Manual Anaximander and the origins of Greek cosmology

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The strangeness disappears, however, when we realize that Anaximander thought that the earth was flat and circular, as suggested by the horizon.

Anaximander and the origins of Greek cosmology | UNIVERSITY OF NAIROBI LIBRARY

For one who thinks, as Anaximander did, that the earth floats unsupported in the center of the universe, the cylinder-shape lies at hand. We may assume that Anaximander somehow had to defend his bold theory of the free-floating, unsupported earth against the obvious question of why the earth does not fall. Aristotle's version of Anaximander's argument runs like this: "But there are some who say that it namely, the earth stays where it is because of equality, such as among the ancients Anaximander.

For that which is situated in the center and at equal distances from the extremes, has no inclination whatsoever to move up rather than down or sideways; and since it is impossible to move in opposite directions at the same time, it necessarily stays where it is. Anaximander's argument returns in a famous text in the Phaedo E4 ff. Even more interesting is that the same argument, within a different context, returns with the great protagonist of the principle of sufficient reason, Leibniz.

In his second letter to Clarke, he uses an example, which he ascribes to Archimedes but which reminds us strongly of Anaximander: "And therefore Archimedes He takes it for granted that if there be a balance in which everything is alike on both sides, and if equal weights are hung on the two ends of that balance, the whole will stay at rest. This is because there is no reason why one side should weigh down, rather than the other". One may doubt, however, whether the argument is not fallacious. Aristotle already thought the argument to be deceiving.

He ridicules it by saying that according to the same kind of argument a hair, which was subject to an even pulling power from opposing sides, would not break, and that a man, being just as hungry as thirsty, placed in between food and drink, must necessarily remain where he is and starve. To him it was the wrong argument for the right proposition. Absolute propositions concerning the non-existence of things are always in danger of becoming falsified on closer investigation.

They contain a kind of subjective aspect: "as far as I know. Already at first sight this qualification sounds strange, for the argument evidently must be wrong, as the earth is not in the center of the universe, although it certainly is not supported by anything but gravity. Nevertheless, we have to wait until Newton for a better answer to the question why the earth does not fall.

When Anaximander looked at the heaven, he imagined, for the first time in history, space. Anaximander's vision implied depth in the universe, that is, the idea that the celestial bodies lie behind one another. Although it sounds simple, this is a remarkable idea, because it cannot be based on direct observation. We do not see depth in the universe. The more natural and primitive idea is that of the celestial vault, a kind of dome or tent, onto which the celestial bodies are attached, all of them at the same distance, like in a planetarium.

One meets this kind of conception in Homer, when he speaks of the brazen or iron heaven, which is apparently conceived of as something solid, being supported by Atlas, or by pillars. Anaximander placed the celestial bodies in the wrong order. He thought that the stars were nearest to the earth, then followed the moon, and the sun farthest away. Some authors have wondered why Anaximander made the stars the nearest celestial bodies, for he should have noticed the occurrence of star-occultations by the moon. This is a typical anachronism, which shows that it not easy to look at the phenomena with Anaximander's eyes.

Nowadays, we know that the stars are behind the moon, and thus we speak of star-occultation when we see a star disappear behind the moon.

But Anaximander had no reason at all, from his point of view, to speak of a star-occultation when he saw a star disappear when the moon was at the same place. So it is a petitio principii to say that for him occultations of stars were easy to observe. Perhaps he observed stars disappearing and appearing again, but he did not observe - could not see it as - the occultation of the star, for that interpretation did not fit his paradigm. The easiest way to understand his way of looking at it - if he observed the phenomenon at all - is that he must have thought that the brighter light of the moon outshines the much smaller light of the star for a while.

Anaximander's order of the celestial bodies is clearly that of increasing brightness. Unfortunately, the sources do not give further information of his considerations at this point. A peculiar feature of Anaximander's astronomy is that the celestial bodies are said to be like chariot wheels the Greek words for this image are presumably his own. The rims of these wheels are of opaque vapor, they are hollow, and filled with fire. This fire shines through at openings in the wheels, and this is what we see as the sun, the moon, or the stars.

Sometimes, the opening of the sun wheel closes: then we observe an eclipse. The opening of the moon wheel regularly closes and opens again, which accounts for the phases of the moon. This image of the celestial bodies as huge wheels seems strange at first sight, but there is a good reason for it. There is no doxographic evidence of it, but it is quite certain that the question of why the celestial bodies do not fall upon the earth must have been as serious a problem to Anaximander as the question of why the earth does not fall.

The explanation of the celestial bodies as wheels, then, provides an answer to both questions. The celestial bodies have no reason whatsoever to move otherwise than in circles around the earth, as each point on them is always as far from the earth as any other. It is because of reasons like this that for ages to come, when Anaximander's concept of the universe had been replaced by a spherical one, the celestial bodies were thought of as somehow attached to crystalline or ethereal sphere-shells, and not as free-floating bodies.

Many authors, following Diels, make the image of the celestial wheels more difficult than is necessary. They say that the light of a celestial bodies shines through the openings of its wheel "as through the nozzle of a bellows. The image of a bellows, somehow connected to a celestial wheel, tends to complicate rather than elucidate the meaning of the text. If we were to understand that every celestial body had such a bellows, the result would be hundreds of nozzles or pipes , extending from the celestial wheels towards the earth.

Anaximander's intention, however, can be better understood not as an image, but as a comparison of the light of the celestial bodies with that of lightning. Lightning, according to Anaximander, is a momentary flash of light against a dark cloud. The light of a celestial body is like a permanent beam of lightning fire that originates from the opaque cloudy substance of the celestial wheel. The doxography gives us some figures about the dimensions of Anaximander's universe: the sun wheel is 27 or 28 times the earth, and the moon wheel is 19 times the earth.

More than a century ago, two great scholars, Paul Tannery and Hermann Diels, solved the problem of Anaximander's numbers.

They suggested that the celestial wheels were one unit thick, this unit being the diameter of the earth. The full series, they argued, had to be: 9 and 10 for the stars, 18 and 19 for the moon, and 27 and 28 for the sun. These numbers are best understood as indicating the distances of the celestial bodies to the earth. In others words, they indicate the radii of concentric circles, made by the celestial wheels, with the earth as the center.

See Figure 1, a plane view of Anaximander's universe. These numbers cannot be based on observation.

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Anaximander and the Origins of Greek Cosmology

In order to understand their meaning, we have to look at Hesiod's Theogony , where it is said that a brazen anvil would take nine days to fall from heaven to earth before it arrives on the tenth day. It is not a bold guess to suppose that Anaximander knew this text.

The agreement with his numbers is too close to neglect, for the numbers 9 and 10 are exactly those extrapolated for Anaximander's star wheel. Hesiod can be seen as a forerunner to Anaximander, for he tried to imagine the distance to the heaven. In the Greek counting system Hesiod's numbers should be taken to mean "a very long time. We may infer that Anaximander, with his number 9 1 x 3 x 3 for the star ring, simply was trying to say that the stars are very far away. Now the numbers 18 and 27 can easily be interpreted as "farther" 2 x 3 x 3, for the moon ring and "farthest" 3 x 3 x 3, for the sun ring.

And this is exactly what we should expect one to say, who had discovered that the image of the celestial vault was wrong but that the celestial bodies were behind one another, and who wished to share this new knowledge with his fellow citizens in a language they were able to understand. Although it is not attested in the doxography, we may assume that Anaximander himself drew a map of the universe, like that in figure 1.

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The numbers, 9, 10, 18, etc. On the other hand, it is quite easy to explain the movements of the celestial bodies with the help of a plan view, by making broad gestures, describing circles in the air, and indicating direction, speed, and inclination with your hands, as is said of a quarrel between Anaxagoras and Oenopides DK 41A2. Almost nothing of Anaximander's opinions about the stars has been handed down to us.

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Probably the best way to imagine them is as a conglomerate of several wheels, each of which has one or more holes, through which the inner fire shines, which we see as stars. The most likely sum-total of these star wheels is a sphere. The only movement of these star wheels is a rotation around the earth from east to west, always at the same speed, and always at the same place relative to one another in the heaven. The sun wheel shows the same rotation from east to west as the stars, but there are two differences.

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The first is that the speed of the rotation of the sun wheel is not the same as that of the stars. We can see this phenomenon by observing how the sun lags behind by approximately one degree per day. The second difference is that the sun wheel as a whole changes its position in the heaven. In summer it moves towards the north along the axis of the heaven and we see a large part of it above the horizon, whereas in winter we only observe a small part of the sun wheel, as it moves towards the south.

This movement of the sun wheel accounts for the seasons. The same holds mutatis mutandis for the moon. Today, we use to describe this movement of the sun and mutatis mutandis of the moon and the planets as a retrograde movement, from west to east, which is a counter-movement to the daily rotation from east to west. In terms of Anaximander's ancient astronomy it is more appropriate and less anachronistic to describe it as a slower movement of the sun wheel from east to west.

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The result is that we see different stars in different seasons, until the sun, at the end of a year, reaches its old position between the stars. Due to the inclination of the axis of the heaven, the celestial bodies do not circle around the earth in the same plane as the earth's - flat - surface, but are tilted. This inclination amounts to about The earth being flat, the inclination must be the same all over its surface.

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This tilting of the heaven's axis must have been one of the biggest riddles of the universe.