From the closed world to the infinite universe, and back

The closed world

For two thousand years the standard picture of the whole was Aristotle’s. In On the Heavens he argued that the cosmos is finite, single, and complete: a nest of spheres with the earth at the center and the sphere of the fixed stars as the outermost shell. Beyond that shell, he wrote, there is “neither place, nor void, nor time” (in the Stocks translation). The question “what is outside?” has no answer because there is no outside. The French historian of science Alexandre Koyré, in a book of 1957, called this the closed world: a universe with a shape, a center, a boundary, and an order of higher and lower places. Courses 1 and 3 describe it in detail.

Koyré’s book, From the Closed World to the Infinite Universe, argued that the change from that world to our own was not only a matter of new facts about the sky. It was two linked changes of thought. One was the loss of the cosmos: the idea of a finite, ordered whole in which each thing has its natural place gave way to a space with no center and no preferred direction. The other was the geometrization of space: the places of the old picture were replaced by the uniform, empty space of geometry. Other historians have qualified his story, and some argue that medieval thinkers were already more open to space beyond the world than Koyré allowed. But it is a good guide to the thread this lesson follows.

Breaking the spheres

An early crack came from a philosopher and cardinal, Nicholas of Cusa. In On Learned Ignorance (1440) he wrote that the world-machine has its center everywhere and its circumference nowhere, because its center and circumference are God. He called the universe “privatively” infinite: without limit, though only God is infinite in the full sense. It was a metaphysical argument, not an observation, and it took the earth out of the center without putting the sun there.

The decisive crack came from Copernicus. In On the Revolutions (1543) he set the earth in motion around the sun, or near it, since he put the sun slightly off the center of the earth’s orbit and kept epicycles. Two consequences of his idea matter here. The first is size. If the earth circles the sun, the nearer stars should seem to shift against the farther ones as the earth moves, as your thumb jumps against the wall when you blink one eye and then the other. This shift, called parallax, was not measured until 1838. Copernicus’s reply was that the heavens are immense compared with the earth’s orbit, so the shift is too small to see. On whether the heavens are finite or infinite he declined to decide: he called the limit “unknown and unknowable” and left the question to the natural philosophers. The second consequence is motion. If the earth spins, the great sphere of the stars does not need to turn once a day. It could stand still, and a sphere at rest does not need to be a sphere. In 1576 the English astronomer Thomas Digges, in an English account of the Copernican system, drew the stars scattered at all depths beyond Saturn, in a region “fixed infinitely up.” In 1584 Giordano Bruno published On the Infinite Universe and Worlds, picturing an infinite universe with no center and countless worlds.

Observation helped. The great comet of 1577 was watched by Tycho Brahe from Denmark and by others elsewhere in Europe, and from the small differences in its position he judged that it lay well beyond the moon, in a region the old picture said was unchanging. A comet that passes through the heavens does not fit among solid crystal shells. Tycho’s own system kept the earth at the center, with the other planets circling the sun and the sun circling the earth, and it too had no room for the shells. René Descartes, in Principles of Philosophy (1644), called the world indefinite, meaning that he could set no limit to it, and kept “infinite” for God. He had held back an earlier book on the world after Galileo’s condemnation in 1633.

Bruno’s fate is often told as science against the Church. The fuller story is less tidy. He was a philosopher and a poet-magus, not an observer or a mathematician, and in 1600 the Church had no official position against Copernicus; his book was suspended only in 1616. The Roman Inquisition tried him from 1593 on a bundle of charges, most of them theological, such as his views on the Trinity, on Christ, and on the soul, and the bundle also included his teaching of an eternal world and of many worlds. He was burned in the Campo de’ Fiori on 17 February 1600. Historians disagree about how heavily the many-worlds charge weighed. It is fair to say he was not burned for that alone, and not fair to say his cosmology had nothing to do with it.

Newton’s endless space

In 1687 Isaac Newton gave the broken world a new frame. His Principia opens with the first law of motion: a body not acted on by a force continues at rest or moves in a straight line at a steady speed. Newton also describes an absolute space that “remains always similar and immovable.” This course draws a strong conclusion: such motion presupposes a space that goes on without end, because a body moving freely never reaches an edge. That is a reading, not a theorem. The law fits a uniform, unbounded, Euclidean space, and it does not fit Aristotle’s cosmos of natural places. But as Einstein’s closed space will show, inertial motion also makes sense in a finite space, so the first law alone does not force infinity.

Endless space brought trouble at once. In 1692 the scholar Richard Bentley asked Newton how a universe of stars attracting one another could avoid collapsing into one lump. In letters to Bentley, Newton replied that matter spread evenly through an infinite space would not fall together, but would form many separate masses; and that balancing everything exactly would be “as hard as to make the sharpest needle stand upright on its point upon a looking glass,” and as hard as doing it for an infinite number of needles. In the second edition of the Principia (1713) he wrote that God had set the stars at immense distances from one another, so that they would not fall on each other. A modern form of the difficulty, due to the astronomer Hugo von Seeliger and the mathematician Carl Neumann in the 1890s, is that in a Newtonian universe filled evenly and endlessly with matter, the total pull on a body has no definite value: the answer depends on how you add up the contributions.

The second trouble is the dark night. If space is endless and filled with stars, every line of sight should end on a star, and the sky should blaze. Kepler raised the riddle in 1610 as an argument for a finite universe; Halley discussed it in 1720, wrongly thinking he had answered it; Heinrich Olbers gave it the name it bears in 1823. Course 7 tells the story and the answer: the universe has a finite age, so light from the most distant stars has not reached us yet. (It is sometimes said that Halley raised both difficulties with Newton. That is not supported: the gravity problem comes from Bentley and Newton in 1692–93, while Halley’s papers of 1720–21 argue for an infinite universe.)

It is also said that after the Principia cosmology “disappeared” for two centuries. That goes too far. In 1750 Thomas Wright pictured the Milky Way as a flat slab of stars seen from inside. Kant in 1755 suggested that the faint nebulae might be other systems like it. In 1761 Johann Lambert imagined clusters nested in larger clusters, and in 1785 William Herschel mapped the shape of the Milky Way by counting stars. What was missing was not cosmological thinking but a physical theory of the universe as a whole that could be tested. The infinite Newtonian universe carried unresolved paradoxes until 1917.

A finite universe with no edge

The next change came with Einstein. He finished the general theory of relativity in November 1915, and in February 1917 he applied it to the universe as a whole, in “Cosmological considerations in the general theory of relativity,” read to the Prussian Academy on 8 February. (Some accounts give 1916.) His model was closed: a space of finite volume and no boundary, like a three-dimensional version of the surface of a globe. Set off in a straight line and, after a very long trip, you come back to where you began, never meeting an edge. He wrote to a colleague that it was a “rather outlandish conception,” and joked that he risked being locked up in a madhouse. Closing space also removed the need for any boundary conditions “at infinity.” To keep his universe from collapsing he added a term to his equations, the cosmological constant. In this reading, it was the return of the cosmos: a finite universe with a shape, after two centuries of the endless one. The likeness to Aristotle’s is only partial, since Aristotle’s universe had an outer boundary and Einstein’s has none. But the point holds: the whole could once again be treated as an object of physics.

Einstein’s universe did not last. In 1922 the Russian mathematician Alexander Friedmann showed that the same equations allow a universe that expands or contracts. In 1927 the Belgian priest and physicist Georges Lemaître proposed an expanding universe, with a first estimate of its rate; Einstein, told of it, is said to have found the idea “abominable.” In 1929 Edwin Hubble’s measurements of galaxies, at the Mount Wilson Observatory in California, showed that the farther away a galaxy is, the faster it recedes. (Galaxy redshifts themselves had been found by Vesto Slipher in the 1910s; the nearby Andromeda galaxy is even moving toward us.) Einstein visited Mount Wilson in January 1931, and that spring he gave up the static model. He did not “discover” expansion; he built the model that expansion overturned. Gamow later reported that Einstein called the cosmological constant his biggest blunder, though doubts remain about the exact words. And in 1931 Lemaître proposed that if the universe expands, then running it backward it began in an extremely dense state, his “primeval atom.”

One claim in this course’s account needs updating: that the evidence for the Big Bang is thin, only the redshift and the background radiation. That was fair in the 1960s. The model now rests on several independent lines: the expansion; the background radiation, found by Arno Penzias and Robert Wilson in 1964–65 and predicted in 1948 by Ralph Alpher and Robert Herman, whose spectrum is a near-perfect thermal one at 2.7255 kelvin; the abundances of hydrogen, helium and deuterium; the pattern of galaxies on large scales; and the stretching in time of the light curves of distant exploding stars, which rules out the old idea of “tired light” that fades as it travels. The course is right that a theory is held for now, and that scientists are free to doubt. The doubt today is about details, such as dark energy, not the broad picture. The best figure for the age of the universe is about 13.8 billion years.

And what of “what was before the Big Bang?” This course says scientists forbid the question, because time began with the bang, as it is meaningless to ask what lies north of the North Pole, and compares Augustine, who is said to have lost patience with those who asked what God did before creating the world. The comparison is better than it looks. In the Confessions (around 400 CE) Augustine reports the joke answer, that God was preparing hell for people who pry into mysteries, and refuses it: it is one thing to answer a question, he says, and another to make sport of the questioner. His own answer is that God made time along with the world, so there was no “then” before it. Stephen Hawking used the pole in a similar way: the no-boundary proposal he and James Hartle made in 1983 pictures a universe with no sharp beginning in time, as there is nothing south of the South Pole. It is one proposal among several, and the question is open, not forbidden: the classical theory breaks down at the earliest moment, and what lies before it belongs to a future theory.

Is space infinite?

And Kant’s question, finite or infinite? Modern cosmology answers part of it. What we can observe is finite: the part from which light has had time to reach us is a ball about 46.5 billion light-years in radius (larger than 13.8 billion because space expanded while the light traveled). Whether the universe is larger than that ball is not known. The Planck satellite and other measurements put space very near flat, with a curvature parameter of 0.0007 plus or minus 0.0019, which fits an infinite space and also a very large finite one. The question is open, and may stay open.

What is cosmology for?

The course ends on a conclusion about people. It says modern cosmology, for all its power, has a human price. Steven Weinberg wrote near the end of his 1977 book The First Three Minutes: “The more the universe seems comprehensible, the more it also seems pointless.” This course takes that as the absurdity of a world pictured in ever finer detail, with no place in it for meaning.

Its answer is bold. Giant instruments, such as China’s 500-meter radio telescope in Guizhou, the gravitational-wave detectors, and the particle colliders, are, in this reading, the temples of our time. Every society, it says, needs a picture of the whole to live in. The Egyptians built pyramids and the Greeks temples; we build telescopes. They do not feed anyone. They defend something people cannot do without, a universe, and so a place that gives life meaning. Asked whether one really believes the Big Bang theory, the answer in this reading is that we take it on trust from those whose job it is, as earlier ages took their world picture from priests. And the course adds a piece of social criticism: that the aliens of science fiction have taken the place of angels, and artificial intelligence the place of gods.