Space

• 1. Introduction

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  Space is one of the few quantities in physics that cannot be defined by anything more fundamental. There is nothing deeper known to build it from. You can measure it, experiment on it, relate it to time and mass, but you cannot reduce it. That stubborn fact sits at the center of a debate that has run since antiquity. Is space a thing in its own right? Is it merely the set of relations between objects? Or is it something our minds supply before we ever open our eyes? Plato wrestled with what the Greeks called khora. Aristotle defined topos, or place, in Book IV of his Physics. Centuries later, physicists came to picture space not as three flat dimensions but as part of a four-dimensional continuum called spacetime. Along the way a spinning bucket of water, an imaginary sphere with a strange climate, and a triangle drawn between mountaintops would each become a weapon in the argument over what space actually is.

• 2. Absolute Versus Relational

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  Isaac Newton insisted that space is absolute. It exists permanently and independently, whether or not any matter sits inside it. Gottfried Leibniz, the German philosopher and mathematician, held the opposite. For him, space was no more than the collection of relations between objects, given by their distance and direction from one another. He summed it up as that which results from places taken together. Leibniz compared space to the ties between family members. People in a family are related, but the relations do not exist apart from the people themselves. He pressed the point with a thought experiment. Imagine two universes exactly alike except for where the material world sits in each. Since no observation could tell them apart, the principle of the identity of indiscernibles says there is no real difference. By the principle of sufficient reason, any theory of space allowing such twin universes must be wrong. Newton answered not with logic but with a bucket. Water hangs from a rope and is set to spin. At first its surface is flat. As the spinning continues, the surface climbs into a concave curve. Stop the bucket, and the water keeps that hollow shape while it keeps turning. The curve cannot come from motion relative to the bucket, Newton reasoned, so it must come from motion relative to space itself. For several centuries that bucket was treated as decisive proof that space exists independently of matter.

• 3. Space In The Mind

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  Immanuel Kant moved the entire question inward. In his Critique of Pure Reason the German philosopher called space a property of our mind, the means by which we represent objects as outside us and all as set in space. Spatial predicates, he wrote, are relations that only attach to the form of intuition, and thus to the subjective constitution of our mind. Without that constitution, the predicates could not attach to anything at all. Kant argued that knowledge of space is synthetic, meaning a claim about space cannot be true merely from the meaning of its words. He contrasted this with the sentence all unmarried men are bachelors, which is true by definition alone. Knowledge of space is also a priori, prior to experience, because space is the form that lets us receive information about the outside world. A person without sight can still grasp spatial attributes through touch, hearing, and smell. Earlier, the philosopher and theologian George Berkeley had tried something narrower. In his Essay Towards a New Theory of Vision he set out to refute the visibility of spatial depth itself.

• 4. The Mechanics Of Motion

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  Galileo overturned the geocentric cosmos that Aristotle and Ptolemy had handed down. He backed the Copernican view that the universe is heliocentric, with a stationary Sun at the center and the planets, the Earth among them, revolving around it. That move created a problem. If the Earth moved, the old Aristotelian belief that its natural tendency was to stay at rest came into doubt. Galileo answered that motion is as natural to an object as rest, and that celestial bodies including the Earth are naturally inclined to move in circles. The idea displaced another Aristotelian notion, that every object drifts toward its designated natural place of belonging. Rene Descartes pushed further, trying to replace the Aristotelian worldview entirely with space and motion governed by natural laws. Cartesian space was Euclidean in structure, infinite, uniform, and flat. He defined it as that which contains matter, and held that matter by definition has spatial extension. The consequence was startling. For Descartes there could be no such thing as empty space. His thinking ran from his famous cogito ergo sum, I think therefore I am, into a sharp split between body and mind now called Cartesian dualism. These Galilean and Cartesian theories formed the foundation of the Scientific Revolution, understood to culminate in Newton's Principia Mathematica in 1687.

• 5. When The Parallel Lines Bent

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  Euclid's Elements rests on five postulates, and one of them tormented mathematicians for centuries. The parallel postulate states that given a straight line and a point not on it, exactly one line through that point runs parallel to the first. Until the 19th century few doubted it. The argument was only whether it needed to be an axiom or could be derived from the others. Around 1830 two men broke it apart separately. The Hungarian Janos Bolyai and the Russian Nikolai Ivanovich Lobachevsky published treatises on a geometry with no parallel postulate, called hyperbolic geometry. There an infinite number of parallel lines pass through the point. The sum of a triangle's angles falls below 180 degrees, and a circle's circumference-to-diameter ratio runs greater than pi. In the 1850s Bernhard Riemann built the mirror image, elliptical geometry, where no parallel lines pass through the point. There triangles exceed 180 degrees and the circle ratio drops below pi. Flat Euclidean space sat between them, with one parallel, exactly 180 degrees, and a ratio of pi. The question was no longer abstract. If space could be curved on paper, it might be curved in fact.

• 6. Testing The Shape Of Space

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  Carl Friedrich Gauss was the first to ask whether the geometry of real space could be measured. The German mathematician thought of testing the angles of an enormous stellar triangle, and reports say he actually tried a small version by triangulating mountaintops in Germany. Henri Poincare, the French mathematician and physicist of the late 19th century, argued such a test was hopeless. He imagined scientists trapped on a large sphere with a peculiar climate, a sphere-world where temperature varies so that all objects expand and contract in the same proportions from place to place. With the right falloff in temperature, measuring rods would deceive the inhabitants into believing they lived on a flat plane rather than a curved surface. They could never in principle tell sphere from plane. The same, Poincare said, holds for whether real space is Euclidean. Which geometry to use was a matter of convention, and since Euclidean geometry is simpler, he assumed it would always be chosen as the true geometry of the world. Albert Einstein would soon give nature a vote in the matter.

• 7. Einstein And Spacetime

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  In 1905 Albert Einstein published his special theory of relativity, fusing space and time into a single construct called spacetime. In it the speed of light in vacuum is the same for every observer. Two events that look simultaneous to one observer are not simultaneous to another moving relative to the first. A moving clock ticks more slowly than a stationary one, and moving objects measure shorter along their direction of travel. His general theory of relativity then recast gravity. Rather than a force acting within spacetime, gravity bends the geometric structure of spacetime itself. Time runs slower where gravitational potential is lower, and light rays bend near a gravitational field. Scientists confirmed these predictions by studying binary pulsars. The equations also predict moving ripples of spacetime called gravitational waves. Indirect evidence turned up in the Hulse-Taylor binary system, but direct detection took longer. LIGO scientists reported the first direct observation of gravitational waves on the 14th of September 2015. This same framework reaches out to the largest question of all. Space appears to have been created in the Big Bang, 13.8 billion years ago, and has been expanding ever since, driven onward by cosmic inflation.

• 8. Space Beyond Physics

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  Australian Aboriginal cultures invert the usual relationship to land. Rather than claiming ownership of it, they consider that they are in fact owned by the land. Geography is the science of identifying and describing places on Earth, using spatial awareness to ask why things sit where they do. Cartography maps those spaces for navigation and visualization, while geostatistics applies statistical concepts to spatial data to estimate what has not been observed. Ownership reaches past the ground into airspace, waters, the radio bands of the electromagnetic spectrum, and even cyberspace. Psychologists began studying how space is perceived in the middle of the 19th century, and the field now treats it as a distinct branch. Their work includes amodal perception, object permanence, and a set of phobias: agoraphobia, the fear of open spaces; astrophobia, the fear of celestial space; and claustrophobia, the fear of enclosed spaces. The understanding of three dimensions is thought to be learned in infancy through unconscious inference, tied closely to hand-eye coordination, and the visual version is called depth perception. Since the 1980s the social sciences have read space as something produced rather than given. Henri Lefebvre's The Production of Space applied Marxist ideas about commodities and capital to treat space as a social product. David Harvey named the time-space compression in The Condition of Postmodernity, the way technology and capital shrink our sense of distance. Edward Soja, in Thirdspace, called the spatial dimension a neglected mode of how we inhabit the world. The argument that began with Plato's khora had become an argument about colonialism, capital, and who gets to define a place.