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)

On Deduction (1800-1849)

"One very reprehensible mode of theory-making consists, after honest deductions from a few facts have been made, in torturing other facts to suit the end proposed, in omitting some, and in making use of any authority that may lend assistance to the object desired; while all those which militate against it are carefully put on one side or doubted." (Henry De la Beche, "Sections and Views, Illustrative of Geological Phaenomena", 1830)

"Facts [...] are not truths; they are not conclusions; they are not even premises, but in the nature and parts of premises. The truth depends on, and is only arrived at, by a legitimate deduction from all the facts which are truly material." (Samuel T Coleridge, "The Table Talk and Omniana of Samuel Taylor Coleridge", 1831)

"The deduction of effect from cause is often blocked by some insuperable extrinsic obstacle: the true causes may be quite unknown." (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)

"Every stage of science has its train of practical applications and systematic inferences, arising both from the demands of convenience and curiosity, and from the pleasure which, as we have already said, ingenious and active-minded men feel in exercising the process of deduction." (William Whewell, "The Philosophy of the Inductive Sciences Founded Upon Their History", 1840)

"These sciences, Geometry, Theoretical Arithmetic and Algebra, have no principles besides definitions and axioms, and no process of proof but deduction; this process, however, assuming a most remarkable character; and exhibiting a combination of simplicity and complexity, of rigour and generality, quite unparalleled in other subjects." (William Whewell, "The Philosophy of the Inductive Sciences", 1840)

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

"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)

"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)