The basic novelty of our age is the combination of this sudden, unique increase in physical power with an equally unprecedented spiritual ebb-tide. To appreciate this novelty one must abandon the limited perspective of European history, and think in terms of the history of the species. Elsewhere I have suggested that the process which led to our present predicament could be represented by two curves similar to temperature charts, one showing the growing physical power of the race, the other its spiritual insight, moral awareness, charity, and related values. For something of the order of several hundred thousand years, from Cro-Magnon man to about 5000 B.C., the first curve would depart little from the horizontal. With the invention of the pulley, the lever and other simple mechanical devices, the muscular strength of man would appear amplified, say, five-fold; after that the curve would again remain horizontal for five or six thousand years. But in the course of the last two hundred years – a stretch less than one-thousandth of the total on the chart – the curve would, for the first time in the history of the species, suddenly rise in leaps and bounds; and in the last fifty years – about one-hundred-thousandth of the total – the curve rises so steeply that it now points almost vertically upward. A single example will illustrate this: after the First World War, less than a generation before Hiroshima, statisticians reckoned that on an average ten thousand rifle bullets, or ten artillery shells, were needed to kill one enemy soldier.
Compared to the first, the second curve will show a very slow rise during the nearly flat pre-historic miles; then it will undulate with indecisive ups and downs through civilized history; finally, on the last dramatic fraction of the chart where the power curve shoots upward like a cobra stabbing at the sky, the spiritual curve goes into a steep decline.
The diagram may be oversimplified, but it is certainly not overdramatized. To draw it true to scale, one would have to use paper about a hundred yards long, but even so the relevant portion would occupy only an inch. We would be obliged to use units of time at first of a hundred thousand, then of a thousand years, while, as we approach the present, the vertical rise of the power-curve is greater in a single year than it was in ten thousand earlier ones.
Thus within the foreseeable future, man will either destroy himself or take off for the stars. It is doubtful whether reasoned argument will play any significant part in the ultimate decision, but if it does, a clearer insight into the evolution of ideas which led to the present predicament may be of some value. The muddle of inspiration and delusion, of visionary insight and dogmatic blindness, of millennial obsessions and disciplined double-think, which this narrative has tried to retrace, may serve as a cautionary tale against the hubris of science – or rather of the philosophical outlook based on it. The dials on our laboratory panels are turning into another version of the shadows in the cave. Our hypnotic enslavement to the numerical aspects of reality has dulled our perception of non-quantitative moral values; the resultant end-justifies-the-means ethics may be a major factor in our undoing. Conversely, the example of Plato's obsession with perfect spheres, of Aristotle's arrow propelled by the surrounding air, the forty-eight epicycles of Canon Koppernigk and his moral cowardice, Tycho's mania of grandeur, Kepler's sun-spokes, Galileo's confidence tricks, and Descartes' pituitary soul, may have some sobering effect on the worshippers of the new Baal, lording it over the moral vacuum with his electronic brain.
March 1955-May 1958
ACKNOWLEDGEMENTS
The author wishes to thank the following for permission to quote from various works: Messrs. Sheed & Ward, London ( The Confessions of St. Augustine, translated by F. J. Sheed); the University of Chicago Press ( Dialogue on the Great World Systems, by Professor Georgio de Santillana, copyright 1953, by the University of Chicago, and The Crime of Galileo, also by Santillana, copyright 1955, by the University of Chicago); Messrs. Edward Arnold (Publishers) Ltd., London ( The Waning of the Middle Ages, by J. Huizinga); Columbia University Press, New York ( Three Copernican Treatises, translated by Professor E. Rosen); The Johns Hopkins Press, Baltimore ( From the Closed World to the Infinite Universe, by Professor Alexandre Koyré); Messrs. Doubleday & Co., Inc., New York ( Discoveries and Opinions of Galileo, translated by Stillman Drake, copyright © 1957, by Stillman Drake); Cambridge University Press ( Science and the Modern World, by A. N. Whitehead ); Messrs. Wm. Collins, Sons & Co. Ltd. and The Macmillan Company, New York ( The Trail of the Dinosaur, ©, by Arthur Koestler, 1955).
NOTES
PREFACE
1
A Study of History, Abridgement of Vols. I-VI by D. C. Somervell , Oxford, 1947. In the complete ten-volume edition there are three brief references to Copernicus, two to Galileo, three to Newton, none to Kepler. All references are by way of asides.
2
Cf. Insight and Outlook, An Inquiry into the Common Foundations of Science, Art and Social Ethics, London and New York, 1949.
PART ONE THE HEROIC AGE
Part 1 Chapter I. DAWN
1
Ency. Brit., 1955 ed., II-582c.
2
Ibid., II-582d.
3
F. Sherwood Taylor: Science Past and Present ( London, 1949), p. 13.
"From the beginning of the reign of Nabonassar, 747 B.C.," Ptolemy reported some 900 years later, "we possess the ancient observations continued practically to the present day." ( Th. L. Heath, Greek Astronomy [ London 1932], p. xiv f.)
The Babylonian observations, incorporated by Hipparchus and Ptolemy into the main body of Greek data, were still an indispensable aid to Copernicus.
4
Plato, Thaetetus, 174 A., quoted by Heath, op. cit., p. 1.
5
Compressed from the Fragments, quoted i.a. by John Burnet , Early Greek Philosophy ( London, 1908), p. 126 seq.
6
Ibid., p. 29.
Part 1 Chapter II. THE HARMONY OF THE SPHERES
1
Cf. John Burnet, Greek Philosophy Part I Thales to Plato ( London, 1914), pp. 42, 54.
2
Aristoxenus of Tarentum, Elements of Harmony, quoted by Burnet, op. cit., p. 41. Aristoxenus, a fourth cent. peripatetic, studied under the Pythagoreans and Aristotle.
For a critical evaluation of the sources on Pythagoras see Burnet Early Greek Philosophy, p. 91 seq.; and A. Delatte, Etudes sur la Litterature Pythagoricienne ( Paris, 1915). For the astronomy of the Pythagoreans, J. L. E. Dreyer, History of the Planetary Systems from Thales to Kepler ( Cambridge, 1906) and Pierre Duhem, Le Système du Monde – Histoire des Doctrines Cosmologiques de Plato à Copernic, Vol. I ( Paris, 1913).
3
The discovery of the sphericity of the earth is variously attributed to Pythagoras and/or Parmenides.
4
Hist. nat., II, p. 84, quoted by Dreyer, op. cit., p. 179.
5
The Merchant of Venice, V.i.
6
Euripides, The Bacchae, a new translation by Philip Vellacott ( London, 1954).
7
Burnet, Early Greek Phil., p. 88.
8
Quoted by B. Farrington: Greek Science ( London, 1953), p. 45.
9
F. M. Cornford, From Religion to Philosophy ( London, 1912), p. 198.
10
Book III, ch. 13. Quoted by Ch. Seltman, Pythagoras, in History Today, August 1956.
11
Quoted by T. Danzig, Number, The Language of Science ( London, 1942), p. 101.
12
Farrington, op. cit., p. 43.
Part 1 Chapter III. THE EARTH ADRIFT
1
Hist. IV, 25, 42; quoted by Dreyer, op. cit., p. 39.
2
Duhem (op. cit., p. 17) is inclined to believe that the counter-earth was always in opposition to the earth, on the other side of the central fire. But in this view (deduced from an ambiguous passage in Pseudo-Plutarch) the antichton would have no practical function. If the earth were to complete a revolution in twenty-four hours round the central fire, her angular velocity
would become prohibitive unless the central fire were quite close; in which case the counter-earth seems to be really needed to prevent her from going up in smoke.
3
Number-lore was indeed the Achilles heel of the Pythagoreans; but lest we become too smug about antique superstitions, what about "Bode's Law"? In 1772, Johannes Daniel Titius of Wittenberg announced that he had discovered a simple (but quite arbitrary) numerical law, according to which the relative distances of all planets from the sun can be expressed by the series 0, 3, 6, 12, 24, etc., by adding 4 to each term. The result is the series 4, 7, 10, 16, 28, 52, 100, 196. This corresponded surprisingly closely to the relative distances of the seven planets known in A.D. 1800; but the eighth planet, with distance 28 did not exist. Accordingly, in that year, a party of six German astronomers set out to look for the missing planet. They found the planetoid Ceres; since then over five hundred planetoids have been discovered in the neighbourhood, presumed to be the fragments of a former full-sized planet in the predicted place. But to the question, why that arbitrary number-sequence should so closely correspond to fact, no satisfactory answer has so far been found.
Planet
Bode's law
Observed distance
Mercury 4
3.9
Venus
7
7.2
Earth
10
10
Mars
16
15.2
?
28
?
Jupiter
52
52
Saturn
100
95
Uranus
196
192
The table reminds one curiously of Mendeleyev's periodical table, before the discovery of isotopes.
4
The explanation is Schiaparelli. Cf. Duhem, op. cit., I, 12.
5
To whom the hypothesis of the earth's rotation on its axis is due, we do not know. Two Pythagoreans are mentioned as responsible for it: Hyketas (some sources call him Niketas) and Ekphantus, both supposedly from Syracuse; but they remain shadows, and we do not know even their dates. Cf. Dreyer, p. 49 seq.; and Duhem, I, p. 21 seq.
6
The precession of the equinoxes was not discovered, or at least not seriously considered, until Hipparchus, who flourished c. 125 B.C.
7
As Venus' angular velocity exceeds that of the earth, she will, when in opposition move clockwise, in conjunction anti-clockwise, as seen from the earth.
8
Yet according to Saidas, when Plato left for Sicily, he left the Academy in Herakleides' charge. Ency. Brit., XI-454d.
9
Schiaparelli Paul Tannery and Pierre Duhem; see Duhem, op. cit., I, p. 410. But there exists no evidence in support of this hypothesis. The "Tychonic" system would have been a logical stepping-stone from Herakleides to Aristarchus; but if somebody advocated it, it should have left some trace. It seems more probable, as Dreyer argues (p. 145 ff.) that Aristarchus performed a kind of mental jump from Fig. B. to Fig. D.
10
Dreyer translation, op. cit., p. 137.
11
De facie in orbe lanae, ch. 6. Quoted by Heath, Greek Astronomy, p. 169.
12
Except for a single Babylonian astronomer named Seleukos, who lived a whole century after Aristarchus and developed a theory of the tides based on the earth's rotation.
13
Heath, The Copernicus of Antiquity ( London, 1920), p. 38.
Part 1 Chapter IV. THE FAILURE OF NERVE
1
Quoted by Farrington, op. cit., p. 81.
2
The Republic of Plato, transl. Thomas Taylor, Book VII.
3
Loc. cit.
4
G. B. Grundy article on "Greece", Ency. Brit., X-78cc.
5
Bertrand Russell, Unpopular Essays( London, 1950), p. 16.
6
Politics, quoted by K. R. Popper, The Open Society and its Enemies ( London, 1945), Vol. II, p. 2.
7
Metaphysics, quoted by Farrington, op. cit., p. 131.
8
Timaeus, 90, 91.
9
Spenser, The Faerie Queene.
10
Phaedo, quoted by Bertrand Russell, A History of Western Philosophy ( London, 1946), p. 159.
11
There has been an unending controversy about a single word, ειλομένην or ιλλομένην in a phrase in Timaeus, 40B, which reads, in Dreyer translation: "But the earth, our nourisher, packed round the axis that extends through the universe, He formed as the guardian and artificer of night and day, the first and most ancient of the gods that have been generated within the universe" (op. cit., p. 71 f.) Burnet reads instead of "packed": "going to and fro" or "backwards and forwards" ( Greek Philosophy, p. 348); Professor A. E. Taylor (quoted by Heath, Greek Astronomy, p. xli) suggests that the phrase must be taken as meaning that the earth is "sliding up and down the axis of the universe", and that Plato was merely quoting a Pythagorean theory (which he evidently got all muddled up), without subscribing to it. Apart from this nebulous sentence, Plato nowhere alludes to any motion of the earth. Plutarch, in discussing the system of Philolaus with its central fire, reports that "These ideas are said to have been entertained by Plato also in his old age; for he too thought that the earth was in a subordinate position, and that the centre of the universe was occupied by some nobler body." ( Plutarch Life of Numa, ch. 11, quoted by Dreyer, p. 82.) Though it is possible that the ageing Plato toyed with the idea of the "central fire" from a quasi-mythological point of view, he again nowhere alludes to it in his writings.
12
Timaeus, 33B-34B, quoted by Heath, op cit., p. 49 f.
13
Farrington, op cit., p. 56.
14
For a concise summing up of Aristotle's and Plato's different attitudes to Change, see Popper, op. cit., Vol. II, pp. 4-6, and particularly Note 11, p. 271 f.
Part I Chapter V. THE DIVORCE FROM REALITY
1
Eudoxus' is the first serious attempt to put astronomy on an exact geometrical basis. His model could lay no claim on representing physical reality, but for sheer geometrical elegance it is unrivalled in pre-Keplerian astronomy, and superior to Ptolemy's. It worked, briefly as follows: The outermost (S 4 ) of the four spheres which form a planet's "nest" reproduced the apparent diurnal rotation; the Axis (A 3 ) of S 3 was perpendicular to the ecliptic, so that its equator turned in the plane of the ecliptic, in the outer planets' zodiacal period, and the inner planets in one year. The two innermost spheres served to account for the movement in latitude, and for the stations and retrogressions. S 2 had its poles on the equator of S 3, i.e. on the zodiacal circle; S 2 rotated in the synodic period of the planet. S 1 rotated in the same period but in the opposite direction; and A 1 was inclined to A 2 at an angle different for each planet. The planet sat on the equator of S 1. The combined rotations of S 1 and S 2 made the planet describe a lemniscate (i.e. an elongated "figure of eight") lying along the zodiac. For details see Dreyer, op. cit., ch. 4; and Duhem, op. cit., I, pp. 111-23.
2
"Nevertheless the theories of Eudoxus and his followers fail to save the phenomena, and not only those which were first noticed at a later date, but even those which were known before, and actually accepted by the authors themselves... I refer to the fact that the planets appear at times to be near to us and at times to have receded. This is indeed obvious to our eyes in the case of some of them; for the star called after Aphrodite and also the star of Ares seem, in the middle of their retrogradations, to be m
any times as large, so much so that the star of Aphrodite actually makes bodies cast shadows on moonless nights. The moon also, even in the perception of our eye, is clearly not always at the same distance from us, because it does not always seem to be of the same size under the same conditions as to medium. The same fact is, moreover, confirmed if we observe the moon by means of an instrument; for it is at one time a disk of eleven fingerbreadths, and again at another time a disk of twelve fingerbreadths, which when placed at the same distance from the observer hides the moon (exactly) so that his eye does not see it." Simplicius on De Caelo, quoted by Heath, op cit., p. 68 f.
3
It is perhaps significant that Ptolemy, alone among famous astronomers, was also a famous map-maker. The re-discovery of his Geography, which was translated into Latin in 1410, marked the beginning of scientific geography in Europe. Copernicus and Kepler, who were also entrusted with map-making, considered it a tedious task to be evaded. Even Hipparchus and Tycho, the greatest star-mapmakers, avoided earthly geography. But it was Hipparchus who outlined the principles of mathematical map-making by regular projection, which Ptolemy adopted. Both the epicyclic universe and the Geography of Ptolemy are painstaking executions of Hipparchus' original designs.
4
From Al-majisty, an Arabic corruption of the Greek Megisty Syntaxis.
5
Dreyer, op. cit., p. 175.
6
Ibid., p. 184. The distance of the sun could not be calculated, even approximately, before the invention of the telescope: Ptolemy gave 610 earth diameters (true value 11,500); but Copernicus again knew no better: his estimate was 571 earth diameters ( Dreyer, pp. 185 and 339). As for the fixed stars, Ptolemy knew that their distance was enormous compared to the solar system; he says that compared to the sphere of the stars "the earth is like a point".
7
Except, of course, the ellipticity of the orbits; but see below, note 15.