceased to exist, space would continue to exist.

To prove this, he proposed the rotating bucket experiment. In this experiment, we tie a bucket to a rope, twist the rope tightly, and then release it. When the rope unwinds, the bucket begins to rotate. Initially, the water inside remains flat, but then, as the bucket rotates, the water begins to rotate with it. As the water rotates at the same speed as the bucket, its surface becomes concave—and here the matter becomes interesting. What is this concavity relative to? Not the bucket, because initially, when only the bucket rotated and the water was stationary relative to it, the surface was flat. Only later did the concavity appear, and even after the bucket was stopped, the concavity persisted for some time. Therefore, this motion must be relative to an independent space. Here the bucket—or in his own term, the vessel—is space. This space is independent of the external world (that is, it exists regardless of whether anything is inside), immobile (and thus serves as a reference point), and mathematical. His assertion that it is mathematical brings Leibniz into the discussion, because the phrase “mathematical” implies that every point is identical and that space or the universe is “God’s sense organ.”^【1】 More precisely, Newton himself explained it this way.

The phrase “space or the universe is God’s sense organ” naturally disturbed Leibniz. Because this phrase could also imply that God depends on the universe. For Leibniz, this was unacceptable. For the reason, you may refer to my essay on The Best Philosopher of Possible Worlds. Moreover, his own theory of possible worlds requires a definition of space. In short, two distinct issues draw Leibniz into the problem of space.

1. First, his monad theory. When describing monads, he said they are “windowless” and cannot interact with anything external, yet each contains a reflection of the entire universe. Thus, monads are not in space; the order of relations among monads constitutes space. Space is the abstract expression of this order in the human mind. Without bodies, there is no space. Using his own example: “Just as the father-son relationship in a family tree cannot exist without people; when people disappear, kinship disappears. Space is the same: without objects, there is no space. Space is the mental representation of relations among objects.”^【2】

2. Second, his objection to Newton’s absolute space theory. This objection is based on the principle of sufficient reason. According to this principle, everything must have a sufficient cause. (Due to the length of the topic, I cannot delve into the principle of sufficient reason.) If Newton’s space existed, we could not explain why God created the universe exactly where it is. If God had moved the universe ten meters to the left, nothing would have changed. But for God, who creates everything for a reason, this is unacceptable. Why is the universe exactly here? If there is no reason why God chose this exact location rather than ten meters to the left or right, then the notion of absolute space cannot be true. (Forgive me, but instead of saying “he solved the problem completely,” I might say “he grew a geranium.”)^【3】

Thus, what Newton called absolute space is rational, appears real, but does not actually exist. Yet the bucket experiment remains. How do we explain it? Leibniz could not explain it—or did not live long enough to do so. About two hundred years later, someone named Ernst Mach, and then Einstein, provided an explanation.

But before that, a figure emerged—indeed, he did not appear from nowhere, he arose: Kant. Kant argued that both Newton and Leibniz were right and wrong. His entry into the issue came while seeking to answer the question: How is knowledge possible? Is it innate or acquired? If geometry, a product of reason, is necessary and universal—as it is—then where does this necessity come from? If geometry is knowledge of space, then what is space? His answer was regarded as revolutionary in his time. He said: Space is neither, as Newton claimed, an independently existing entity outside us, nor, as Leibniz claimed, an abstraction of relations among objects. Space is an innate form of human perception. It precedes experience but is not independent of it; it makes experience possible. We do not find space in the world; we perceive the world spatially because our minds are structured that way. In short, things are not in space; we perceive things spatially (“I probably created you inside my head,” he says, as if, yet there is a real kunefe out there).^【4】 We do this through a kind of innate lens. Let me explain: Imagine a computer program. First, we need a coordinate plane. Then we write a program, and as a result, we see the table to the right of the tree and the person in front of them. Here the coordinate system precedes the image. Without coordinates, we could not see anything. The coordinate system is Kant’s lens; the software places the objects, and what appears on the screen is how we perceive objects. Space is not part of experience; it is what makes experience possible.

Kant’s view explained the necessity of geometry but could not answer where this lens comes from. Let us clarify how he explained geometry: If space were an independent external entity, we would have to learn geometry through experience, and it could not be necessary or universal. If space were merely an abstract relation, geometry would be merely a logical game and could not tell us anything about the world. But if space is the mind’s way of perceiving the world, then geometry describes the mind’s own rules. Since the mind constructs the world according to these rules, geometry is confirmed in every experience. Thus, it is both necessary and informative about the world.

Years later, Ernst Mach responded to Newton’s bucket experiment by saying it is relative to the entire universe. Later, Einstein unified space with time. He said everything influences everything else. Einstein transformed space and time from mere “containers” or “glasses” into a dynamic structure—spacetime—that is bent and stretched by mass and interacts physically. The idea that space or the universe is continuously expanding gained wider acceptance. Yet even though Einstein presented it as a physical reality, the debate continues: Is our perception of space real, or is it merely an illusion? Viewers of The Matrix, before reading the next paragraph, answer this: Why does a handkerchief bleed, not a tooth or a fingernail?^【5】 And now this: Which of the views discussed in this essay appear in the film?

The Matrix also addresses this issue (according to many of the philosophers discussed here). For example, Plato’s distinction between the world of Forms and the real world: For Plato, the world of Forms is the true reality, and the world we see is merely a copy. In The Matrix, it is the reverse: humans live inside the copy and cannot perceive the truth. Descartes’s evil demon is precisely the Matrix itself. Moreover, Kant’s idea that “space is really our way of seeing” is illustrated in the “there is no spoon” scene.

To summarize the philosophers’ views on space in one sentence each:

Plato: Space is the formless intermediary between two worlds.

Aristotle: Space is the inner surface of the container surrounding a body.

Descartes: Space is matter itself; there is no void.

Newton: Space is an absolute container independent of bodies.

Leibniz: Space is the mental abstraction of relations among bodies.

Kant: Space is the innate perceptual framework through which the mind experiences the world.

Einstein: Space is a dynamic structure, intertwined with time, that is curved and deformed by matter.

Note: This text was composed and expanded using artificial intelligence to organize and develop my knowledge on the subject (e.g., Khora, Mach). I had originally constructed the computer program analogy incorrectly; its correction and final form were completed with the assistance of artificial intelligence.