About the same time that Anaximander was inventing solid hemispheres and rings to hold and move the heavenly bodies round about a flat earth, Pythagoras was founding a school in southern Italy which gave to the world a very different scheme. One of the characteristics of his school was secrecy, its methods were oral, and his later followers were fond of attributing to their master everything which had gradually grown out of his teaching: it is difficult therefore to say with certainty what he himself taught. It has often been stated by modern writers that he anticipated Copernicus, and discovered that the earth revolves round the sun. Though this is a mistake, we may venture to believe that Pythagoras taught that the earth is a sphere, hanging freely in space.

We are so familiar with this idea from childhood, that it is difficult to imagine what a tremendous innovation it was. Pythagorean noviciates, doubtless after solemn initiation and preparation, were told: This earth, which seems to you the floor of the world, with heaven stretched over it like a tent, is a round globe, with men like you living on the other side of it, and yet they do not fall, and earth does not fall, for it is poised in the centre of the world, and has no tendency to fall in one direction rather than in another. Earth, itself a perfect sphere, is in the centre of an infinitely greater sphere, the star-set heaven; and within this seven heavenly bodies move in perfect circles, each at its proper distance and pace, all needing no support and no force to drive them, for harmony is the motive power of the Cosmos. Their distances are proportional to the intervals between musical notes, and as they circle they make heavenly music, which we should hear did we not always hear it, like one who lives beside a waterfall[28]. There is no below, and no above, for above is below and below above to our antipodes: there is but the centre, where we live, and Heaven is all around.

How did Pythagoras reach this great and startling truth of the round unsupported earth?

His school relied more on experiment and observation than the Ionian, and the colonizing Greeks of Italy had travelled. They might have noticed the curvature of the sea, and the varying height of the Pole Star according to latitude. We know that in early days the Greeks were struck by the remarkable fact that the brilliant star Canopus (second only to Sirius in brightness), which was invisible in Greece, could just be seen close to the southern horizon in Rhodes, and was well seen in Egypt. Then the moon may have helped once more. When it was understood that lunar eclipses only happen at full moon, when we are between her and the sun, and that they may therefore be explained by the earth’s shadow falling on the moon, then, since the edge of that shadow is always a circle, it is demonstrable that the body throwing that shadow can have no form but that of a ball.

Sun and moon are obviously round: it was guessed that they also are globes rather than discs, and the spherical shape of all heavenly bodies was a doctrine of the later if not the earliest Pythagoreans.

Whatever may have been the steps which led to these two great discoveries that Earth is a sphere, and that the apparent path of every celestial body is a circle, the sphere and the circle were soon accepted as the only forms suitable for celestial bodies and their orbits. The founder of the school was a great mathematician, and it is not strange that these forms should have commended themselves to his disciples. The sphere, which has its surface everywhere similar, and its contents greater than those of any other figure with equal surface, was the “most perfect” of solids; and the circle, which has no beginning and no end, is alike in every part, and presents ideas of haunting suggestiveness to the geometer, was the “most perfect” of lines.

In the system of Pythagoras we first find the five planets distinctly enumerated, and playing as important parts as sun and moon. Number was the principle of this universe, and the planets with sun and moon made the sacred number of seven. Among the Greeks, and through the middle ages, all these bodies are spoken of as planets or “wanderers,” in distinction from the “fixed” stars which do not appear to move amongst themselves. These seven “planets” represented the seven notes of a musical scale, and the star sphere made up the octave. Pythagoras is said to have been the first to teach that Phosphor and Hesperus, the morning and the evening star, were the same. When, however, we ask what was the order of the planets in his scheme, we meet with many conflicting reports, and a serious difficulty suggests itself. If the planets had really been observed with care, it must have been seen that their motions could not be accounted for by simple circular movement. The large oscillations of Mercury and Venus on either side of the sun would strike an observer before he thought of tracing their movements among the stars, and noting that they made a circuit of the zodiac. Similarly, the other planets are most conspicuous, rising after sunset and remaining long visible through the night, at the very time of their retrograde movements, so these must have been noticed if a long enough series of observations had been made to distinguish them from one another. The only solution of the difficulty seems to be that Pythagoras, on the journeys into Egypt and Babylon which he is said to have made, learned that there exist planets to the number of five, which move in regular periods, and he may also have learned the length of their zodiacal periods at the same time, or perhaps these were only known to his school much later. If the order assigned to them was that which was finally and generally accepted by the ancient world, the periods must have been known, for this is the only possible clue to the order Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. The planet with shortest period (the moon, with a month) was naturally placed by the Greeks nearest to earth, with the smallest circle to traverse, and so on outwards.

It is very possible, however, that the early Pythagoreans, at least, did not venture to assert more than that there were five planets, without assigning to them any order, for Aristotle tells us that their universe was divided thus:—

From Earth to Moon was the Ouranos, or sky, within which exists all that is changing and corruptible.

Cosmos, the place of ordered movement, was the region of Sun, Moon, and Planets.

Olympos, the place of pure elements, held the stars; the region of Celestial Fire came beyond this, and the Apeiron, the Infinite Space, or Infinite Air, from which the world draws its breath, was outside all.

The diagram shows, then, the earliest form of the Pythagorean universe. But they did not remain content with this. Out of it grew a most interesting scheme (referred to by Dante), which is usually attributed to one Philolaus, of whom hardly anything is known, not even his date.

It seems to have struck Philolaus as a difficulty that the seven planets, which were circling round Earth in the same direction but at very different distances and speeds, and also the immense sphere of stars beyond, were all sweeping together at the same time in an opposite direction, and at the almost incredible pace of one revolution in a day. The brilliant idea occurred to him: Leave the stars at rest, let the seven planets revolve in their seven orbits, the nearer to the centre the faster, and let earth herself revolve fastest of all, viz. in twenty-four hours, in the same direction. If she keeps one face always turned towards the centre, like the moon, this will account quite as well for the apparent diurnal revolution of all the heavenly bodies, and the change of day and night on the earth.

Philolaus did not make Earth remain stationary and simply turn on her axis, which would have had just the same effect on the apparent motions of the heavens; for it seemed more natural that she should revolve as did the rest. The five naked eye planets are all mentioned by name in his scheme.

Was the centre, deprived of Earth, to be left empty? No, the centre was the Watch Tower of Zeus, the Hearth of the Universe, and here they placed the purest element, fire. It was invisible to us, because we live on the side of the earth-sphere turned away from the centre; and also invisible to us was another planet, Antichthon, or Counter-Earth, for this revolved within our orbit, and also in twenty-four hours. It was added to the system, because the addition of Earth as a heavenly body spoiled the sacred number of seven, but by adding Antichthon, and counting the star sphere as another, the total was brought up to ten, another sacred number.

The objection was made that, if Earth is moving in space, this must bring about a change in the apparent sizes of sun and moon, as Earth is nearer or farther from them, but the Pythagoreans were quite ready to believe that all the heavenly bodies are so distant that this journey of Earth makes no difference to their apparent size or brightness. The planets were thought to be worlds like ours, and inhabited; and it was even guessed that plants and animals on the moon must be fifteen times as strong as ours, apparently because there the average day consists of nearly fifteen of our days (of twenty-four hours), and the nights are equally long.

It was the braver of the Pythagoreans to shake the steady earth from her centre, and set her whirling in the depths of space, that they realized, as no one had done before, how large she must be; for Greece and the surrounding lands, the Middle and the other seas, instead of making the whole of the earth, were now understood to be only a portion of a great globe.

Here, then, is a conception of the Universe widely different from Homer’s. The little flat disc has become a great round ball, a planet among planets, swiftly moving through space; the crystal dome that tenderly covered it like a bell-glass over some fragile flower, has lifted, and the vast sphere is seen, infinitely distant, and studded with enormous stars. Man himself is now a tiny creature on a great earth, and his world but one among many, but if he is humiliated by his insignificance, is he not elevated by the vastness of his outlook?

But not even here did the Greeks stop. It was taking a less startling step than they had already taken, to reach the truth that Earth was merely rotating on her axis once in a day, and so causing the apparent diurnal revolution of the heavens. This step was taken (it is said) by a Pythagorean called Hicetas of Syracuse, who is quoted as saying that the earth, “while it turns and twists itself with the greatest velocity round its axis, produces all the same phenomena as if the heavens were moved and the earth were standing still.” We are told also that “Heracleides of Pontus and Ecphantus the Pythagorean let the earth move, not progressively, but in a turning manner like a wheel fitted with an axis, from west to east round its own centre.”

A brilliant guess,[29] which seems fully justified by facts, has recently explained the personalities of these two mysterious Pythagoreans of unknown date, Hicetas and Ecphantus, whose names have been coupled for centuries with that of Heracleides, as teaching the rotation of Earth on her axis. It seems that they resemble the Shadow in Hans Andersen’s tale, which became a man and lived apart from the man to whom it originally owed its existence, for it is now thought that they were speakers introduced by Heracleides into one of his dramatic dialogues to discuss astronomy.

Heracleides, therefore, was the sole author of this remarkable discovery.

In this way Earth was restored to her central position, but as a rotating sphere, and the later Pythagoreans apparently tried to reconcile their new scheme with the old by calling Antichthon the uninhabited hemisphere of Earth, and placing the central fire within the earth.