What is clear, however, is that Heraclitus was searching – in the authentically Milesian way – for a logical interpretation of nature. For him, fire was the key transforming agent, ‘the lightning that drives the universe’: ‘Fire comes to life by the death of the Earth, and Air by the death of Fire; Water lives by the death of Air and the Earth by the death of Water’. ‘Everything flows’ through the metamorphosis of one element into another so that ‘all becoming is a struggle’ and ‘the world is a harmony of tensions, by turns taut and relaxed, like the strings on a lyre or a bow’. This is the language of a visionary. It is not surprising that ‘the great Heraclitus’ was for Nietzsche the symbol of the ‘Dionysiac profundities’.
But Heraclitus believed that everything obeyed an immutable law, by means of which ‘the ambient milieu is provided’ with reason. ‘There is only one wisdom: to know the Thought which guides all things through the Whole’, and he who penetrates the ‘heart of the universe’will be able to cure the ills of the universe and even the ills of human beings. Surely this idea of a superior law, intelligible to human reason, which the sage must pursue in order to control nature, corresponds fairly precisely to our modern idea of science, the explanation of a world ‘uniformly constituted for all, not created by any god or man, but which has always existed and always will exist, a fire continually burning, flaring up and dying down in due order’.
The zigzag progress of science
After about 530, Ionia was no longer prosperous and independent, but the torch which had been lit there had barely died down before it was rekindled elsewhere, in the cities of Sicily and Greater Greece. These were the centres for the parallel endeavours of Pythagoras and the Eleatic School, idealist reactions against Ionian positivism.
Pythagoras was born in c. 582 and left Samos in 532. Fleeing from the Persians, he took refuge at Croton where he became not only the leader of a school of thought but also the leader of a religious sect, whose central concerns were purification and asceticism. His explanation of the origin of the universe – he had his own, needless to say – nevertheless led from Pythagoreanism to that most abstract of sciences, mathematics.
For Pythagoras and his disciples, number was the key to the universe, as Fire had been for Heraclitus. Number had an existence of its own, outwith the human mind, ‘and everything which can be known’, as a fourth-century commentator put it, ‘possesses a Number, without which it can neither be comprehended nor known’. This myth directed the Pythagoreans towards the study of the properties of number: lucky and unlucky numbers, numbers squared and cubed; the miraculous nature of the number 10 which is the sum of the first four numbers 1, 2, 3 and 4. This led them to discover proportions (ratios), arithmetical, geometrical, harmonic; in geometry, ‘they called the point One, the straight line Two, the plane Three and the solid Four, according to the number of points it took to define each item, a point, a line, an area and a volume’. Such reflections even led them to calculate the orbits of the sun and the planets, to account for their real as opposed to their apparent movements, to study acoustics and music, and to assert thatthe earth was a sphere. Their best-known, though not most important discovery, was what we know as Pythagoras’ theorem, according to which, in every right-angled triangle, the square of the hypotenuse is equal to the squares of the other two sides.
But one day the apprentice mathematicians found themselves faced with the enigma of the irrational numbers. A number is irrational in relation to another when it has no common measure with the latter, and no quotient which can be expressed in either a whole number or a fraction. For example: the relation between the diameter of a circle and its circumference is an irrational number. In fact it was the right-angled isosceles triangle which revealed the existence of irrational numbers. Let us suppose that in such an isosceles triangle the two sides of the right angle are one unit long. The hypotenuse will be equal to the square root of z. This simple answer, which is how we would put it, was not available at the time, but it could easily be demonstrated that the hypotenuse was smaller than 2 (the sum of the two other sides) and larger than 1 so it could not be represented by a whole number. And neither could it be represented by a fraction (this would take longer to demonstrate). It followed that on any given vector, the number of points was not finite, as the Pythagoreans had previously thought: as well as whole numbers, fractions and irrational numbers continued into infinity.
But in that case, reducing the world to numbers can no longer be seen as simplifying its image, if the number of numbers is infinite. ‘Mathematics was born from Pythagoreanism’, one historian concludes, ‘and like a boomerang, it rebounded on it.’
The reaction was not slow to appear, a negation of the Pythagorean view of numbers, from the city of Elea or Velia on the coast of Lucania in the first half of the fifth century. Parmenides (born c. 530) centred his enquiries on Being, an overall immutable truth, to be distinguished from opinion, or Non-Being, which was merely the appearance of things. He rejected the ‘multiple’, that is the theories of the Ionians and Pythagoreans, as belonging with appearances – hence the controversy. It was in defence of his master, and in defiance of common sense, that Zeno came up with his famous paradoxes: Achilles can never catch up with the tortoise; the arrow never reaches its destination, etc. It would take too long to explain how these images are both absurd and not absurd. They become almost reasonable if they are viewed as a rejoinder to Pythagorean ideas, an attempt to demonstrate that the latter were absurd. Reasoning in this way about the absurd marks the beginning of logic, or dialectic as Aristotle would call it, and once more the zigzag progress of science benefited.
After this orgy of logic-chopping, we might note the return to the concrete with the experiments of Empedocles of Agrigento (500-430), which demonstrated the role of air, the pressure it exerted and the need to substitute air for vapour among the elements. The same would be true of the arguments of Democritus, who was the first philosopher to speak of tiny invisible particles, or ‘atoms’, or to be precise ‘the indivisibles’. The living architecture of the world was made up of a profusion of atoms rather than a profusion of numbers. In the light of present-day atomic physics and chemistry, his world view, as revealed by a turn of phrase here and there, sometimes seems deceptively modern.
Science in the age of Pericles
By the fifth century BC at any rate, the problem of science was unambiguously posed, while at the same time a conflict arose between pure and applied science.
Socrates and Plato were idealists: their quarry was that timid and elusive bird, the human soul, imprisoned only briefly in the world of men. Science for them was simply a form of meditation, a road towards an eternal and disembodied thought. No one was allowed into Plato’s Academy unless he was proficient at geometry. When asked ‘What does God do all day?’ he replied ‘Geometry’. But practical or applied science was anathema to him. In the Gorgias, Plato had described the merits of a military engineer: ‘Yet you despise him and his skill, you call him engineer as an insult, and you would not wish to marry your son to his daughter, nor marry his daughter yourself.’ When Archytas of Tarentum made wooden doves fly in the air, and became enthusiastic about other mechanical toys, Plato fumed: ‘He is corrupting geometry… stripping it of dignity by forcing it to descend from the immaterial and purely intelligible to corporeal and embodied objects; to make use of vile matter which requires manual labour and is used for servile trades.’ These are anecdotes but the tale they tell is clear.
This divorce between Greek science and the urge to make mechanical experiments corresponded to a recent change in Greek society. Michel Rostovtzeff noted that ‘Greek art of the archaic and classical periods never neglected the depiction of trades’. Pottery thus offers us a series of tableaux of everyday life, but art would subsequently turn away from ‘mechanical’ subjects, deemed contemptible. ‘What are known as the mechanical arts’, Xenophon tells is, ‘carry a social stigma and are rightly scorned in our cities.’
; Public opinion in Athens was unsympathetic to scientific experiment for other reasons. Astronomers and scholars appeared to be men lacking piety, in other words they demystified the heavens and the stars which were traditionally revered as deities. Protagoras was banished, and Anaxagoras put in prison, which he was able to escape only with the help of Pericles himself: but he subsequently left Athens, which was no haven of free thought. Even Socrates thought it was pointless to ask questions about the orbits of stars and the movements of the planets or their causes. It is true that Plato probably helped give astronomy a better name, but only when he came round to the view of his disciples, namely that the observable movements of the planets may seem random (the word planet in Greek means wanderer) but this is only apparent: their real movements are perfectly regular and therefore, like the stars, obey some divine order. Why then condemn astronomy, which was moving away from the tiresome theories of the Pythagoreans and (since ‘the natural laws were once more subordinate to the authority of divine principles’ as Plutarch put it) was returning to its state of innocence? But Plato’s approval of astronomy is ambiguous and still disregards the research of the Ionians into natural causes which might explain the structure of the universe. The desacralization of the Greek world was thus neither complete nor rapid.
Fifth-century science nevertheless benefited from the fruitful results of thought which turned inwards and not to the outside world. The Platonic distinction between the role of thought and that of perception as instruments of knowledge was to be essential to the future of science. The same was true of the acute sense of mathematical abstraction which brought Platonic philosophy together with pure science. But one cannot altogether escape the impression that at the most creative high point of philosophical thought, the rejection of empirical and experimental science closed off certain paths which had previously been open.
Aristotle of Stagira
In a sense it was Aristotle who saved for posterity a substantial part of ancient scientific thought. Born in Stagira on the Macedonian coast, the son of a doctor who trained him in medical practice from an early age, Aristotle was then initiated into Pythagorean mathematics and the philosophy of Plato, his maitre a penser, in Athens. He developed the quasi-theological side of Platonic astronomy, but in the end abandoned mathematics for human science and biology. This odd training explains the encyclopedic nature of his readily comprehensible work, a pedagogical summa which was for centuries to be a source of inspiration for Islam and then the west. Medicine, mathematics, logic, physics, astronomy, natural sciences, political psychology, ethics – all human knowledge was tackled by Aristotle. In the field of zoology he was even an original thinker and in two of his books, the Mechanics and the Meteorology, he veered towards experimental science. It is true that these works may well be spurious. But the general truth remains that Aristotle definitely moved away from Platonic idealism and poetry. The emphasis was no longer on the soul, that divine spark, but on the human being as a thinking and mortal being, and even on the physiological bases of the movements of the soul, the imagination, the memory and the passions. The Idea no longer had an independent existence apart from its material support.
Finally, Aristotelian physics formed for the first time a coherent system, ‘a highly elaborated theory even though not mathematically formulated’. It was of course a false theory: Aristotle himself was confused by the distinction between natural movements and violent movements. There are natural movements which are perpetual, as he saw it, such as the rotation of the celestial spheres. And since in the order of the cosmos everything had its place, natural movement tended to return it to that place: the stone I hold in my hand, if I drop it, will try to return to the centre of the earth, and will stop on the ground: vapour being lighter than air will float up naturally, and so on. Violent, non-natural movement required traction or propulsion. This mightseem logical, except of course that everyday experience tends to contradict it: if a stone is thrown, it shows the anomaly of a mobile object continuing its course without an agent. Aristotle was not troubled by this and explained the anomaly by a reaction of the ambient environment, a whirlwind action which propelled the object onward. ‘A brilliant explanation’, according to A. Koyre, ‘despite its erroneousness, since it rescued the system; and it was thanks to this that scientific thought managed to survive the vicissitudes of history until the age of Galileo’. It would be centuries before the principle of inertia was formulated.
The splendour of Alexandria
Alexander’s conquests led to a prodigious expansion of the Hellenic world. Surveyors, geometers, engineers, geographers and astronomers all benefited from this sudden opening up of great spaces: they now had direct access to Babylonian and Egyptian sources. Greek science now discovered much more about the distances between heavenly bodies, the precession of equinoxes and the geography of distant lands. Should we agree with S. F. Mason (1953) that Alexander’s conquests pushed Greek science towards the practical and the applied, as happened to French science after the Napoleonic conquests?
Alexandria, founded by Alexander in 332, became the capital of an independent Egypt in 323. Under Ptolemy I Soter, who reigned until Z85, and his son Ptolemy II Philadelphus (282-246) this metropolis upon which the teeming life of Egypt concentrated had soon become the richest, most densely populated and most ethnically varied city in the Mediterranean. The new pharaohs, who were hungry for prestige and sympathetic to the arts and sciences, soon became patrons to scholars from throughout the Ancient World. They created in Alexandria what one might call a Centre for Scientific Research. The dates of the foundation of the museum (the Temple of the Muses) and the libraries are not known for certain. But the resources available (countless books, dissection rooms, zoological and botanical gardens, an observatory) offered scholars both their living expenses and the means to do their research. The museum was a kind of research academy. Everybody who was anybody went to Alexandria, just as in the eighteenth century no European intellectual could afford to ignore Paris.
After Aristotle, Athens still had some fine days ahead of it: it could boast Aristotle’s own successors at the Lyceum (Theophrastus, director from 322 to 287, was succeeded by Straton who had spent time in Alexandria); Epicurus; Zeno of Citium, the founder of the Stoic school (born in 335 in Citium in Cyprus, died c. 264 in Athens); Pyrrhon of Elis, the earliest of the Sceptics, who came to Athens in 336 and died in about 290. And Rhodes was also a notable centre until about 166, as was Pergamum in Asia Minor. All the same, the critical mass of Hellenic culture and science had emigrated to the new cosmopolitan city of Alexandria.
What is miraculous is that this Alexandrian splendour should have survived at such a high level for two hundred years, two centuries of an intellectual life so rich that its achievements cannot be summed up in a few lines, especially since scientific thought moved away from the traditional syntheses and began to branch out into different sciences. Thinkers were no longer referred to as sages or philosophers, but as mathematicians: Euclid (c. 300), Archimedes (287-212), who only passed through Alexandria, if he was there at all; Apollonius of Perge, c. 200; grammarians such as Dionysius Thrax, c. 290; atomists such as Herophilus and Erasistratus at about the same time; or astronomers, like Aristarchus (310-230), Eratosthenes (273-192) and Hipparchus (fl. 125).
This burgeoning of individual sciences corresponded to immense advances in knowledge. After a slow process of maturation, there was an explosion in every sector. Euclid in his Elements attempted a systematic presentation of mathematics. Archimedes, alongside bold statements such as ‘give me a point of leverage and I will lift the world’, invented the measurement of the circumference of the circle by approximation: if two polygons are imagined, one inscribed inside the circle and the other outside, and if one then imagines them as having an infinite number of sides which can be measured, sooner or later their perimeters will coincide with the circumference of the circle. He also prefigured infinitesimal calculus. Apollonius of Perge worked on conies. Mechanic
s was born – Archimedes again – while Aristarchus measured, or tried to measure, the distance between the earth, the moon and the sun, and Eratosthenes measured the terrestrial meridian. Hipparchus was able to predict eclipses. Herophilus in 300distinguished between veins and arteries, Isistra identified the lymphatic channels. The most sensational of all these achievements was probably that of Aristarchus (c. 3io-z3o): according to Archimedes, he pronounced that the earth rotates on its axis in a day and goes round the sun in a year. According to a report by Plutarch, he had to suffer constant insults and narrowly escaped being tried for impiety. These two details may be accurate and may be connected: the notion of the sun being at the centre of the universe was in fact abandoned because it clashed with religious views at the time.
‘Spartacus’ revenge’
Despite all these achievements, Alexandrian science reached a dead end. The problem about the fate of science during the Roman period has often been posed. Taking my courage in both hands, let me say that the usual answers seem questionable.
The Mediterranean in the Ancient World Page 37