Science in classical antiquity

"If someone associates with a true Pythagorean, what will he will get from him, and in what quantity? I would say: statesmanship, geometry, astronomy, arithmetic, harmonics, music, medicine, complete and god-given prophecy, and also the higher rewards — greatness of mind, of soul, and of manner, steadiness, piety, knowledge of the gods and not just supposition, familiarity with blessed spirits and not just faith, friendship with both gods and spirits, self-sufficiency, persistence, frugality, reduction of essential needs, ease of perception, of movement, and of breath, good color, health, cheerfulness, and immortality."

"Discovery attends on every quest, Except for renegades who shirk the toil. Now certain men have pushed discovery Into the sphere of heaven. Some part they know,— How planets rise and set and wheel about, And of the sun’s eclipse. If men have probed Worlds far remote, can problems of this earth, This common home to which we’re born, defy them?"

"Give me a place to stand and with a lever I will move the whole world."

"It seems to me that they do well to study mathematics, and it is not at all strange that they have correct knowledge about each thing, what it is. For if they knew rightly the nature of the whole, they were also likely to see well what is the nature of the parts. About geometry, indeed, and arithmetic and astronomy, they have handed us down a clear understanding, and not least also about music. For these seem to be sister sciences; for they deal with sister subjects, the first two forms of being."

"It has fallen to the lot of one people, the ancient Greeks, to endow human thought with two outlooks on the universe neither of which has blurred appreciably in more than two thousand years. ...The first was the explicit recognition that proof by deductive reasoning offers a foundation for the structure of number and form. The second was the daring conjecture that nature can be understood by human beings through mathematics, and that mathematics is the language most adequate for idealizing the complexity of nature into appreciable simplicity. Both are attributed by persistent Greek tradition to Pythagoras in the sixth century before Christ. ...there is an equally persistent tradition that it was Thales... who first proved a theorem in geometry. But there seems to be no claim that Thales... proposed the inerrant tactic of definitions, postulates, deductive proof, theorem as a universal method in mathematics."

"The Pythagorean mathematical concepts, abstracted from sense impressions of nature, were... projected into nature and considered to be the structural elements of the universe. [Pythagoreans] attempted to construct the whole heaven out of numbers, the stars being... material points. ...they identified the regular geometric solids... with the different sorts of substances in nature. ...This confusion of the abstract and the concrete, of rational conception and empirical description, which was characteristic of the whole Pythagorean school and of much later thought, will be found to bear significantly on the development of the concepts of calculus. It has often been inexactly described as mysticism, but such stigmatization appears to be somewhat unfair. Pythagorean deduction a priori having met with remarkable success in its field, an attempt (unwarranted...) was made to apply it to the description of the world of events, in which the Ionian hylozoistic interpretations a posteriori had made very little headway. This attack on the problem was highly rational and not entirely unsuccessful, even though it was an inversion of the scientific procedure, in that it made induction secondary to deduction."

"Ionian philosophers... had sought to identify a first principle for all things. Thales had thought to find this in water, but others preferred to think of air or fire as the basic element. The Pythagoreans had taken a more abstract direction, postulating that number... was the basic stuff behind phenomena; this numerical atomism... had come under attack by the followers of Parmenides of Elea... The fundamental tenet of the was the unity and permanence of being... contrasted with the Pythagorean ideas of multiplicity and change. Of Parmenides' disciples the best known was Zeno the Eleatic... who propounded arguments to prove the inconsistency in the concepts of multiplicity and divisibility."

"[T]he authority of Anaximenes was so great that both Leukippos and Demokritos adhered to his theory of a disc-like earth. ...This, in spite of the fact that the spherical form of the earth was already a commonplace in circles affected by Pythagoreanism."

"[T]he religious revival... suggested the view that philosophy was above all a "way of life." Science too was a "purification," a means of escape from the "wheel." This is the view expressed so strongly in Plato’s Phaedo, which was written under the influence of Pythagorean ideas."

"The Pythagoreans held, [Aristotle] tells us that there was "boundless breath" outside the heavens, and that it was inhaled by the world. In substance, this is the doctrine of Anaximenes, and... it was that of Pythagoras... Xenophanes denied it. ...[F]urther development of the idea is ...due to Pythagoras ...We are told that, after the first unit had been formed ...the nearest part of the Boundless was first drawn in and limited; and... the Boundless thus inhaled... keeps the units separate from each other. It represents the interval between them. This is a... primitive way of describing... discrete quantity."

"Aristotle is... decided in his opinion that Pythagoreanism was intended to be a cosmological system like the others. "Though the Pythagoreans... made use of less obvious s and elements than the rest, seeing that they did not derive them from sensible objects, yet all their discussions and studies had reference to nature alone. They describe the origin of the heavens, and they observe the phenomena of its parts, all that happens to it and all it does." They apply their first principles entirely to these things, "agreeing... with the other natural philosophers in holding that reality was just what could be perceived by the senses, and is contained within the compass of the heavens," though "the first principles and causes of which they made use were... adequate to explain realities of a higher order than the sensible.""

"When the Pythagoreans returned to Southern Italy, they must have found views... there which... demanded a partial reconstruction of their own system. ...Empedokles founded a philosophical society, but ...influence[d] ...the medical school of these regions; and ...Philolaos played a part in the history of medicine."

"The account of the doctrine given by Plato is... in accordance with the view that it was of medical origin. Simmias says: "Our body being... strung and held together by the warm and the cold, the dry and the moist... [etc.,] our soul is a sort of temperament and attunement of these, when... mingled... well and in due proportion. If, then, our soul is an attunement,... when the body has been relaxed or strung up out of measure by diseases and other ills, the soul must... perish at once." This is... an application of the theory of Alkmaion, and is in accordance with... the Sicilian school of medicine. It completes the evidence that the Pythagoreanism of the end of the fifth century was an adaptation of the old doctrine to the new principles introduced by Empedokles."

"The planetary system which Aristotle attributes to "the Pythagoreans" and Aetios to Philolaos is... remarkable. The earth is no longer in the middle of the world; its place... taken by a central fire, which is not... the sun. Round this fire revolve ten bodies. First comes the Antichthon or , and next the earth, which thus becomes one of the planets. After the earth comes the moon, then the sun, the five planets, and the heaven of the fixed stars. We do not see the central fire and the antichthon because... [our] side of the earth... is always turned away from them.., explained by the analogy of the moon. ...[M]en living on the other side of it would never see the earth. ...[A]ll these bodies rotate on their axes in the same time as they revolve round the central fire."

"Plato states it as ...a novelty that the earth does not require ...support ...to keep it in its place. ...Anaxagoras had not been able to shake himself free of that idea, and Demokritos still held it."

"The... inference from the Phaedo would... be that the theory of a spherical earth, kept in the middle of the world by its equilibrium, was that of Philolaos... If so, the doctrine of the central fire would belong to a somewhat later generation of the school, and Plato may have learnt it from Archytas and his friends after he had written the Phaedo."

"[I]t is... incredible that the heaven of the fixed stars should have been regarded as stationary. That would have been the most startling paradox that any scientific man had yet propounded, and we should have expected the comic poets and popular literature generally to raise the cry of atheism... [W]e should have expected Aristotle to say something... He made the circular motion of the heavens the... keystone of his system, and would have regarded... a stationary heaven as blasphemous. ...[H]e argues against those who, like the Pythagoreans and Plato, regarded the earth as in motion; but he does not attribute the view that the heavens are stationary to any one. There is no necessary connexion between the two ideas. All the heavenly bodies may be moving as rapidly as we please, provided that their relative motions are such as to account for the phenomena."

"[T]he Aristotelian doctrine of inertia was a doctrine of rest—it was motion, not rest, that always required to be explained."

"[T]he peculiar character of that Aristotelian universe... things... in motion had to be accompanied by a mover all of the time. A universe... [that] had the door half-way open for spirits...unseen hands had to be in constant operation... sublime Intelligences had to roll the planetary spheres... Alternatively, bodies had to be endowed with souls and aspirations... [M]atter itself seemed to possess mystical qualities."

"For out of olde feldes, as men seith, Cometh al this new corn fro yeer to yere; And out of olde bokes, in good feith, Cometh al this newe science that men lere."

"[T]he Pythagorean One, or Monad, splits into two principles, male and female, the Even and the Odd, which are the elements of all numbers and so of the universe. ...One is not simply a numerical unit, which gives rise to other numbers by ...addition. That conception belongs to the later atomistic number-doctrine ...In the earlier Pythagoreanism, we must think of the One (which is not itself a number at all) as analogous to Anaximander's ἄπειρον. It is the primary, undifferentiated group-soul, or , of the universe, and numbers must arise from it by a process of differentiation or 'separating out' (ἀπόκρισις). Similarly, each of these numbers is not a collection of units, built up by addition, but itself a sort of minor group-soul—a distinct 'nature,' with various mystical properties. In the same way, it is by dividing up the whole interval of the that the harmonic proportions are determined."

"Pythagorean science... will inevitably reproduce the later and inconsistent conception of the atomic, indestructible, individual soul. ...The later Pythagoreans of the fifth century 'construct the whole world out of numbers, but they suppose the units to have magnitude. As to how the first unit with magnitude arose, they appear to be at a loss'... because they could not realise that this physical doctrine was ...a reflection of the belief in a plurality of immortal souls, which contradicted their older faith that Soul was a Harmony—a bond linking all things in one. This Soul had formerly been the One God manifest in the logos; now it is broken up into a multitude of individual atoms, each claiming an immortal and separate persistence. And the material world suffers a corresponding change. In place of the doctrine of procession from the Monad, bodies are built up out of numbers, now conceived as collections of ultimate units, having position and magnitude. Thus, Pythagoreanism is led... from a temporal monism to a spatial pluralism—a doctrine of number-atoms hardly distinguishable from the atoms of Leukippus and Democritus, who, as Aristotle says, like these Pythagoreans, 'in a sense make all things to be numbers and to consist of numbers.' But the development of this number-atomism was predestined by religious representations of the nature of soul older than Pythagoreanism itself, and already contained in the blend of Dionysiac and Olympian conceptions inherited by Pythagoras from ."

"The tendency which impelled Pythagorean science towards a materialistic atomism is only the recoil of that same tendency which exalted Pythagoras, from his position as the indwelling daemon of his church, to the distant heaven of the immortals. It is the tendency to dualism. When God ceases to be the immanent Soul of the world, living and dying in its ceaseless round of change, and ascends to the region of immutable perfection, it is because man has acquired a soul of his own, a little indestructible atom of immortality, a self-subsistent individual. 'Nature' likewise loses her unity, continuity, and indwelling life, and is remodelled as an aggregate of little indestructible atoms of matter. But note the consequence: she, too, is now self-subsistent. The world of matter becomes the undisputed dominion of , or Chance, or Necessity—of Moira, ', . There is no place in it for the God who has vanished beyond the stars."

"Greek and medieval knowledge accepted the world in its qualitative variety, and regarded nature's processes as having ends, or in technical phrase as teleological. New science was expounded so as to deny the reality of all qualities in real, or objective, existence."

"With the discovery of the law of inertia and the subsequent downfall of the Aristotelian theory of motion on which Kepler had based his work, his physical theories soon became outmoded and were then rendered obsolete by Newton's work. Yet Kepler's laws of planetary motion remained, so that Edmond Halley could write in his review of Newton's Principia that the first eleven propositions were found to agree with the phenomena of celestial motions, as discovered by the great sagacity and diligence of Kepler."

"Scientific thought is a development of pre-scientific thought."

"The Egyptians were also busy with agriculture, dairying, pottery, glass-making, weaving, ship-building, and carpentry of every sort. This technical activity rested upon a basis of empirical knowledge... To deny it the name of science because it was, perhaps, handed down by tradition to apprentices instead of being written in a book is not wholly just. Technical problems also certainly clamoured for solution in connection with their gold-work, weaving, pottery, hunting, fishing, navigation, basket-work, culture of cereals, culture of flax, baking and brewing, vine-growing and wine-making, stone-cutting and stone-polishing, carpentry, joinery, boat-building, and the many other processes so accurately figured on the walls of the tombs of the nobles at Sakara. In all these techniques lay the germ of science."

"Progress was often achieved by a "criticism from the past"… After Aristotle and Ptolemy, the idea that the earth moves - that strange, ancient, and "entirely ridiculous", Pythagorean view was thrown on the rubbish heap of history, only to be revived by Copernicus and to be forged by him into a weapon for the defeat of its defeaters. The Hermetic writings played an important part in this revival, which is still not sufficiently understood, and they were studied with care by the great Newton himself. Such developments are not surprising. No idea is ever examined in all its ramifications and no view is ever given all the chances it deserves. Theories are abandoned and superseded by more fashionable accounts long before they have had an opportunity to show their virtues. Besides, ancient doctrines and "primitive" myths appear strange and nonsensical only because their scientific content is either not known, or is distorted by philologists or anthropologists unfamiliar with the simplest physical, medical or astronomical knowledge."

"[F]itness to support desirable conduct on the part of citizens or, briefly, to support moral behavior, has served through the ages as a reason for the acceptance of a theory. In antiquity, the physics of Aristotle and Plato seemed to be fitter, in this respect, than the physics of Epicurus. According to the first, the celestial bodies were made of a nobler material than our earth, while according to the "materialistic" doctrine of Epicurus, all these bodies consisted of the same elements. This latter doctrine, however, made it more difficult to teach the existence of a difference between material and spiritual beings. Since a great many educators and statesmen have been convinced that the belief in this difference is important for the education of good citizens, the Epicurean doctrine was rejected by powerful groups. ...Plato ...in his description of "good government" included the requirement that the followers of Epicurean philosophy should be silenced."

"We may... go to our... statement from Aristotle's treatise on the Pythagoreans, that according to them the universe draws in from the Unlimited time and breath and the void. The cosmic nucleus starts from the unit-seed, which generates mathematically the number-series and physically the distinct forms of matter. ...it feeds on the Unlimited outside and imposes form or limit on it. Physically speaking this Unlimited is [potential or] unformed matter... mathematically it is extension not yet delimited by number or figure. ...As apeiron in the full sense, it was... duration without beginning, end, or internal division—not time, in Plutarch's words, but only the shapeless and unformed raw material of time... As soon... as it had been drawn or breathed in by the unit, or limiting principle, number is imposed on it and at once it is time in the proper sense. ...the Limit, that is the growing cosmos, breathed in... imposed form on sheer extension, and by developing the heavenly bodies to swing in regular, repetitive circular motion... it took in the raw material of time and turned it into time itself."

"There is an enormous difference between modern science and Greek philosophy, and that is just the empiristic attitude... Since the time of Galileo and Newton, modern science has been based upon a detailed study of nature and upon the postulate that only such statements should be made, as have been verified or at least can be verified by experiment. The idea that one can single out some events from nature by an experiment... to find out what is the constant law in the continuous change, did not occur to the Greek philosophers. Therefore, modern science has from its beginning stood on a much more modest, but at the same time much firmer, basis than ancient philosophy. Therefore, the statements of modern physics are in some way meant much more seriously than the statements of Greek philosophy."

"Nicomachus... mentions the customary Pythagorean divisions of quantum and the science that deals with each. Quantum is either discrete or continuous. Discrete quantum in itself considered, is the subject of Arithmetic; if in relation, the subject of Music. Continuous quantum, if immovable, is the subject of Geometry; if movable, of Spheric (Astronomy). These four sciences formed the of the Pythagoreans. With the (which Nicomachus does not mention) of Grammar, Logic, and Rhetoric, they composed the seven liberal arts taught in the schools of the Roman Empire."

"The Neo-Pythagoreans treated all the divisions of philosophy. In Metaphysics they held that the Unit and the (indeterminate) Two are the basis of all things. the Unit being the form, and the Two the matter. ...The Unit being the prior principle may be identified with Deity, and, as such, was thought of either as the former [creator] of indefinite matter into individual things, or, as in Neo-Platonism, as the transcendent origin of the derivative Unit and Two. Another mode of conception was to identify the numbers with the Platonic Ideas and then to think of the Unit as comprehending them in the same manner as the mind comprehends its thoughts and gives them form. In Logic the Neo-Pythagoreans were for the most part imitators of Aristotle. Their Physics was Aristotelian and Stoic. ...In all this Neo-Pythagoreanism has little originality."

"All "if" statements about the past are as dubious as prophecies of the future are. It seems fairly plausible that if Alexander or Ghengis Khan had never been born, some other individual would have filled his place and executed the design of the Hellenic or Mongolic expansion; but the Alexanders of philosophy and religion, of science and art, seem less expendable; their impact seems less determined by economic challenges and social pressures; and they seem to have a much wider range of possibilities to influence the direction, shape and texture of civilizations."

"We are tempted 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... There are tunnels on the road, whose length 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."

"I could easily believe that Aristotle had stumbled, but not that, on entering physics, he had totally collapsed. Might not the fault be mine rather than Aristotle's... Perhaps his words had not always meant to him and his contemporaries quite what they meant to me and mine. ...I was sitting at my desk with the text of Aristotle's Physics ...Suddenly the fragments in my head sorted themselves out in a new way, and fell into place... My jaw dropped, for all at once Aristotle seemed a very good physicist... of a sort I'd never dreamed possible. Now I could understand why... [and] what he'd said, and... his authority... Statements that had... seemed egregious mistakes, now seemed at worst near misses within a powerful and generally successful tradition. That sort of experience—the pieces suddenly sorting themselves out and coming together in a new way—is the first general characteristic of revolutionary change... Though scientific revolutions leave much piecemeal mopping up to do, the central change... involves... relatively sudden and unstructured transformation in which... the flux of experience sorts itself out... and displays patterns... not visible before."

"Although modern Science includes ideas not less transcendental than those included in ancient Science... As abstract expressions of the observed order of nature they are liable at any moment to be displaced in favour of expressions more accurate. They serve as guides and starting-points in research. They are not believed in as absolute existences. In ancient science they were held to be absolute existences, which it was the primary object of research to find, and which, when disclosed to the imagination, required no confrontation with reality."

"He who is ignorant of Motion, says Aristotle, is necessarily ignorant of all natural things. ...Not only was he entirely in the dark respecting the Laws, he was completely wrong in his conception of the nature of Motion. ...He thought that every body in motion naturally tends to rest."

"The attitude of Aristotelian physics toward lawfulness takes a new direction. ...The highest degree of lawfulness, beyond mere frequency, was characterized by the idea of the always eternal."

"Why was the Tetraktys so revered? Because to the eyes of the sixth century BC Pythagoreans, it seemed to outline the entire nature of the universe. In geometry — the springboard to the Greeks' epochal revolution in thought — the number 1 represented a point... 2 represented a line... 3 represented a surface... and 4 represented a three-dimensional tetrahedral solid... The Tetraktys, therefore appeared to encompass all the perceived dimensions of space."

"On the question whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt — mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician — mathematics was God! ...By setting the stage, and to some extent the agenda, for the next generation of philosophers — Plato in particular — the Pythagoreans established a commanding position in Western thought."

"All things that are of perishable body must needs have been consumed by infinite time and ages past. But if through that space of time past there have been bodies from which this sum of things subsists being made again, imperishable indeed must their nature be; therefore things cannot severally return to nothing."

"There is so great a difference and distinction in these things that what is one man's meat is another man's rank poison."

"There is a fault in this regard which you should earnestly crave to escape, and shun error with exceeding fearfulness—do not suppose that the clear senses and light of the eyes was made in order that we might made be able to see before us; or that the ends of the thighs and calves were jointed and placed upon the foundation of the feet, only to enable us to march forward with long forward strides; that the forearms again were fitted upon sturdy upper arms, and ministering hands given on either side, only that we might be able to do what should be necessary for life. Such explanations, and all other such that men give, put effect for cause and are based on perverted reasoning; since nothing is born in us simply in order that we may use it, but that which is born creates the use. There was no sight before the eyes with their light were born, no speaking of words before the tongue was made; but rather the origin of the tongue came long before speech, and the ear was made long before sound was heard, in a word all the members, as I think, existed before their use: then they could not have grown up for the sake of use."

"By what law all things were made, how bound they are to abide in it, how impotent to annul the strong statutes of time."

"A part of the soil again is reduced to dissolution by rain, and the scraping rivers nibble their banks away. Besides, whatever she takes her part in nourishing, she increases [and is herself diminished; but when the nursling perishes, it is all] given back; and since beyond all doubt she is seen to be at once the mother of all and the universal sepulchre, therefore you see that the earth is diminished and is increased and grows again."

"I now return to the world’s infancy, what first the fields of earth in their tender age thought fit to bring forth into the regions of light with new birth-throes and to commit to the wayward winds."

"Even now many living creatures arise from the earth, formed by the rain and the warm heat of the sun, so that it is less wonderful if then more and larger ones arose, which grew up when earth and air were young. First the race of winged things and the different birds issued from their eggs being hatched in the springtime, even as now in summer the cicalas of their own accord leave their flimsy husks, to seek life and living. Then first, look you, the earth gave forth the generations of mortal creatures. For there was great abundance of heat and moisture in the fields."

"Many species of animals must have perished at that time, unable by procreation to forge out the chain of posterity: for whatever you see feeding on the breath of life, either cunning or courage or at least quickness must have guarded and kept that kind from its earliest existence; many again still exist, entrusted to our protection, which remain, commended to us because of their usefulness. Firstly, the fierce brood of lions, that savage tribe, has been protected by courage, the wolf by cunning, by swiftness the stag."

"When they had got them huts and skins, and fire, and woman mated with man was appropriated to one, [and the laws of wedlock] became known, and they saw offspring born to them, then first the human race began to grow soft. For the fire saw to it that their shivering bodies were less able to endure cold under the canopy of heaven."