History of science
study of the historical development of science and scientific knowledge
The history of science is the study of the historical development of science and scientific knowledge, including both the natural sciences and social sciences.
- listed alphabetically by author
- Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle, as in natural science, where sufficient proof can be brought to show that the movement of the heavens is always of uniform velocity. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astrology the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them.
- Five geometers—Clairaut, Euler, D'Alembert, Lagrange and Laplace—shared among them the world of which Newton had revealed the existence. They explored it in all directions, penetrated into regions believed inaccessible, pointed out countless phenomena in those regions which observation had not yet detected, and finally—and herein lies the imperishable glory—they brought within the domain of a single principle, a unique law, all that is most subtle and mysterious in the motions of the celestial bodies. Geometry also had the boldness to dispose of the future; when the centuries unroll themselves they will scrupulously ratify the decisions of science.
- Studies serve for delight, for ornament, and for ability. Their chief use for delight, is in privateness and retiring; for ornament, is in discourse; and for ability, is in the judgment and disposition of business. For expert men can execute, and perhaps judge of particulars, one by one; but the general counsels, and the plots and marshalling of affairs, come best from those that are learned. To spend too much time in studies, is sloth; to use them too much for ornament, is affectation; to make judgment wholly by their rules, is the humour of a scholar [scholastic]. They perfect nature, and are perfected by experience. For natural abilities are like natural plants, that need proyning by study; and studies themselves do give forth directions too much at large, except they be bounded in by experience. Crafty men contemn studies; simple men admire them; and wise men use them. For they teach not their own use; but that is a wisdom without [outside of] them, and above them, won by observation.
Read not to contradict and confute, nor to believe and take for granted, nor to find talk and discourse, but to weigh and consider. Some books are to be tasted, others to be swallowed, and some few to be chewed digested. That is, some books are to be read only parts; others to be read, but not curiously; and some few to be read wholly, and with diligence and attention. Some books also may be read by deputy, and extracts made of them by others; but that would be only in less important arguments, and the meaner sort of books: else distilled books are, like common distilled waters, flashy things. Reading maketh a full man; conference a ready man; and writing an exact man. And, therefore, if a man write little, he had need have a great memory; if he confer little, he had need have a present wit; and if he read little, he had need have much cunning, to seem to know that he doth not.
- The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws.
- Let such a history be once provided and well set forth, and let there be added to it such auxiliary and light-giving experiments... and the investigation of nature and of all sciences will be the work of a few years. ...In this way, and in this way only, can the foundations of a true and active philosophy be established; and then will men wake as from deep sleep.
- This history I call Primary History, or the Mother History.
- Francis Bacon, De Parascevis ad Inquisitionem (Parasceve) in The Great Instauration (1620).
- Atomism began life as a philosophical idea that would fail virtually every contemporary test of what should be regarded as 'scientific'; yet, eventually, it became the cornerstone of physical science.
- John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation (1991) p. 3.
- Scanning the past millennia of human achievement reveals just how much has been achieved during the last three hundred years since Newton set in motion the effective mathematization of Nature. We found that the world is curiously adapted to a simple mathematical description. It is enigma enough that the world is described by mathematics; but by simple mathematics, of the sort that a few years energetic study now produces familiarity with, this is an enigma within and enigma.
- John D. Barrow, New Theories of Everything (2007)
- Maxwell in particular noted that the phenomena of electromagnetism did not fit into the scheme of Newtonian mechanics. Whereas it had been thought that only the distance between two objects determined the force one exerted on the other, electric charges in motion, such as are met with in electric currents, were found to produce effects not encountered when charges are at rest. Celestial bodies will only attract each other; electric charges at rest will either attract or repel... they will exert forces only in the direction of the connecting straight line. Oersted discovered that an electric current (...charges in motion) will exert a force on a magnetic needle at right angles to the connecting straight line. Previous observations in astronomy had tended to show that the force between two bodies depended only on their instantaneous configuration, but Hertz showed by experiment that electromagnetic disturbances propagate as waves, at a finite rate of speed. Hence the force experienced by one body can be understood and explained only in terms of the history of the other.
- Peter G. Bergmann, The Riddle of Gravitation: From Newton to Einstein to Today's Exciting Theories (1968) pp. 25-26.
- Maxwell succeeded in casting all known electromagnetic effects into a mathematical form that has endured to this day... known as Maxwell's field equations. Based on Faraday's earlier work, Maxwell stressed the notion of fields, in contrast to Newton's emphasis on the direct action of bodies on each other across empty space (action at a distance). Faraday and Maxwell regarded the effect on an electrically charged body as giving rise to stresses in its immediate surroundings. These in turn produce stresses in ever widening circles, gradually diminishing... These stresses... thought of as capable of existence in otherwise empty space, are called fields... intermediaries between material particles and which assume the burden of Newton's action at a distance.
- Peter G. Bergmann, The Riddle of Gravitation: From Newton to Einstein to Today's Exciting Theories (1968) p. 26.
- In every age there is a turning point, a new way of seeing and asserting the coherence of the world. It is frozen in the statues of Easter Island that put a stop to time—and in the medieval clocks of Europe that once also seemed to say the last word about the heavens for ever. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or of man. But in retrospect, what commands our attention as much are the continuities—the thoughts that run or recur from one civilization to another.
- Jacob Bronowski, The Ascent of Man (1973) Ch. 1 Lower than the Angels.
- If I were giving this lecture fifty years from now, the word "gravitation" would be as old-fashioned as the word "phlogiston" is to us. Relativity has certainly demoted gravitation as a real explanation, just as Priestley's and Lavoisier's analyses and decoding of chemical reactions destroyed the word "phlogiston."
- Jacob Bronowski, The Origins of Knowledge and Imagination (1978)
- An invention acts rather like a trigger, because, once it's there, it changes the way things are, and that change stimulates the production of another invention, which in turn, causes change, and so on. Why those inventions happened, between 6,000 years ago and now, where they happened and when they happened, is a fascinating blend of accident, genius, craftsmanship, geography, religion, war, money, ambition... Above all, at some point, everybody is involved in the business of change, not just the so-called "great men." Given what they knew at the time, and a moderate amount of what's up here [pointing to head], I hope to show you that you or I could have done just what they did, or come close to it, because at no time did an invention come out of thin air into somebody's head, [snaps fingers] like that. You just had to put a number of bits and pieces, that were already there, together in the right way.
- James Burke, Connections (1979).
- How curious, after all, is the way in which we moderns think about our world! And it is all so novel, too. The cosmology underlying our mental processes is but three centuries old—a mere infant in the history of thought—and yet we cling to it with the same embarrassed zeal with which a young father fondles his new-born baby.
- Edwin Arthur Burtt, The Metaphysical Foundations of Modern Physical Science; a Historical and Critical Essay (1925).
- Considering the part played by the sciences in the story of our Western civilization, it is hardly possible to doubt the importance which the history of science will sooner or later acquire both in its own right and as the bridge which has been so long needed in between the Arts and the Sciences.
- Herbert Butterfield, The Origins of Modern Science (1957) Introduction
- In spite of all the allegations of self-love, the facts at first associated with the name of a particular man end by being anonymous, lost forever in the ocean of Universal Science. Thus the monograph imbued with individual human quality becomes incorporated, stripped of sentamentalisms, in the abstract doctrine of the general treatise. To the hot sun of actuality will succeed—if they do succeed—the cold beams of the history of learning.
- Santiago Ramón y Cajal, Autobiographía (1923)
- A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton’s theory of mechanics explained Kepler’s law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton’s theory of mechanics explained not only Kepler’s laws, but also Galileo’s findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud’s theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed.
- John L. Casti in "Correlations, Causes, and Chance," Searching for Certainty: How Scientists Predict the Future (1990).
- This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is now seen to be an enigma only as an individual; in the mass he is a mathematical problem.
- The book, as far as I am aware, is the first attempt to connect the natural sciences into a history of creation.
- Robert Chambers, Vestiges of the Natural History of Creation (1844).
- The progress of knowledge is very irregular, somewhat resembling the movements of an army, of which some battalions are in vigorous health, while others are sickly or overburdened with baggage. The experimental marches on at a good pace; the observational proceeds but slowly; the speculative is left far in the rear.
- Robert Chambers, Edinburgh Papers: Testimony, its posture in the scientific world, Volume 3 (1859).
- History of science played a very important role for me. Before I knew well how to do an experiment, I knew why Joliot has missed the neutron, why his wife missed the fission, why they succeeded in having artificial radioactivity, and even why they almost missed the other things, by doing very nice experiments, but didn't come to the conclusion. That is science. Science is doubt, is research. It is not something which is—and that is the danger of teaching—which is too academic and which the people explain [to] you... it is like the logic thing that comes out of the computer, which is not true. You have intuition, you have passion.
- The most important ploy that nineteenth-century European scholars devised to avoid acknowledging that the roots of civilization are Afroasiatic was to minimize the importance of Egyptian, Sumerian, and Semitic contributions and to focus instead almost entirely on the Greeks. According to this idea, the Egyptians, Sumerians, and Semites established rather static and uninteresting cultures, while the really worthwhile developments in the rise of civilization were the work of the dynamic and sophisticated Greeks, who were considered to be of Aryan stock because their language is part of the Indo-European family. ...It was claimed that the Greeks developed their culture all on their own, with virtually no contribution from the earlier civilizations.
- Clifford D. Conner, A People's History of Science (2005).
- In the nineteenth century C.E., a small but influential group of German scholars led by Karl Otfried Müller decided that the ancient Greek authors did not know what they were talking about—that their traditions of external influences were simply "myths." …They were convinced that the principle of historical explanation was race, and they believed they had discovered the "scientific laws of race." …only the white race ...had the natural ability to create advanced civilizations. ...This "racial science" …served as a useful ideology to explain the "natural right" of white Europeans to dominate the darker peoples of the world.
- Clifford D. Conner, A People's History of Science (2005).
- Modern science will continue to be blindly destructive as long as its operations are determined by the anarchism of market economic forces. The problem to be solved is whether science, technology, and industry can be brought under genuinely democratic control in the context of a global planned economy, so that all of us can collectively put our hard-won scientific knowledge to mutually beneficial use. I am confident it can be accomplished, but will it? If so, there is reason for optimism. If not... well, to paraphrase Keynes, "in the not-so-long run we're all dead."
- Clifford D. Conner, A People's History of Science (2005).
- The strategic act by which Grosseteste and his thirteenth- and fourteenth-century successors created modern experimental science was to unite the experimental habit of the practical arts with the rationalism of twelfth-century philosophy.
- A.C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100-1700 (1953).
- Before the eighth century [B.C.] no scientific astronomy was possible owing to the absence of one indispensable condition, namely, the possession of an exact system of chronology. The old calendar already in use about the year 2500, and perhaps earlier, was composed of twelve lunar months. But as twelve lunar periods make only 354 days, a thirteenth month was from time to time inserted to bring the date at which the festivals recurred each year, into harmony with the seasons. It was only little by little that greater precision was attained by observing at what date the heliac rising of certain fixed stars took place. ...By degrees, direct observation of celestial phenomena, intended either to enable soothsayers to make predictions or to fix the calendar, led to the establishment of the fact that certain... phenomena recurred at regular intervals, and the attempt was then made to base predictions on the calculation of this recurrence or periodicity. This necessitated a strict chronology, at which the Babylonians did not arrive till the middle of the eighth century B.C.: in 747 they adopted the so-called "era of Nabonassar." ...the moment when, doubtless owing to the establishment of a lunisolar cycle, they kept properly constructed chronological tables. Farther back there was no certainty in regard to the calculation of time. It is from that moment that the records of eclipses begin which Ptolemy used, and which are still sometimes employed by men of science for the purpose of testing their lunar theories.
- When we realize the important rôle played by space-time in our attempts to avoid a belief in absolute rotation, we can well understand that the doctrine of the relativity of all motion would have been absurd in Newton's day. ...any speaker prior to, say, the year 1900 could never have anticipated the discovery of space-time, for its sole justification arose from the negative experiments in optics and electrodynamics attempted at about that time. As for Newton, not only did he not know nothing of the non-mechanical negative experiments, but in addition, the equations of electrodynamics had not been discovered... even if he had conceived of space-time through some divine inspiration, he could never have utilised it for the purpose of establishing the relativity of all motion. His ignorance of non-Euclidean geometry would have rendered the task impossible. In fact, space-time, in the seventeenth century, would have been a hindrance, and the sole result of its premature introduction into science would have been to muddle everything up and render the discovery of Newton's law of gravitation well-nigh impossible.
And this brings us to another point which is often true in physical science. Premature discoveries are apt to do more harm than good. ...had the astronomers of the seventeenth century possessed more perfect telescopes, had they recognized that the planets (Mercury, in particular) did not obey Kepler's laws rigorously, Newton's law might never have been discovered. At all events, its correctness would have been questioned seriously and mathematicians might have lost courage and doubted their ability to discover natural laws. Leverrier, for example, might have lacked the necessary assurance to carry out his lengthy calculations leading to the discovery of Neptune. In short, physical science proceeds by successive approximations, and too rapid jumps in the accretion of knowledge are liable to be disastrous.
- A. D'Abro, The Evolution of Scientific Thought from Newton to Einstein (1927) pp. 428-429
- The present century has witnessed the emergence of two grand theories of mathematical physics: the Theory of Relativity and the Quantum Theory. Both theories were conceived for coordinating certain bodies of facts which the classical theories were unable to interpret; and neither theory would have seen the day had it not been for the increased refinement of experimental measurements which rendered the disclosure of these facts possible. But although the two theories were born under similar circumstances, they soon branched in opposite directions. The theory of relativity has developed into a doctrine whose principle field of application is found in the world of large-scale phenomena, whereas the quantum theory has become identified with the atomic and subatomic worlds. To this extent the theories are complimentary.
- A. D'Abro, The Decline of Mechanism (in Modern Physics) (1939) Preface
- Inasmuch as both Rayleigh's and Wien's laws of radiation, though incorrect, appear to express facts correctly at opposite limits of temperature and frequency, we may presume that the correct law must have an intermediary form, passing over into Rayleigh's when [temperature] T is large and [frequency] ν small, and into Wein's when the reverse situation... Planck, guided by these considerations, devised a new theory of radiation which he called the "Quantum Theory." From this theory Planck was able to derive a radiation law which satisfied Wien's relation, ...the displacement law [when the temperature is increased, intensities of all the frequencies increase, while the radiation of maximum intensity is directly proportional to the absolute temperature] and Stefan's law, and which was in excellent agreement with experimental measurements at all temperatures.
- A. D'Abro, The Rise of the New Physics, Its Mathematical and Physical Theories (1939) Vol. 2. p. 457
- 1. Small particles called atoms exist and compose all matter; 2. They are indivisible and indestructible; 3. Atoms of the same chemical element have the same chemical properties and do not transmute or change into different elements.
- The genesis of all science can be traced to the contemplation of... occult influences. Astrology preceded astronomy, chemistry grew out of alchemy, and the theory of numbers had its precursor in a sort of numerology which to this day persists in otherwise unaccountable omens and superstitions.
- While we cannot place Pythagoras among the great or event near-great mathematicians, his position in the history of scientific thought remains unchallenged. ...dictum "Number rules the universe" ...in the broad modern sense ...is there anything in the dictum to which a modern scientist could not or would not subscribe? The theories of relativity and quanta have shaken the physical sciences to the very foundation, forcing the physicist to cast overboard such principles as conservation of energy or economy of action, and to revise the very concepts of space, time, matter, cause and effect. Still, number reigns as firmly in the new physics as it did in the old.
- Tobias Dantzig, The Bequest of the Greeks (1955)
- Great is the power of steady misrepresentation; but the history of science shows that fortunately this power does not long endure.
- Charles Darwin, On the Origin of Species (1859) Ch. 15: "Recapitulation and Conclusion"
- The rise of the scientific spirit was a notable feature of the Renaissance: men no longer accepted without question the opinions of the ancients about the universe and the laws governing the natural world; dogma was subjected to experiment, and when it failed to survive the test it was rejected and new theories were formulated. Thus science in the modern sense was born, and rapid progress was made in mathematics, physics, chemistry, and biology. But the immediate consequences for technology were confined to a few specialized fields; in the main, technological progress still depended upon the empirical methods by practical men. On the whole, up to 1750 science probably gained more from technology than vice versa. Among the notable exceptions... were the navigational instruments that played so important a part in the great voyages of exploration and in surveying and cartography; the application of the principle of the pendulum to time-measurement; and, particularly, the growing exploitation of chemistry. However, the new outlook on natural phenomena was only one manifestation of a healthy scepticism: technological processes which often had changed very little for centuries were carefully scrutinized to see what improvements could usefully be made. The Royal Society, founded in 1660 to further the investigation of natural phenomena by observation and experiment, in its early days directed at least as much of its attention to the improvement of existing arts and industries as to the advancement of fundamental scientific knowledge. Among the Society's early activities was the founding of Greenwich Observatory in 1675 for the strictly practical purpose of 'finding out the longitude for perfecting navigation'.
- T. K. Derry & Trevor I. Williams, A Short History of Technology: From the Earliest Times to A.D. 1900 (1960) Ch. 1 General Historical Survey, "The Emergence of the Modern World"
- Growing skill in the working of metals is... exemplified by the development of the instrument-maker's craft. To many... we make reference elsewhere—for example, clocks, navigational instruments and balances. ...Brass, ivory, and closed-grained woods, such as box and pear, were the principal materials of the instrument-makers, with brass becoming increasingly favoured because of its rigidity and permanence. For the shaping of metal the lathe was a valuable tool, and the clock-makers in particular developed it greatly for precision work. The engraving of scales was, of course, a most important part of the work: until the advent of mechanical devices, this was done with simple engraving tools and punches, the design being first set out by geometrical methods. The earliest products of the instrument-makers were made mainly for astronomical purposes or to apply astronomical methods in navigation: they included astrolabes, cross-staffs, quadrants, sundials, and orreries, as well as basic geometrical instruments such as compasses and rules. From the seventeenth century, however, a variety of new instruments, or much improved versions of old ones, began to appear. The needs of surveyors led to the elaboration of the hodometer... enabling distances to be measured... Improvements in artillary called for more accurate sighting of cannon, and by the beginning of the seventeenth century the gunner's level had been highly developed. The invention of the telescope and microscope introduced new problems both in the making of lenses and of the instruments in which they were mounted: the new instruments were a regular part of the instrument-maker's trade from about 1660. From 1700 the revolution in science was making still further demands on the craft, and air-pumps, thermometers, barometers, electrical machines, and other instruments were called for in constantly increasing quantities.
- T. K. Derry & Trevor I. Williams, A Short History of Technology: From the Earliest Times to A.D. 1900 (1960) Ch.4 The Extraction and Working of Metals, "Instrument-making"
- 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. Sounds, colors, ends, as well as goods and bads, were regarded as purely subjective — as mere impressions in the mind. Objective existence was then treated as having only quantitative aspects — as so much mass in motion, its only differences being that at one point in space there was a larger aggregate mass than at another, and that in some spots there were greater rates of motion than at others. Lacking qualitative distinctions, nature lacked significant variety. Uniformities were emphasized, not diversities; the ideal was supposed to be the discovery of a single mathematical formula applying to the whole universe at once from which all the seeming variety of phenomena could be derived. This is what a mechanical philosophy means.
- Les hypothèses ne sont point le produit d'une création soudaine, mais le résultat d'une évolution progressive.
[Hypotheses are not the product of sudden creation, but the result of progressive évolution.]
- Science and religion are two human enterprises sharing many common features. They share these features also with other enterprises such as art, literature and music. The most salient features of all these enterprises are discipline and diversity. Discipline to submerge the individual fantasy in a greater whole. Diversity to give scope to the infinite variety of human souls and temperaments. Without discipline there can be no greatness. Without diversity there can be no freedom. Greatness for the enterprise, freedom for the individual—these are the two themes, contrasting but not incompatible, that make up the history of science and the history of religion.
- Freeman Dyson, Infinite in All Directions (1988)
- Science as subversion has a long history. ...Davis and Sakharov belong to an old tradition in science that goes all the way back to the rebels Benjamin Franklin and Joseph Priestley in the eighteenth century, to Galileo and Giordano Bruno in the seventeenth and sixteenth. If science ceases to be a rebellion against authority, then it does not deserve the talents of our brightest children. ...We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice.
- Freeman Dyson, The Scientist As Rebel (2006).
- The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. ...A study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. ...Two people who came early and strongly under the influence of Spengler's philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. ...Weyl and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics. In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant.
- Freeman Dyson, The Scientist As Rebel (2006).
- Progress in science is often built on wrong theories that are later corrected. It is better to be wrong than to be vague.
- Freeman Dyson, The Scientist As Rebel (2006).
- According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought... scientists will need only the rules of logic and knowledge of the existence of God. For four hundred years since Bacon and Descartes... science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature's secrets by itself, but both together have been amazingly successful. For four hundred years English scientists have tended to be Baconian and French scientists Cartesian. Faraday and Darwin and Rutherford were Baconians; Pascal and Laplace and Poincaré were Cartesians. Newton was at heart a Cartesian, using pure thought... to demolish the Cartesian dogma of vortices. Marie Curie was at heart a Baconian, boiling tons of crude uranium ore to demolish the dogma of the indestructibility of atoms.
- The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science.
- ...The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein's amazing revelations have likewise sunk into the commonplaces of educated thought.
- If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz.
- Albert Einstein, "Clerk Maxwell's Influence on the Evolution of the Idea of Physical Reality" in Essays in Science (1934)
- 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)
- I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today—and even professional scientists—seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth.
- Albert Einstein, Letter to Robert A. Thorton (Dec 7, 1944) EA-674, Einstein Archive, Hebrew University, Jerusalem.
- What Luther's burning of the Papal Bull was in the religious field, in the field of natural science was the great work of Copernicus, in which he, although timidly... threw down a challenge to ecclesiastical superstition. From then on natural science was in essence emancipated from religion, although the complete settlement of accounts in all details has gone on to the present day and in many minds is still far from being complete. But from then on the development of science went forward with giant strides, increasing, so to speak, proportionately to the square of the distance in time from its point of departure, as if it wanted to show the world that for the motion of the highest product of organic matter, the human mind, the law that holds good is the reverse of that for the motion of inorganic matter.
- The impression that science is over has occurred many times in various branches of human knowledge, often because of an explosion of discoveries made by a genius or a small group of men in such a short time that average minds could hardly follow and had the unconscious desire to take breath, to get used to the unexpected things that came to be revealed. Dazzled by these new truths, they could not see beyond. Sometimes an entire century did not suffice to produce this accommodation.
- Charles Fabry, La vie et l'oeuvre scientifique de Augustin Fresnel (1927), p. 13
- Christians believed in a teleological cosmos, one created by an omniscient God, a Grand Designer, for a specific purpose. This comforting view was threatened by the new statistical methods in physics, and also by Darwin's theory of evolution, which assumes that chance may intervene between generations to introduce new characteristics.
- Patricia Fara, Science A Four Thousand Year History (2009).
- 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.
- Benjamin Farrington, Science in Antiquity (1950).
- 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.
- Paul Feyerabend, Against Method (1975) p. 48
- Our freedom to doubt was born out of a struggle against authority in the early days of science. It was a very deep and strong struggle: permit us to question — to doubt — to not be sure. I think that it is important that we do not forget this struggle and thus perhaps lose what we have gained.
- Richard Feynman, in "The Value of Science," address to the National Academy of Sciences (Autumn 1955)
- By the way, what I have just outlined is what I call a “physicist’s history of physics,” which is never correct. What I am telling you is a sort of conventionalized myth-story that the physicists tell to their students, and those students tell to their students, and is not necessarily related to the actual historical development, which I do not really know!
- Richard Feynman, QED: The Strange Theory of Light and Matter (1985), Ch. 1 : Introduction
- For indeed it is one of the lessons of the history of science that each age steps on the shoulders of the ages which have gone before. The value of each age is not its own, but is in part, in large part, a debt to its forerunners. And this age of ours if, like its predecessors, it can boast of something of which it is proud, would, could it read the future, doubtless find also much of which it would be ashamed.
- Fundamental changes in science have always been accompanied by deeper digging toward the philosophical foundations. Changes like the transition from the Ptolomaic to the Copernican system, from Euclidean to non-Euclidean geometry, from Newtonian to relativistic mechanics... have brought about a radical change in our common-sense explanation of the world. From all these considerations everyone who is to get a satisfactory understanding of twentieth century science will have to absorb a good deal of philosophical thought. But he will soon feel the same thing holds for a thorough understanding of the science which originated in any period of history.
- Philipp Frank, Philosophy of Science: The Link Between Science and Philosophy (1957)
- Toward the last quarter of the nineteenth century, it was accepted more and more that the phenomena of electromagnetism were not to be reduced to Newtonian mechanics, but were to be reduced from a separate system of principles, of which, in turn, the Newtonian laws were a special case. The "state of a system" is no longer described by the velocity at a certain point x, y, z and at a time t, but by the electric and magnetic field strengths at x, y, z and at a time t. A causal law in the theory of the electromagnetic field is now an equation that allows us to compute from the present distribution of field strengths the future value of field strengths. Mathematically, the causal laws look exactly like those in mechanics except that the velocities u, v, w are replaced by the field strengths. This theory... has been generalized into a "general field theory."
- Philipp Frank, Philosophy of Science: The Link Between Science and Philosophy (1957) p. 272.
- [A]mong several theories that are set up to account for a certain domain of observed facts, one will stand out as the best... the theory should be accepted which shows "more" agreement with observed facts... However, this... cannot be the only criterion... If this were so, the best theory would be the mere description of facts; but this would be no theory at all. ...the actual advance of science has always been engineered by a criterion of economy and simplicity. The criteria of Reichenbach and Carnap, which are based, like John Stuart Mill's inductive logic, upon agreement with observations, have to be complemented by the criterion of economy and simplicity which was advanced in the history of science by men like William Ockham, Isaac Newton, and Ernst Mach. In our twentieth century, the importance of crieteria other than mere agreement with observation was stressed by von Mises and Bronowski.
- Philipp Frank, Philosophy of Science: The Link Between Science and Philosophy (1957) p. 350.
- [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.
- Included in this “almost nothing,” as a kind of geological afterthought of the last few million years, is the first development of self-conscious intelligence on this planet—an odd and unpredictable invention of a little twig on the mammalian evolutionary bush. Any definition of this uniqueness, embedded as it is in our possession of language, must involve our ability to frame the world as stories and to transmit these tales to others. If our propensity to grasp nature as story has distorted our perceptions, I shall accept this limit of mentality upon knowledge, for we receive in trade both the joys of literature and the core of our being.
- Stephen Jay Gould, "Literary Bias on the Slippery Slope" in Bully for Brontosaurus (1991).
- I... praise the newly opened halls of fossil mammals at the American Museum of Natural History. ...teaching us about evolutionary trees by organizing the entire hall as a central trunk and set of branches... placing our brains in our feet and letting us learn by walking. ...the chosen geometry of evolutionary organization... violates the traditional picture of life's history, thus illustrating... an important principle in the history of science: the central role of pictures, graphs, and other forms of visual representation in channeling and constraining our thought. ...Words are an evolutionary afterthought. ...My colleagues have actually done it. ...They have ordered all the fossils into an unconventional iconographic tree that fractures the bias of progress. ...so that we can preambulate along the tree of life and absorb the new scheme viscerally by walking... They have taken Colbert's radical idea and arranged all the fossils by their branching order, not by their later "success" or "advancement." Groups that branch early, appear early in the hall... Sea cows and elephants are at the end of the hall, horses in the middle, and primates near the beginning.
- Stephen Jay Gould, "Evolution by Walking", Dinosaur in a Haystack: Reflections in Natural History (1995)
- In this oversimplified view of scientific progress, we advance along a pathway of accumulating knowledge, guided by a timeless method of accurate observation and relentless logic. ... T. H. Huxley's The Crayfish... argues that the study of organisms has progressed through the same three stages followed by all sciences... an initial phase of gathering information without theoretical guidance (Huxley calls this... Natural History... "accurate, but necessarily incomplete and unmethodized knowledge"); a second stage of systemizing and organization... still without guiding theory (called Natural Philosophy); and... the... synthetic climax... Physical Science, "this final stage of knowledge, [where] the phenomena of nature are regarded as one continuous series of causes and effects." ...In this system... Linnaeus occupies the middle rung. ...I would agree with most modern historians of science in branding this... as misleading, and unfair... [T]wo aspects of this older positivist view... lack validity and impede understanding: ...the notion of a timeless scientific method based on rigorously objective observation and logic, and ...that earlier systems were either theory-free or theory-poor because explanation can only follow accurate description.
Theory-free science makes about as much sense as value-free politics. Both... are oxymoronic. All thinking about the natural world must be informed by theory... The old... theories may have been wrong, but they were as persuasive (and restrictive) in the structuring of knowledge as any more accurate and later system... [W]e cannot collect information without a theory to organize our searches and observations.
- Stephen Jay Gould, "The First Unmasking of Nature", Dinosaur in a Haystack: Reflections in Natural History (1995)
- Henry Fairfield Osborn, the dominant paleontologist of his era, and long time director of the American Museum of Natural History, gave the "standard version in his popular book of 1918, The Origin and Evolution of Life... "Lamarck attributed the lengthening of the [giraffe's] neck to the inheritance of bodily modifications caused by the neck-stretching habit. Darwin attributed the lengthening of the neck to the constant selection of individuals and races which were born with the longest necks. Darwin was probably right." …The version has held ever since.
- Stephen Jay Gould, "The Tallest Tale" in Leonardo's Mountain of Clams and the Diet of Worms (1998).
- Progress in science proceeds in fits and starts. Some periods are filled with great breakthroughs; at other times researchers experience dry spells. Scientists put forward results... theoretical and experimental. The results are debated... sometimes... discarded, sometimes... modified, and sometimes they provide inspirational jumping-off points for new and more accurate ways of understanding... a zig zag path toward what we hope will be ultimate truth, a path that began with humanity's earliest attempts to fathom the cosmos and whose end we cannot predict. Whether string theory is an incidental rest stop... a landmark turning point, or... the final destination we do not know. But the last two decades of research by hundreds of... physicists and mathematicians from numerous countries have given us well-founded hope that we are on the right and possibly final track.
- Brian Greene, The Elegant Universe (1999, 2003) Ch. 1 "Tied Up with a String."
- Kuhn... (like Popper and many other predecessors) thought the primary work of science was theoretical. He esteemed theory, and although he had a good sense of experimentation, presented it as of secondary importance. Since the 1980s there has been a substantial shift in emphasis, with historians, sociologists, and philosophers attending seriously to experimental science.
- Ian Hacking, Introduction to The Structure of Scientific Revolutions: 50th Anniversary Edition by Thomas S. Kuhn (2012).
- The whole history of science has been the gradual realization that events do not happen in an arbitrary manner, but that they reflect a certain underlying order, which may or may not be divinely inspired.
- Stephen Hawking, A Brief History of Time (1988) Ch. 8.
- Everything is theoretically impossible, until it is done. One could write a history of science in reverse by assembling the solemn pronouncements of highest authority about what could not be done and could never happen.
- Robert A. Heinlein, The Rolling Stones (1952)
- 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.
- Werner Heisenberg, Physics and Philosophy: The Revolution in Modern Science (1958)
- Of the splendid constellation of great names... we admire the living and revere dead far too warmly and too deeply to suffer us sit in judgment on their respective claims to in this or that particular discovery; to balance mathematical skill of one against the experimental dexterity of another, or the philosophical acumen a third. So long as "one star differs from another in glory,"—so long as there shall exist varieties, or even incompatibilities of excellence,—so long will the admiration of mankind be found sufficient for all who merit it.
- In former times the Mathematician and the Physicist were usually one and the same man. Even as late as the eighteenth century this was very generally the case; it was in the nineteenth century that the increasing complexity of both Sciences produced that separation of the two departments which has become continually more marked, and has reached its extreme point in our own time. ...The chief drawback is that each specialist, from lack of interest in, and knowledge of, the progress of the other great department, is apt to miss that large source of inspiration in his own study which is supplied by the other one.
- E. W. Hobson, Mathematics, from the points of view of the Mathematician and of the Physicist (1912) an address delivered to the Mathematical and Physical Society of University College London, p. 4.
- Mathematical thinking has played a very important part in the formation of the fundamental concepts of the Physicist; very often this part has been a dominant one. Many of these concepts could only have received a precise meaning and... taken definite forms as the result of the work of Mathematicians... For example, the conception of Energy, and the exact meaning of the... law of the Conservation of Energy, emerged as results of the development of the abstract side of molar mechanics, which determined the mode in which the kinetic energy of moving bodies and potential energy as work are defined as measurable quantities. Only by the transference and extension of these notions to the molecular domain did the conception involved in the modern doctrine become possible. The doctrine... had been established before Joule and Mayer commenced their work, and was a necessary presupposition of their further development. Joule was able to determine the mechanical equivalent of heat only owing to the fact that mechanical work was already regarded as a measurable quantity, measured in a manner which had been fixed in the course of the development of the older Mathematical Mechanics. The notion of Potential, fundamental in Electrical Science, and which every Physicist, and every Electrical Engineer, constantly employs, was first developed as a Mathematical conception during the eighteenth century in connection with the theory of the attractions of gravitating bodies. It was transferred to the electrical domain by George Green and others, together with a good deal of detailed mathematics connected with it which had previously been applied to the gravitational potential function.
- E. W. Hobson, Mathematics, from the points of view of the Mathematician and of the Physicist (1912) an address delivered to the Mathematical and Physical Society of University College London, pp. 6-7.
- Science has only existed for a few hundred years, and its most spectacular achievements have occurred within the last century. Viewed from a historical perspective, the modern era of rapid scientific and technological progress appears to be not a permanent feature of reality, but an abberation, a fluke, a product of a singular convergence of social, intellectual, and political factors.
- John Horgan, The End of Science (1996)
- The history of civilization details the steps by which men have succeeded in building up an artificial world within the cosmos. Fragile reed as he may be, man, as Pascal says, is a thinking reed: there lies within him a fund of energy, operating intelligently and so far akin to that which pervades the universe, that it is competent to influence and modify the cosmic process. In virtue of his intelligence the dwarf bends the Titan to his will. In every family, in every polity that has been established, the cosmic process in man has been restrained and otherwise modified by law and custom; in surrounding nature, it has been similarly influenced by the art of the shepherd, the agriculturist, the artisan. As civilization has advanced, so has the extent of this interference increased; until the organized and highly developed sciences and arts of the present day have endowed man with a command over the course of non-human nature greater than that once attributed to the magicians. ...a right comprehension of the process of life and of the means of influencing its manifestations is only just dawning upon us. We do not yet see our way beyond generalities; and we are befogged by the obtrusion of false analogies and crude anticipations. But Astronomy, Physics, Chemistry, have all had to pass through similar phases, before they reached the stage at which their influence became an important factor in human affairs. Physiology, Psychology, Ethics, Political Science, must submit to the same ordeal. Yet it seems to me irrational to doubt that, at no distant period, they will work as great a revolution in the sphere of practice.
- Great courageous spirits like Abelard and Saint Thomas Aquinas dared to introduce into Catholicism the concepts of Aristotelian logic, and thus founded scholastic philosophy. But when the Church took the sciences under her wing, she demanded that the forms in which they moved be subjected to the same unconditioned faith in authority as were her own laws. And so it happened that scholasticism, far from freeing the human spirit, enchained it for many centuries to come, until the very possibility of free scientific research came to be doubted. At last, however, here too daylight broke, and mankind, reassured, determined to take advantage of its gifts and to create a knowledge of nature based on independent thought. The dawn of the day in history is known as the Renaissance or the Revival of Learning.
- Carl Gustav Jacob Jacobi, "Über Descartes Leben und seine Methode die Vernunft Richtig zu Leiten und die Wahrheit in den Wissenschaften zu Suchen," "About Descartes' Life and Method of Reason.." (Jan 3, 1846) C. G. J. Jacobi's Gesammelte werke Vol. 7 p.309, as quoted by ** Tobias Dantzig, Number: The Language of Science (1930).
- The Copernican revolution... revealed that the earth is not the center of the universe... The second, the Darwinian revolution... revealed that we are not created divinely or uniquely but instead evolved from simpler animals by a process of natural selection. The third great revolution, the Freudian revolution of Vienna 1900, revealed that we do not consciously control our own actions but are instead driven by unconscious motives. This... later led to the idea that human creativity... stems from conscious access to underlying, unconscious forces.
- Eric Kandel, The Age of Insight (2012)
- When Galilei let balls of a particular weight, which he had determined himself, roll down an inclined plain, or Torricelli made the air carry a weight, which he had previously determined to be equal to that of a definite volume of water; or when, in later times, Stahl changed metal into lime, and lime again into metals, by withdrawing and restoring something, a new light flashed on all students of nature. They comprehended that reason has insight into that only, which she herself produces on her own plan, and that she must move forward with the principles of her judgments, according to fixed law, and compel nature to answer her questions, but not let herself be led by nature, as it were in leading strings, because otherwise accidental observations made on no previously fixed plan, will never converge towards a necessary law, which is the only thing that reason seeks and requires. Reason, holding in one hand its principles, according to which concordant phenomena alone can be admitted as laws of nature, and in the other hand the experiment, which it has devised according to those principles, must approach nature, in order to be taught by it: but not in the character of a pupil, who agrees to everything the master likes, but as an appointed judge, who compels the witnesses to answer the questions which he himself proposes. Therefore even the science of physics entirely owes the beneficial revolution in its character to the happy thought, that we ought to seek in nature (and not import into it by means of fiction) whatever reason must learn from nature, and could not know by itself, and that we must do this in accordance with what reason itself has originally placed into nature. Thus only has the study of nature entered on the secure method of a science, after having for many centuries done nothing but grope in the dark.
- It is not an unusual phenomenon in the history of science that views which were once considered antiquated and out of date suddenly come into favor again, though in a more or less modified form. An extremely interesting case of this kind is presented by the revolution in our ideas of electric phenomena which has taken place within the last 10 years...
The modern theory of electrical and allied optical phenomena... [i.e.,] the "electron theory," means practically a return to views as laid down in the sixties and seventies by Wilhelm Weber and Zöllner, but modified by the results of Maxwell's and Hertz's researches. W. Weber imagined electric phenomena as the actions of elementary electrical particles—so called "electric atoms"—whose mutual influence depended not only upon their positions but also upon their relative velocities and accelerations. ...most of the laws of electrodynamics when expressed from the standpoint of pure phenomenology in the shape of differential equations, are much more simple and convenient than Weber's formulæ. ...Faraday and Maxwell brought about a general feeling that... a finite rate of propagation would have to take the place of action at a distance. ...Maxwell's formulæ [were] wholly void ...of atomistic conceptions ...According to Maxwell... the vibrations of light were not mechanical, but electrical vibrations of the ether, and the two constants by which Maxwell defined the electric and magnetic behaviour of every body (the dielectric constant and the magnetic permeability) had also to be the determining elements in its refractive power. Although the condition... was well fulfilled in a number of bodies, ...many bodies, notably water...sufficed to prove the inadequacy of the theory... To this was added the dependence of the refractive index upon the colour [frequency], for which the original theory gave no explanation whatever.
H. A. Lorentz showed that the foundations of an electromagnetic theory of dispersion could be laid in a manner quite analogous to the mechanical theory, by regarding every molecule as the origin of electric vibrations of a definite period. He says:—"Let there be in every material particle several material points charged with electricity, of which, however, only one be movable, and have the charge e and the mass μ." Lorentz derives the equations of dispersion from this fundamental assumption of vibrating charged particles. ...
In his Faraday Memorial Address of 1881 Helmholtz points out that Faraday's law necessarily implies the existence of electric atoms. ...when a neutral molecule—say NaCl—splits up in +Na and -CI when dissolved in water, it is most probable that both the sodium and the chlorine atom had their charges beforehand... equal and opposite. But if we consider a ray of light traversing a crystal of salt, the charges and the atoms they accompany must be thrown into vibrations, and must influence the propagation of the light. ...
In the years 1890-93 a number of works appeared by F. Richarz, H. Ebert and G. Johnstone Stoney, mostly dealing with the mechanism of the emission of luminous vapours, and in which attempts are made, on the basis of the kinetic theory of gases, to determine the magnitude of the elementary electrical quantity, called by Stoney... the now universally accepted name of electron. ...that one electron contains about 10-10 electrostatic units. ...a whole series of other methods... tend to very similar values. ...
In 1896 a pupil of Lorentz, P. Zeeman, discovered a phenomenon whose existence Faraday had vainly sought for in 1862. If a luminous vapour, say a sodium flame, is brought into a strong magnetic field, the spectrum lines of the vapour show peculiar changes, consisting of a doubling or trebling, according to the line of vision. These changes are predicted by Lorentz's theory. The Zeeman phenomenon further permitted a determination of the inert mass connected with the vibrating charges, and then a striking result was obtained: the vibrating electron is always negatively charged, while the positive charge is stationary. ...The original and almost tacit assumption that the whole ion—i.e., the chemical atom plus its valency charge—was in oscillation must, therefore, be abandoned. We must suppose that the charge, just as is the case in electrolysis, has also an independent mobility in the light-emitting molecule, and that the mass concerned in the Zeeman phenomenon is that of the electron itself.
We thus arrive at a view which nearly coincides with the old conception of Weber, but with the important difference that instead of a direct action at a distance we have an action transmitted by the ether, and further, that we have now a perfectly distinct numerical estimate of the magnitude of the electric atoms.
- Historically, the investigations of oscillatory motions was motivated by the desire to improve methods of telling time. ...In the seventeenth century the need to measure small periods of time accurately for the purpose of telling longitude at sea caused scientists to search for increasingly accurate clocks. The search resulted in some major successes that were at least as valuable for the advancement of mathematics and the study of other phenomena of nature, such as light and sound, as they were for the specific problem of measuring time.
Scientists naturally concentrated on any physical phenomena that seemed to be periodic or repetitive and might therefore be related to the periodic motion of the planets. Two phenomena recommended themselves for closer investigation, the motion of an object or bob... on a spring, and the motion of a pendulum. The first of those attracted the attention of Robert Hooke... Suppose d is the increase or decrease in the length of the spring resulting from extension or contraction. Hooke found that the restoring force the spring exerts is proportional to d; that is, the force is a constant k, say, times d. This is the meaning of [Ut tensio, sic vis ("as the extension, so the force")]...
- Morris Kline, Mathematics and the Physical World (1959)
- 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).
- If conquerors be regarded as the engine-drivers of History, then the conquerors of thought are perhaps the pointsmen who, less conspicuous to the traveller's eye, determine the direction of the journey.
- 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).
- Rationality is very much connected with the tradition in science for the last 300 years, when you're going to end up with some sort of understandable explanation of something. And I would be disappointed if that were the case.
- Science as we now understand the word is of later birth. If its germinal origin may be traced to the early period when Observation, Induction, and Deduction were first employed, its birth must be referred to that comparatively recent period when the mind,—rejecting the primitive tendency to seek in supernatural agencies for an explanation of all external phenomena,—endeavoured, by a systematic investigation of the phenomena themselves to discover their invariable order and connection.
- The separation of Science from Knowledge was effected step by step as the Subjective Method was replaced by the Objective Method: i.e., when in each inquiry the phenomena of external nature ceased to be interpreted on premisses suggested by the analogies of human nature.
- George Henry Lewes, Aristotle: a Chapter from the History of Science (1864).
- 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.
- George Henry Lewes, Aristotle: a Chapter from the History of Science (1864).
- 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.
- George Henry Lewes, Aristotle: a Chapter from the History of Science (1864).
- The gist and kernel of mechanical ideas has in almost every case grown up in the investigation of very simple and special cases of mechanical processes; and the analysis of the history of the discussions concerning these cases must ever remain the method at once the most effective and the most natural for laying this gist and kernel bare. ...[I]t is the only way in which a real comprehension of the general upshot of mechanics is to be attained.
- The history of the development of mechanics, is... indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example of the processes by which natural science generally is developed.
- We now propose to enter more minutely into subject of our inquiries, and at the same time, without making the history of mechanics the chief topic discussion, to consider its historical development so far as this is requisite to an understanding of the present state of mechanical science... Apart from the consideration that we cannot afford to neglect the great incentives that it is in our power to derive from the foremost intellects of all epochs, incentives which taken as a whole are more fruitful than the greatest men of the present day are able to offer, there is no grander, no more intellectually elevating spectacle than that of the utterances of the fundamental investigators in their gigantic power.
Possessed as yet of no methods, for these were created by their labors, and are only rendered comprehensible to us by their performances, they grapple with and subjugate the object of their inquiry, and imprint upon it the forms of conceptual thought. They that know the entire course of the development of science, will, as a matter of course, judge more freely and more correctly of the significance of any present scientific movement than they, who limited in their views, to the age in which their own lives have been spent, contemplate merely the momentary trend that the course of intellectual events takes at the present moment.
- The history of the development of mechanics is quite indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example of the processes by which natural science generally is developed.
- Ernst Mach, The Science of Mechanics: A Critical and Historical Account of Its Development (1893) Introduction, Tr. Thomas J. McCormack.
- The acquisition of the most elementary truth does not devolve upon the individual alone: it is pre-effected in the development of the race.
- Ernst Mach, The Science of Mechanics: A Critical and Historical Account of Its Development (1893) Tr. Thomas J. McCormack.
- Know that this Universe, in its entirety, is nothing else but one individual being; that is to say, the outermost heavenly sphere, together with all included therein, is as regards individuality beyond all question a single being like Said and Omar. The variety of its substances—I mean the substances of that sphere and all its component parts—is like the variety of the substances of a human being: just as, e.g., Said is one individual, consisting of various solid substances, such as flesh, bones, sinews of various humours, and of various spiritual elements; in like manner this sphere in its totality is composed of the celestial orbs, the four elements and their combinations; there is no vacuum whatever therein, but the whole space is filled up with matter. Its centre is occupied by the earth, earth is surrounded by water, air encompasses the water, fire envelopes the air, and this again is enveloped by the fifth substance (quintessence). These substances form numerous spheres, one being enclosed within another so that no intermediate empty space, no vacuum, is left. One sphere surrounds and closely joins the other. All the spheres revolve with constant uniformity, without acceleration or retardation; that is to say, each sphere retains its individual nature as regards its velocity and the peculiarity of its motion; it does not move at one time quicker, at another slower. Compared with each other, however, some of the spheres move with less, others with greater velocity. The outermost, all-encompassing sphere, revolves with the greatest speed; it completes its revolution in one day, and causes every thing to participate in its motion, just as every particle of a thing moves when the entire body is in motion; for all existing beings stand in the same relation to that sphere as a part of a thing stands to the whole. These spheres have not a common centre; the centres of some of them are identical with the centre of the Universe, while those of the rest are different from it. Some of the spheres have a motion independent of that of the whole Universe, constantly revolving from East to West, while other spheres move from West to East. The stars contained in those spheres are part of their respective orbits; they are fixed in them, and have no motion of their own, but participating in the motion of the sphere of which they are a part, they themselves appear to move. The entire substance of this revolving fifth element is unlike the substance of those bodies which consist of the other four elements, and are enclosed by the fifth element.
- Through the constant revolution of the fifth element, with all contained therein, the four elements are forced to move and to change their respective positions, so that fire and air are driven into the water, and again these three elements enter the depth of the earth. Thus are the elements mixed together; and when they return to their respective places, parts of the earth, in quitting their places, move together with the water, the air and the fire. In this whole process the elements act and react upon each other. The elements intermixed, are then combined, and form at first various kinds of vapours; afterwards the several kinds of minerals, every species of plants, and many species of living beings, according to the relative proportion of the constituent parts. All transient beings have their origin in the elements, into which again they resolve when their existence comes to an end. The elements themselves are subject to being transformed from one into another; for although one substance is common to all, substance without form is in reality impossible, just as the physical form of these transient beings cannot exist without substance.
- Maimonides, The Guide of the Perplexed (ca. 1190 AD) Part I, Ch. LXXII, A Parallel Between the Universe and Man, as in The Guide of the Perplexed of Maimonides (1881) pp.294-295, Tr. Michael Friedländer.
- [T]he principal part in the human body, namely, the heart, is in constant motion, and is the source of every motion noticed in the body; it rules over the other members, and communicates to them through its own pulsations the force required for their functions. The outermost sphere by its motion rules in a similar way over all other parts of the universe, and supplies all things with their special properties. Every motion in the universe has thus its origin in the motion of that sphere; and the soul of every animated being derives its origin from the soul of that same sphere.
- The history of science shews that even during the phase of her progress in which she devotes herself to improving the accuracy of the numerical measurement of quantities with which she has long been familiar, she is preparing the materials for the subjugation of the new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers. I might bring forward instances gathered from every branch of science... But the history of the science of terrestrial magnetism affords us a sufficient example of what may be done by experiments in concert, such as we hope some day to perform in our Laboratory.
- James Clerk Maxwell, Introductory Lecture on Experimental Physics at Cambridge (October, 1871), re-edited by W. D. Niven, The Scientific Papers of James Clerk Maxwell (2003) Vol. 2, p. 241
- [T]he application of algebra to geometry... far more than any of his metaphysical speculations, has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.
- Do what we will, we always, more or less, construct our own universe. The history of science may be described as the history of the attempts, and the failures, of men " to see things as they are."
- With the development of the sciences and with the articulation of the machine in practical life, the realm of order was transferred from the absolute rulers, exercising a personal control, to the universe of impersonal nature and to a particular group of artifacts and customs we call the machine. The royal formula of purpose—"I will"—was translated into the causal terms of science—"It must." By partly supplanting the crude desire for personal dominion by an impersonal curiosity and by the desire to understand, science prepared the way for a more effective conquest of the external environment and ultimately for a more effective control of the agent, man, himself.
- Lewis Mumford, Technics and Civilization (1934) Ch. 7 "Assimilation of the Machine"
- These independent objects of Newtonian physics might move, touch each other, collide, or even, by a certain stretch of the imagination, act at a distance: but nothing could penetrate them except in the limited way that light penetrated translucent substances. This world of separate bodies, unaffected by the accidents of history or geographic location, underwent a profound change with the elaboration of the new concepts of matter and energy that went forward from Faraday and von Mayer through Clerk-Maxwell and Willard Gibbs and Ernest Mach to Planck and Einstein. The discovery that solids, liquids, and gases were phases of all forms of matter modified the very conceptions of substance, while the identification of electricity, light, and heat as aspects of a protean energy, and the final break-up of "solid" matter into particles of this same ultimate energy lessened the gap, not merely between various aspects of the physical world, but between the mechanical and the organic. Both matter in the raw and the more organized and internally self-sustaining organisms could be described as systems of energy in more or less stable, more or less complex, states of equilibrium.
- Lewis Mumford, Technics and Civilization (1934) Ch.8 "Orientation"
- The history of science is rich in the example of the fruitfulness of bringing two sets of techniques, two sets of ideas, developed in separate contexts for the pursuit of new truth, into touch with one another.
- While, by the present methods of teaching, a knowledge of science in its present state of advancement is imparted very successfully, eminent and far-sighted men have repeatedly been obliged to point out a defect which too often attaches to the present scientific education of our youth. It is the absence of the historical sense and the want of knowledge of the great researches upon which the edifice of science rests.
- If we study the history of science we see happen two inverse phenomena, so to speak. Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities.
...What is more complicated than the confused movements of the planets? What simpler than Newton's law?
...In the kinetic theory of gases, one deals with molecules moving with great velocities, whose paths, altered by incessant collisions, have the most capricious forms... The observable result is Mariotte's simple law. ...The law of great numbers has reestablished simplicity in the average.
...No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations.
- Zoologists maintain that the embryonic development of an animal recapitulates in brief the whole history of its ancestors throughout geologic time. It seems it is the same in the development of minds. The teacher should make the child go over the path his fathers trod; more rapidly, but without skipping stations. For this reason the history of science should be our first guide.
- Henri Poincaré, Science and Method (1914)
- In my presentation I... follow the genetic method. The essential idea... is that the order in which knowledge has been acquired by the human race will be a good teacher for its acquisition by the individual. The sciences came in a certain order; an order determined by human interest and inherent difficulty. Mathematics and astronomy were the first sciences really worth the name; later came mechanics, optics, and so on. At each stage of its development the human race has had a certain climate of opinion, a way of looking, conceptually, at the world. The next glimmer of fresh understanding had to grow out of what was already understood. The next move forward, halting shuffle, faltering step, or stride with some confidence, was developed upon how well the [human] race could then walk. As for the human race, so for the human child. But this is not to say that to teach science we must repeat the thousand and one errors of the past, each ill-directed shuffle. It is to say that the sequence in which the major strides forward were made is a good sequence in which to teach them. The genetic method is a guide to, not a substitute for, judgement.
- George Pólya, Mathematical Methods in Science (1977)
- The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error. But science is one of the very few human activities — perhaps the only one — in which errors are systematically criticized and fairly often, in time, corrected. This is why we can say that, in science, we often learn from our mistakes, and why we can speak clearly and sensibly about making progress there.
- Karl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (1963) Ch. 1 "Science : Conjectures and Refutations"
- Let us not... contend about merit, but let us all be intent on forwarding the common enterprize, and equally enjoy any progress we may make towards succeeding in it; and above all, let us acknowledge the guidance of that Great Being, who has put a spirit in man, and whose inspiration giveth him understanding.
- The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of center towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation.
- [S]cientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation...
- Up until the publication of Thomas Kuhn's The Structure of Scientific Revolutions in 1962, the history, philosophy, and sociology of science maintained an internalist approach to scientific knowledge claims. Science was seen as somehow above any social, political, or cultural influences, and therefore, the examinations of scientific knowledge focused on areas such as 'discoveries,' 'famous men,' and 'the scientific revolution in the West.' When Kuhn opened the door to the possibility that external factors were involved in the development of scientific paradigms, science studies assumed a more critical tone.
- Diane M. Rodgers "Debugging the Link Between Social Theory and Social Insects" (2009).
- 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).
- Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science — by far the most successful claim to knowledge accessible to humans — teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us.
- Carl Sagan, The Demon-Haunted World: Science as a Candle in the Dark (1995) Ch. 2, Science and Hope, p. 28
- The history of science—especially physics—has in part been the tension between the natural tendency to project our everyday experience on the universe and the universe's noncompliance...
- Carl Sagan, The Varieties of Scientific Experience: A Personal View of the Search for God (2006)
- The relativity and quantum theories provide good examples of one of the most characteristic features in the development of scientific ideas—namely the fact that every major advance, resulting in a new representation which post factum can be seen to have reduced the earlier picture to one whose results approximate closely to those of the newer one in special cases, has been connected with a revolutionary change in outlook, and with a radical revision of the epistemological and metaphysical foundations of the earlier picture. It is at such turning-points that scientific thought is most clearly revealed as creative speculation, kept within certain boundaries, and corrected, by facts and experimental evidence... akin to that sphere of inspiration which brings about the great creations of art: both constitute sudden and unpredictable insights into reality which no artificial and mechanical devices, such as computers, could ever achieve. ...science in the making can be seen to be as much an experiment with ideas as a search after significant experimental data.
- Shmuel Sambursky, Physical Thought from the Presocratics to the Quantum Physicists (1974).
- The history of science should be the leading thread in the history of civilization.
- The history of science familiarizes us with the ideas of evolution and the continuous transformation of human things... It shows us that if the accomplishments of mankind as a whole are grand, the contributions of each is small.
- George Sarton, (ca. 1917) as quoted by William Thompson Sedgwick, Harry Walter Tyler, A Short History of Science (1917)
- 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).
- The historical order is very interesting, but accidental and capricious; if we would to understand the growth of knowledge, we cannot be satisfied with accidents, we must explain how knowledge was gradually built up.
- George Sarton, A History of Science Vol.1 Ancient Science Through the Golden Age of Greece (1952).
- The history of science should not be an instrument to defend any kind of social or philosophic theory; it should be used only for its own purpose, to illustrate impartially the working of reason against unreason, the gradual unfolding of truth, in all its forms, whether pleasant or unpleasant, useful of useless, welcome or unwelcome.
- George Sarton, A History of Science Vol.1 Ancient Science Through the Golden Age of Greece (1952).
- Men of science have made abundant mistakes of every kind; their knowledge has improved only because of their gradual abandonment of ancient errors, poor approximations, and premature conclusions.
- George Sarton,A History of Science Vol.2 Hellenistic Science and Culture in the Last Three Centuries B.C. (1959).
- Science, especially evolutionary sciences, can only proceed from learning about theories of hypotheses that do not stand the test of time.
- Jeffrey H. Schwartz, What the Bones Tell Us (1997)
- 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.
- The history of science on the part of students will give them a better understanding of the broad tendencies which have determined the general course of scientific progress, will enlarge their appreciation of the work of successive generations, and tend to guard them against falling into those ancient pitfalls which have bordered the paths of progress.
- Two points should be specially emphasized in connection with the general theory of relativity.
First, it is a purely physical theory, invented to explain empirical physical facts, especially the identity of gravitational and inertial mass, and to coordinate and harmonize different chapters of physical theory, especially mechanics and electromagnetic theory. It has nothing metaphysical about it. Its importance from a metaphysical or philosophical point of view is that it aids us to distinguish in the observed phenomena what is absolute, or due to the reality behind the phenomena, from what is relative, i.e. due to the observer.
Second, it is a pure generalization, or abstraction, like Newton's system of mechanics and law of gravitation. It contains no hypothesis, as contrasted with the atomic theory or the theory of quanta, which are based on hypothesis. It may be considered as the logical sequence and completion of Newton's Principia. The science of mechanics was founded by Archimedes, who had a clear conception of the relativity of motion, and may be called the first relativist. Galileo, who was inspired by the reading of the works of Archimedes, took the subject up where his great predecessor had left it. His fundamental discovery is the law of inertia, which is the backbone of Newton's classical system of mechanics, and retains the same central position in Einstein's relativistic system. Thus one continuous line of thought can be traced through the development of our insight into the mechanical processes of nature... characterized by the sequence... Archimedes, Galileo, Newton, Einstein.
- Willem de Sitter, The Astronomical Aspect of the Theory of Relativity (1933)
- Descartes's so-called dualism is often taken to represent a fundamental revolution in ideas and the starting point of modern philosophy. ...but in substance his work is... better understood as an attempt to conserve the old truths in the face of new threats. His dualism was in essence an armistice... between the established religion and the emerging science of his time. ...isolating the mind from the physical world... ensured that many of the central doctrines of orthodoxy—immortality of the soul, the freedom of will, and, in general, the "special" status of humankind—were rendered immune to any possible contravention by the scientific investigation of the physical world. ...
For men such as Descartes, Malebranche, and Leibniz, solving the mind-body problem was vital to preserving the theological and political order inherited from the Middle Ages... For Spinoza, it was a means of destroying that same order and discovering a new foundation for human worth.
- Matthew Stewart, The Courtier and the Heritic (2006)
- Lagrange's "Mécanique analytique" is perhaps his most valuable work and still amply repays careful study. ...the full power of the newly developed analysis was applied to the mechanics of points and rigid bodies. The results of Euler, of D'Alembert, and of the other mathematicians of the Eighteenth Century were assimilated and further developed from a consistent point of view. Full use of Lagrange's own calculus of variations made the unification of the varied principles of statistics and dynamics possible... Newton's geometrical approach was now fully discarded; Lagrange's book was a triumph of pure analysis.
- Dirk Jan Struik, A Concise History of Mathematics (1948) Ch. 8 The Eighteenth Century.
- The development of human thought and achievement, as a whole, has not been, as commonly supposed, a continual upward progression, nor even the equivalent of a continuous series of ascertained results. Thoughts and inventions, which seemed on the verge of practical fruition, have often been reduced to nothingness, even at the most decisive moment, through some combination of untoward circumstances; yes, even the very memory of a pathway broken into the Land of Promise is often obliterated and what seemed accomplished fact has had to be recreated by laborious work covering years, decades and even centuries. Just the simplest, most natural and, in the end, almost self-evident facts are the hardest to evolve and elucidate, just what was most decisive and potent of result has been time and again overlooked by the seeker after truth. ...The gold of historic thought, indeed, is as little to be found in the street as the gold of actual daily strife, and it is by no means the task of the historian of broad general scope to give the initial clew to its discovery. He, indeed, can only reproduce the past with fidelity and exactitude. The intuition of the true investigator and pathfinder of today and tomorrow must find its own way to new guiding principles from the work of yesterday, before yesterday, and the distant past.
- Where Francis Bacon had provided the manifesto for experimental science, René Descartes... did the same for scientific theory. And though in the three hundred years since 1650, there have been occasional conflicts between the Baconian and Cartesian tendencies in modern science, their opposition has been creative, and out of it have come many of our most profound insights.
- This subject crosses most cultures and places... It might even be argued that this discipline was the link that brought geometric models of the cosmos together with numerical computation in a synthesis that allowed theory to be converted into prediction: the birth of the exact sciences. All this makes it hard to believe that trigonometry has never been given a proper book-length historical treatment in English.
- Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (2009) Preface, p.xi.
- One cannot genuinely practice the history of a scientific subject without also living and breathing the science itself.
- Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (2009) Preface, p.xii.
- Our technology is based entirely on mathematics and physics. ...The unprecedented growth of natural science in the 17th century was followed ineluctably by the rationalism of the 18th, by the deification of reason... Science is the most significant phenomenon of modern times, the principal ingredient of our civilization — alas!
...the 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.
- The treatment of the kinetics of a material system by the method of generalised coordinates was first introduced by Lagrange, and has since his time been greatly developed by the investigations of different mathematicians.
Independently of the highly interesting, although purely abstract science of theoretical dynamics which has resulted from these investigations, they have proved of great and continually increasing value in the application of mechanics to thermal, electrical and chemical theories, and the whole range of molecular physics.
- The important thing for the progress of physics is not the decision that a theory is true, but the decision that it is worth taking seriously—worth teaching to graduate students, worth writing textbooks about, above all, worth incorporating into one’s own research.
- Steven Weinberg, Dreams of a Final Theory (1992), Chap. 5 : Tales of Theory and Experiment
- The effect of these researches has been, a persuasion, that we need not despair of seeing, even in our own time, a renovation of sound philosophy, directed by the light which the History of Science sheds. Such a reform, when its Epoch shall arrive, will not be the work of any single writer, but the result of the intellectual tendencies of the age.
- Our species, from the time of its creation, has been travelling onwards in pursuit of truth; and now that we have reached a lofty and commanding position, with the broad light of day around us, it must be grateful to look back on the line of our past progress;—to review the journey.
- William Whewell, History of the Inductive Sciences (1837).
- The main object of the work was to present such a survey of the advances already made in physical knowledge, and of the mode in which they have been made, as might serve as a real and firm basis for our speculations concerning the progress of human knowledge, and the processes by which sciences are formed.
- William Whewell, History of the Inductive Sciences (1837).
- The present generation finds itself the heir of a vast patrimony of science; and it must needs concern us to know the steps by which these possessions were acquired, and the documents by which they are secured to us and our heirs for ever.
- William Whewell, History of the Inductive Sciences (1837).
- The earlier truths are not expelled but absorbed, not contradicted but extended; and the history of each science, which may thus appear like a succession of revolutions, is, in reality, a series of developements.
- In all modern history, interference with science in the supposed interest of religion, no matter how conscientious such interference may have been, has resulted in the direst evils both to religion and to science, and invariably; and, on the other hand, all untrammelled scientific investigation, no matter how dangerous to religion some of its stages may have seemed for the time to be, has invariably resulted in the highest good both of religion and of science.
- 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...
- Andrew Dickson White, A History of the Warfare of Science with Theology in Christendom (1896).
- The physical doctrine of the atom has got into a state which is strongly suggestive of the epicycles of astronomy before Copernicus.
- Alfred North Whitehead, Science and the Modern World (1925).
- We are indeed a blind race, and the next generation, blind to its own blindness, will be amazed at ours.
- Lancelot Law Whyte, Accent on Form: An Anticipation of the Science of Tomorrow p. 33 (1955).
- Understanding what M-theory really is—the physics it embodies—would transform our understanding of nature at least as radically as occurred in any of the major scientific upheavals of the past.
- This statement appears to us to be conclusive with respect to the insufficiency of the undulatory theory, in its present state, for explaining all the phenomena of light. But we are not therefore by any means persuaded of the perfect sufficiency of the projectile system: and all the satisfaction that we have derived from an attentive consideration of the accumulated evidence, which has been brought forward, within the last ten years, on both sides of the question, is that of being convinced that much more evidence is still wanting before it can be positively decided. In the progress of scientific investigation, we must frequently travel by rugged paths, and through valleys as well as over mountains. Doubt must necessarily succeed often to apparent certainty, and must again give place to a certainty of a higher order; such is the imperfection of our faculties, that the descent from conviction to hesitation is not uncommonly as salutary, as the more agreeable elevation from uncertainty to demonstration. An example of such alternations may easily be adduced from the history of chemistry. How universally had phlogiston once expelled the aërial acid of Hooke and Mayow. How much more completely had phlogiston given way to oxygen! And how much have some of our best chemists been lately inclined to restore the same phlogiston to its lost honours! although now again they are beginning to apprehend that they have already done too much in its favour. In the mean time, the true science of chemistry, as the most positive dogmatist will not hesitate to allow, has been very rapidly advancing towards ultimate perfection.
- Notwithstanding the broad foundation for mechanics laid by Newton in his Principia, and notwithstanding the indefatigable labors of Clairaut, d'Alembert, the Bernoullis, and Euler, there was near the end of the eighteenth century no comprehensive treatise on the science. Its leading principles and methods were fairly well known, but scattered through many works, and presented from divers points of view. It remained for Lagrange to unite them into one harmonious system. Mechanics had not yet freed itself from the restrictions of geometry, though progress since Newton's time had been constantly toward analytical... methods. The emancipation came with Lagrange's Mécanique Analytique published one hundred and one years after the Principia.
- The history of the rainbow from the age of myth to contemporary optics is an example wrought in miniature of our unfolding penetration of and relation to natural phenomena. ...Yet while engaging in itself, the history of the rainbow hides within it another story far more significant than an external history of science. For the changing images of the rainbow reflect to us momentous changes in the fabric of consciousness itself. The history of light, the rainbow, and more generally the history of science continue to act as a text in which we read the psychogenesis of the mind.
- Arthur Zajonc, Catching the Light: The Entwined History of Light and Mind (1993)
- Atomic theory
- Classical mechanics
- History of mathematics
- History of medicine
- History of non-Euclidean geometry
- History of optics
- Philosophy of science
- Scientific Revolution
- Unification in science and mathematics
- Henry Smith Williams, A History of Science Vol. 1–4 online text @WorldWideSchool.org