In the previous chapter I concentrated on the broad outlines and the metaphysical implications of Aristotle's universe, without going into astronomical detail. Thus I spoke of the classic nine spheres, from the moon's sphere to that of the Prime Mover (which alone were, in fact, remembered during the Middle Ages), without mentioning that each of these nine spheres was actually a nest of spheres-within-spheres. In reality, Aristotle used altogether fifty-four spheres to account for the motions of the seven planets. The reason for this additional investment of twenty spheres is interesting. Eudoxus and Calippus were not concerned with constructing a model that would be physically possible; they were not concerned with the real machinery of the heavens; they constructed a purely geometrical device, which, they knew, could exist only on paper. Aristotle wanted to do better, and transform it into a true physical model. The difficulty about this was that all adjoining spheres must be mechanically connected, yet the individual motion of each planet must not be transmitted to the others. Aristotle tried to solve this problem by inserting a number of "neutralizing" spheres, which turned in the opposite direction to the "working spheres", between two successive nests; in this manner, the effect of the motions of, say, Jupiter on his neighbour was eliminated, and the nest of Mars could be started from scratch, as it were. But insofar as the reproduction of the actual planetary motions is concerned, Aristotle's model was no improvement.
Besides, another difficulty remained. While each sphere participated in the motion of the next larger one enclosing it, it needed a special moving force to impart to it its independent rotation on its own axis; which meant, that there had to be no less than fifty-five "unmoved movers", or spirits, to keep the system going.
It was an extremely ingenious system – and completely mad, even by contemporary standards; as shown by the fact that in spite of Aristotle's enormous prestige, it was quickly forgotten and buried. Yet it was only the first of several equally ingenious and equally mad systems which astronomers created out of their tortured brains, in obedience to Plato's post-hypnotic suggestion that all heavenly motion must be circular motion centred round the earth.
There was also a certain dishonesty about it. The spheres of Eudoxus could account – however imprecisely – for the existence of "stations" and "retrogressions" in the progress of a planet; but it could never account for the variations in size and brightness, caused by variations of the planet's distance from the earth. These were particularly evident in the case of Venus and Mars, and most of all, the moon: thus central eclipses of the sun are "annular" or "total", according to the moon's momentary distance from the earth. Now all this was known before Eudoxus, and thus to Eudoxus himself as well as to Aristotle; 2 yet their system simply ignores the fact: however complicated the planet's motion is, it is confined to a sphere centred on the earth, and its distance to the earth can therefore never vary.
It was this unsatisfactory state of affairs which gave rise to the unorthodox branch of cosmology developed by Herakleides and Aristarchus (see Chapter III). The system of Herakleides eliminated (though merely for the inner planets) both the most conspicuous scandals: the "stations-and-retrogressions", and the varying distances from the earth. Moreover, it explained (as a glance at Fig. B on p. 46 will show) the logical relatedness of the two scandals: why Venus was always brightest when she was moving crabwise, and vice versa. When Herakleides and/or Aristarchus made the remaining planets, including the earth, move round the sun, Greek science was on the straight road to the modern universe; then abandoned it again. Aristarchus' sun-centred model was discarded as a freak; and academic science marched on triumphantly from Plato, via Eudoxus, and Aristotle's fifty-five spheres, to an even more ingenious and improbable artefact: the maze of epicyclcs devised by Claudius Ptolemy.
If we call Aristotle's world an onion universe, we might as well call Ptolemy's the Ferris Wheel universe. It was begun by Apollonius of Perga in the third century B.C., developed by Hipparchus of Rhodes in the century that followed, and completed by Ptolemy of Alexandria in the second century A.D. The Ptolemaic system remained, with minor modifications, the last word in astronomy until Copernicus.
Any rhythmic movement, even the dance of a bird, can be imagined as being caused by a clockwork in which a great number of invisible wheels co-operate to produce the motions. Ever since "uniform circular motion" had become the law governing the heavens, the task of astronomy was reduced to designing, on paper, just such imaginary clockworks which explained the dance of the planets as a result of the gyrations of perfectly circular, ethereal components. Eudoxus had used spheres as components; Ptolemy used wheels.
It is perhaps easiest to visualize the Ptolemaic universe not as an ordinary clockwork, but a system of "Big Wheels" or "Ferris Wheels" as one sees them in amusement parks – a huge, upright, slowly revolving wheel with seats or small cabins hanging suspended from its rim. Let us imagine the passenger safely strapped to his seat in the little cabin, and let us further imagine that the machinery has gone crazy – the cabin, instead of hanging down quietly from the rim of the Big Wheel, rotates wildly round the pivot from which it is suspended, while the pivot itself revolves slowly with the Wheel. The unhappy passenger – or planet – is now describing a curve in space which is not a circle, but is nevertheless produced by a combination of circular motions. By varying the size of the Wheel, the length of the arm by which the cabin is suspended, and the speeds of the two rotations, an amazing variety of curves can be produced, such as the one shown on the diagram – but also kidney-shaped curves, garlands, ovals, and even straight lines!
Seen from the earth, which is in the centre of the Big Wheel, the planet-passenger in the cabin will move clockwise until he reaches the "stationary point" S 1, then regress anti-clockwise to S 2, then move again clockwise to S 3, and so on. * The rim of the Big Wheel is called the deferent, and the circle described by the cabin is called the epicycle. By choosing a suitable ratio between the diameters of epicycle and deferent, and suitable velocities for each, it was possible to achieve a fair approximation to the observed motions of the planet, insofar as the "stations and retrogressions", and its varying distances from the earth were concerned.
These, however, were not the only irregularities in the planetary motions. There was yet another scandal, due (as we today know) to the fact that their orbits are not circular, but elliptic, that is, oval-shaped; they "bulge". To do away with this anomaly, another device was brought in, called a "movable eccentric": the hub of the Big Wheel no longer coincided with the earth, but moved on a small circle in the vicinity of the earth; and in this manner a suitably eccentric, i.e. "bulgy" orbit, was produced.†
____________________
*
At this point the reader may think that I am repeating myself – for the diagram on this page seems to express the same idea as Fig. B on p. 46 – the idea of Herakleides. But there is a difference: in Herakleides' scheme the planet's epicycle is centred on the sun. In Ptolemy's, it is centred on nothing. It is a purely geometrical construction.
†
The "movable eccentric" is in fact merely a kind of epicycle-in-reverse; and since the two are geometrically interchangeable, I shall use the term "epicycle" for both.
Egg-shaped Orbit of Mercury, according to Ptolemy: E = Earth; M = Mercury.
In the figure above, the hub of the Big Wheel moves clockwise on the small circle, from A to B; the point on the rim from which the cabin is suspended moves anti-clockwise in an egg-shaped curve from a to b; and the cabin spins round the final epicycle. But this was not enough; in the case of some recalcitrant planets it was found necessary to suspend a second cabin from the cabin suspended on the Big Wheel, with a different radius and a different speed; and then a third, fourth and fifth, until the passenger in the ultimate cabin di
d indeed describe a trajectory more or less conforming to the one he was meant to describe.
By the time the Ptolemaic system was perfected, the seven passengers, sun, moon and five planets, needed a machinery of not less than thirty-nine wheels to move through the sky; the outermost wheel, which carried the fixed stars, made the number an even forty. This system was still the only one recognized by academic science in Milton's day – and was caricatured by him in a famous passage of Paradise Lost:
From man or angel the great Architect
Did wisely to conceal, and not divulge,
His secret to be scanned by them who ought
Rather admire; or, if they list to try
Conjecture, he his fabric of the Heavens
Hath left to their disputes, perhaps to move
His laughter at their quaint opinions wide
Hereafter, when they come to model Heaven
And calculate the stars, how they will wield
The mighty frame, how build, unbuild, contrive
To save appearances, how gird the sphere
With centric and eccentric scribbled o'er,
Cycle and epicycle, orb in orb.
Alphonso X of Castile, called the Wise, who was a pious man and a great patron of astronomy, put the matter more succinctly. When he was initiated into the Ptolemaic system, he sighed: 'If the Lord Almighty had consulted me before embarking upon the Creation, I should have recommended something simpler.'
3. The Paradox
There is something profoundly distasteful about Ptolemy's universe; it is the work of a pedant with much patience and little originality, doggedly piling "orb in orb". All the basic ideas of the epicyclic universe, and the geometrical tools for it, had been perfected by his predecessor, Hipparchus; but Hipparchus had only applied them to the construction of orbits for the sun and moon. Ptolemy completed the unfinished job, without contributing any idea of great theoretical value. 3
Hipparchus flourished around 125 B.C., more than a century after Aristarchus; and Ptolemy flourished around A.D. 150, nearly three centuries after Hipparchus. In this span of time, nearly equal to the duration of the Heroic Age, practically no progress was made. The landmarks were thinning out, and were soon to vanish altogether in the desert; Ptolemy was the last great astronomer of the Alexandrian School. He picked up the threads which had been left trailing behind Hipparchus, and completed the pattern of loop entwined in loop. It was a monumental and depressing tapestry, the product of tired philosophy and decadent science. But nothing else turned up to replace if for nearly a millennium and a half. Ptolemy Almagest 4, remained the Bible of astronomy until the beginning of the seventeenth century.
To get this extraordinary phenomenon into a proper perspective, one must not only be on one's guard against the wisdom of hindsight, but also against the opposite attitude, that kind of benevolent condescension which regards the past follies of Science as the unavoidable consequences of ignorance or superstition: "our forebears just did not know better". The point I shall try to make is that they did know better; and that to explain the extraordinary cul de sac into which cosmology had manoeuvred itself, we must look for more specific causes.
In the first place, the Alexandrian astronomers can hardly be accused of ignorance. They had more precise instruments for observing the stars than Copernicus had. Copernicus himself, as we shall see, hardly bothered with star-gazing; he relied on the observations of Hipparchus and Ptolemy. He knew no more about the actual motions in the sky than they did. Hipparchus' Catalogue of the fixed stars, and Ptolemy's Tables for calculating planetary motions, were so reliable and precise that they served, with some insignificant corrections, as navigational guides to Columbus and Vasco da Gama. Eratosthenes, another Alexandrian, computed the diameter of the earth as 7,850 miles, with an error of only 1/2 per cent; 5 Hipparchus calculated the distance of the moon as 301/4 earth diameters – with an error of only 0.3 per cent. 6
Thus, insofar as factual knowledge is concerned, Copernicus was no better off, and in some respects worse off, than the Greek astronomers of Alexandria who lived at the time of Jesus Christ. They had the same observational data, the same instruments, the same know-how in geometry, as he did. They were giants of "exact science". Yet they failed to see what Copernicus saw after, and Herakleides-Aristarchus had seen before them: that the planets' motions were obviously governed by the sun.
Now I have said before that we must beware of the word "obvious"; but in this particular case its use is legitimate. For Herakleides and the Pythagoreans had not been led to the heliocentric hypothesis by a lucky guess, but by the observed fact that the inner planets behaved like satellites of the sun, and that the outer planets' retrogressions and changes in earth-distance were equally governed by the sun. Thus, by the end of the second century B.C., the Greeks had all the major elements of the puzzle in their hands, 7 and yet failed to put them together; or rather, having put them together, they took them to pieces again. They knew that the orbits, periods and velocities of the five planets were connected with, and dependent on, the sun – yet in the system of the universe which they bequeathed to the world, they managed to ignore completely this all-important fact.
This mental snow-blindness is all the more remarkable as, qua philosophers, they were aware of the dominant part played by the sun which, qua astronomers, thy nevertheless denied.
A few quotations will illustrate this paradox. Cicero, for instance, whose knowledge of astronomy is, of course, entirely based on Greek sources, writes in The Republic: "The sun ... ruler, prince and leader of the other stars, sole and ordering principle of the universe (is) so large that its light brightens and fills the all... The orbits of Mercury and Venus follow him as his companions" 8
Pliny writes a century later: "The sun is carried around in the midst of the planets, directing not only the calendar and the earth but also the stars themselves and the sky." 9
Plutarch speaks in a similar vein in On the Face in the Moon Disc:
"But in general how can we say: the earth is in the centre – in the centre of what? The universe is infinite; and the infinite, which has neither beginning nor end, has no centre either... The universe does not assign any fixed centre to the earth, which drifts homelessly and unsteadily through the infinite emptiness without a proper goal..." 10
In the fourth century A.D., when darkness was finally closing in on the world of antiquity, Julian the Apostate wrote about the sun: "He leads the dance of the stars; his foresight guides all generation in nature. Around him, their King, the planets dance their rounds; they revolve around him in the perfect harmony of their distances which are exactly circumscribed, as the sages affirm, who contemplate the events in the skies..." 11
Lastly Macrobius, who lived around 400 A.D., comments on the passage from Cicero which I have just quoted:
"He calls the sun the ruler of the other stars because the sun regulates their progression and retrogression within spatial limits, for there are spatial limits which confine the planets in their advance and regress relative to the sun. Thus the force and power of the sun regulates the course of the other stars within fixed limits." 12
Here, then, is evidence that to the very end of the antique world, the teaching of Herakleides and Aristarchus was well remembered; that a truth, once found, can be hidden away, buried under the surface, but not undone. And yet the Ptolemaic earth-centred universe, ignoring the specific role of the sun, held the monopoly in scientific thought for fifteen centuries. Is there an explanation for this remarkable paradox?
It has been frequently suggested that the explanation is fear of religious persecution. But all the evidence quoted in support of this view consists of a single, facetious remark by a character in Plutarch dialogue On the Face in the Moon Disc, which I have mentioned before. The character, Lucius, is playfully accused of "turning the universe upside down" by pretending that the moon consists of solid matter like the earth; he is then invited to explain his views further:
" Luc
ius smiled and said: 'Very well; only do not bring against me a charge of impiety such as Cleanthes used to say that it behoved Greeks to bring against Aristarchus of Samos for moving the Hearth of the Universe, because he tried to save the phenomena by the assumption that the heaven is at rest, but that the earth revolves in an oblique orbit, while also rotating about its own axis.'" 13
However, the charge was never brought; neither Aristarchus, who was held in the highest esteem, nor Herakleides or any other adherent of the earth's motion, was persecuted or indicted. If Cleanthes had really tried to have anybody indicted on the grounds of "moving the Hearth of the Universe", then the first person charged with impiety would have been the venerated Aristotle; for Aristarchus merely made the Hearth move with the earth through space, whereas Aristotle removed the Hearth to the periphery of the world, deprived the earth altogether of the divine presence, and made it the lowliest place in the world. In reality, the "Hearth of the Universe" was no more than a poetic allusion to the Pythagorean Central Fire, and it would be absurd to regard it as a religious dogma. Cleanthes himself was a mystically inclined, and rather sour Stoic philosopher, who wrote a hymn to Zeus and despised science. His attitude to Aristarchus, a scientist and a Samian to boot, that island from which no good has ever come, was evidently "the fellow deserves to be hanged". Apart from this bit of academic gossip in Plutarch, there is no mention in any of the sources of religious intolerance toward science in the Hellenistic Age. 14