science

"[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 were at the bottom arithmetical; and the study of simple fractions was called 'music' right down until the late Middle Ages."

"[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?"

"[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."

"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."

"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."

"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.""

"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."

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

"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."

"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."

"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 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 , as the geometrical . 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."

"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."

"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."

"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."

"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..."

"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."

"Neu regio foret ulla suis animantibus orba, Astra tenent cæleste solum, formæque deorum."

"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."

"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."

"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."

"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."

"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."

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

"[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."

"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."

"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."

"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."

"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."

"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."

"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."

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

"While most s emphasized the reality of change — in particular, the Atomists, followers of 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 '). 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."

"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."

"[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 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."

"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 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."

"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 "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."

"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."

"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."

"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."

"[A] giant net (similar to a trawl) would be erected in outer space, constructed in a hexagonal mesh pattern. This net would be stretched out and a tension sufficient to rotate the entire net would be maintained by . The rotation would be begun by special rockets and... continue because it was in a vacuum. The diameter of each hexagon would be about 10 kilometers, and the entire mirror would have a circular disk shape with a diameter of about 100 to 200 kilometers. Within each hexagon, a round mirror approximately 10 kilometers in diameter, would be installed. ...[Each] single mirror would be capable of being [independently] tilted... initiated by... electric s."

"Oberth... began the book Men in Outer Space: New Projects for Rockets and Space Travel... written in the style accessible to the general reader. ...Published in 1955 in German, it was translated into English, French, Italian, Dutch, and even in Croatian! ...Oberth's new book was indeed "cosmic," and this gave it a cardinal distinction from his classic book of the 1920s. ...A supplemental chapter ...is devoted to "s," a theme which occupied Oberth all his life. A short description ...is already present in the 1923 book. In 1929, when he published his fundamental work, Ways to Space Travel, he included a much more comprehensive description... in the chapter... "Space Stations." ...[A]lmost the entire chapter is devoted to space mirrors. In the 1954 book... a new varient... is presented. Eventually in Bucharest in 1978, an entire book (in German) was devoted to this theme. ...[T]he primary purpose for the space mirror would today be called an ecological one ...At the time ...there was ...no robotics technology, and he assumed all the work after ...erection ...would ...be carried out manually by astronauts."

"shields for planets such as Venus or Mars would... be large, complex structures requiring vast amounts of lunar or asteroidal material... and long-range transportation... One... stepping stone to understanding and mastering the technologies and processes... would be the construction of a shield to offset the greenhouse effect on... Earth. Such... would not require interplanetary capabilities."

"The time required for the removal of... [[w:Greenhouse gases|[greenhouse] gases]] from the atmosphere by natural processes is... uncertain: current estimates are several centuries. The uncertainties... [have] led to calls for... restrictions on the generation of greenhouse gases. ...The existence of a possible technical solution could... have a major short-term impact in influencing short term consumption restrictions, even if the solution could not be implemented until the next century."

"Enough of this. They are only dreams of the future. Bold ones? Perhaps, but we have already experienced... bolder ideas. Who would have believed in 1894 that, a few years later, one would see through a person by means of Roentgen rays? PHILANDER's statement (Medical Fairy Tales), "Man will be made transparent like a jelly-fish", was bolder than this dream of the future; that required finding something completely new, while here we are dealing with laws of nature already known.—Accomplishing these things will certainly require the conversion of enormous energies. But were not hundred times greater sums of money expended during the World War? In one year, the nations of Europe spend more on smoking and drinking than the whole sodium reflector would cost. War and narcotics are quite unnecessary things, yet more money is spent on them than on something useful. Should not mankind, in an exceptional case, also save something for constructive work?"

"Ref: Philander, Medizinische Märchen"