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This deeper 20th-century insight (or, some may prefer, mere technicality) notwithstanding, every generation tends to believe devoutly in the finality of its own science, always for the same excellent reasons: what we experience presents us with puzzles. We put our trust in plausible solutions, of which we can say, ‘Of course, that explains it!’ We choose the explanations that seem to make the best sense of things as we know them, and of things as we believe future generations will probably know them (to the best of our ability to predict). After all, that is the most anyone can ask of science in any era. But it isn’t final, unassailable truth. We criticize our ancestors for not bearing that in mind, while we continue to err in the selfsame manner.

Carrying our modern world-view along on a visit to the past is notoriously inadvisable, but, in this chapter and the next, doing so selectively would not be a bad idea. Leave behind scient
ism
, the popular belief that current science is final Truth. Instead, bring along a less naive scientific world-view that recognizes the open-endedness of science. Bring along the
concept
of relative motion. With those things in mind, you’ll be prepared to appreciate and sympathize as two of the most brilliant intellects in history account for the observed movement of pinpoints of light in the heavens.

Almost no information whatsoever exists about the life or personality of Claudius Ptolemaeus, known to us as Ptolemy, except that he worked at Alexandria during the second century
AD
and died in about 180. There is no record of where he was born, and the name Ptolemy doesn’t indicate he was a member of the ruling family. Like Eratosthenes, Ptolemy was interested in a wide range of subjects including acoustics, music theory, optics, descriptive geography and mapmaking. Some of his maps were still in use as late as the 16th century. More significantly, Ptolemy drew together, from previous ideas and knowledge and out of his own mathematical genius, an astronomy that would dominate Western thinking about the universe for 1,400 years.

Ptolemy inherited an intellectual tradition that placed an unmoving Earth at the centre of the universe and that insisted that all heavenly movement occurred in perfect circles and spheres. Among his contemporaries who thought about such matters, most had come to assume that the physical appearance of things must be taken into serious account when one tried to figure out the structure of the universe. To be believed, an explanation must ‘save the appearances’. That may seem so obvious that it is hardly worth mentioning, but it isn’t an assumption present in all cultures nor was it supported by all schools of thought in the Greek and Hellenistic worlds.

The ‘appearance of things’, for Ptolemy, included what Hipparchus and others had recorded in star catalogues. Ptolemy also brought to his task an in-depth knowledge of previous attempts to explain and predict planetary movement as it is seen from the Earth. The origins of the longing to understand that movement are lost in pre-history, but Plato, in the fourth century
BC,
focused it in the question: ‘What are the uniform and ordered
movements
by the assumption of which the apparent movements of the planets can be accounted for?’ The ancient attempts to answer him, beginning with his pupil, the mathematician Eudoxus of Cnidus, were ingenious. Science historians disagree about how much Ptolemy’s work was a synthesis of some of these earlier ideas and how much it owed to his personal genius. Either way it’s clear he was a brilliant mathematician, and his achievement is almost unparalleled in the history of science.

When trying to understand Ptolemy it helps to pay an imaginary visit to a fair or amusement park.

Look first at a carousel designed for very young children. The horses do nothing else but move in a large circle. We’ll put a light on the head of one horse, switch off all other lights, situate ourselves at the centre of the carousel in such a way that we don’t turn with the carousel, and set it going The light circles us steadily, never varying in speed or brightness, never changing direction.

If the Earth were the centre and were not moving or rotating, and if all the planets were orbiting it in circular orbits, we could expect to see each planet as we see the light on this carousel. That is, roughly, the way we see the Moon and the Sun, though their movements include irregularities that foil any attempt to describe them quite that simply. But we definitely do not see the planets moving in this manner, and neither did ancient astronomers and stargazers. Even as early as Plato and Eudoxus, those who studied the heavens knew that a model with simple circular orbits centred on the Earth couldn’t adequately explain what was going on up there.

To illustrate one particularly mysterious problem: on the darkened carousel, suppose we see the light move ahead for a while, pause, reverse, then move forward again. The pattern continues to repeat itself. How to account for this movement? Someone might suggest that the light isn’t attached to a horse’s head at all. Instead it’s on the cap of the ticket-taker who is moving around among the horses. But the movement looks too
regular
for that. Not quite random enough. Try again. Suppose the light is at the end of a rope, and someone riding one of the horses is swinging the light around his or her head as one would a stone in a long slingshot prior to launching it. Putting that movement together with the overall circular movement of the carousel might explain the apparent reversing, as the light circles
toward
the back of the rider’s head. Or, if we want to stay with the notion that the light is on a horse’s head, perhaps the horse isn’t fixed directly to the floor of the carousel but instead is part of a mini-carousel attached near the edge of the large carousel. In other words, in addition to being carried around in the big circle of the carousel, the horse is also moving around in a smaller circle, chasing its own tail. This last scheme would be something like
Figure 2.1.
We could still accurately say that we are at the centre of the carousel and everything on it is moving around us. Also, all movement is in perfect circles, no matter how complicated and uncircular it may appear to our eyes.

Figure 2.1

The carousel is rotating, and on its periphery, the smaller disc is rotating on its own axis so that the horse with the light on its head (asterisk) is chasing its tail. From the centre of the carousel it seems to us that the light moves forward, stops, reverses its motion a little while, stops again and moves forward once more.

Figure 2.2
is an idealized picture of the pattern such a light might trace in time-lapse photography taken from a helicopter hovering over the carousel. From our position at the centre (E) we wouldn’t see the loops. The light would appear to go forward, then pause, then back up, then pause, then repeat the
pattern
. With the fair fully illuminated, it’s easy to account for movement like that in terms of perfect circles, but it would require considerable mathematical insight to do so if we could see nothing but a few moving lights.

Figure 2.2

With the naked eye and a view of only a portion of the sky at any one time, those who studied the movements of the stars, Sun, Moon and planets before the invention of the telescope were left to account for what they saw in much the way we would have to do in our amusement park plunged into darkness. Tiny lights that move smoothly for a time, then pause and reverse, or seem to grow brighter and dimmer, to speed up and slow down. That’s what Aristotle, Plato, Aristarchus and Ptolemy saw. That is also what Copernicus saw, for he too lived before there were telescopes. All they had beyond that were charts and catalogues of what their forebears had observed. Even assuming those notations were made with consummate skill and care (which was not always the case), given the lack of standardization and the discrepancy of calendars between one society and another, the interpretation of those records was not a straightforward matter. Telescopes appeared in the 17th century, but until the 20th century no one had a view of the planets from anywhere else but on the Earth. What a daunting task – one might think an utterly impossible task – it was to make sense of it, to design, as it were, carnival rides that could underlie and explain all that motion.

The arrangement with small carousels riding on large carousels is like one of the models that Ptolemy (long before such rides existed) took from his predecessors and incorporated into his astronomy. There are technical words to describe it: the ‘reversing’ movement of a planet is
retrogression
. The smaller circles around which the planets move (chasing their tails) are
epicycles
. The circumference on the carousel at which the centres of the epicycles are attached is the
deferent
.
Figure 2.3
makes these definitions clearer.

By adjusting the size, direction and speed of the epicycles,
it’s
possible to account for many irregularities in the way the planets move as viewed from the Earth in an Earth-centred system. It’s also possible to explain irregularities in the movements of the Sun and Moon and variations in a planet’s brightness. The epicycles place the planet sometimes closer to us, sometimes further away.

Figure 2.3

The planet moves in a small circle (epicycle) while that small circle moves along a large circle (deferent). The deferent is centred on the Earth.

A second device that Ptolemy inherited from earlier astronomy and liked better as an explanation for the Sun’s movement had the planet or the Sun orbiting in a circle with the orbit centred not precisely on the Earth but on a point a small distance away from the Earth, as in
Figure 2.4.
The technical name for the displaced circle is the
eccentric
. In this
model
also the planet will be closer to Earth in one part of its orbit than in another, which makes sense of variations in its brightness when viewed from Earth, and also of apparent changes in its speed.

Figure 2.4

In this model, the circular orbit (the eccentric) is centred on a point a small distance away from the Earth.