Place, void and extension

Where are you?

Ask three people, “Where are you?” The first says, “Second row, by the window.” The second, standing in a room that has just been cleared, says, “In an empty room.” The third, holding a tape measure, says, “In a space about four meters by five.” All three are right, and each means a different kind of space.

The first answer is about place: what surrounds you and how you stand to it, a row, a window, a direction. The second is about void: emptiness that can take something in, as when we make room or clear a shelf. The third is about extension, the size and shape of things: length, width, height. Move a table anywhere and it keeps them.

Each kind suggests a theory of what space is. If space is place, it is a web of relations among things. This is the relational view, and in 1716 Leibniz, writing to Samuel Clarke, called space “an order of coexistences.” If space is void, it is a real thing in its own right, an empty container that is there whether or not anything fills it. Its name is substantivalism, and relationism against substantivalism is the standard split in modern philosophy of space. If space is extension, it is a property of bodies: Descartes held that a body’s length, breadth and depth is exactly what makes it a body, so that space and matter are one.

Be clear about what is ours. The sort into place, void and extension is this course’s own device, not a standard classification, and in life the three overlap. It has an ancestor, though. In Physics IV.4, Aristotle weighs four candidates for what a place could be: the shape of a thing, its matter, an interval between the inner surfaces of its container, and the container’s boundary. He picks the boundary. The interval is extension, and an interval with nothing in it is the void.

In this course’s telling, modern thought joined void and extension into one object: an endless, empty, three-dimensional box with a fixed geometry, in which all motion happens. Newton’s Principia (1687) is the name to remember, and Lesson 2 tells the story. Place shrank into a position, a point named by coordinates. (Newton still gave place some size; the point came later, with coordinates and point masses.) The course asks what that exchange gained and what it cost. This lesson goes back to the Greeks, who argued over place and the void.

A nothing that is?

Leucippus and Democritus, in the later fifth century BCE, taught that everything is made of “the full and the empty”: atoms, tiny bodies solid all the way through, and the void between them. Aristotle reports that they called the full “what is” and the empty “what is not,” and held that the second is no less real than the first (Metaphysics I.4). They needed the void for two jobs. Without empty space nothing could move. And without gaps nothing would mark where one thing ends and the next begins, so there would be one lump, not many things.

Democritus apparently coined a word for it. Cutting the front off Greek meden, “nothing,” he made den, “thing,” and said, as Plutarch reports, that the thing exists no more than the nothing, since the void too has a nature of its own. So the atomists accepted that the void is “what is not,” and still said that it is.

Opposition came from Elea, in southern Italy. Parmenides (about 500 BCE) argued that what is not cannot be thought or said, so what is must be whole and continuous: in Burnet’s translation, “everything is full of what is.” His surviving fragments do not argue about the void as such. The explicit argument is by a later thinker of his school, Melissus of Samos, an admiral who commanded the Samian fleet that beat the Athenians at sea in 441–440 BCE. Nothing is empty, he wrote, “for what is empty is nothing,” and being has nowhere to go. No void, no motion. The atomists accepted that the void is not-being and denied that it therefore cannot be. Epicurus (341–270 BCE) kept their void, writing that “the whole of being consists of bodies and space,” and the Roman poet Lucretius put the argument into Latin verse.

Aristotle against the void

Aristotle (384–322 BCE) sided with the Eleatics on the void, but not on their reasons or on their conclusion that nothing moves. His case is in Physics IV.6–9. He starts from his opponents’ definition: a void is “place with nothing in it” (here and below, the Hardie and Gaye translation). On his own definition of place (next section), a place needs a container to bound it, so an empty place would have nothing to be a place of. That is an implication, not his argument, which is about motion.

1. No natural motion. Earth falls and fire rises by nature. In a void, up would not differ from down, so nothing could have a natural motion.
2. No reason to stop. Nothing could say why a body set moving in a void should stop: “why should it stop here rather than here?” It would go on forever unless something stronger stopped it. Aristotle meant this as an absurdity. It reads like Newton’s first law of motion.
3. Speed. Speed depends on a body’s weight and on the medium’s resistance. A void resists nothing, so every body would move equally fast, which he finds impossible.
4. The cube. If a void is a separate extension, how would a cube placed in it differ from the equal stretch of void it fills?

He also answers the atomists. Motion needs no void, because bodies can “make room for one another.” Thinning and thickening need none either: the same stuff can become more or less extended, as a thing becomes hot from cold. And what looks empty is not, because air is a body, as you feel by squeezing an air-filled wine-skin or shutting air into a water-clock. His verdict at the end of Book IV: “it is evident that void does not exist.”

“Nature abhors a vacuum” is not Aristotle’s sentence. He argues that a void is impossible or unnecessary, not that nature recoils from it. The slogan is a Latin formula of the schools that, according to the historian Edward Grant, begins to appear in the thirteenth century. Aristotle’s view won out in the schools.

Testing the void

The test came about two thousand years later, and it began with a nuisance: a suction pump will not lift water higher than about ten meters, and Galileo knew it. Around 1640–43 in Rome, Gasparo Berti stood a water-filled tube of about that height upright, and the water sank until a space opened above it (the year is uncertain). In 1643–44 Evangelista Torricelli proposed, and Vincenzo Viviani carried out, a smaller version with mercury, which is far heavier than water. A glass tube, closed at one end and filled with mercury, was turned upside down into a dish of mercury, and the column sank to about 76 centimeters, a little under thirty inches, leaving an empty space at the top. In a letter of 11 June 1644, the first written account, Torricelli said that we live submerged at the bottom of an “ocean of air” and that its weight balances the mercury. Berti came earlier, but Torricelli’s was the first easy, repeatable vacuum and the first explained by the weight of air.

Blaise Pascal heard of it in 1646. If the weight of the air held the mercury up, he reasoned, the column should stand lower on a mountain, with less air above. Pascal was ill and in Paris, so his brother-in-law Florin Périer made the test on 19 September 1648, at the Puy de Dôme near Clermont. Two checked tubes began in a convent garden. One stayed there under a friar’s watch, and Périer carried the other roughly a kilometer higher. At the summit the mercury stood about 8.5 centimeters lower, and on the way down it rose again. Pascal concluded that the weight of the air, not nature’s horror of emptiness, held it up.

Otto von Guericke (1602–1686), mayor of Magdeburg, built an air pump about 1650 and made the void a public show. He pumped the air out of two copper hemispheres, and two teams of eight horses could not pull them apart. That is the picture in his book Experimenta nova (1672); retellings differ on the number of horses, and we follow the book. Against Aristotle, Guericke argued for an infinite empty space.

This course argues that the experiments mattered for more than a fact. A void had been a problem for two thousand years, and it became respectable only as the school philosophy built on Aristotle began to give way. That is the thesis, and Lesson 2 continues it.

Aristotle’s place

Aristotle’s theory of place, his topos, begins with an everyday fact: we say where something is by saying what is around it. Your keys are in the drawer, the drawer is in the desk, the desk is in the room. In Physics IV.4 Aristotle makes that exact. Place, he concludes, is “the innermost motionless boundary of what contains.” In plain words: the place of a thing is the inner surface of whatever surrounds it, and that surface has to be treated as standing still.

Why still? Take Aristotle’s boat. It floats on a river, and the water touching its hull flows past. That water cannot be the boat’s place, he says, because it acts as a vessel and not as a place. Instead it is “the whole river that is place”: taken as a whole, the river stays where it is.

Aristotle also says what a place must be like. It contains the thing, is neither smaller nor larger than it, and can be left behind: you stand up, your place stays, and someone else can sit in it. Why not form, matter or an interval? Form is the boundary of the thing itself, while a place bounds the container. Matter contains nothing. And no permanent stretch of extension sits between the container’s surfaces, since a vessel’s contents can be swapped.

The second half of the theory says where things go. Each simple body has a natural place and, if nothing hinders it, is carried there: “Each is carried to its own place, if it is not hindered.” Earth goes toward the center and fire away from it, with water and air between: in the usual picture, nested shells, with the earth at the center and the heavens outside. A stone let go falls by nature. A stone thrown upward moves by force, and only while something keeps pushing. Think of the first kind as each thing going home; that is a modern picture, not Aristotle’s own image. Course 3 tells this physics at more length.

The same logic ends at the edge of the world. Aristotle’s chain of containers has to stop somewhere, and it stops at the outermost heaven. Nothing outside contains it, so by his own definition the heaven as a whole is “not anywhere.” Its parts have places, because each touches the next, but the whole has none. He accepts this (Physics IV.5). The Greek cosmos itself is the subject of Course 19, Lesson 3. He also records a puzzle that goes back to Zeno of Elea: if everything that exists is in a place, then a place is in a place too, and so on without end.

Plato offered a third idea. In the Timaeus he adds a “third kind,” the receptacle of all becoming, also called chōra: a seat for everything that comes to be, with no features of its own. Whether it is space, matter or something between, scholars dispute.

Modern physics threw Aristotle’s place out, so it is easy to think the theory died young. It did not. Until the seventeenth century it was the school definition of place. Philoponus, in the sixth century CE, rejected it and argued that place is the three-dimensional extension equal to the size of the body, not a surface. And Descartes’ “external place,” in his Principles of Philosophy (1644), is usually read as a reworking of the same surface idea.

Place, 位 and 宇 in Chinese

Chinese did not need Aristotle to say that where you are is part of who you are. The idea sits inside the word 位, which means a position in space and a rank in society at once. The old dictionary Shuowen jiezi defines it as the places arranged left and right in a court (列中庭之左右谓之位) and builds it from 人, “person,” and 立, “to stand.” The Yijing uses it both ways. When high and low are laid out, noble and humble have their positions (卑高以陈，贵贱位矣), and later the sage’s great treasure is position (圣人之大宝曰位).

Confucius took the link for granted. “One who is not in the position does not plan its affairs,” runs Analects 8.14 (不在其位，不谋其政, bù zài qí wèi, bù móu qí zhèng; our translation). The saying is repeated in Book 14, where Zengzi, a disciple, adds a gloss: the gentleman’s thoughts do not go beyond his position (君子思不出其位). Two other classical words for place are 处 (chǔ, to dwell; as a noun, chù, a place) and 所 (suǒ).

In his essay on the Yueyang Tower, dated 1046, the statesman Fan Zhongyan wrote of the worthy person: in the high halls of the court he worries about the people, and far away among the rivers and lakes he worries about the ruler (居庙堂之高，则忧其民；处江湖之远，则忧其君). A modern proverb says the seat decides the head, meaning that where you sit decides what you think, a cynical and different idea. Fan’s point is that the worthy person worries in either place.

Now space itself. The Huainanzi, a Han dynasty collection, defines a famous pair: 往古来今谓之宙，四方上下谓之宇，道在其间，而莫知其所. Past and present, from the old to the now, is called zhòu, time. The four directions and above and below are called yǔ, space. The Way lies in between, “and no one knows where.” Together they make 宇宙 (yǔzhòu), still the word for “universe.” The Shuowen glosses 宇 as the eaves of a house. The Mohist Canon, compiled most likely between the late fourth and mid third century BCE, defines space through places: 宇，弥异所也, which on the usual reading says that yǔ spreads across different places. Its word for place is the 所 from above. So one of the earliest Chinese definitions of space on record is built from places.

Chinese culture also built a practice around choosing places. 风水 (fēngshuǐ, “wind and water”) is the art of siting graves, houses and cities by the lie of the land. The Zangshu (“Book of Burial”) explains the name: qi, the vital energy of Chinese thought, rides the wind and scatters, and stops at water, so the ancients gathered and guided it (气乘风则散，界水则止). Tradition credits the book to Guo Pu (276–324), but scholars doubt that, and the text in use was edited by Song and Yuan scholars. Fengshui is a real historical practice, and it shows how seriously Chinese culture took place. There is no scientific support for its claims that qi flows along terrain or that a building’s orientation changes the luck or health of those inside.