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Science in classical antiquity

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Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals (e.g., establishing a reliable calendar or determining how to cure a variety of illnesses) as well as more abstract investigations belonging to natural philosophy. Classical antiquity is traditionally defined as the period between the 8th century BC (beginning of Archaic Greece) and the 6th century AD (after which there was medieval science). It is typically limited geographically to the Greco-Roman West, Mediterranean basin, and Ancient Near East, thus excluding traditions of science in the ancient world in regions such as China and the Indian subcontinent.


CONTENT
A, B, C, D, E, F-G, H-I, J-K, L, M-O, P-R, S, T, U-Z
See also, External links

Quotes

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listed alphabetically by author

A

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  • 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.

B

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  • 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.
    • Carl B. Boyer, The History of the Calculus and Its Conceptual Development (1949).
  • 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 Eleatics 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.
    • John Burnet, Early Greek philosophy (1892) p. 83, footnote 2.
  • [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.
    • John Burnet, Early Greek philosophy (1892) p. 89.
  • 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.
    • John Burnet, Early Greek philosophy (1892) p. 120.
  • 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 first principles 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."
    • John Burnet, Early Greek philosophy (1892) Ch. VII The Pythagoreans, pp. 331-332. Footnote: Aristotle, Metaphysics A, 8. 990 a 3 & a 5.
  • 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.
    • John Burnet, Early Greek philosophy (1892) Ch. VII The Pythagoreans, pp. 339-340.
  • 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.
    • John Burnet, Early Greek philosophy (1892) Ch. VII The Pythagoreans, p. 344.
Antichthon with only
Central fire, Earth & Sun.
  • 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 Counter-earth, 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.
    • John Burnet, Early Greek philosophy (1892) Ch. VII The Pythagoreans, pp. 344-345.
  • 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.
    • John Burnet, Early Greek philosophy (1892) Ch. VII The Pythagoreans, p. 345. Footnote:The primitive character of the astronomy taught by Demokritos as compared with that of Plato is the best evidence of the value of the Pythagorean researches.
  • 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.
    • John Burnet, Early Greek philosophy (1892) Ch. VII The Pythagoreans, pp. 345-346.
  • [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.
    • John Burnet, Early Greek philosophy (1892) Ch. VII The Pythagoreans, p. 347.
  • [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.

C

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  • 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 physis, 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 octave that the harmonic proportions are determined.
    • F. M. Cornford, From Religion to Philosophy: A Study in the Origins of Western Speculation (1912) p. 210.
  • 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 Orphism.
    • F. M. Cornford, From Religion to Philosophy: A Study in the Origins of Western Speculation (1912) pp. 212-213. Footnote on 5thC quote: Aristotole, Metaphysics 16, 10800 18 ff. See Burnet, Early Greek Philosophy, p. 336 ff.
  • 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 Destiny, or Chance, or Necessity—of Moira, Lachesis, Ananke. There is no place in it for the God who has vanished beyond the stars.
    • F. M. Cornford, From Religion to Philosophy: A Study in the Origins of Western Speculation (1912) p. 213.

D

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  • 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.
    • A.M. Duncan, Judith V. Field, The Harmony of the World (1997), Preface, Vol.209

E

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  • Scientific thought is a development of pre-scientific thought.
    • Albert Einstein, "The Problem of Space, Ether, and the Field in Physics," Mein Weltbild, Amsterdam: Querido Verlag (1934) in Ideas and Opinions (1954)

F-G

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  • 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.
    • Philipp Frank, Philosophy of Science: The Link Between Science and Philosophy (1957) p. 354.
  • 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.
    • W. K. C. Guthrie, A History of Greek Philosophy Vol. 1, "The Earlier Presocratics and the Pythagoreans" (1962)

H-I

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  • 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.

J-K

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  • 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.
    • Arthur Koestler, The Sleepwalkeers: A History of Man's Changing Vision of the Universe (1959).
  • 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.
    • Arthur Koestler, The Sleepwalkeers: A History of Man's Changing Vision of the Universe (1959).
  • 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.
    • Thomas Kuhn, "What Are Scientific Revolutions?" 1982. In: Thomas S. Kuhn. The Road Since Structure: Philosophical Essays, 1970-1993, with an Autobiographical Interview. University of Chicago Press, 2002. p. 16.

L

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  • 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.
    • Kurt Lewin. The conflict between Aristotelian and Galileian modes of thought in contemporary psychology, 1931. p. 147.
The Tetractys
  • 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.
  • When a wind gathering together from some one quarter through the hollow places beneath the earth throws itself forward, and bears hard, thrusting with great force into the lofty caverns, the earth leans over in the direction of the wind's headlong force. Then those buildings which are built up above the earth, and each all the more, the more they tower up towards heaven, lean suspended, pushing forward in the same direction, and the beams dragged forward hang over ready to go. And yet people fear to believe that this great universe has waiting for it some period of destruction and ruin, although they see the earth's mighty mass leaning over. Yet if the winds should never blow backwards, no force could curb the world back or hold it back in its rush to perdition. As it is, because in turns they do blow back gathering force, and rally as it were and come back, and then are driven back in retreat, for this reason the earth more often threatens to fall than it does fall; for it inclines forward and then again springs back, and brings back its overhanging weights to their proper place. This then is how all buildings totter, the top more than the middle, the middle than the foundation, the foundation the merest trifle.
    • Lucretius, De rerum natura, VI, 558–77 (Tr. W. H. D. Rouse)
    • In 373 or 272 BC Helice and Bura were destroyed by earthquake; Aegium is the chief Achaean town in the neighbourhood.

M-O

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  • Galileo's comprehension of the concept of acceleration, which he defined as a change of velocity either in magnitude or direction... was an abstract idea that no one seems to have thought much about before. And in using it to test the still accepted Aristotelian precept that a moving object requires a force to maintain it, Galileo easily demonstrated that it is not motion but rather acceleration which cannot occur without an external force. Deliberately rejecting common sense as a prejudiced witness, he let nature herself speak...
  • Neu regio foret ulla suis animantibus orba,
    Astra tenent cæleste solum, formæque deorum.
    • Creation nowhere lacks inhabitants:
      Heaven has its stars, and moving shapes of gods.
      • Ovid, Metamorphoses, I, 72 (Trans. W. F. H. King)

P-R

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  • As a moral philosopher, many of his precepts relating to the conduct of life will be found in the verses which bear the name of the Golden Verses of Pythagoras. It is probable they were composed by some one of his school, and contain the substance of his moral teaching. The speculations of the early philosophers did not end in the investigation of the properties of number and space. The Pythagoreans attempted to find, and dreamed they had found, in the forms of geometrical figures and in certain numbers, the principles of all science and knowledge, whether physical or moral. The figures of Geometry were regarded as having reference to other truths besides the mere abstract properties of space. They regarded the unit, as the point; the duad, as the line; the triad, as the surface; and the tetractys, as the geometrical volume. They assumed the pentad as the physical body with its physical qualities. They seem to have been the first who reckoned the elements to be five in number, on the supposition of their derivation from the five regular solids. They made the cube, earth; the pyramid, fire; the octohedron, air; the icosahedron, water; and the dodecahedron, aether. The analogy of the five senses and the five elements was another favourite notion of the Pythagoreans.
  • Histories of scientific thought tend to obscure the revolutionary state of knowledge in the age of Archimedes—the Hellenistic period—toning down the differences between it, the natural philosophy of classical Greece two centuries earlier, and even the prescientific knowledge of ancient Egypt and Mesopotamia.
    • Lucio Russo, "The Erasure of the Scientific Revolution" in The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (2004).

S

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  • It is childish to assume that science began in Greece; the Greek "miracle" was prepared by millenia of work in Egypt, Mesopotamia and possibly in other regions. Greek science was less an invention than a revival.
    • George Sarton, A History of Science Vol.1 Ancient Science Through the Golden Age of Greece (1952).
  • Hellenic science is a victory of rationalism, which appears greater, not smaller, when one is made to realize that it had been won in spite of the irrational beliefs of the Greek people; all in all, it was a triumph of reason in the face of unreason. Some knowledge of Greek superstitions is needed not only for a proper appreciation of that triumph but also for the justification of occasional failures, such as the many Platonic aberrations.
    • George Sarton, A History of Science Vol.1 Ancient Science Through the Golden Age of Greece (1952).
  • That the Babylonians were Syrians, I believe that nobody will deny. Consequently, they are greatly mistaken who say that it is not possible that the Syrians know something of such matters (astronomy), since these Syrians were the inventors and the first Masters in these matters. Ptolemy again renders witness to this in the "Syntax" (Almageste), because when he chooses an origin for the computation of the Sun, the Moon and the five planets, he does not start with the years of Greek kings, but with those of the kings of Babylon, that is, Nebuchadnezzar, king of the Assyrians. I said Nebuchadnezzar, not the one of whom the prophet Daniel was the contemporary, but another more ancient. Ptolemy has thus given in the "Syntax" that the years that have passed since this first Nebuchadnezzar ---- i.e. of the Babylonian and Persian kings ---- until Philip (Arrhidaeus) the Macedonian, the successor of Alexander the founder of Alexandria, (are in the number of) four hundred and twenty-four years. There he rightly shows that he found among the Babylonians, and not among the Greeks, the beginning and foundation of the calculations which he made. It is thus on this foundation that he built and that he piled up the many calculations that he made.
  • While most sophists emphasized the reality of change — in particular, the Atomists, followers of Leucippus and Democritus — the Pythagoreans stressed the study of the unchangeable elements in nature and society. In their search for the eternal laws of the universe they studied geometry, arithmetic, astronomy, and music (the quadrivium). Their most outstanding leader was Archytas of Tarentum...and to whose school, if we follow... E. [Eva] Frank, much of the Pythagorean brand of mathematics may be ascribed.

T

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  • [T]he ancients possessed a considerable acquaintance with many operations of technical chemistry... Their methods were probably jealously guarded and handed down by successive members of the crafts as precious secrets. ...But, under the conditions in which their industries were prosecuted, the scientific spirit was not free to develop, for science depends essentially upon free inter-communication of facts ...Moreover, the great intellects of antiquity, for the most part, had little sympathy with the operations of artisans, who, at least among the Greeks and Romans, were, for the most part, slaves. Philosophers taught that industrial work tended to lower the standard of thought. The priests, in most ages, have looked more or less askance at attempts, on the part of the laity, to inquire too closely into the causes of natural phenomena. The investigation of nature in early times was impossible for religious reasons.
    There was an outcry in Athens when the thunderbolts of Zeus were ascribed to the collision of clouds. Anaxagoras, Diogenes of Apollonia, Plato, Aristotle, Diagoras, and Protagoras were charged by the priests with blasphemy and driven into exile. Prodikos, who deified the natural forces, as did Empedokles the primal elements, was executed for impiety. Sacerdotalism in Athens had no more sympathy with science than had the Holy Congregation in Italy when it banned the writings of Copernicus, Kepler, and Galileo, and sent Giordano Bruno to the stake. The educated Greeks had no interest in observing or in explaining the phenomena of technical processes. However prone they might be to speculation, they had no inclination to experiment or to engage in the patient accumulation of the knowledge of physical facts. ...The influence of a spurious Aristotelianism, which lasted through many centuries and even beyond the time of Boyle, was wholly opposed to the true methods of science, and it was only when philosophy had shaken itself free from scholasticism that chemistry, as a science, was able to develop.
  • Kenny has shown the Aquinas' Five Ways—his five proofs of God's existence—are absolutely dependent on Aristotelian physics... Aquinas... was one of the leading scholars of Aristotelian physics... and... was primarily responsible for... [its] general acceptance throughout Europe. We could call Aquinas a great physicist as well as a great theologian, for, although Aristotelian physics was wrong, it was an essential precursor of modern physics.
    • Frank J. Tippler, The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead (1994) p. 329. Ref: Anthony Kenny, The Five Ways: St. Thomas Aquinas' Proof of God's Existence (1969) p. 329.
  • [T]he most striking result of the Greeks' faith that the world could be understood in terms of rational principles was the invention of abstract mathematics. The most grandiose ambition they conceived was to explain all the properties of Nature in arithmetical terms alone. This was the aim of the Pythagoreans... [T]hey... knew that the phenomena of the Heavens recurred in a cyclical manner; and... discovered ...that the sound of a vibrating string ...is simply related to the length ...and its 'harmonics' always go with simple fractional lengths. ...[S]ince the Pythagoreans were a religious brotherhood... they thought that this search would lead to more than explanations alone. If one discovered the mathematical harmonies in things, one should... discover how to put oneself in harmony with Nature. ...[T]hey had ...positive grounds for thinking that both astronomy and acoustics were at the bottom arithmetical; and the study of simple fractions was called 'music' right down until the late Middle Ages.

U-Z

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  • [T]he most important question for the history of culture is: How did our modern natural science come about?
    It will be conceded that most historical writings either do not consider this question at all, or else deal with it in a very unsatisfactory manner. For example, which are the histories of Greek culture that mention the names of Theaetetus and of Eudoxus, two of the greatest mathematicians of all times? Who realizes that, from the historical point of view, Newton was the most important figure of the 17th century?
  • Without the stupendous work of Ptolemy, which completed and closed antique astronomy, Kepler's Astronomia Nova, and hence the mechanics of Newton, would have been impossible. Without the conic sections of Apollonius, which Newton knew thoroughly, his development of the law of gravitation is equally unthinkable. And Newton's integral calculus can be understood only as a continuation of Archimedes' determination of areas and volumes. The history of mechanics as an exact science begins with the law of the lever, the laws of hydrostatics and the determination of mass centers by Archimedes. ...all the developments which converge in the work of Newton, those of mathematics, of mechanics and of astronomy, begin in Greece.
  • It is said, that Alexander the Great wrote to his former tutor to this effect; "You have not done well in publishing these lectures; for how shall we, your pupils, excel other men, if you make that public to all, which we learnt from you." To this Aristotle is said to have replied; "My Lectures are published and not published; they will be intelligible to those who heard them, and to none beside." This may very easily be a story invented and circulated among those who found the work beyond their comprehension; and it cannot be denied, that to make out the meaning and reasoning of every part, would be a task very laborious and difficult, if not impossible.
  • Herein lies the truth of all bibles, and especially of our own. ...they are eminently precious, not as a record of outward fact, but as a mirror of the evolving heart, mind, and soul of man. They are true because they have been developed in accordance with the laws governing the evolution of truth in human history, and because in poem, chronicle, code, legend, myth, apologue, or parable they reflect this development of what is best in the onward march of humanity. To say that they are not true is as if one should say that a flower or a tree or a planet is not true; to scoff at them is to scoff at the law of the universe. In welding together into noble form, whether in the book of Genesis, or in the Psalms, or in the book of Job, or elsewhere, the great conceptions of men acting under earlier inspiration, whether in Egypt, or Chaldea, or India, or Persia, the compilers of our sacred books have given to humanity a possession ever becoming more and more precious; and modern science, in substituting a new heaven and a new earth for the old—the reign of law for the reign of caprice, and the idea of evolution for that of creation...

Bibliography

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See also

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Wikipedia
Wikipedia
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