The Sleepwalkers
4. Knowing and Un-Knowing
Thus neither ignorance, nor the threats of an imaginary Alexandrian inquisition, can serve to explain why the Greek astronomers, after having discovered the heliocentric system, turned their backs on it. 15 However, they never did so entirely; as the passages previously quoted, from Cicero and Plutarch to Macrobius, indicate, they knew that the sun governed the motions of the planets, but at the same time closed their eyes to the fact. But perhaps it is this irrationality itself which provides the clue to the solution, by jolting us out of the habit of treating the history of science in purely rational terms. Why should we allow artists, conquerors and statesmen to be guided by irrational motives, but not the heroes of science? The post-Aristotelian astronomers denied the rule of the sun over the planets and affirmed it at the same time; while conscious reasoning rejects such a paradox, it is in the nature of the unconscious that it may simultaneously affirm and deny, say yes and no to the same question; to know and to un-know, as it were. Greek science in the age of decline was faced with an insoluble conflict, which resulted in a split of the mind; and this "controlled schizophrenia" continued throughout the Dark and Middle Ages, until it came to be almost taken for granted as the normal condition of man. It was maintained, not by threats from outside, but by a kind of censor planted inside the mind, who kept it separated into strictly non-communicating compartments.
Their main concern was "to save the appearances". The original meaning of this ominous phrase was that a theory must do justice to the observed phenomena, or "appearances"; in plain words, that it must agree with the facts. But gradually, the phrase came to mean something different. The astronomer "saved" the phenomena if he succeeded in inventing a hypothesis which resolved the irregular motions of the planets along irregularly shaped orbits into regular motions along circular orbits – regardless whether the hypothesis was true or not, i.e. whether it was physically possible or not. Astronomy, after Aristotle, becomes an abstract sky-geometry, divorced from physical reality. Its principal task is to explain away the scandal of noncircular motions in the sky. It serves a practical purpose as a method for computing tables of the motions of the sun, moon and planets; but as to the real nature of the universe, it has nothing to say.
Ptolemy himself is quite explicit about this: "We believe that the object which the astronomer must strive to achieve is this: to demonstrate that all the phenomena in the sky are produced by uniform and circular motions..." 16 And elsewhere: "Having set ourselves the task to prove that the apparent irregularities of the five planets, the sun and moon can all be represented by means of uniform circular motions, because only such motions are appropriate to their divine nature... We are entitled to regard the accomplishment of this task as the ultimate aim of mathematical science based on philosophy." 17 Ptolemy also makes it clear why astronomy must renounce all attempts to explain the physical reality behind it: because the heavenly bodies, being of a divine nature, obey laws different from those to be found on earth. No common link exists between the two; therefore we can know nothing about the physics of the skies.
Ptolemy was a wholehearted Platonist; the effect of the twin-stars on the course of science now makes itself fully felt. The divorce which they effected between the four elements of the sublunary region and the fifth element of the heavens, leads directly to a divorce of sky-geometry from physics, of astronomy from reality. The split world is reflected in the split mind. It knows that in reality the sun has a physical influence on the planets; but reality is no longer its concern. 18
The situation is summed up in a striking passage by Theon of Smyrna, a contemporary of Ptolemy. After expressing his opinion that Mercury and Venus may, after all, be revolving round the sun, he goes on to say that the sun should be called the heart of the universe, which is both "a world and an animal". "But," he reflects, "in animated bodies the centre of the animal is different from the centre of its mass. For instance, for us who are both men and animals, the centre of the animated creature is in the heart, always in motion and always warm, and therefore the source of all the faculties of the soul, of desire, imagination and intelligence; but the centre of our volume is elsewhere, about the navel... Similarly ... the mathematical centre of the universe is where the earth is, cold and immovable, but the centre of the world as an animal is in the sun, which is, so to say, the heart of the universe." 19
The passage is both appealing and appalling; it strikes a note which will reverberate throughout the Dark and Middle Ages. It appeals to the archetypal craving to comprehend the world as a live, pulsating animal; and it appalls by its unholy mix-up of allegorical and physical statements, by its pedantic variations on the inspired Platonic leg-pull. The contrast between navel and heart is witty but unconvincing; it does not explain why two planets should revolve round the heart and the other three round the navel. Did Theon and his readers believe in this sort of thing? The answer is, apparently, that one compartment of their minds did, the other did not; the process of divorcement was nearly completed. Observational astronomy was still progressing; but what a regression in philosophy compared to the Pythagorean, and even the Ionian, school of seven centuries before!
5. The New Mythology
It looks as if the wheel had come full circle, back to the early Babylonians. They too had been highly competent observers and calendar-makers, who combined their exact science with a mythological dream-world. In the universe of Ptolemy, interlocking canals of perfect circles have replaced the heavenly waterways, along which the star-gods sail their barges on their precisely charted journeys. The Platonic mythology of the sky was more abstract and less colourful, but as irrational and dreamborn as the older one.
The three fundamental conceits of this new mythology were: the dualism of the celestial and sub-lunary worlds; the immobility of the earth in the centre; and the circularity of all heavenly motion. I have tried to show that the common denominator of the three, and the secret of their unconscious appeal, was the fear of change, the craving for stability and permanence in a disintegrating culture. A modicum of split-mindedness and double-think was perhaps not too high a price to pay for allaying the fear of the unknown.
But whether the price was high or low, it had to be paid: the universe was put into the deep freeze, science was paralyzed, and the manufacture of artificial moons and nuclear warheads was delayed by a millennium or more. Whether, sub specie aeternitatis, this was a Good Thing or a Bad Thing, we shall never know; but as far as our limited topic is concerned, it was clearly a bad thing. The earth-centred, dualistic, circular view of the cosmos excluded all progress and all compromise for fear of endangering its main principle, stability. Thus, it could not even be admitted that the two inner planets circled round the sun, because once you gave way on this apparently harmless minor point, the next logical step would be to extend the idea to the outer planets and to the earth itself – as the development of the Herakleidian deviation had clearly shown. The frightened mind, always on the defensive, is particularly aware of the dangers of yielding an inch to the devil.
The anxiety complex of the late Greek cosmologists becomes almost palpable in a curious passage 20 by Ptolemy himself, in which he defends the immobility of the earth. He starts with the usual commonsense argument that if the earth moved, "all the animals and all separate weights would be left behind floating on the air" – which sounds plausible enough, though the Pythagoreans and atomists had long before Ptolemy realized its fallacious nature. But then Ptolemy continues to say that if the earth were really moving, it would "at its great speed, have fallen completely out of the universe itself". Now this is not plausible even on a naive level, for the only motion attributed to the earth was a circular motion round the sun, which entailed no risk of falling out of the universe, just as the sun incurred no such risk by circling the earth. Ptolemy, of course, knew this quite well – or, more precisely, one compartment of his mind knew it, while the other was hypnotized by the fear that once the earth's stability was shaken, the w
orld would fly to pieces.
The myth of the perfect circle had an equally deep-rooted, spell-binding power. It is, after all, one of the oldest symbols; the ritual of drawing a magic circle around a person protects him against hostile spirits and perils of the soul; it marks off a place as an inviolable sanctuary; it was commonly used in tracing out the sulcus primigenius, the first furrow, when founding a new city. Apart from being a symbol of stability and protection, the circle, or wheel, had a technological plausibility, as it were, as a suitable element for any machine. But on the other hand, the planetary orbits were evidently not circles; they were eccentric, bulging, oval – of egg-shaped. They could be made to appear as the product of a combination of circles by geometrical artifices, but only at the price of renouncing any semblance of physical reality. There exist some fragmentary remains, dating from the first century A.D., of a small-sized Greek planetarium – a mechanical model designed to reproduce the motions of sun, moon, and perhaps also of the planets. But its wheels, or at least some of them, are not circular – they are egg-shaped. 21 A glance at the orbit of Mercury in the Ptolemaic system on p. 68 shows a similar eggshaped curve staring into one's face. All these pointers were ignored, relegated into limbo as a sacrifice to circle-worship.
And yet there was nothing a priori frightening about oval or elliptic curves. They too were "closed" curves, returning into themselves, and displayed a reassuring symmetry and mathematical harmony. By an ironical coincidence, we owe the first exhaustive study of the geometrical properties of the ellipse to the same man, Apollonius of Perga, who, never realizing that he had the solution in his hands, started the development of the epicyclic monster-universe. We shall see that, two thousand years later, Johannes Kepler, who cured astronomy of the circular obsession, still hesitated to adopt elliptical orbits, because, he wrote, if the answer were as simple as that, "then the problem would already have been solved by Archimedes and Apollonius". 22
6. The Cubist Universe
Before bidding farewell to the Greek world, an imaginary parallel may help to bring matters into focus.
In 1907, simultaneously with the Cézanne memorial exhibition in Paris, a collection of the master's letters was published. A passage in one of the letters ran:
"Everything in nature is modelled on the sphere, the cone and the cylinder. One must teach oneself to base one's painting on these simple figures – then one can accomplish anything one likes."
And further:
"One must treat nature by reducing its forms to cylinder, sphere, and cone, all put into perspective, meaning that each side of an object, each plane, is directed towards a central plane." 23
This pronouncement became the gospel of a school of painting known under the misnomer "Cubism". Picasso's first "Cubist" picture was in fact constructed entirely of cylinders, cones and circles; while other members of the movement saw nature in terms of angular bodies – pyramids, and bricks, and octaeders. *
____________________
*
The name of the movement derives from a slighting remark by Matisse, who said of a landscape by Braque that it was "entirely constructed in little cubes". 24
But whether they painted in terms of cubes, cylinders, or cones, the declared aim of the Cubists was to resolve every object to a configuration of regular geometrical solids. Now the human face is not constructed out of regular solids any more than the orbits of the planets are made of regular circles; but in both cases it is possible to "save the phenomena": in Picasso Femme au Miroir, the reduction of the model's eyes and upper lip to an interplay of spheres, pyramids and parallelepipedes, displays the same ingenuity and inspired madness as Eudoxus' spheres pivoting within spheres.
It is rather depressing to imagine what would have happened to painting if Cezanne's Cubist pronouncement had been turned into a dogma, as Plato's spherist pronouncement was. Picasso would have been condemned to go on painting more elaborate cylindrical bowls to the bitter end; and lesser talents would have found out soon that it is easier to save the phenomena with compass and ruler on graph-paper under a neon lamp, than by facing the scandals of nature. Luckily, Cubism was only a passing phase, because painters are free to choose their style; but the astronomers of the past were not. The style in which the cosmos was presented had, as we saw, a direct bearing on the fundamental questions of philosophy; and later, during the Middle Ages it acquired a bearing on theology. The curse of "spherism" upon man's vision of the universe lasted for two thousand years.During the last few centuries, from about A.D. 1600 onwards, the progress of science has been continuous and without a break; so we are tempted to extend the curve back into the past and to fall into the mistaken belief that the advance of knowledge has always been a continuous, cumulative process along a road which steadily mounts from the beginnings of civilization to our present dizzy height. This, of course, is not the case. In the sixth century B.C., educated men knew that the earth was a sphere; in the sixth century A.D., they again thought it was a disc, or resembling in shape the Holy Tabernacle.
In looking back at the part of the road travelled so far, we may well wonder at the shortness of those stretches where the progress of science was guided by rational thought. There are tunnels on the road, whose length in time is measured in miles, alternating with stretches in full sunlight of no more than a few yards. Up to the sixth century B.C., the tunnel is filled with mythological figures; then for three centuries there is a shrill light; then we plunge into another tunnel, filled with different dreams.
CHRONOLOGICAL TABLE TO PART ONE*
600 B.C.
Orphic Mystery cult
Ionian Philosophers
500 “
Pythagorean Brotherhood (c. 530–450)
Philolaus (5th cent.)
400 “
Herakleides (c. 375–310)
Plato (c. 428–348)
Eudoxus and Calippus (4th cent.)
Aristotle (384–322)
300 “
Aristarchus (c. 310–230)
Apollonius (250–220)
200 “
END OF GREEK HELIOCENTRIC COSMOLOGY
Hipparchus (c. 125)
0
A.D. 100
Ptolemy (c. 150)
“ 200
[GEOCENTRIC COSMOLOGY BROUGHT TO PERFECTION]
Compilers
Pliny the Elder (c. 23–79)
Plutarch (c. 46–120)
Theon of Smyrna (2nd cent.)
Macrobius (c. 400)
Chalcidius Martianus Capella
(5th cent.)
Simplicius (c. 535)
[SOURCES FOR THE EARLY MIDDLE AGES]
*
Only the main lines of development of cosmological systems are represented.
PART TWO DARK INTERLUDE
I THE RECTANGULAR UNIVERSE
1. The City of God
PLATO had said that mortal man was prevented from hearing the Harmony of the Spheres by the grossness of his bodily senses; the Christian Platonists said that he lost that faculty with the Fall.
When Plato's images strike an archetypal chord, they continue to reverberate on unexpected levels of meaning, which sometimes reverse the messages originally intended. Thus one might venture to say that it was Plato who caused that Fall of philosophy which made his followers deaf to the harmonies of nature. The sin which led to the Fall was the destruction of the Pythagorean union of natural and religious philosophy, the denial of science as a way of worship, the splitting up
of the very texture of the universe into a vile lowland and ethereal highlands, made of different materials, governed by different laws.
This "dualism of despair", as one might call it, was carried over into medieval philosophy by the Neoplatonists. It was the legacy of one bankrupt civilization: Greece at the age of the Macedonian conquest, to another bankrupt civilization: the Latin world at the age of its conquest by the Germanic tribes. From the third century A.D. to the end of the Empire, Neoplatonism had reigned without a rival at the three main centres of philosophy, Alexandria, Rome, and the Athenian Academy. By that process of natural selection in the realm of ideas which we have already seen at work, the Middle Ages took over precisely those elements in Neoplatonism which appealed to their mystic aspirations toward the Kingdom of Heaven, and which echoed their despair of this world as "the lowest and vilest element in the scheme of things"; 1 while the more optimistic aspects of Neoplatonism were ignored. Of Plato himself only the Timaeus, that masterpiece of ambiguity, was available in Latin translation (the knowledge of Greek was dying out); and though Plotinus, the most influential among the Neoplatonists, affirmed that the material world partook to some extent of the goodness and beauty of its Creator, he was best remembered for the saying that he "blushed because he had a body". It was in this distorted and extreme form that Neoplatonism was absorbed into Christianity after the collapse of the Roman Empire, and became the main link between antiquity and medieval Europe.