Johann H Lambert - Collected Quotes

"All this, it has been said, is not only possisible, but analogous to what actually happens. Does not Jupiter disturb the motion of Saturn? Does not the Moon cause the Earth to vacillate on her axis? And, does she not elevate and depress, alternately, the waves of the ocean?" (Johann H Lambert, "The System of the World", 1800)

"All those discoveries, which have been, and in process of time may be made, exalt the glory of the immortal Newton, who derived this admirable law from the depths of his own genius." (Johann H Lambert, "The System of the World", 1800)

"But, as the universe is an extremely complex machine; the arrangement of the various parts of which it is composed, its preservation, and the play and energy of its springs, depend on an infinite number of general as well as particular laws. The most general admit of no exception. The exceptions attach on the detail; their number increases in proportion as the laws are specrfſed and particularized, and thus become more and more limited and restricted by other laws. Hence the exceptions themselves iorm new laws and means employed for a higher end. Apparent disorder in the parts is thus absorbed in the order of the whole, and the small defects gradually vanish in the eye of the philosopher as he proceeds to view nature on a more extended scale." (Johann H Lambert, "The System of the World", 1800)

"If we admit the existence of a Supreme Disposer. who brought order out of Chaos, and gave form to the universe, it will follow that the universe is a perfect work, the impression, the character, the reflected image of the perfections of its author." (Johann H Lambert, "The System of the World", 1800)

"If we are convinced that every thing is formed by design, that every thing is in its proper link of the chain, that the world is the expression of the perfections of God, we will be inclined also to believe that all the heavenly bodies are inhabited, and, that universal space is replenished with as many globes as it can contain. We cannot bring ourselves to leave blanks and chasms in so perfect a work. In every situation that affords a point of view we will place an observatory and an observer." (Johann H Lambert, "The System of the World", 1800)

"If we could demonstrate that every body which revolves on its axis must likewise move in an orbit, we could no longer refuse this Jast motion to our Sun, since we know he has the first. Probably the mechanism of the world requires the combination of these two motions, though we do not distinctly see the eause of it." (Johann H Lambert, "The System of the World", 1800)

"In astronomy the scenery is continually shifting, and the modes of language vary in proportion as this inexhaustible science makes progress in improvement, and supplies us with new theories. Ptolemy spake the language ot the people: to Copernicus we are indebted for the language of astronomy; which Tycho Brahe in some measure confounded: Kepler and Newton rectified his faults, and gave to astronomical language a superior degree of elegance and perfection. The discoveries of the present and future times will introduce in this respect farther changes. All these different modes of language will, nevertheless, continue to be always intelligible; and may always be preserved in a certain degree, and within certain limitations." (Johann H Lambert, "The System of the World", 1800)

"In order to supply the defects of experience, we will have recourse to the probable conjectures of analogy, conclusions which we will bequeath to our posterity to be ascertained by new observations, which, if we augur rightly, will serve to establish our theory and to carry it gradually nearer to absolute certainty." (Johann H Lambert, "The System of the World", 1800)

"Is it not truly wonderful, that, in the constitution of the universe, time and space should every where be so happily combined, that notwithstanding the infinity of wheels and springs which mutually depend on each other, and which are all necessary to the play of the machine, the visible order of nature should, nevertheless, every where preserve the same air of simplicity aud uniformity." (Johann H Lambert, "The System of the World", 1800)

"Nothong is more simple than the plan of the Solar System: we have only to conceive the Sun in one of the focuses of the eliptic orbits, Which the planets and comets describe around him. We will bestow our chief attention on comets, as on them will depend all the merit of novelty to be found in the following theory." (Johann H Lambert, "The System of the World", 1800)

"The curves which the law of attraction may oblige the heavenly bodies to describe, are not confined to the elipse and circle; the sections of the cone are equally within its province, because they all have a focus wherein attraction may reside." (Johann H Lambert, "The System of the World", 1800)

"The law of attraction, which extends its dominion over every atom of matter, suffers nothing within the universe to be in a state of absolute rest: Motion obtains every where; all bodies of whatever description gravitate one towards another; all the wheels in this vast machine are going round; nature tolerates no dead and useless masses. The universe is a whole whose different members or systems can only be combined by reciprocal action and re- action, from which motion results as a- necessary consequence." (Johann H Lambert, "The System of the World", 1800)

"The law of gravitation extends universally over all matter. The fixed stars obeying central forces move in orbits. The milky way comprehends several systems of fixed stars; those that appear out of the tract of the milky way form but one system which is our own. The sun being of the number of fixed stars, revolves round a centre like the rest. Each system has its centre, and several systems taken together have a common centre, Assemblages of their assemblages have likewise theirs. In fine, there is à universal centre for the whole world round which all things revolve." (Johann H Lambert, "The System of the World", 1800)

"The system of Copernicus is, in fact, only a theory; but we have seen that astronomy can come at the truth only by carefully bringing under a review every possible hypothesis.This science, however, has made astonishing progress; by converting, at different periods apparent arrangements into such as are more conformable to what actually exista, we have left behind various theories founded in appearances, and penetrated, if not fully and demonstrably, at least in the way ot fair conjecture, even to the real and genuine order of things." (Johann H Lambert, "The System of the World", 1800)

"Universal order and harmony consist in resemblances infinitely diversified, or in endless varieties referred back to a point of re-union." (Johann H Lambert, "The System of the World", 1800)

"Upon the whole, we may draw this conclusion, that the heavens are made to endure, and the things of the earth to pass away. Nature changes in small, and is maintained and preserved in great. The vast clock of the firmament can only develape its springs in the course of numberless epoques which succeed each other, and each in the epoque to which it is assigned." (Johann H Lambert, "The System of the World", 1800)

"We suppose the existence of a wise and beneficent Being who presided over the formation of the World, and who is pleased to display his infinite perfections on this illustrious theatre." (Johann H Lambert, "The System of the World", 1800)

"We will found our hypothesis in the general laws of motion, whose effects are every where the same, and whose influence extends to the utmost limits of matter." (Johann H Lambert, "The System of the World", 1800)

"We would then see each of those bodies in the place and at the distance most convenient for it, each pursuing a route from which it must not depart, and which, as it should seem, had been traced out for it by rule and compass. Order and symmetry would result from apparent confusion; and such would be the case with respect to every thing that appears disorderly to us, provided we had data enough to refer those appearances to the whole of which they make a part." (Johann H Lambert, "The System of the World", 1800)

"We would wish to discover the Plan of the Universe, and the means employed by the Eternal Architect in the execution of his magnificent design. We will first contemplate the System of which we make a part, and of which our Sun is the center. Thence we will ascend towards those Suns and those innumerable Worlds which are scattered through the immensity of space." (Johann H Lambert, "The System of the World", 1800)

Note:

"The System of the World" (1800) is an abridged version of "Cosmologische Briefe über die Einrichtung des Weltbaues" [*Cosmological Letters on the Arrangement of the World-Structure]" (1761)

🪐On Astronomy (1800-1824)

"In astronomy the scenery is continually shifting, and the modes of language vary in proportion as this inexhaustible science makes progress in improvement, and supplies us with new theories. Ptolemy spake the language ot the people: to Copernicus we are indebted for the language of astronomy; which Tycho Brahe in some measure confounded: Kepler and Newton rectified his faults, and gave to astronomical language a superior degree of elegance and perfection. The discoveries of the present and future times will introduce in this respect farther changes. All these different modes of language will, nevertheless, continue to be always intelligible; and may always be preserved in a certain degree, and within certain limitations." (Johann H Lambert, "The System of the World", 1800)

"The system of Copernicus is, in fact, only a theory; but we have seen that astronomy can come at the truth only by carefully bringing under a review every possible hypothesis.This science, however, has made astonishing progress; by converting, at different periods apparent arrangements into such as are more conformable to what actually exista, we have left behind various theories founded in appearances, and penetrated, if not fully and demonstrably, at least in the way ot fair conjecture, even to the real and genuine order of things." (Johann H Lambert, "The System of the World", 1800)

"Astronomy and Pure Mathematics are the magnetic poles toward which the compass of my mind ever turns." (Carl Friedrich Gauss, [letter to Bolyai], 1803) 

"The present state of the system of nature is evidently a consequence of what is in the preceding moment, and if we conceive of an intelligence which at a given instant knew all the forces acting in nature and the position of every object in the universe - if endowed with a brain sufficiently vast to make all necessary calculations - could describe with a single formula the motions of the largest astronomical bodies and those of the smallest atoms. To such an intelligence, nothing would be uncertain; the future, like the past, would be an open book." (Pierre-Simon Laplace, "Essay on Probabilities", 1814)

"Astronomy is the science of the harmony of infinite expanse." (Richard Maltravers, cca. 1822)

"Little comes to us through time as a complete monument; much comes as remnants; much as techniques, as practical manual; some things because of their close affinity to man, like mathematics; other things because they are always encouraged, like astronomy and geography; other things because of man’s needs, like medicine; and finally some things, because the human being, without wanting to, continues to produce them, like music and the other fine arts." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1822)

On Literature: On Astronomy (From Fiction to Science-Fiction)

"It [the revelation of chaos] is treated scientifically; everything is explained by geology and astronomy, and in that way. It shows you exactly how a star is formed; nothing can be so pretty! A cluster of vapour, the cream of the milky way, a sort of celestial cheese, churned into light [...]" (Benjamin Disraeli, "Tancred, or The New Crusade", 1847)

"If [...] you are restless and anxious about the future, study astronomy at once. Your troubles will be reduced amazingly. But your study will reduce them in a singular way, by reducing the importance of everything." (Thomas Hardy, "Two on a Tower", 1882)

"The vastness of the field of astronomy reduces every terrestrial thing to atomic dimensions." (Thomas Hardy, "Two on a Tower", 1882)

"The demonstration must be against learning-science. But not every science will do. The attack must have all the shocking senselessness of gratuitous blasphemy. Since bombs are your means of expression, it would be really telling if one could throw a bomb into pure mathematics. But that is impossible... What do you think of having a go at Astronomy?" (Joseph Conrad, "The Secret Agent: A Simple Tale", 1907) 

"He knew not how to look at a landscape nor at a sky. Of plants and trees he was as exquisitely ignorant as of astronomy. It had not occurred to him to wonder why the days are longer in summer, and he vaguely supposed that the cold of winter was due to an increased distance of the earth from the sun. Still, he had learnt that Saturn had a ring and sometimes he unconsciously looked for it in the firmament, as for a tea-tray." (Arnold Bennett, "Clayhanger", 1910)

"Astronomy, as nothing else can do, teaches men humility." (Arthur C Clarke, "The Challenge of the Spaceship", 1954)

🪐On Astronomy (1975-1999)

"Astronomy is a great human endeavor, international in its ideals and performance, and shared by thousands of scientists, technicians, engineers, and craftsmen. Its instruments are the most beautifully precise, exquisitely delicate, and incredibly sensitive that the genius of man can produce." (Herbert Friedman," The Amazing Universe", 1975)

"It is a striking thought that ten years of radio astronomy have taught humanity more about the creation and organization of the universe than thousands of years of religion and philosophy." (Paul Davies, "Space and Time in the Modern Universe", 1977) 

"Each of the major sciences has contributed an essential ingredient in our long retreat from an initial belief in our own cosmic importance. Astronomy defined our home as a small planet tucked away in one corner of an average galaxy among millions; biology took away our status as paragons created in the image of God; geology gave us the immensity of time and taught us how little of it our own species has occupied." (Stephen J Gould, "Uniformity and Catastrophe", 1977)

"Studying the behavior of large whales has been likened to astronomy. The observer glimpses his subjects, often at long range; he cannot do experiments, and he must continually try to infer from data that are usually inadequate." (Hal Whitehead, "Why Whales Leap", Scientific American Vol. 252 (3), 1985) 

"Thus, astronomy was probably the first exact science, practiced long before the concept of science as such had been formulated. (Mathematics may have been earlier, but I do not consider it a natural science: the mother of many kings is not necessarily a queen.)" (Erwin Chargaff, "Serious Questions: An ABC of Skeptical Reflections", 1986)

"There is no such thing as 'pure' science. By this I mean that physics impinges on astronomy on the one hand and chemistry and biology on the other. And not only does each support neighbors, but derives sustenance from them."(Melvin Calvin, "Following the Trail of Light: A Scientific Odyssey", [autobiography] 1992)

🪐On Astronomy (2000-)

"A more extreme form of exponential growth was probably responsible for the start of the universe. Astronomer and physicists now generally accept the Big Bang theory, according to which the universe started at an unimaginably small size and then doubled in a split second 100 times, enough to make it the size of a small grapefruit. This period of 'inflation' or exponential growth then ended, and linear growth took over, with an expanding fireball creating the universe that we know today." (Richar Koch, "The Power Laws", 2000)

"Symmetry is ubiquitous. Symmetry has myriad incarnations in the innumerable patterns designed by nature. It is a key element, often the central or defining theme, in art, music, dance, poetry, or architecture. Symmetry permeates all of science, occupying a prominent place in chemistry, biology, physiology, and astronomy. Symmetry pervades the inner world of the structure of matter, the outer world of the cosmos, and the abstract world of mathematics itself. The basic laws of physics, the most fundamental statements we can make about nature, are founded upon symmetry." (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"A map is a graphical representation of geographical or astronomical features, but this may range from a sketch of a subway system, to an interactive, zoomable, or animated map on a computer which constantly changes in front of the eyes." " (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)

"[...] transcendental numbers, those numbers that lie beyond those that arise through euclidean geometry and ordinary algebraic equations. [...] The transcendentals are the numbers that fill the huge void between the more familiar algebraic numbers and the collection of all decimal expansions: to use an astronomical comparison, the transcendentals are the dark matter of the number world." (Peter M Higgins, "Number Story: From Counting to Cryptography", 2008)

"There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics" (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music" (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood." (Paul Lockhart, "A Mathematician's Lament", 2009)

"There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics" (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music" (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood." (Paul Lockhart, "A Mathematician's Lament", 2009)

"Good statistics are not a trick, although they are a kind of magic. Good statistics are not smoke and mirrors; in fact, they help us see more clearly. Good statistics are like a telescope for an astronomer, a microscope for a bacteriologist, or an X-ray for a radiologist. If we are willing to let them, good statistics help us see things about the world around us and about ourselves - both large and small - that we would not be able to see in any other way." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

🪐On Astronomy (1950-1974)

"The most interesting feature of this science astronomy (and of all science) is our eager ignorance." (Harlow Shapley, "Astronomy", Scientific American Vol. 183 (3), 1950) 

"It is not only the smallest features of the Universe that are controlled by the laws of physics. The behavior of matter on the very large scale that concerns us in astronomy is also determined by physics. The heavenly bodies dance like puppets on strings. If we are to understand why they dance as they do, it is necessary to find out how the strings are manipulated." (Fred Hoyle, "Frontiers of Astronomy", 1955)

"The astronomer seems at first sight to be the most helpless of all scientists. He cannot experiment with the Universe. It is a significant matter of nomenclature that whereas we speak of experimental work in other sciences we speak of observational work in astronomy." (Fred Hoyle, "Frontiers of Astronomy", 1955)

"The pursuit of the good and evil are now linked in astronomy as in almost all science.... The fate of human civilization will depend on whether the rockets of the future carry the astronomer's telescope or a hydrogen bomb." (Bernard Lovell, "The Individual and the Universe", 1959) 

"Astronomy differs from most sciences in that we cannot do experiments; the astronomer must build up from his existing observations a picture or 'model' of the Universe, and then look for further effects which should be observable if his model is correct." (Martin Ryle, "Radio Astronomy and Cosmology", Proceedings of the Royal Institution Vol. 38 (173), 1961

"They are to astronomy what atoms are to physics. Each galaxy is a stellar system somewhat like our Milky Way, and isolated from its neighbors by nearly empty space. In popular terms, each galaxy is a separate universe unto itself." (Allan Sandage, "The Hubble Atlas of Galaxies", 1961) 

"Physics can teach us only what the laws of nature are today. It is only Astronomy that can teach us what the initial conditions for these laws are." (Eugene P Wigner, "The Case for Astronomy", Proceedings of the American Philosophical Society Vol. 8 (1), 1964)

"No one can date that remote epoch when astronomy 'began' - we can say only that the fascination of the heaven is as old as man’s ability to think; as ancient as his capacity to wonder and to dream. And in company with most of the special enchantments of human life, the unique appeal of astronomy is incommunicable; easily understood through direct experience, but not to be precisely defined or explained. Nor should any explanation be thought necessary. The area of astronomy is both intellectual and aesthetic; it combines the thrill of exploration and discovery, the fun of sight-seeing, and the sheer pleasure of firsthand acquaintance with incredibly wonderful and beautiful things." (Robert Jr Burnham, "Burnham’s Celestial Handbook", 1966)

"Throughout science there is a constant alternation between periods when a particular subject is in a state of order, with all known data falling neatly into their places, and a state of puzzlement and confusion, when new observations throw all neatly arranged ideas into disarray." (Sir Hermann Bondi, "Astronomy and the Physical Sciences", 1966)

"Astronomy was the cradle of the natural sciences and the starting point of geometrical theories." (Cornelius Lanczos, "Space Through the Ages", 1970)

"The picture of the universe presented by astronomy is one of dismal stretches of time and space and unparalled desolation. In the eternal abyss of space - bleak, cold, and dark — there are no signs of a Cosmic Consciousness." (Woolsey Teller, "TheAtheism of Astronomy", 1972) 

"Yet nature does not always prefer conventional explanations, least of all in astronomy." (Roger Penrose, "Black Holes", Scientific American Vol. 226 (5), 1972)

"Astronomy is not the apex of science or of invention. But it is a test of the

cast of temperament and mind that underlies a culture." (Jacob Bronowski, "The Ascent of Man", 1973)

"The pre-eminence of astronomy rests on the peculiarity that it can be treated mathematically; and the progress of physics, and most recently biology, has hinged equally on finding formulations of their laws that can be displayed as mathematical models." (Jacob Bronowski, "The Ascent of Man", 1973)

🪐On Astronomy (1925-1949)

"Most sciences progress by pursuing nature into the realms of infinitely small, but for astronomy and cosmogony progress lies in the direction of the infinitely great, or, to be more exact, of the unthinkably great." (James Jeans, "Annual Report of the Board of Regents of the Smithsonian Institution" 1926) 

"In our recognition that order is universal, a fact confirmed by myriads of observations of patient, indefatigable, and devoted investigators, the old saying that 'an irreverent astronomer is mad' can apply with equal force to the physicist. Man learns something of his own minute and colossal stature, and he comes to feel that his own intelligence, which enables him to make such sublime discoveries, is the supreme achievement of evolution." (Harvey B Lemon, "Atomic Structure", 1927)

"Probably, what characterizes all scientists, whatever they may be, archivists, mathematicians, chemists, astronomists, physicists, is that they do not seek to reach a practical conclusion by their work." (Charles Richet, "The Natural History of a Savant", 1927)

"They [astronomy, mechanics and physics] search for reality beyond the realm of common thought up to unutterable abstractions consisting only of equations of symbols." (Alexis Carrel, "Man, The Unknown", 1935) 

"A circle no doubt has a certain appealing simplicity at the first glance, but one look at a healthy ellipse should have convinced even the most mystical of astronomers that that the perfect simplicity of the circle is akin to the vacant smile of complete idiocy. Compared to what an ellipse can tell us, a circle has nothing to say." (Eric T Bell, "The Handmaiden of the Sciences", 1937)

"Our conception of space is, in a fashion similar to that of natural numbers, depending on a constructive grip on all possible places. Let us consider a metallic disk in a plane E. Places on the disk can be marked in concreto by scratching little crosses on the plate. But relatively to two axes of coordinates and a standard length scratched into the plate we can also put ideal marks in the plane outside the disk by giving the numerical values of their two coordinates. Each coordinate varies over the a priori constructed range of real numbers. ln this way astronomy uses our solid earth as a base for plumbing the sidereal spaces." (Hermann Weyl, "The Mathematical Way of Thinking", 1940)

"Microscopical anatomy is like mathematics in books on astronomy or physics - something to be avoided if possible. Yet physiology without cell structure means less than Einstein without calculus." (George W Corner, "The Hormones in Human Reproduction", 1942) 

🪐On Astronomy (1900-1924)

"A generation ago, men thought the 'perfect science', for so we love to, call astronomy, could advance only by increasing a little the exact precision of observation." (Harold Jacoby, "Practical Talks by an Astronomer", 1902)

"The so-called problems of astronomy are not separate and independent, but are rather the parts of one great problem, that of increasing our knowledge of the universe in its widest extent." (Simon Newcomb, "The Reminiscences of an Astronomer", 1903)

"In astronomy, the law of gravitation is plainly better worth knowing than the position of a particular planet on a particular night, or even on every night throughout a year. There are in the law a splendor and simplicity and sense of mastery which illuminate a mass of otherwise uninteresting details [...]" (Bertrand Russell, "On History,  Independent Review, 1904)

"If we turn to the problems to which the calculus owes its origin, we find that not merely, not even primarily, geometry, but every other branch of mathematical physics - astronomy, mechanics, hydrodynamics, elasticity, gravitation, and later electricity and magnetism - in its fundamental concepts and basal laws contributed to its development and that the new science became the direct product of these influences. [...] The calculus is the greatest aid we have to the appreciation of physical truth in the broadest sense of the word." (William Osgood,"The Calculus in Colleges in Colleges and Technical Schools", Bulletin of the American Mathematical Society, 1907)

"So completely is nature mathematical that some of the more exact natural sciences, in particular astronomy and physics, are in their theoretic phases largely mathematical in character, while other sciences which have hitherto been compelled by the complexity of their phenomena and the inexactitude of their data to remain descriptive and empirical, are developing towards the mathematical ideal, proceeding upon the fundamental assumption that mathematical relations exist between the forces and the phenomena, and that nothing short, of the discovery and formulations of these relations would constitute definitive knowledge of the subject. Progress is measured by the closeness of the approximation to this ideal formulation." (Jacob W A Young, "The Teaching of Mathematics", 1907)

"[Astronomy] is a science of hairbreadths and fractions of a second. It exists only by the rigid enforcement of arduous accuracy and unwearying diligence. Whatever secrets the universe still has in store for man will only be communicated on these terms." (Agnes Mary Clerke, "A Popular History of Astronomy During the Nineteenth Century", 1908) 

"In no realm of nature is the principle of cause and effect more conspicuous than in astronomy; and we fall into the habit of thinking of its laws as not only being unchangeable in our universe, but necessary to the conception of any universe that might have been substituted in its place." (George L Forbes, "History of Astronomy", 1909

"Much of the skill of the true mathematical physicist and of the mathematical astronomer consists in the power of adapting methods and results carried out on an exact mathematical basis to obtain approximations sufficient for the purposes of physical measurements." (Ernst W Hobson, Nature Vol. 84, [address] 1910)

"Much of the skill of the true mathematical physicist and of the mathematical astronomer consists in the power of adapting methods and results carried out on an exact mathematical basis to obtain approximations sufficient for the purposes of physical measurements. It might perhaps be thought that a scheme of Mathematics on a frankly approximative basis would be sufficient for all the practical purposes of application in Physics, Engineering Science, and Astronomy, and no doubt it would be possible to develop, to some extent at least, a species of Mathematics on these lines. Such a system would, however, involve an intolerable awkwardness and prolixity in the statements of results, especially in view of the fact that the degree of approximation necessary for various purposes is very different, and thus that unassigned grades of approximation would have to be provided for. Moreover, the mathematician working on these lines would be cut off from the chief sources of inspiration, the ideals of exactitude and logical rigour, as well as from one of his most indispensable guides to discovery, symmetry, and permanence of mathematical form. The history of the actual movements of mathematical thought through the centuries shows that these ideals are the very life-blood of the science, and warrants the conclusion that a constant striving toward their attainment is an absolutely essential condition of vigorous growth. These ideals have their roots in irresistible impulses and deep-seated needs of the human mind, manifested in its efforts to introduce intelligibility in certain great domains of the world of thought." (Ernest W Hobson, [address] 1910)

"The ordinary mathematical treatment of any applied science substitutes exact axioms for the approximate results of experience, and deduces from these axioms the rigid mathematical conclusions. In applying this method it must not be forgotten that the mathematical developments transcending the limits of exactness of the science are of no practical value. It follows that a large portion of abstract mathematics remains without finding any practical application, the amount of mathematics that can be usefully employed in any science being in proportion to the degree of accuracy attained in the science. Thus, while the astronomer can put to use a wide range of mathematical theory, the chemist is only just beginning to apply the first derivative, i. e. the rate of change at which certain processes are going on; for second derivatives he does not seem to have found any use as yet." (Felix Klein, "Lectures on Mathematics", 1911)

"For thought raised on specialization the most potent objection to the possibility of a universal organizational science is precisely its universality. Is it ever possible that the same laws be applicable to the combination of astronomic worlds and those of biological cells, of living people and the waves of the ether, of scientific ideas and quanta of energy? .. Mathematics provide a resolute and irrefutable answer: yes, it is undoubtedly possible, for such is indeed the case. Two and two homogenous separate elements amount to four such elements, be they astronomic systems or mental images, electrons or workers; numerical structures are indifferent to any element, there is no place here for specificity." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)

"Similarly, many a young man, hearing for the first time of the refraction of stellar light, has thought that doubt was cast on the whole of astronomy, whereas nothing is required but an easily effected and unimportant correction to put everything right again." (Ernst Mach," The Analysis of Sensations: And the Relation of the Physical to the Psychical", 1914)

"In the great sciences, like astronomy and geology, one gets wholes; the imagination has play-room. The cosmic laws launch him upon a shoreless sea. One is blown upon by a breeze from eternity. The same with biology in the light of evolution." (John Burroughs, 

"Under the Apple-Trees", 1916) 

"The development of mathematics is largely a natural, not a purely logical one: mathematicians are continually answering questions suggested by astronomers or physicists; many essential mathematical theories are but the reflex outgrowth from physical puzzles." (George A L Sarton, "The Teaching of the History of Science", The Scientific Monthly, 1918)

"The main object of astronomy, as of all science, is not the collection of facts, but the development, on the basis of collected facts, of satisfactory theories regarding the nature, mutual relations, and probable history and evolution of the objects of study." (Henry N Russell, "Some Problems of Sidereal Astronomy", Proceedings of the National Academy of Sciences Vol. 5 (10), 1919) 

"Astronomy is truly the handmaid of science, and the road to knowledge. For if the heavens declare the glory of God, that science which opens a door to the investigation into the heavens, which declare God's glory, and furnishes the means of illustration of the firmament, where God's handiwork is seen and exhibited, is a Divine Science." (Henry Fitz, "The Layman's Legacy Or Twenty-five Sermons On Important Subjects", 1923)

🪐On Astronomy (1875-1899)

"Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined; it is as limitless as the space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity as the consciousness, the life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud and cell and is forever ready to burst forth into new forms of vegetable and animal existence." (James J Sylvester, The Educational Times", 1877)

"It [astronomy] is, above all others, a science that cultivates the imagination. Yet its theories and distances are based upon rigorous mathematical demonstrations. Thus the study has at once the beauty of poetry and the exactness of Geometry." (Joel D Steele," The Story of the Stars: New Descriptive Astronomy", 1884) 

"[Astronomy] is a science of hairbreadths and fractions of a second. It exists only by the rigid enforcement of arduous accuracy and unwearying diligence. Whatever secrets the universe still has in store for man will only be communicated on these terms." (Agnes M Clerke, "A Popular History of Astronomy during the Nineteenth Century", 1885)

"[Astronomy] seems to have the strongest hold on minds which are not intimately acquainted with its work. The view taken by such minds is not distracted by the technical details which trouble the investigator, and its great outlines are seen through an atmosphere of sentiment, which softens out the algebraic formulae with which the astronomer is concerned into those magnificent conceptions of creation which are the delight of all minds, trained or untrained." (Simon Newcomb, Harper’s Magazine, 1885)

"Although the astronomer has achieved many successes in studying comets, yet these objects still remain outside the surveyed fields of astronomy - now, as in the old days when men spoke of sun and moon, planet and stars, as including all the members of the heavenly host." (Richard A Proctor, "The Twentieth Century, Whence Came the Comets?", Vol. 29 (111), 1886) 

"Between mathematicians and astronomers some misunderstanding exists with respect to the meaning of the term 'convergence'. Mathematicians [...] stipulate that a series is convergent if the sum of the terms tends to a predetermined limit even if the first terms decrease very slowly. Conversely, astronomers are in the habit of saying that a series converges whenever the first twenty terms, for example, decrease rapidly even if the following terms might increase indefinitely. [...] Both rules are legitimate; the first for theoretical research and the second for numerical applications. Both must prevail, but in two entirely separate domains of which the boundaries must be accurately defined. Astronomers do not always know these boundaries accurately but rarely exceed them; the approximation with which they are satisfied usually keeps them far on this side of the boundary. In addition, their instinct guides them and, if they are wrong, a check on the actual observation promptly reveals their error [...]" (Henri Poincaré, "New Methods in Celestial Mechanics" ["Les méthodes nouvelles de la mécanique céleste"], 1892)

"Astronomy is the most accurate of the sciences. All the truths which it teaches are absolutely demonstrated, and cannot be disputed by any mind which gives itself the trouble, or rather the pleasure, to gain information in the study of this admirable science."Camille Flammarion," Popular Astronomy: A General Description of the Heavens" Book I, 1894)

"Astronomy, the oldest and most juvenile of the sciences, may still have some surprises in store. May anti-matter be commended to its care!" (Arthur Schuster, "Letter to the Editor, Potential Matter - A Holiday Dream", Nature Vol. 58 (1503), 1898) 

"Certainly, if a system moves under the action of given forces and its initial conditions have given values in the mathematical sense, its future motion and behavior are exactly known. But, in astronomical problems, the situation is quite different: the constants defining the motion are only physically known, that is with some errors; their sizes get reduced along the progresses of our observing devices, but these errors can never completely vanish." (Jacques Hadamard, "Les surfaces à courbures opposées et leurs lignes géodésiques", Journal de mathématiques pures et appliquées 5e (4), 1898)

🪐On Astronomy (1825-1849)

"All Science is necessarily prophetic, so truly so, that the power of prophecy is the test, the infallible criterion, by which any presumed Science is ascertained to be actually & verily science. The Ptolemaic Astronomy was barely able to prognosticate a lunar eclipse; with Kepler and Newton came Science and Prophecy." (Samuel T Coleridge, "On the Constitution of the Church and State", 1830)

"Contemplated as one grand whole, astronomy is the most beautiful monument of the human mind; the noblest record of its intelligence." (Pierre-Simon Laplace," The Systems of the World", 1830)

"Of all the natural sciences, astronomy is that which presents the longest series of discoveries. The first appearance of the heavens is indeed far removed from that enlarged view, by which we comprehend at the present day, the past and future states of the system of the world." (Pierre-Simon Laplace," The Systems of the World" Vol. 1, 1830)

"The discovery of other systems in the boundless regions of space was the triumph of astronomy - to trace the same system through various transformations - to behold it at successive eras adorned with different hills and valleys, lakes and seas, and peopled with new inhabitants, was the delightful need of geological research." (Charles Lyell," Principles of Geology", 1830)

"The progress of astronomy depends on these three things: the measure of time, that of angles, and the perfection of optical instruments. The two first are nearly as perfect as we could wish; it is therefore to the improvement of the latter that our attention should be directed." (Pierre-Simon Laplace," The Systems of the World" Vol. 1, 1830)

"We may therefore define Astronomy as the science by which we discover the laws of the geometrical and mechanical phenomena presented by the heavenly bodies." (Auguste Comte, “The Positive Philosophy”, 1830)

"Astronomy is, not without reason, regarded, by mankind, as the sublimest of the natural sciences. Its objects, so frequently visible, and therefore familiar, being always remote and inaccessible, do not lose their dignity." (Benjamin Silliman Jr, "Elements of Chemistry", 1830-1831)

"The term ‘science’ should be kept for disciplines such as mathematics or astronomy, whose object is pure knowledge. That every theory of art may contain discrete sciences goes without saying, and need not worry us. But it is also to be noted that no science can exist without some element of art: in mathematics, for instance, the use of arithmetic and algebra is an art. But art may go still further. The reason is that, no matter how obvious and palpable the difference between knowledge and ability may be in the totality of human achievement, it is still extremely difficult to separate them entirely in the individual." (Carl von Clausewitz, "On War", 1832)

"Physical astronomy is the science which compares and identifies the laws of motion observed on earth with the motions that take place in the heavens; and which traces, by an uninterrupted chain of deduction from the great principle that governs the universe, the revolutions and rotations of the planets, and the oscillations of the fluids at their surfaces; and which estimates the changes the system has hitherto undergone, or may hereafter experience - changes which require millions of years for their accomplishment." (Mary Somerville, "The Connection of the Physical Sciences", 1834)

"That the study of mathematics and their application to astronomy are full of interest will be allowed by all who have devoted their time and attention to these pursuits; and they only can estimate the delight of arriving at truth, whether it be in the discovery of a world, or of a new property of numbers." (Mary Somerville, "Mechanism of the Heavens, Preliminary Dissertation", 1831)

"No science is more worthy of cultivation and encouragement than that which, calculating time by the aid of Astronomy, adjusts the results of observations thus obtained to the ordinary use and instruction of man." (Elias Hiam Lindo, "A Jewish Calendar for Sixty-Four Years", 1838)

"In the progressive growth of astronomy, physics or mechanical science was developed, and when this had been, to a certain degree, successfully cultivated, it gave birth to the science of chemistry." (Justus von Liebig, "Familiar Letters on Chemistry", 1844)

"The knowledge whose content makes up astronomy is the gain from more than 2,000 years' work on one of the most abundant objects of human knowledge, in which the foremost minds of all times have summoned up all the resources of genius and diligence." (Carl Friedrich Gauss, [letter to Heinrich C Schumacher] 1845)

"Geology and Astronomy are, in truth, sciences whose discoveries have realized the wildest imaginings of the poet, and whose realities infinitely surpass, in grandeur and sublimity, the most imposing fictions of romance." (Gideon Mantell, "Relics from the Wreck of a Former World", 1847)

🪐On Astronomy (1850-1874)

"He must have studied astronomy to little purpose, who can suppose man to be the only object of his Creator's care, or who does not see in the vast and wonderful apparatus around us provision for other races of animated beings." (John Herschel, "A Treatise on Astronomy", 1851)

"Mathematics is the Queen of the Sciences, and arithmetic the Queen of Mathematics. She frequently condescends to do service for astronomy and other natural sciences, but to her belongs, under all circumstances, the foremost place." (Sartorius von Waltershausen, "Gauss zum Gedächtniss", 1856) 

"The great problems which offer themselves on all hands for solution, problems which the wants of the age force upon us as practically interesting, and with which its intellect feels itself competent to deal, are far more complex in their conditions, and depend on data which to be of use must be accumulated in far greater masses, collected over an infinitely wider field, and worked upon with a greater and more systematized power than has sufficed for the necessities of astronomy. The collecting, arranging, and duly combining these data are operations which, to be carried out to the extent of the requirements of modern science, lie utterly beyond the reach of all private industry, mean, or enterprise. Our demands are not merely for a slight and casual sprinkling to refresh and invigorate an ornamental or luxurious product, but for a copious, steady, and well-directed stream, to call forth from a soil ready to yield it, an ample, healthful, and remunerating harvest." (Sir John F W Herschel, "Essays from the Edinburgh and Quarterly Reviews with Addresses and Other Pieces", 1857)

"The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics." (Whewell, William, "The Philosophy of the Inductive Sciences" , 1858)

"Astronomy is the science of which the human mind may most justly boast. It owes this indisputable pre-eminence to the elevated nature of its object, to the grandeur of its means of investigation, to the certainty, the utility, and the unparalleled magnificence of its results." (François Arago, "Biographies of Distinguished Scientific Men", [Eulogy on Laplace] 1859)

"There are some questions in Astronomy, to which we are attracted rather on account of their peculiarity, as the possible illustration of some unknown principle, than from any direct advantage which their solution would afford to mankind." (James C Maxwell, "On the Stability of the Motion of Saturn's Rings" 1859) 

"On certain occasions, the eyes of the mind can supply the want of the most powerful telescopes, and lead to astronomical discoveries of the highest importance." (François Arago, "Biographies of Distinguished Scientific Men", 1859)

"Like astronomy, which with mathematical certainty has measured the spaces of the heavens, so does modern geology, by taking a retrospective view of the millions of years which have passed, lift the veil which has so long concealed the history of the earth and has given rise to all kinds of religious and mysterious dreams." (Ludwig Büchner, "Force and Matter", 1864) 

"The degree in which each mind habitually substitutes signs for images will be, CETERIS PARIBUS [with other conditions remaining the same], the degree in which it is liable to error. This is not contradicted by the fact that mathematical, astronomical, and physical reasonings may, when complex, be carried on more successfully by the employment of signs; because in these cases the signs themselves accurately represent the abstractness of the relations. Such sciences deal only with relations, and not with objects; hence greater simplification ensures greater accuracy. But no sooner do we quit this sphere of abstractions to enter that of concrete things, than the use of symbols becomes a source of weakness. Vigorous and effective minds habitually deal with concrete images." (George H Lewes, "The Principles of Success in Literature", 1865)

"The periodic law has given to chemistry that prophetic power long regarded as the peculiar dignity of its sister science, astronomy," (Dmitri Mendeleev. "Principles of Chemistry", 1871) 

"Astronomy is one of the sublimest fields of human investigation. The mind that grasps its facts and principles receives something of the enlargement and grandeur belonging to the science itself. It is a quickener of devotion." (Horace Mann, "Thoughts Selected From the Writings of Horace Mann", 1872)

"Astronomy, although the oldest and in many respects the most perfect of the sciences, in many of its questions is still in its infancy." (François Arago, "Scientific Miscellany, The Galaxy" Vol. XIII, 1872) 

🪐On Astronomy (1700-1799)

"Among all the mathematical sciences which have been continually improved, and are daily improving in the world, the first place has, as it were, by general consent, been always given to Astronomy." (John Keill, "An Introduction to the True Astronomy", 1721)

"There is nothing in Nature that does more show the piercing Force of Human Understanding, the sublimity of its Speculations and deep researchers, than true Astronomy. It raises our Minds above our Senses, and even in contradiction to them, shows us the true System of the World: the faculty of Reason by which we have made these great discoveries in the Heavens must needs be derived from Heaven, since no Earthly Principle can attain so great a Perfection." (John Keill, "An Introduction to the True Astronomy", 1721)

"Astronomy is a science which, in all ages and countries flourishing in arts and politeness, has engaged the attention of the curious: it has not only employed the pens of the most eloquent orators and embellished the writings of poets of the most elevated genius; but has also been cultivated by the greatest princes, the ablest statesmen, and the wisest philosophers [...]" (Roger Long, "Astronomy, in Five Books" Vol. I, 1742)

"Astronomy was born of superstition; eloquence of ambition, hatred, falsehood, and flattery; geometry of avarice; physics of an idle curiosity; and even moral philosophy of human pride. Thus the arts and sciences owe their birth to our vices." (Jean-Jacques Rousseau,"A Discourse on the Moral Effects of the Arts and Sciences", 1750)

"For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the mathematics, of which sort are perspective, music, astronomy, cosmography, architecture, engineery, and divers others." (Francis Bacon, 1753) 

"Astronomy is the science which treats of the motions of the heavenly bodies, and all the phenomena arising therefrom." (William Emerson, "A System of Astronomy", cca. 1760)

"Astronomy was the daughter of idleness, geometry the daughter of interest; and if we did but examine poetry, we should certainly find her to be the daughter of love." (Bernard Le Bovier de Fontenelle, "Conversations on the Plurality of Worlds - The First Evening", 1761) 
"Astronomy is perhaps the science whose discoveries owe least to chance, in which human understanding appears in its whole magnitude, and through which man can best learn how small he is." (Georg C Lichtenberg, Notebook C,1772-1773)

"Astronomy is the science of which the human mind may most justly boast. It owes this indisputable pre-eminence to the elevated nature of its object, to the grandeur of its means of investigation, to the certainty, the utility, and the unparalleled magnificence of its results." (François Arago,Annual Report of the Board of Regents of the Smithsonian Institution, - 1874) 

"The direct tendency of (Astronomy) is to dilate the heart with universal benevolence, and to enlarge its views." (David Rittenhouse, [oration], 1775) 

"That which is now called natural philosophy, embracing the whole circle of science, of which astronomy occupies the chief place, is the study of the works of God, and of the power and wisdom of God in his works, and is the true theology." (Thomas Paine, "The Age of Reason", 1793)

"Astronomy, considered in the most general way, is a great problem of mechanics, the arbitrary data of which are the elements of the celestial movements; its solution depends both on the accuracy of observations and on the perfection of analysis." (Pierre-Simon Laplace,"Celestial Mechanics", [preface] 1799)

"To say that physiology is made up of the physics of animals, is to give a very inaccurate idea of it; as well might we say that astronomy is the physiology of the stars." (Xavier Bichat, "Physiological Researches on Life and Death", 1799)

🪐On Astronomy (1600-1699)

"For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated to use with sufficient dexterity, without the aid and intervention of Mathematic: of which sort are Perspective, Music, Astronomy, cosmography, Architecture, Machinery, and some others." (Sir Francis Bacon, "De Augmentis", Bk. 3 [The Advancement of Learning], 1605)

"As in every discipline, so in astronomy, too, the conclusions that we teach the reader are seriously intended, and our discussion is no mere game." (Johannes Kepler, "Astronomia Nova" ["New Astronomy"],1609)

"Provide ship or sails adapted to the heavenly breezes, and there will be some who will not fear even that void. [...] So, for those who will come shortly to attempt this journey, let us establish the astronomy: Galileo, you of Jupiter, I of the moon." (Johannes Kepler

[open letter to Galileo Galilei] 1610)

"To command the professors of astronomy to confute their own observations is to enjoin an impossibility, for it is to command them not to see what they do see, and not to understand what they do understand, and to find what they do not discover." (Galileo Galilei, "Letter to the Grand Duchess Christina", 1615)

"Astronomy has two ends, to save the appearances and to contemplate the true form of the edifice of the world." (Johannes Kepler, "Epitome of Copernican Astronomy" ["Epitome Astronomiae Copernicanae"], 1617)

"It is surely harmful to souls to make it a heresy to believe what is proved. The prohibition of astronomy would be an open contempt of a hundred texts of the Holy Scriptures, which teach us that the glory and the greatness of Almighty God are admirably discerned in all His works, and divinely read in the open book of the heavens." (Galileo Galilei, "Dialogue Concerning the Two Chief World Systems", 1632)

"This [experimentation] is the custom - and properly so - in those sciences where mathematical demonstrations are applied to natural phenomena, as is seen in the case of perspective, astronomy, mechanics, music, and others where the principles, once established by well-chosen experiments, become the foundations of the entire superstructure." (Galileo Galilei, "Dialogues and Mathematical Demonstrations Concerning Two New Sciences", 1638)

"As astronomy is the daughter of idleness, geometry is the daughter of property." (Bernard Le Bovier de Fontenelle, "Conversations on the Plurality of Worlds", 1686)

"My soul is not mercenary enough for geometry, nor is it tender enough for poetry; but I have as much time to spare as astronomy requires." (Bernard Le Bovier de Fontenelle, "Conversations on the Plurality of Worlds", 1686)

🪐On Astronomy (1500-1599)

"As far as hypotheses go, let no one expect anything in the way of certainty from astronomy, since astronomy can offer us nothing certain, lest, if anyone take as true that which has been constructed for another use, he go away from this discipline a bigger fool than when he came to it." (Nicholas Copernicus, "De Revolutionibus Orbium Coelestium" ["On the Revolutions of the Heavenly Spheres"], 1543)

"All this you should know exists in man and realize that the firmament is within man, the firmament with its great movements of bodily planets and stars which result in exaltations, conjunctions, oppositions and the like, as you call these phenomena as you understand them. Everything which astronomical theory has searched deeply and gravely by aspects, astronomical tables and so forth,—this self-same knowledge should be a lesson and teaching to you concerning the bodily firmament. For, none among you who is devoid of astronomical knowledge may be filled with medical knowledge." (Paracelsusm "Astronomia Magna" [aka "Philosophia Sagax"], cca 1537–1538 [published 16th century])

"Medicine rests upon four pillars - philosophy, astronomy, alchemy, and ethics." (Paracelsus, cca. 1540)

"The scorn which I had reason to fear on account of the novelty and unconventionality of my opinion almost induced me to abandon completely the work which I had undertaken.... Astronomy is written for astronomers. To them my work too will seem, unless I am mistaken, to make some contribution." (Nicolaus Copernicus, "De Revolutionibus Orbium Coelestium" ["On the Revolutions of the Heavenly Spheres"], 1543)

"For astronomy is not only pleasant, but also very useful to be known: it cannot be denied that this art unfolds the admirable wisdom of God." (John Calvin, *Commentary on the Book of Genesis", 1554)

"I wanted to become a theologian; for a long time I was unhappy. Now, behold, God is praised by my work even in astronomy." (Johannes Kepler, [letter to Michael Maestlin] 1595) 

🪐On Astronomy (-1499)

"Astronomy compels the soul to look up upward and leads us from this world to another." (Plato, cca. 400 BC)

"In astronomy, as in geometry, we should employ problems, and let the heavens alone if we would approach the subject in the right way and so make the natural gift of reason to be of any real use." (Plato, cca. 400 BC)

"At the Egyptian city of Naucratis there was a famous old god whose name was Theuth; the bird which is called the Ibis was sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters." (Plato, cca. 400 BC)

"From astronomy we find the east, west, south, and north, as well as the theory of the heavens, the equinox, solstice, and courses of the stars. If one has no knowledge of these matters, he will not be able to have any comprehension of the theory of sundials." (Vitruvius, "De architectura" ["The Ten Books On Architecture"], cca. 15BC) 

"Let him [who would be an architect] be educated, skillful with the pencil, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens." (Vitruvius, "De architectura" ["The Ten Books On Architecture"], cca. 15BC) 

"Mathematical science […] has these divisions: arithmetic, music, geometry, astronomy. Arithmetic is the discipline of absolute numerable quantity. Music is the discipline which treats of numbers in their relation to those things which are found in sound." (Cassiodorus, cca. 6th century)

"More evidently still astronomy attains through arithmetic the investigations that pertain to it, not alone because it is later than geometry in origin - for motion naturally comes after rest - nor because the motions of the stars have a perfectly melodious harmony, but also because risings, settings, progressions, retrogressions, increases, and all sorts of phases are governed by numerical cycles and quantities. So then we have rightly undertaken first the systematic treatment of this, as the science naturally prior, more honorable, and more venerable, and, as it were, mother and nurse of the rest; and here we will take our start for the sake of clearness." (Nicomachus of Gerasa," Arithmetic", cca. 100 AD)

"Two other sciences in the same way will accurately treat of 'size': geometry, the part that abides and is at rest, [and] astronomy, that which moves and revolves." (Nicomachus of Gerasa," Arithmetic", cca. 100 AD)

 "Astronomy itself is a venerable science, and might become a stepping stone to something more august, a science which I think is a convenient passage to mystical theology, for the happy body of heaven has matter underneath it, and its motion has seemed to the leaders in philosophy to be an imitation of mind. It proceeds to its demonstrations in no uncertain way, for it uses as its servants geometry and arithmetic, which it would not be improper to call a fixed standard of truth." (Synesius, "On an Astrolabe", cca. 5th century)

William Herschel - Collected Quotes

"We may strongly suspect that there is not, in strictness of speaking, one fixed star in the heavens, and reasons which I shall adduce will render this so obvious that there can hardly remain a doubt of the general motion of all the starry systems, and, consequently, of the solar one among the rest." (William Herschel, "On the Proper Motion of the Sun and Solar System", Philosophical Transactions of the Royal Society of London Vol. 73, 1783)

"If we indulge a fanciful imagination and build worlds of our own, we must not wonder at our going wide from the path of truth and nature; but these will vanish like the Cartesian vortices, that soon gave way when better theories were offered." (William Herschel, "The Construction of the Heavens", Philosophical Transactions of the Royal Society of London Vol. LXXV, 1785) 

"The subject of the Construction of the Heavens is of so extensive and important a nature, that we cannot exert too much attention in our endeavors to throw all possible light upon it." (William Herschel, "The Construction of the Heavens", Philosophical Transactions of the Royal Society of London Vol. LXXV, 1785) 

"The phenomena of nature, especially those that fall under the inspection of the astronomer, are to be viewed, not only with the usual attention to facts as they occur, but with the eye of reason and experience." (William Herschel, "An Account of Three Volcanoes in the Moon", Philosophical Transactions of the Royal Society of London Vol. 67, 1787)

"It is sometimes of great use in natural philosophy to doubt of things that are commonly taken for granted; especially as the means of resolving any doubt, when once it is entertained, are often within our reach." (William Herschel, "Investigation of the Powers the Prismatic Colours to Heat and Illuminate Objects", Philosophical Transactions of the Royal Society of London Vol. 90, 1800)

"Familiar objects and events are far from presenting themselves to our senses in that aspect and with those connections under which science requires them to be viewed, and which constitute their rational explanation." (William Herschel, "Outlines of Astronomy", 1849)

"I have looked farther into space than ever human being did before me. I have observed stars of which the light, it can be proved, must take two millions of years to reach this earth!" (William Herschel)

"There are two kinds of happiness or contentment for which we mortals are adapted; the first we experience in thinking and the other in feeling. The first is the purest and most unmixed. Let a man once know what sort of a being he is; how great the being which brought him into existence, how utterly transitory is everything in the material world, and let him realize this without passion in a quiet philosophical temper, and I maintain that then he is happy; as happy indeed as it is possible for him to be." (William Herschel [letter to Jacob Herschel)

"When an object is once discovered by a superior power, an inferior one will suffice to see if afterwards." (William Herschel)

Edward Everett - Collected Quotes

"Truth travels down from the heights of philosophy to the humblest walks of life, and up from the simplest perceptions of an awakened intellect to the discoveries which almost change the face of the world. At every stage of its progress it is genial, luminous, creative." (Edward Everett, [address] 1835)

"It usually happens in scientific progress, that when a great fact is at length discovered, it approves itself at once to all competent judges. It furnishes a solution to so many problems, and harmonizes with so many other facts, - that all the other data as it were crystallize at once about it." (Edward Everett, "The Uses of Astronomy", 1856)

"The great object of all knowledge is to enlarge and purify the soul, to fill the mind with noble contemplations, to furnish a refined pleasure, and to lead our feeble reason from the works of nature up to its great Author and Sustainer." (Edward Everett, "The Uses of Astronomy", 1856)

"Beyond the little arithmetic required for the ordinary economies of life, the mass of college-bred men, unless engaged in the business of instruction or in pursuits which directly involve their application, from the time they leave their places of education, of whatever name, give up the Mathematics as a useless and hopeless abstraction." (Edward Everett, [address] 1857)

"The Mathematics, like language, (of which indeed they may be considered a species,) comprehending under that designation the whole science of number, space, form, time, and motion, as far as it can be expressed in abstract formulas, are evidently not only one of the most useful, but one of the grandest of studies." (Edward Everett, [address] 1857)

"The great truths with which it [mathematics] deals, are clothed with austere grandeur, far above all purposes of immediate convenience or profit. It is in them that our limited understandings approach nearest to the conception of that   absolute and infinite, towards which in most other things they aspire in vain. In the pure mathematics we contemplate absolute truths, which existed in the divine mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven." (Edward Everett, "Orations and Speeches" Vol. 8, 1870)

"[Arithmetic] is another of the great master-keys of life. With it the astronomer opens the depths of the heavens; the engineer, the gates of the mountains; the navigator, the pathways of the deep. The skillful arrangement, the rapid handling of figures, is a perfect magician's wand." (Edward Everett)

Johannes Kepler - Collected Quotes

"I undertake to prove that God, in creating the Universe and regulating the order of the cosmos, had in view the five regular bodies of geometry known since the days of Pythagoras and Plato, and that he has fixed according to those dimensions, the number of heavens, their proportions and the relations of their movements." (Johannes Kepler, "The Mystery of the Cosmos", 1596)

"Geometry existed before the creation. It is co-eternal with the mind of God. It is God himself. Where there is matter there is geometry. [...] It is absolutely necessary that the work of such a creator be of the greatest beauty [...]" (Johannes Kepler, "The Mystery of the Cosmos", 1596) 

"It is very difficult to write mathematics books today. If one does not take pains with the fine points of theorems, explanations, proofs and corollaries, then it won’t be a mathematics book; but if one does these things, then the reading of it will be extremely boring." (Johannes Kepler, "Astronomia Nova", 1609)

"Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God." (Johannes Kepler, "Conversation with the Sidereal Messenger" ["Dissertatio cum Nuncio Sidereo"], [open letter to Galileo Galilei] 1610)

"That faculty which perceives and recognizes the noble proportions in what is given to the senses, and in other things situated outside itself, must be ascribed to the soul. It lies very close to the faculty which supplies formal schemata to the senses, or deeper still, and thus adjacent to the purely vital power of the soul, which does not think discursively […] Now it might be asked how this faculty of the soul, which does not engage in conceptual thinking, and can therefore have no proper knowledge of harmonic relations, should be capable of recognizing what is given in the outside world. For to recognize is to compare the sense perception outside with the original pictures inside, and to judge that it conforms to them." (Johannes Kepler, "Harmonices Mundi" ["Harmony of the World", 1619)

"A mind accustomed to mathematical deduction, when confronted with the faulty foundations resists a long, long time, like an obstinate mule, until compelled by beating and curses to put its foot into that dirty puddle." (Johannes Kepler)

"As in every discipline, so in astronomy, too, the conclusions that we teach the reader are seriously intended, and our discussion is no mere game." (Johannes Kepler)

"It is a right, yes a duty, to search in cautious manner for the numbers, sizes, and weights, the norms for everything [God] has created. For He himself has let man take part in the knowledge of these things […] For these secrets are not of the kind whose research should be forbidden; rather they are set before our eyes like a mirror so that by examining them we observe to some extent the goodness and wisdom of the Creator." (Johannes Kepler)

"[...] it is the most widely accepted axiom in the natural science that Nature makes use of the fewest possible means" (Johannes Kepler)

"The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics." (Johannes Kepler)

"What else can the human mind hold besides numbers and magnitudes? These alone we apprehend correctly, and if piety permits to say so, our comprehension is in this case of the same kind as God’s, at least insofar as we are able to understand it in this mortal life." (Johannes Kepler)

"We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way." (Johannes Kepler)

Eugene P Wigner - Collected Quotes

"The regularities in the phenomena which physical science endeavors to uncover are called the laws of nature. The name is actually very appropriate. Just as legal laws regulate actions and behavior under certain conditions but do not try to regulate all action and behavior, the laws of physics also determine the behavior of its objects of interest only under certain well-defined conditions but leave much freedom otherwise." (Eugene P Wigner, "Events, Laws of Nature, and Invariance principles", [Nobel lecture] 1914)

"The simplicities of natural laws arise through the complexities of the languages we use for their expression." (Eugene P Wigner, 1959)

"Nothing in our experience suggests the introduction of [complex numbers]. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications in Pure and Applied Mathematics 13 (1), 1960)

"Somebody once said that philosophy is the misuse a terminology which was invented just for this purpose. In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose."  (Eugene Wigner, "The of Mathematics in the Natural Sciences," Communications on Pure Applied Mathematics 13 (2), 1960)

"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)

"The mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. This shows that the mathematical language has more to commend it than being the only language which we can speak; it shows that it is, in a very real sense, the correct language." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications in Pure and Applied Mathematics 13 (1), 1960)

"[…] mathematics is the science of skillful operations with concepts and rules invented just for this purpose." (Eugene P Wigner, 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)

"The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications in Pure and Applied Mathematics 13 (1), 1960)

"Physics does not endeavour to explain nature. In fact, the great success of physics is due to a restriction of its objectives: it only endeavours to explain the regularities in the behavior of objects." (Eugene P Wigner, "Events, Laws of Nature, and Invariance Principles", [Nobel Lecture], 1963)

"We have ceased to expect from physics an explanation of all events, even of the gross structure of the universe, and we aim only at the discovery of the laws of nature, that is the regularities, of the events." (Eugene P Wigner, "Events, Laws of Nature, and Invariance Principles", [Nobel Lecture], 1963)

"We know many laws of nature and we hope and expect to discover more. Nobody can foresee the next such law that will be discovered. Nevertheless, there is a structure in laws of nature which we call the laws of invariance. This structure is so far-reaching in some cases that laws of nature were guessed on the basis of the postulate that they fit into the invariance structure." (Eugene P Wigner, "The Role of Invariance Principles in Natural Philosophy", 1963)

“Physics can teach us only what the laws of nature are today. It is only Astronomy that can teach us what the initial conditions for these laws are.” (Eugene P Wigner, “The Case for Astronomy”, Proceedings of the American Philosophical Society Vol. 8 (1), 1964)

"It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature." (Eugene P Wigner, "Symmetries and Reflections: Scientific Essays", 1967)

"I believe that the present laws of physics are at least incomplete without a translation into terms of mental phenomena." (Eugene P Wigner, "Physics and the Explanation of Life", 1970)

"In science, it is not speed that is the most important. It is the dedication, the commitment, the interest and the will to know something and to understand it - these are the things that come first." (Eugene P Wigner, [interview by István Kardos] 1978)

"Part of the art and skill of the engineer and of the experimental physicist is to create conditions in which certain events are sure to occur." (Eugene P Wigner, "Symmetries and Reflections", 1979)

"Physics is becoming so unbelievably complex that it is taking longer and longer to train a physicist. It is taking so long, in fact, to train a physicist to the place where he understands the nature of physical problems that he is already too old to solve them." (Eugene P Wigner) 

"The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it." (Eugene P Wigner) 

 

"With thermodynamics, one can calculate almost everything crudely; with kinetic theory, one can calculate fewer things, but more accurately; and with statistical mechanics, one can calculate almost nothing exactly." (Eugene P Wigner)