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Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That�s what will lend meaning to the creed our fathers once declared.”
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Home > Category Index for Science Quotations > Category Index F > Category: Foundation

Foundation Quotes (177 quotes)


“Facts, facts, facts,” cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science.
From the first chapter of an unfinished book, The Thought: A Logical Inquiry (1918), collected in Arthur Sullivan (ed.), Logicism and the Philosophy of Language: Selections from Frege and Russell (2003), 215.
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“Normal science” means research firmly based upon one or more past scientific achievements, achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice.
The Structure of Scientific Revolutions (1962), 10.
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[Euclid's Elements] has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her. And hence she was called, in the dialect of the Pythagoreans, ‘the purifier of the reasonable soul.’
From a lecture delivered at the Royal Institution (Mar 1873), collected postumously in W.K. Clifford, edited by Leslie Stephen and Frederick Pollock, Lectures and Essays, (1879), Vol. 1, 296.
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[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error. (c.1267)
Translation by Robert Burke, Opus Majus of Roger Bacon (1928), vol 1, 124. In Fred R. Shapiro, The Yale Book of Quotations (2006), 39.
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[Philosopher Lao-tse] is not dogmatic, and he does not go in for big, universal ideas. For instance, I like what he says about failure and success, “Failure is the foundation of success and the means by which it is achieved. Success is the lurking place of failure; but who can tell when the turning point will come?”
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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[The body of law] has taxed the deliberative spirit of ages. The great minds of the earth have done it homage. It was the fruit of experience. Under it men prospered, all the arts flourished, and society stood firm. Every right and duty could be understood because the rules regulating each had their foundation in reason, in the nature and fitness of things; were adapted to the wants of our race, were addressed to the mind and to the heart; were like so many scraps of logic articulate with demonstration. Legislation, it is true occasionally lent its aid, but not in the pride of opinion, not by devising schemes inexpedient and untried, but in a deferential spirit, as a subordinate co-worker.
From biographical preface by T. Bigelow to Austin Abbott (ed.), Official Report of the Trial of Henry Ward Beecher (1875), Vol. 1, xii.
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Engineering, too, owes its most useful materials to the achievements of chemists in identifying, separating, and transforming materials: structural steel for the framework of bridges and buildings, portland cement for roadways and aqueducts, pure copper for the electrical industries, aluminum alloys for automobiles and airplanes, porcelain for spark plugs and electrical insulators. The triumphs of engineering skill rest on a chemical foundation.
In Fundamental Chemistry, and Elementary Textbook for College Classes (1936), 8.
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Primo enim paranda est Historia Naturalis et Experimentalis, suffidens et bona; quod fundamentum rei est: neque enim fingendum, aut excogitandum, sed inveniendum, quid natura faciat aut ferat.
For first of all we must prepare a Natural and Experimental History, sufficient and good; and this is the foundation of all; for we are not to imagine or suppose, but to discover, what nature does or may be made to do.
In Novum Organum, Book 2, Aphorism 10. As translated in Francis Bacon and James Spedding with ‎Robert Leslie Ellis (eds.), 'The New Organon', The Works of Francis Bacon: Translations of the Philosophical Works (1858), Vol. 4, 127. Also seen in epigraphs as a shorter quote, “Non fingendum, aut excogitandum, sed inveniendum, quid natura faciat aut ferat,” which can also be translated as “We have not to imagine or to think out, but to find out what Nature does or produces.”
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A fateful process is set in motion when the individual is released “to the freedom of his own impotence” and left to justify his existence by his own efforts. The autonomous individual, striving to realize himself and prove his worth, has created all that is great in literature, art, music, science and technology. The autonomous individual, also, when he can neither realize himself nor justify his existence by his own efforts, is a breeding call of frustration, and the seed of the convulsions which shake our world to its foundations.
In The Passionate State of Mind (1955), 18.
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A human being is part of the whole, called by us “Universe”; a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest—a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. Nobody is able to achieve this completely but the striving for such achievement is, in itself, a part of the liberation and a foundation for inner security.
In Letter (4 Mar 1950), replying to a grieving father over the loss of a young son. In Dear Professor Einstein: Albert Einstein’s Letters to and from Children (2002), 184.
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A mind is accustomed to mathematical deduction, when confronted with the faulty foundations of astrology, resists a long, long time, like an obstinate mule, until compelled by beating and curses to put its foot into that dirty puddle.
As quoted in Arthur Koestler, The Sleep Walkers: A History of Man’s Changing Vision of the Universe (1959), 243, citing De Stella Nova in Pede Serpentarii (1606).
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A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value. It seems to me that what is important is the force of this superpersonal content and the depth of the conviction concerning its overpowering meaningfulness, regardless of whether any attempt is made to unite this content with a divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly, a religious person is devout in the sense that he has no doubt of the significance and loftiness of those superpersonal objects and goals which neither require nor are capable of rational foundation. They exist with the same necessity and matter-of-factness as he himself. In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals and constantly to strengthen and extend their effect. If one conceives of religion and science according to these definitions then a conflict between them appears impossible. For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary.
…...
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A scientific writer can scarcely encounter anything more undesirable than, after completing a work, to have one of the foundations shaken. I became aware of this situation through a letter from Mr. Bertrand Russell as the printing of this volume neared completion.
In Epilog, Grundgestze der Arithmetic (1903), Vol. 2, 253. Russell wrote in 1901, just as Frege was about to publish Volume 2 of his last major work. English translation by Webmaster using Google translate and online dictionaries, from the original German: “Einem wissenschaftlichen Schriftsteller kann kaum etwas Unerwünschteres begegnen, als dass ihm nach Vollendung einer Arbeit eine der Grundlagen seines Baues erschüttert wird. In diese Lage wurde ich durch einen Brief des Herrn Bertrand Russell versetzt, als der Druck dieses Bandes sich seinem Ende näherte.” The translation in John E. Hopcroft, 'Turing Machines', Scientific American (May 1984), 250, No. 5, 95, gives: “A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.”
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A soil adapted to the growth of plants, is necessarily prepared and carefully preserved; and, in the necessary waste of land which is inhabited, the foundation is laid for future continents, in order to support the system of the living world.
In 'Concerning and System of the Earth, its Duration and Stability', a Dissertation presented to the Royal Society of Edinburgh (Mar-Apr 1785). The surviving Abstract is excerpted in Frank H. T. Rhodes, Richard O. Stone and Bruce D. Malamud (eds.), Language of the Earth: A Literary Anthology (2002, 2nd. ed. 2008), 110.
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Aeroplanes are not designed by science, but by art in spite of some pretence and humbug to the contrary. I do not mean to suggest that engineering can do without science, on the contrary, it stands on scientific foundations, but there is a big gap between scientific research and the engineering product which has to be bridged by the art of the engineer.
In John D. North, 'The Case for Metal Construction', The Journal of the Royal Aeronautical Society, (Jan 1923), 27, 11.
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After … the general experimental knowledge has been acquired, accompanied with just a sufficient amount of theory to connect it together…, it becomes possible to consider the theory by itself, as theory. The experimental facts then go out of sight, in a great measure, not because they are unimportant, but because … they are fundamental, and the foundations are always hidden from view in well-constructed buildings.
In Electromagnetic Theory (1892), Vol. 2, 1.
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Agriculture is the backbone of the livelihood security system of nearly 700 million people in the country and we need to build our food security on the foundation of home grown food.
In 'Interview: We need to build our food security: MS Swaminathan', The Economic Times (11 Feb 2010), on economictimes.indiatimes.com website.
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Agriculture is the foundation of manufactures, since the productions of nature are the materials of art.
In The History of the Decline and Fall of the Roman Empire (1841), Vol. 1, 33.
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All the human culture, all the results of art, science and technology that we see before us today, are almost exclusively the creative product of the Aryan. This very fact admits of the not unfounded inference that he alone was the founder of all higher humanity, therefore representing the prototype of all that we understand by the word 'man.' He is the Prometheus of mankind from whose shining brow the divine spark of genius has sprung at all times, forever kindling anew that fire of knowledge which illuminated the night of silent mysteries and thus caused man to climb the path to mastery over the other beings of the earth ... It was he who laid the foundations and erected the walls of every great structure in human culture.
Mein Kampf (1925-26), American Edition (1943), 290. In William Lawrence Shirer, The Rise and Fall of the Third Reich (1990), 86-87.
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All these delusions of Divination have their root and foundation from Astrology. For whether the lineaments of the body, countenance, or hand be inspected, whether dream or vision be seen, whether marking of entrails or mad inspiration be consulted, there must be a Celestial Figure first erected, by the means of whole indications, together with the conjectures of Signs and Similitudes, they endeavour to find out the truth of what is desired.
In The Vanity of the Arts and Sciences (1530), translation (1676), 108.
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Among the studies to which the [Rockefeller] Foundation is giving support is a series in a relatively new field, which may be called molecular biology, in which delicate modern techniques are being used to investigate ever more minute details of certain life processes.
In 'Molecular Biology', Annual Report of the Rockefeller Foundation (1938), 203-4. Reprinted in a letter to Science (6 Nov 1970), 170, 582.
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An old foundation is worthy of all respect, but it must not take from us the right to build afresh wherever we will.
In The Maxims and Reflections of Goethe (1906), 188.
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And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art…
From 'Preface' in Course in the Art of Measurement with Compass and Ruler (1525). As quoted in Stacey Bieler, Albrecht Durer: Artist in the Midst of Two Storms (2017), 189.
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Any one who has studied the history of science knows that almost every great step therein has been made by the “anticipation of Nature,” that is, by the invention of hypotheses, which, though verifiable, often had very little foundation to start with; and, not unfrequently, in spite of a long career of usefulness, turned out to be wholly erroneous in the long run.
In 'The Progress of Science 1837-1887' (1887), Collected Essays (1901), Vol. 1, 62.
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As regards religion, on the other hand, one is generally agreed that it deals with goals and evaluations and, in general, with the emotional foundation of human thinking and acting, as far as these are not predetermined by the inalterable hereditary disposition of the human species. Religion is concerned with man’s attitude toward nature at large, with the establishing of ideals for the individual and communal life, and with mutual human relationship. These ideals religion attempts to attain by exerting an educational influence on tradition and through the development and promulgation of certain easily accessible thoughts and narratives (epics and myths) which are apt to influence evaluation and action along the lines of the accepted ideals.
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As to what Simplicius said last, that to contend whether the parts of the Sun, Moon, or other celestial body, separated from their whole, should naturally return to it, is a vanity, for that the case is impossible, it being clear by the demonstrations of Aristotle that the celestial bodies are impassible, impenetrable, unpartable, etc., I answer that none of the conditions whereby Aristotle distinguishes the celestial bodies from the elementary has any foundation other than what he deduces from the diversity of their natural motions; so that, if it is denied that the circular motion is peculiar to celestial bodies, and affirmed instead that it is agreeable to all naturally moveable bodies, one is led by necessary confidence to say either that the attributes of generated or ungenerated, alterable or unalterable, partable or unpartable, etc., equally and commonly apply to all bodies, as well to the celestial as to the elementary, or that Aristotle has badly and erroneously deduced those from the circular motion which he has assigned to celestial bodies.
Dialogue on the Great World Systems (1632). Revised and Annotated by Giorgio De Santillana (1953), 45.
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At that point, my sense of dissatisfaction was so strong that I firmly resolved to start thinking until I should find a purely arithmetic and absolutely rigorous foundation of the principles of infinitesimal analysis. … I achieved this goal on November 24th, 1858, … but I could not really decide upon a proper publication, because, firstly, the subject is not easy to present, and, secondly, the material is not very fruitful.
(1872). As quoted in Ernst Hairer and Gerhard Wanner, Analysis by Its History (2008), 177.
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Be discontented. Be dissatisfied. Be as restless as the billows on the boundless sea. Let your discontent break mountain-high against the wall of prejudice and swamp it to the very foundation.
John Hope
Speech to a Black debating society in Nashville, Tennessee (1896).Excerpted in Ridgely Torrence, The Story of John Hope (1948), 114.
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Botany is based on fixed genera.
Philosophia Botanica (1751), aphorism 209. Trans. Frans A. Stafleu, Linnaeus and the Linnaeans: The Spreading of their Ideas in Systematic Botany, 1735-1789 (1971), 64.
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Both religion and natural science require a belief in God for their activities, to the former He is the starting point, and to the latter the goal of every thought process. To the former He is the foundation, to the latter, the crown of the edifice of every generalized world view.
Lecture, 'Religion and Natural Science' (1937) In Max Planck and Frank Gaynor (trans.), Scientific Autobiography and Other Papers (1949), 184.
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But shall gravity be therefore called an occult cause, and thrown out of philosophy, because the cause of gravity is occult and not yet discovered? Those who affirm this, should be careful not to fall into an absurdity that may overturn the foundations of all philosophy. For causes usually proceed in a continued chain from those that are more compounded to those that are more simple; when we are arrived at the most simple cause we can go no farther ... These most simple causes will you then call occult and reject them? Then you must reject those that immediately depend on them.
Mathematical Principles (1729), 27.
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But when we face the great questions about gravitation Does it require time? Is it polar to the 'outside of the universe' or to anything? Has it any reference to electricity? or does it stand on the very foundation of matter–mass or inertia? then we feel the need of tests, whether they be comets or nebulae or laboratory experiments or bold questions as to the truth of received opinions.
Letter to Michael Faraday, 9 Nov 1857. In P. M. Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1990), Vol. 1, 1846-1862, 551-2.
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Cell genetics led us to investigate cell mechanics. Cell mechanics now compels us to infer the structures underlying it. In seeking the mechanism of heredity and variation we are thus discovering the molecular basis of growth and reproduction. The theory of the cell revealed the unity of living processes; the study of the cell is beginning to reveal their physical foundations.
Recent Advances in Cytology (1937), 562.
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Chemistry is like a majestic skyscraper. The concrete secure foundation of chemistry consists of countless experimentally observed facts. The theories, principles and laws developed from these observations are like an elevator which runs from the bottom to the top of the edifice.
Ernest R. Toon and George L. Ellis (eds.), Foundations of Chemistry (1968), 1.
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Clarity about the aims and problems of socialism is of greatest significance in our age of transition. Since, under present circumstances, free and unhindered discussion of these problems has come under a powerful taboo, I consider the foundation of this magazine to be an important public service.
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Copernicus, the most learned man whom we are able to name other than Atlas and Ptolemy, even though he taught in a most learned manner the demonstrations and causes of motion based on observation, nevertheless fled from the job of constructing tables, so that if anyone computes from his tables, the computation is not even in agreement with his observations on which the foundation of the work rests. Therefore first I have compared the observations of Copernicus with those of Ptolemy and others as to which are the most accurate, but besides the bare observations, I have taken from Copernicus nothing other than traces of demonstrations. As for the tables of mean motion, and of prosthaphaereses and all the rest, I have constructed these anew, following absolutely no other reasoning than that which I have judged to be of maximum harmony.
Dedication to the Duke of Prussia, Prutenicae Tabulae (1551), 1585 edition, as quoted in Owen Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler (1993), 227.
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Could the waters of the Atlantic be drawn off so as to expose to view this great seagash which separates continents, and extends from the Arctic to the Antarctic, it would present a scene the most rugged, grand and imposing. The very ribs of the solid earth, with the foundations of the sea, would be brought to light.
(1860)
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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During the half-century that has elapsed since the enunciation of the cell-theory by Schleiden and Schwann, in 1838-39, it has became ever more clearly apparent that the key to all ultimate biological problems must, in the last analysis, be sought in the cell. It was the cell-theory that first brought the structure of plants and animals under one point of view by revealing their common plan of organization. It was through the cell-theory that Kolliker and Remak opened the way to an understanding of the nature of embryological development, and the law of genetic continuity lying at the basis of inheritance. It was the cell-­theory again which, in the hands of Virchaw and Max Schultze, inaugurated a new era in the history of physiology and pathology, by showing that all the various functions of the body, in health and in disease, are but the outward expression of cell­-activities. And at a still later day it was through the cell-theory that Hertwig, Fol, Van Beneden, and Strasburger solved the long-standing riddle of the fertilization of the egg, and the mechanism of hereditary transmission. No other biological generalization, save only the theory of organic evolution, has brought so many apparently diverse phenomena under a common point of view or has accomplished more far the unification of knowledge. The cell-theory must therefore be placed beside the evolution-theory as one of the foundation stones of modern biology.
In The Cell in Development and Inheritance (1896), 1.
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Energy conservation is the foundation of energy independence.
Tom Allen
Title of press release (22 Sep 2005), 'Energy Conservation Is the Foundation of Energy Independence' on co-sponsoring the Energy Efficiency Cornerstone Act.
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Even more difficult to explain, than the breaking-up of a single mass into fragments, and the drifting apart of these blocks to form the foundations of the present-day continents, is the explanation of the original production of the single mass, or PANGAEA, by the concentration of the former holosphere of granitic sial into a hemisphere of compressed and crushed gneisses and schists. Creep and the effects of compression, due to shrinking or other causes, have been appealed to but this is hardly a satisfactory explanation. The earth could no more shrug itself out of its outer rock-shell unaided, than an animal could shrug itself out of its hide, or a man wriggle out of his skin, or even out of his closely buttoned coat, without assistance either of his own hands or those of others.
The Rhythm of Ages (1940), 9-10.
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Facts are certainly the solid and true foundation of all sectors of nature study ... Reasoning must never find itself contradicting definite facts; but reasoning must allow us to distinguish, among facts that have been reported, those that we can fully believe, those that are questionable, and those that are false. It will not allow us to lend faith to those that are directly contrary to others whose certainty is known to us; it will not allow us to accept as true those that fly in the face of unquestionable principles.
Memoires pour Servir a l'Histoire des Insectes (1736), Vol. 2, xxxiv. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 165.
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Facts, and facts alone, are the foundation of science... When one devotes oneself to experimental research it is in order to augment the sum of known facts, or to discover their mutual relations.
Precis elementaire de Physiologie (1816), ii. Trans. J. M. D. Olmsted, François Magendie: Pioneer in Experimental Physiology and Scientific Medicine in XIX Century France (1944), 62.
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Few will deny that even in the first scientific instruction in mathematics the most rigorous method is to be given preference over all others. Especially will every teacher prefer a consistent proof to one which is based on fallacies or proceeds in a vicious circle, indeed it will be morally impossible for the teacher to present a proof of the latter kind consciously and thus in a sense deceive his pupils. Notwithstanding these objectionable so-called proofs, so far as the foundation and the development of the system is concerned, predominate in our textbooks to the present time. Perhaps it will be answered, that rigorous proof is found too difficult for the pupil’s power of comprehension. Should this be anywhere the case,—which would only indicate some defect in the plan or treatment of the whole,—the only remedy would be to merely state the theorem in a historic way, and forego a proof with the frank confession that no proof has been found which could be comprehended by the pupil; a remedy which is ever doubtful and should only be applied in the case of extreme necessity. But this remedy is to be preferred to a proof which is no proof, and is therefore either wholly unintelligible to the pupil, or deceives him with an appearance of knowledge which opens the door to all superficiality and lack of scientific method.
In 'Stücke aus dem Lehrbuche der Arithmetik', Werke, Bd. 2 (1904), 296.
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For, Mathematical Demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick, are the only Truths, that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth, according as their Subjects are more or less capable of Mathematical Demonstration.
Inaugural lecture of Christopher Wren in his chair of astronomy at Gresham College (1657). From Parentelia (1741, 1951), 200-201.
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Formal thought, consciously recognized as such, is the means of all exact knowledge; and a correct understanding of the main formal sciences, Logic and Mathematics, is the proper and only safe foundation for a scientific education.
In Number and its Algebra (1896), 134.
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Fortunately I experienced Max Wertheimer's teaching in Berlin and collaborated for over a decade with Wolfgang Köhler. I need not emphasize my debts to these outstanding personalities. The fundamental ideas of Gestalt theory are the foundation of all our investigations in the field of the will, of affection, and of the personality.
From A Dynamic Theory of Personality. Selected papers (1935), 240.
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God has not revealed all things to man and has entrusted us with but a fragment of His mighty work. But He who directs all things, who has established and laid the foundation of the world, who has clothed Himself with Creation, He is greater and better than that which He has wrought. Hidden from our eyes, He can only be reached by the spirit.
From Quaestiones Naturales as translated in Charles Singer, From Magic to Science (1958), 57.
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Had there not been in zoology men who devoted themselves to such seemingly unimportant studies as the differentiation of the species of mosquitoes, we should not have been able to place on a firm foundation the aetiology of malaria and yellow fever.
From address, 'A Medical Retrospect'. Published in Yale Medical Journal (Oct 1910), 17, No. 2, 65.
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He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer. I believe that it is impossible to do this, and to study geometry as it admits of being studied and am conscious it can be taught, without finding the reason invigorated, the invention quickened, the sentiment of the orderly and beautiful awakened and enhanced, and reverence for truth, the foundation of all integrity of character, converted into a fixed principle of the mental and moral constitution, according to the old and expressive adage “abeunt studia in mores”.
In 'A Probationary Lecture on Geometry, in Collected Mathematical Papers (1908), Vol. 2, 9. [The Latin phrase, “abeunt studia in mores” translates as “studies pass on into character”. —Webmaster]
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I can assure you, reader, that in a very few hours, even during the first day, you will learn more natural philosophy about things contained in this book, than you could learn in fifty years by reading the theories and opinions of the ancient philosophers. Enemies of science will scoff at the astrologers: saying, where is the ladder on which they have climbed to heaven, to know the foundation of the stars? But in this respect I am exempt from such scoffing; for in proving my written reason, I satisfy sight, hearing, and touch: for this reason, defamers will have no power over me: as you will see when you come to see me in my little Academy.
The Admirable Discourses (1580), trans. Aurele La Rocque (1957), 27.
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I do not … reject the use of statistics in medicine, but I condemn not trying to get beyond them and believing in statistics as the foundation of medical science. … Statistics … apply only to cases in which the cause of the facts observed is still [uncertain or] indeterminate. … There will always be some indeterminism … in all the sciences, and more in medicine than in any other. But man’s intellectual conquest consists in lessening and driving back indeterminism in proportion as he gains ground for determinism by the help of the experimental method..
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 138-140.
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I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.
The Anatomy of Science (1926), 6-7.
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I hold every man a debtor to his profession; from the which as men of course do seek to receive countenance and profit, so ought they of duty to endeavour themselves, by way of amends, to be a help and ornament thereunto. This is performed, in some degree, by the honest and liberal practice of a profession; where men shall carry a respect not to descend into any course that is corrupt and unworthy thereof, and preserve themselves free from the abuses wherewith the same profession is noted to be infected: but much more is this performed, if a man be able to visit and strengthen the roots and foundation of the science itself; thereby not only gracing it in reputation and dignity, but also amplifying it in profession and substance.
Opening sentences of Preface, Maxims of Law (1596), in The Works of Francis Bacon: Law tracts. Maxims of the Law (1803), Vol. 4, 10.
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I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially [science] of nature, requires a pure portion, lying at the foundation of the empirical, and based upon a priori knowledge of natural things. … To the possibility of a determinate natural thing, and therefore to cognise it à priori, is further requisite that the intuition corresponding à priori to the conception should be given; in other words, that the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.
From Preface to The Metaphysical Foundations of Natural Science (1786), as translated by Ernest Belford Boax, in Kant’s Prolegomena: And The Metaphysical Foundations of Natural Science (1883), 140.
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I regard sex as the central problem of life. And now that the problem of religion has practically been settled, and that the problem of labor has at least been placed on a practical foundation, the question of sex—with the racial questions that rest on it—stands before the coming generations as the chief problem for solution. Sex lies at the root of life, and we can never learn to reverence life until we know how to understand sex.
Studies in the Psychology of Sex (1897), Vol. 1, xxx.
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I submit a body of facts which cannot be invalidated. My opinions may be doubted, denied, or approved, according as they conflict or agree with the opinions of each individual who may read them; but their worth will be best determined by the foundation on which they rest—the incontrovertible facts.
Experiments and Observations on the Gastric Juice, and the Physiology of Digestion (1833), Preface.
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I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
In 'Reflections on my Eightieth Birthday', Portraits from Memory (1956), 54.
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I wanted to preserve the spontaneity of thought in speech… [and to] guard the spontaneity of the argument. A spoken argument is informal and heuristic; it singles out the heart of the matter and shows in what way it is crucial and new; and it gives the direction and line of the solution so that, simplified as it is, still the logic is right. For me, this philosophic form of argument is the foundation of science, and nothing should be allowed to obscure it.
On his philosophy in presenting the TV series, from which the book followed. In 'Foreward', The Ascent of Man, (1973), 14-15.
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I wish the lecturers to treat their subject as a strictly natural science, the greatest of all possible sciences, indeed, in one sense, the only science, that of Infinite Being, without reference to or reliance upon any supposed special exception or so-called miraculous revelation. I wish it considered just as astronomy or chemistry is.
Statement in deed of foundation of the Gifford Lectures on natural theology (1885).
Quoted in Michael A. Arbib and Mary B. Hesse, The Construction of Reality (1986), 1.
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If finally, the science should prove that society at a certain time revert to the church and recover its old foundation of absolute faith in a personal providence and a revealed religion, it commits suicide.
In The Degradation of the Democratic Dogma (1919), 131.
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If human thought is a growth, like all other growths, its logic is without foundation of its own, and is only the adjusting constructiveness of all other growing things. A tree cannot find out, as it were, how to blossom, until comes blossom-time. A social growth cannot find out the use of steam engines, until comes steam-engine-time.
Lo! (1931, 1941), 20.
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If you disregard the very simplest cases, there is in all of mathematics not a single infinite series whose sum has been rigorously determined. In other words, the most important parts of mathematics stand without a foundation.
In Letter to a friend, as quoted in George Finlay Simmons, Calculus Gems (1992), 188.
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If you do not rest on the good foundation of nature, you will labour with little honor and less profit.
As quoted in George Clausen, Six Lectures on Painting: Delivered to the Students of the Royal Arts in London, January, 1904 (1906), 30.
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If you have built castles in the air, your work need not be lost; that is where they should be. Now put the foundations under them.
In last chapter 'Conclusion', from Walden: or, Life in the Woods (1854), collected in The Writings of Henry David Thoreau (1894), Vol. 2, 499.
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In 1912 I went to a book sale and bought ten books for fifty cents. One of the books was by Ostwald The Scientific Foundations of Analytical Chemistry. Ostwald wrote at the beginning of that book that analytical chemists are the maidservants of other chemists. This made quite an impression on me, because I didn't want to be a maidservant.
Comment during interview, Beckman Center (15 March 1984), as recorded on tape held by The Chemical Heritage Foundation, Philadelphia. Quotation provided by W. H. Brock.
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In an objective system … any mingling of knowledge with values is unlawful, forbidden. But [the] … “first commandment” which ensures the foundation of objective knowledge, is not itself objective. It cannot be objective: it is an ethical guideline, a rule for conduct. True knowledge is ignorant of values, but it cannot be grounded elsewhere than upon a value judgment…
In Chance and Necessity (1970), 176.
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In geology we cannot dispense with conjectures: [but] because we are condemned to dream let us ensure that our dreams are like those of sane men—e.g. that they have their foundations in truth—and are not like the dreams of the sick, formed by strange combinations of phantasms, contrary to nature and therefore incredible.
Introducione alla Geologia, Part I (1811), trans. Ezio Vaccari, 81.
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In mathematics it is notorious that we start from absurdities to reach a realm of law, and our whole (mathematical) conception of the world is based on a foundation which we believe to have no existence.
In The Dance of Life (1923), 86.
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In neurophysiology we have none of those vast tidal waves of discovery which shake the world to its foundations and which have such incalculable consequences for good or evil.
From Speech (10 Dec 1963) at the Nobel Banquet in Stockholm, Sweden. Collected inGöran Liljestrand (ed.), Les Prix Nobel en 1963, (1964).
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In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
In 'Die Theorie der algebraischen Zahlkorper', Vorwort, Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 4.
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In the beginning God created Heaven and Earth … Which beginning of time, according to our Cronologie, fell upon the entrance of the night preceding the twenty third day of Octob. in the year of the Julian Calendar, 710 [or 4004 B.C.]. Upon the first day therefore of the world, or Octob. 23. being our Sunday, God, together with the highest Heaven, created the Angels. Then having finished, as it were, the roofe of this building, he fell in hand with the foundation of this wonderfull Fabrick of the World, he fashioned this lowermost Globe, consisting of the Deep, and of the Earth; all the Quire of Angels singing together and magnifying his name therefore … And when the Earth was void and without forme, and darknesse covered the face of the Deepe, on the very middle of the first day, the light was created; which God severing from the darknesses, called the one day, and the other night.
In 'Annals of the Old Testament', The Annals of the World (1658), excerpted in Louis A. Ruprecht, God Gardened East: A Gardener's Meditation on the Dynamics of Genesis (2008), 53-54.
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In the distant future I see open fields for far more important researches. Psychology will be based on a new foundation, that of the necessary acquirement of each mental power and capacity by gradation. Light will be thrown on the origin of man and his history.
On The Origin of Species by Means of Natural Selection (1859, 1882), 428 .
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In the future I see open fields for more important researches. Psychology will be securely based on the foundation already laid by Mr. Herbert Spencer, that of the necessary acquirement of each mental power and capacity by graduation.
Origin of Species
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In the Life of Darwin by his son, there is related an incident of how the great naturalist once studied long as to just what a certain spore was. Finally he said, “It is this, for if it isn’t, then what is it?” And all during his life he was never able to forget that he had been guilty of this unscientific attitude, for science is founded on certitude, not assumption.
In Elbert Hubbard (ed. and publ.), The Philistine (May 1908), 26, No. 6, 172.
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In the medical field [scientific ignorance] could lead to horrendous results. People who don’t understand the difference between a controlled experiment and claims by some quack may die as a result of not taking medical science seriously. One of the most damaging examples of pseudoscience is false memory syndrome. I’m on the board of a foundation exposing this problem.
As quoted by Lawrence Toppman, 'Mastermind', The Charlotte Observer (20 Jun 1993), 6E. As quoted and cited in Dana Richards, 'Martin Gardner: A “Documentary”', collected in Elwyn R. Berlekamp and Tom Rodgers (ed.) The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner (1999), 11.
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In the real changes which animals undergo during their embryonic growth, in those external transformations as well as in those structural modifications within the body, we have a natural scale to measure the degree or the gradation of those full grown animals which corresponds in their external form and in their structure, to those various degrees in the metamorphoses of animals, as illustrated by embryonic changes, a real foundation for zoological classification.
From Lecture 4, collected in Twelve Lectures on Comparative Embryology: Delivered Before the Lowell Institute in Boston: December and January 1848-9 (1849), 29.
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In the school of political projectors, I was but ill entertained, the professors appearing, in my judgment, wholly out of their senses; which is a scene that never fails to make me melancholy. These unhappy people were proposing schemes for persuading monarchs to choose favourites upon the score of their wisdom, capacity, and virtue; of teaching ministers to consult the public good; of rewarding merit, great abilities, and eminent services; of instructing princes to know their true interest, by placing it on the same foundation with that of their people; of choosing for employment persons qualified to exercise them; with many other wild impossible chimeras, that never entered before into the heart of man to conceive, and confirmed in me the old observation, that there is nothing so extravagant and irrational which some philosophers have not maintained for truth.
Gulliver's Travels (1726, Penguin ed. 1967), Part III, Chap. 6, 232.
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Injustice or oppression in the next street...or any spot inhabited by men was a personal affront to Thomas Addis and his name, from its early alphabetical place, was conspicuous on lists of sponsors of scores of organizations fighting for democracy and against fascism. He worked on more committees than could reasonably have been expected of so busy a man... Tom Addis was happy to have a hand in bringing to the organization of society some of the logic of science and to further that understanding and to promote that democracy which are the only enduring foundations of human dignity.
Kevin V. Lemley and Linus Pauling, 'Thomas Addis: 1881-1949', Biographical Memoirs, National Academy of Sciences, 63, 27-29.
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It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
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It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophising? Such might indeed be the right thing to do a time when the physicist believes he has at his disposal a rigid system of fundamental laws which are so well that waves of doubt can't reach them; but it cannot be right at a time when the very foundations of physics itself have become problematic as they are now … when experience forces us to seek a newer and more solid foundation.
‘Physics and Reality’, Franklin Institute Journal (Mar 1936). Collected in Out of My Later Years (1950), 58.
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It is a natural inquiry to ask—To what most nearly are these new phenomena [the newly-born science of radioactivity and the spontaneous disintegration of elements] correlated? Is it possible to give, by the help of an analogy to familiar phenomena, any correct idea of the nature of this new phenomenon “Radioactivity”? The answer may surprise those who hold to the adage that there is nothing new under the sun. Frankly, it is not possible, because in these latest developments science has broken fundamentally new ground, and has delved one distinct step further down into the foundations of knowledge.
In The Interpretation of Radium: Being the Substance of Six Free Popular Lectures Delivered at the University of Glasgow (1909, 1912), 2. The original lectures of early 1908, were greatly edited, rearranged and supplemented by the author for the book form.
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It is idle to expect any great advancement in science from the superinducing and engrafting of new things upon old. We must begin anew from the very foundations, unless we would revolve for ever in a circle with mean and contemptible progress.
From Novum Organum (1620), Book 1, Aphorism 31. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 52.
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It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory...
'On the Generalized Theory of Gravitation', Scientific American (Apr 1950), 13. In David H. Levy (Ed.), The Scientific American Book of the Cosmos (2000), 19.
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Mathematics … is necessarily the foundation of exact thought as applied to natural phenomena.
In An Introduction to Mathematics (1911), 8.
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Mathematics is the study which forms the foundation of the course [at West Point Military Academy]. This is necessary, both to impart to the mind that combined strength and versatility, the peculiar vigor and rapidity of comparison necessary for military action, and to pave the way for progress in the higher military sciences.
In Congressional Committee on Military Affairs, 1834, United States Bureau of Education, Bulletin 1912, No. 2, 10.
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Mathematics, once fairly established on the foundation of a few axioms and definitions, as upon a rock, has grown from age to age, so as to become the most solid fabric that human reason can boast.
In Essays on the Intellectual Powers of Man, 4th. Ed., 461.
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Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.
In 'A Plea for the Mathematician', Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.
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My interest in Science had many roots. Some came from my mother … while I was in my early teens. She fell in love with science,… [from] classes on the Foundations of Physical Science. … I was infected by [her] professor second hand, through hundreds of hours of conversations at my mother’s knees. It was from my mother that I first learned of Archimedes, Leonardo da Vinci, Galileo, Kepler, Newton, and Darwin. We spent hours together collecting single-celled organisms from a local pond and watching them with a microscope.
From 'Richard E. Smalley: Biographical', collected in Tore Frängsmyr (ed.), Les Prix Nobel: The Nobel Prizes 1996 (1997).
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Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules [i.e. atoms] out of which these systems are built—the foundation stones of the material universe—remain unbroken and unworn. They continue to this day as they were created—perfect in number and measure and weight.
Lecture to the British Association at Bradford, 'Molecules', Nature (1873), 8, 437-441. Reprinted in James Clerk Maxwell and W. D. Niven, editor, The Scientific Papers of James Clerk Maxwell (2003), 377. By
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Nature, the parent of all things, designed the human backbone to be like a keel or foundation. It is because we have a backbone that we can walk upright and stand erect. But this was not the only purpose for which Nature provided it; here, as elsewhere, she displayed great skill in turning the construction of a single member to a variety of different uses.
It Provides a Path for the Spinal Marrow, Yet is Flexible.
Firstly, she bored a hole through the posterior region of the bodies of all the vertebrae, thus fashioning a suitable pathway for the spinal marrow which would descend through them.
Secondly, she did not make the backbone out of one single bone with no joints. Such a unified construction would have afforded greater stability and a safer seat for the spinal marrow since, not having joints, the column could not have suffered dislocations, displacements, or distortions. If the Creator of the world had paid such attention to resistance to injury and had subordinated the value and importance of all other aims in the fabric of parts of the body to this one, he would certainly have made a single backbone with no joints, as when someone constructing an animal of wood or stone forms the backbone of one single and continuous component. Even if man were destined only to bend and straighten his back, it would not have been appropriate to construct the whole from one single bone. And in fact, since it was necessary that man, by virtue of his backbone, be able to perform a great variety of movements, it was better that it be constructed from many bones, even though as a result of this it was rendered more liable to injury.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, 57-58, as translated by William Frank Richardson, in 'Nature’s Skill in Creating a Backbone to Hold Us Erect', On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), 138.
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No one must think that Newton’s great creation can be overthrown in any real sense by this [Theory of Relativity] or by any other theory. His clear and wide ideas will for ever retain their significance as the foundation on which our modern conceptions of physics have been built.
In 'Time, Space, and Gravitation', The Times (28 Nov 1919). Excerpted in David E. Rowe and Robert J. Schulmann, Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb (2007), 104.
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Nomenclature, the other foundation of botany, should provide the names as soon as the classification is made... If the names are unknown knowledge of the things also perishes... For a single genus, a single name.
Philosophia Botanica (1751), aphorism 210. Trans. Frans A. Stafleu, Linnaeus and the Linnaeans: The Spreading of their Ideas in Systematic Botany, 1735-1789 (1971), 80.
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Of all the constituents of the human body, bone is the hardest, the driest, the earthiest, and the coldest; and, excepting only the teeth, it is devoid of sensation. God, the great Creator of all things, formed its substance to this specification with good reason, intending it to be like a foundation for the whole body; for in the fabric of the human body bones perform the same function as do walls and beams in houses, poles in tents, and keels and ribs in boats.
Bones Differentiated by Function
Some bones, by reason of their strength, form as it were props for the body; these include the tibia, the femur, the spinal vertebrae, and most of the bony framework. Others are like bastions, defense walls, and ramparts, affording natural protection to other parts; examples are the skull, the spines and transverse processes of the vertebrae, the breast bone, the ribs. Others stand in front of the joints between certain bones, to ensure that the joint does not move too loosely or bend to too acute an angle. This is the function of the tiny bones, likened by the professors of anatomy to the size of a sesame seed, which are attached to the second internode of the thumb, the first internode of the other four fingers and the first internodes of the five toes. The teeth, on the other hand, serve specifically to cut, crush, pound and grind our food, and similarly the two ossicles in the organ of hearing perform a specifically auditory function.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, 1, as translated by William Frank Richardson, in 'Nature of Bone; Function of Bones', On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), 1.
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On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
'The Work of Nicholas Bourbaki'American Mathematical Monthly (1970), 77, 134. In Carl C. Gaither, Alma E. Cavazos-Gaither, Mathematically Speaking: a Dictionary of Quotations (), 194.
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On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
Considerations on the Doctrine of Phlogiston (1796), 57-8.
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One of the most conspicuous and distinctive features of mathematical thought in the nineteenth century is its critical spirit. Beginning with the calculus, it soon permeates all analysis, and toward the close of the century it overhauls and recasts the foundations of geometry and aspires to further conquests in mechanics and in the immense domains of mathematical physics. … A searching examination of the foundations of arithmetic and the calculus has brought to light the insufficiency of much of the reasoning formerly considered as conclusive.
In History of Mathematics in the Nineteenth Century', Congress of Arts and Sciences (1906), Vol. 1, 482. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 113-114.
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Our civilization is an engineering civilization, and the prosperous life of the large population, which our earth now supports has become possible only by the work of the engineer. Engineering, however, is the application of science to the service of man, and so to-day science is the foundation, not only of our prosperity, but of our very existence, and thus necessarily has become the dominant power in our human society.
In 'Religion and Modern Science', The Christian Register (16 Nov 1922), 101, 1089. The article is introduced as “the substance of an address to the Laymen’s League in All Soul’s Church (5 Nov 1922).
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Our commercial and mercantile law was no sudden invention. It was not the work of a day, or of one set of minds… In the incipient, the early existence of this system, a single maxim obtained force, others succeeded; one rule of right formed a nucleus around which other kindred rules might cling; the necessities of trade originated customs, customs ripened into law; a few feeble decisions of courts laid the foundation for others; the wisdom and experience of each succeeding generation improved upon the wisdom and experience of generations that were past; and thus the edifice arose, perfect in its parts, beautiful in its proportions.
From biographical preface by T. Bigelow to Austin Abbott (ed.), Official Report of the Trial of Henry Ward Beecher (1875), Vol. 1, xi-xii.
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Our most distinguished “man of science” was the then veteran John Dalton. He was rarely absent from his seat in a warm corner of the room during the meetings of the Literary and Philosophical Society. Though a sober-minded Quaker, he was not devoid of some sense of fun; and there was a tradition amongst us, not only that he had once been a poet, but that, although a bachelor, two manuscript copies were still extant of his verses on the subject of matrimonial felicity; and it is my belief there was foundation for the tradition. The old man was sensitive on the subject of his age. Dining one day ... he was placed between two ladies ... [who] resolved to extract from him some admission on the tender point, but in vain. Though never other than courteous, Dalton foiled all their feminine arts and retained his secret. ... Dalton's quaint and diminutive figure was a strongly individualized one.
In Reminiscences of a Yorkshire Naturalist (1896), 73-74.
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People have noted with admiration how the progress of scientific enquiry is like the growth of a coral reef; each generation of little toilers building a sure foundation on which their successors may build yet further. The simile is apt in many ways, and in one way in particular that is worth considering. When we see how industrious and how prolific are the coral insects, our chief astonishment should be, not how vast are the structures they have built, but how few and scattered. Why is not every coast lined with coral? Why is the abyss if ocean not bridged with it. The answer is that coral only lives under certain limitations; it can only thrive at certain depths, in water of certain temperatures and salinities; outside these limits it languishes and dies. Science is like coral in this. Scientific investigators can only work in certain spots of the ocean of Being, where they are at home, and all outside is unknown to them...
Scientific Method: An Inquiry into the Character and Validy of Natural Law (1923), 195. Quoted in Wilson Gee, Social science research methods (1950), 182.
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Problems in human engineering will receive during the coming years the same genius and attention which the nineteenth century gave to the more material forms of engineering.
We have laid good foundations for industrial prosperity, now we want to assure the happiness and growth of the workers through vocational education, vocational guidance, and wisely managed employment departments. A great field for industrial experimentation and statemanship is opening up.
Letter printed in Engineering Magazine (Jan 1917), cover. Quoted in an article by Meyer Bloomfield, 'Relation of Foremen to the Working Force', reproduced in Daniel Bloomfield, Selected Articles on Employment Management (1919), 301.
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Prophetic of infidel times, and indicating the unsoundness of our general education, “The Vestiges of the Natural History of Creation,” has started into public favour with a fair chance of poisoning the fountains of science, and sapping the foundations of religion.
Review of the 4th edition of Chambers’ Book, 'Vestiges of the Natural History of Creation', The North British Review, 1845, 3, 471.
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Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.
Arithmetices Principia, (1889)
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Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.
Malay Archipelago
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Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”
In History of Mathematics (1893), 67.
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Science is wonderful at destroying metaphysical answers, but incapable of providing substitute ones. Science takes away foundations without providing a replacement. Whether we want to be there or not, science has put us in the position of having to live without foundations. It was shocking when Nietzsche said this, but today it is commonplace; our historical position—and no end to it is in sight—is that of having to philosophise without 'foundations'.
In Hilary Putnam (ed.), The Many Faces of Realism: The Paul Carns Lectures (1987), 29. Excerpt 'Realism and Reasonableness', in Joseph Margolis and Jacques Catudal, The Quarrel between Invariance and Flux (2001), 122.
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Scientific wealth tends to accumulate according to the law of compound interest. Every addition to knowledge of the properties of matter supplies the physical scientist with new instrumental means for discovering and interpreting phenomena of nature, which in their turn afford foundations of fresh generalisations, bringing gains of permanent value into the great storehouse of natural philosophy.
From Inaugural Address of the President to British Association for the Advancement of Science, Edinburgh (2 Aug 1871). Printed in The Chemical News (4 Aug 1871), 24, No. 610., 53.
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So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us.
To the German Society of Scientists and Physicists, Braunschweig, Germany (Sep 1896). As quoted in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 20. Wiechert was reporting his measurement of the mass of the moving particles in a cathode ray beam (electrons).
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Some of my cousins who had the great advantage of University education used to tease me with arguments to prove that nothing has any existence except what we think of it. … These amusing mental acrobatics are all right to play with. They are perfectly harmless and perfectly useless. ... I always rested on the following argument. … We look up to the sky and see the sun. Our eyes are dazzled and our senses record the fact. So here is this great sun standing apparently on no better foundation than our physical senses. But happily there is a method, apart altogether from our physical senses, of testing the reality of the sun. It is by mathematics. By means of prolonged processes of mathematics, entirely separate from the senses, astronomers are able to calculate when an eclipse will occur. They predict by pure reason that a black spot will pass across the sun on a certain day. You go and look, and your sense of sight immediately tells you that their calculations are vindicated. So here you have the evidence of the senses reinforced by the entirely separate evidence of a vast independent process of mathematical reasoning. We have taken what is called in military map-making “a cross bearing.” When my metaphysical friends tell me that the data on which the astronomers made their calculations, were necessarily obtained originally through the evidence of the senses, I say, “no.” They might, in theory at any rate, be obtained by automatic calculating-machines set in motion by the light falling upon them without admixture of the human senses at any stage. When it is persisted that we should have to be told about the calculations and use our ears for that purpose, I reply that the mathematical process has a reality and virtue in itself, and that onie discovered it constitutes a new and independent factor. I am also at this point accustomed to reaffirm with emphasis my conviction that the sun is real, and also that it is hot— in fact hot as Hell, and that if the metaphysicians doubt it they should go there and see.
In My Early Life (1930).
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Sometime between 1740 and 1780, electricians were for the first time enabled to take the foundations for their field for granted. From that point they pushed on to more concrete and recondite problems.
From The Structure of Scientific Revolutions (1970, 2012), 21-22.
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Statistical accounts are to be referred to as a dictionary by men of riper years, and by young men as a grammar, to teach them the relations and proportions of different statistical subjects, and to imprint them on the mind at a time when the memory is capable of being impressed in a lasting and durable manner, thereby laying the foundation for accurate and valuable knowledge.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5-6.
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Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified.
Concluding remark in 'Consistency and Completeness—A Résumé', The American Mathematical Monthly (May 1956), 63, No.5, 305.
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Terrorist attacks can shake the foundations of our biggest buildings, but they cannot touch the foundation of America. These acts shatter steel, but they cannot dent the steel of American resolve.
Address to the US after hijack attacks on the US World Trade Centers and Pentagon, September 11, 2001
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The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.
In Tobias Dantzig and Joseph Mazur (ed.), Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 99.
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The art of healing is like an unroofed temple, uncovered at the top and cracked at the foundation.
Quoted by Isaac Jennings, in Medical Reform; a Treatise on Man's Physical Being and Disorders (1847), 33.
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The assumption of an absolute determinism is the essential foundation of every scientific enquiry.
Physikalische Abhandlungen und Vorträge (1958), Vol 3, 89. Translated in J. L. Heilbron, The Dilemmas of an Upright Man (1986) 66.
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The doctrine of foods is of great ethical and political significance. Food becomes blood, blood becomes heart and brain, thoughts and mind stuff. Human fare is the foundation of human culture and thought. Would you improve a nation? Give it, instead of declamations against sin, better food. Man is what he eats [Der Mensch ist, was er isst].
Advertisement to Moleschott, Lehre der Nahrungsmittel: Für das Volk (1850).
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The end of our foundation [Salomon's House in the New Atlantis] is the knowledge of Causes and the secret motions of things; and the enlarging of the bounds of Human Empire, to the effecting of all things possible.
In Francis Bacon and William Rawle (ed.), The Works of Francis Bacon: Philosophical Works (1887), 156.
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The End of our Foundation is the knowledge of Causes; and secret motions of things; and the enlarging of the bounds of Human Empire, to the effecting of all things possible.
'New Atlantis' (1626) in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1887-1901), Vol. 3, 156.
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The existence of life must be considered as an elementary fact that can not be explained, but must be taken as a starting point in biology, in a similar way as the quantum of action, which appears as an irrational element from the point of view of classical mechanical physics, taken together with the existence of elementary particles, forms the foundation of atomic physics. The asserted impossibility of a physical or chemical explanation of the function peculiar to life would in this sense be analogous to the insufficiency of the mechanical analysis for the understanding of the stability of atoms.
'Light and Life', Nature, 1933, 131, 458.
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The first step in wisdom is to know the things themselves; this notion consists in having a true idea of the objects; objects are distinguished and known by classifying them methodically and giving them appropriate names. Therefore, classification and name-giving will be the foundation of our science.
Systema Naturae (1735), trans. M. S. J. Engel-Ledeboer and H. Engel (1964), 19.
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The Foundation of Empire is Art & Science. Remove them, or Degrade them, & the Empire is No More. Empire follows Art, & not Vice Versa as Englishmen suppose.
Marginal note (c. 1808) written in his copy of The Works of Sir Joshua Reynolds (1798), at foot of first page of table of contents. As given in William Blake, Edwin John Ellis (ed.) and William Butler Yeats (ed.), The Works of William Blake (1893), Vol. 2, 319.
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The foundation of morality should not be made dependent on myth nor tied to any authority lest doubt about the myth or about the legitimacy of the authority imperil the foundation of sound judgment and action.
In a letter to a minister in Brooklyn, N.Y. (20 Nov 1950), third paragraph, as quoted in Helen Dukas and Banesh Hoffmann (eds.), Albert Einstein: The Human Side (1979, 1981), 95.
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The foundations of population genetics were laid chiefly by mathematical deduction from basic premises contained in the works of Mendel and Morgan and their followers. Haldane, Wright, and Fisher are the pioneers of population genetics whose main research equipment was paper and ink rather than microscopes, experimental fields, Drosophila bottles, or mouse cages. Theirs is theoretical biology at its best, and it has provided a guiding light for rigorous quantitative experimentation and observation.
'A Review of Some Fundamental Concepts and Problems of Population Genetics', Cold Spring Harbor Symposia on Quantitative Biology, 1955, 20, 13-14.
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The function of Latin literature is its expression of Rome. When to England and France your imagination can add Rome in the background, you have laid firm the foundations of culture. The understanding of Rome leads back to the Mediterranean civilisation of which Rome was the last phase, and it automatically exhibits the geography of Europe, and the functions of seas and rivers and mountains and plains. The merit of this study in the education of youth is its concreteness, its inspiration to action, and the uniform greatness of persons, in their characters and their staging. Their aims were great, their virtues were great, and their vices were great. They had the saving merit of sinning with cart ropes.
In 'The Place of Classics in Education', The Aims of Education: & Other Essays (1917), 106.
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The great artifice of regarding small deviations from the truth as being the truth itself is at the same time the foundation of wit, where the whole thing would often collapse if we were to regard these deviations in a spirit of philosophical rigor.
Aphorism from Georg Christoph Lichtenberg and R.J. Hollingdale (trans.) 'Notebook A: 1765-1770', The Waste Books (1990), 4. Also seen translated as, “The great trick of regarding small departures from the truth as the truth itself—on which is founded the entire integral calculus—is also the basis of our witty speculations, where the whole thing would often collapse if we considered the departures with philosophical rigour,” for example, as quoted in FractalVision: Put Fractals to Work For You (1992), 5, citing Aphorisms: 1764-1799.
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The great doctors all got their education off dirt pavements and poverty—not marble floors and foundations.
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
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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. Considering this as the ultimate end of science, no branch of it can surely claim precedence of Astronomy. No other science furnishes such a palpable embodiment of the abstractions which lie at the foundation of our intellectual system; the great ideas of time, and space, and extension, and magnitude, and number, and motion, and power. How grand the conception of the ages on ages required for several of the secular equations of the solar system; of distances from which the light of a fixed star would not reach us in twenty millions of years, of magnitudes compared with which the earth is but a foot-ball; of starry hosts—suns like our own—numberless as the sands on the shore; of worlds and systems shooting through the infinite spaces.
Oration at Inauguration of the Dudley Astronomical Observatory, Albany (28 Jul 1856). Text published as The Uses of Astronomy (1856), 36.
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The highest principles for our aspirations and judgments are given to us in the Jewish-Christian religious tradition. It is a very high goal which, with our weak powers, we can reach only very inadequately, but which gives a sure foundation to our aspirations and valuations.
…...
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The instinct for collecting, which began as in other animals as an adaptive property, could always in man spread beyond reason; it could become a hoarding mania. But in its normal form it provides a means of livelihood at the hunting and collecting stage of human evolution. It is then attached to a variety of rational aptitudes, above all in observing, classifying, and naming plants, animals and minerals, skills diversely displayed by primitive peoples. These skills with an instinctive beginning were the foundation of most of the civilised arts and sciences. Attached to other skills in advanced societies they promote the formation of museums and libraries; detached, they lead to acquisition and classification by eccentric individuals, often without any purpose or value at all.
As quoted in Richard Fifield, 'Cytologist Supreme', New Scientist (16 Apr 1981), 90, No. 1249, 179; citing C.D. Darlington, The Little Universe of Man (1978).
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The introduction of men into the lying in chamber in place of female attendants, has increased the suffering and dangers of childbearing women, and brought multiplied injuries and fatalities upon mothers and children; it violates the sensitive feelings of husbands and wives and causes an untold amount of domestic misery. The unlimited intimacy between a male profession and the female population silently and effectually wears away female delicacy and professional morality, and tends probably more than any other cause in existence, to undermine the foundation of public virtue.
Man-midwifery Exposed and Corrected (1848) quoted in The Male Midwife and the Female Doctor: The Gynecology Controversy in Nineteenth Century America Charles Rosenburg and Carroll Rovenberg Smith (Editors) publ. Arno, 1974.
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The laws of Coexistence;—the adaptation of structure to function; and to a certain extent the elucidation of natural affinities may be legitimately founded upon the examination of fully developed species;—But to obtain an insight into the laws of development,—the signification or bedeutung, of the parts of an animal body demands a patient examination of the successive stages of their development, in every group of Animals.
'Lecture Four, 9 May 1837', The Hunterian Lectures in Comparative Anatomy, May-June 1837, ed. Phillip Reid Sloan (1992), 191.
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The laws of nature, as we understand them, are the foundation of our knowledge in natural things. So much as we know of them has been developed by the successive energies of the highest intellects, exerted through many ages. After a most rigid and scrutinizing examination upon principle and trial, a definite expression has been given to them; they have become, as it were, our belief or trust. From day to day we still examine and test our expressions of them. We have no interest in their retention if erroneous. On the contrary, the greatest discovery a man could make would be to prove that one of these accepted laws was erroneous, and his greatest honour would be the discovery.
Experimental researches in chemistry and physics (1859), 469.
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The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search for truth. So it does more harm than good.
From Novum Organum (1620), Book 1, Aphorism 12. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 48-49.
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The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adhering to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depends upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.
Address to the University of Cambridge upon being elected Lucasian Professor of Mathematics (14 Mar 1664). In Mathematical Lectures (1734), xxviii.
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The method I take to do this is not yet very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course (as a Specimen of the Political Arithmetic I have long aimed at) to express myself in Terms of Number, Weight, or Measure; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature.
From Essays in Political Arithmetic (1679, 1755), 98.
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The more I meditate on the principles of the theory of functions—and I do this unremittingly the stronger becomes my conviction that the foundations upon which these must be built are the truths of Algebra…
From Letter (3 Oct 1875), to Professor Schwartz. As quoted and translated in Ernst Hairer and Gerhard Wanner, Analysis by Its History (2008), 177. From the original German in Mathematische Werke (1875, 1895), Vol. 2, 235, “Je mehr ich über die Principien der Functionentheorie nachdenke—und ich thue dies unablässig—, um so fester wird meine Überzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss…”
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The National Science Foundation asked the great “breakthrough” scientists what they felt to be the most dominantly favorable factor in their educational experience. The answer was almost uniformly, “Intimate association with a great, inspiring teacher.”
In "How Little I Know", in Saturday Review (12 Nov 1966), 152. Excerpted in Buckminster Fuller and Answar Dil, Humans in Universe (1983), 70.
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The night before Easter Sunday of that year (1920) I awoke, turned on the light, and jotted down a few notes on a tiny slip of thin paper. Then I fell asleep again. It occurred to me at six o’clock in the morning that during the night I had written down something most important, but I was unable to decipher the scrawl. The next night, at three o’clock, the idea returned. It was the design of an experiment to determine whether the hypothesis of chemical transmission that I had uttered seventeen years ago was correct. I got up immediately, went to the laboratory, and performed a simple experiment on a frog heart according to the nocturnal design. I have to describe this experiment briefly since its results became the foundation of the theory of chemical transmission of the nervous impulse. The hearts of two frogs were isolated, the first with its nerves, the second without. Both hearts were attached to Straub cannulas filled with a little Ringer solution. The vagus nerve of the first heart was stimulated for a few minutes. Then the Ringer solution that had been in the first heart during the stimulation of the vagus was transferred to the second heart. It slowed and its beats diminished just as if its vagus had been stimulated. Similarly, when the accelerator nerve was stimulated and the Ringer from this period transferred, the second heart speeded up and its beats increased. These results unequivocally proved that the nerves do not influence the heart directly but liberate from their terminals specific chemical substances which, in their turn, cause the well-known modifications of the function of the heart characteristic of the stimulation of its nerves.
'An Autobiographic Sketch', Perspectives in Biology and Medicine (1960), 4, 17.
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The only sure foundations of medicine are, an intimate knowledge of the human body, and observation on the effects of medicinal substances on that. The anatomical and clinical schools, therefore, are those in which the young physician should be formed. If he enters with innocence that of the theory of medicine, it is scarcely possible he should come out untainted with error. His mind must be strong indeed, if, rising above juvenile credulity, it can maintain a wise infidelity against the authority of his instructors, and the bewitching delusions of their theories.
In letter to Caspar Wistar (21 Jun 1807), collected in Thomas Jefferson Randolph (ed.), Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson (1829), Vol. 4, 93.
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The physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations for he himself knows best and feels most surely where the shoe pinches. … he must try to make clear in his own mind just how far the concepts which he uses are justified … The whole of science is nothing more than a refinement of everyday thinking. It is for this reason that the critical thinking of the physicist cannot possibly be restricted by the examination of the concepts of his own specific field. He cannot proceed without considering critically a much more difficult problem, the problem of analyzing the nature of everyday thinking.
‘Physics and Reality’, Franklin Institute Journal (Mar 1936). Collected in Out of My Later Years (1950), 59.
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The pure culture is the foundation for all research on infectious disease.
'Zur Untersuchungen von Pathologen Organismen', Mittheilungen aus dem Kaiserlichen Gesundheitsamte (1881), 1, 1-48. Quoted in English in Thomas D. Brock, Robert Koch: A Life in Medicine and Bacteriology (1988), 94.
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The sciences are monuments devoted to the public good; each citizen owes to them a tribute proportional to his talents. While the great men, carried to the summit of the edifice, draw and put up the higher floors, the ordinary artists scattered in the lower floors, or hidden in the obscurity of the foundations, must only seek to improve what cleverer hands have created.
From Mémoires présentés par divers Savants à l'Académie des Sciences (1776), Introduction, 4. As translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics (1990), Vol. 1, 533.
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The scientific man does not aim at an immediate result. He does not expect that his advanced ideas will be readily taken up. His work is like that of the planter—for the future. His duty is to lay the foundation for those who are to come, and point the way.
In 'The Problem of Increasing Human Energy', Century Illustrated Monthly Magazine (Jun 1900), 60, 211.
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The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. ... it was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.
Introduction to a paper on magnetic monopoles, 'Quantised singularities in the electromagnetic field', Proceedings of the Royal Society of Lonndon (1931), A, 133 60. In Helge Kragh, Dirac: a Scientific Biography (1990), 208.
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The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.
Mathematics in Western Culture (1953), 382.
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The tiny creatures of the undergrowth were the first creatures of any kind to colonise the land. They established the foundations of the land’s ecosystems and were able to transcend the limitations of their small size by banding together in huge communities of millions.
From BBC TV series Life in the Undergrowth (2005), as quoted in BBC press release (10 Oct 2005).
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The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms. From this it has come about that our entire contemporary culture, inasmuch as it is based on the intellectual penetration and the exploitation of nature, has its foundations in mathematics. Already Galileo said: one can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are mathematical figures.
Radio broadcast (8 Sep 1930). As quoted in Michael Fitzgerald and Ioan James, The Mind of the Mathematician (2007), 6-7.
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The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject. … The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty. It would probably be a good thing also to give a preference to those branches of mathematics that have an interesting group of transformations underlying them, since transformations play an important role in modern physical theory, both relativity and quantum theory seeming to show that transformations are of more fundamental importance than equations.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 122.
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The true foundation of theology is to ascertain the character of God. It is by the aid of Statistics that law in the social sphere can be ascertained and codified, and certain aspects of the character of God thereby revealed. The study of statistics is thus a religious service.
As quoted by Florence Nightingale David in Games, Gods, and Gambling: A History of Probability and Statistical Ideas (1962, 1998), 103. David introduced the quote by saying “Florence Nightingale, after some lengthy calculations, wrote:”.
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The very foundation of our science is only an inference; far the whole of it rests an the unprovable assumption that, all through the inferred lapse of time which the inferred performance of inferred geological processes involves, they have been going on in a manner consistent with the laws of nature as we know them now.
'The Value of Outrageous Geological Hypotheses', Science, 1926, 63, 465-466.
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There are four classes of Idols which beset men’s minds. To these for distinction’s sake I have assigned names,—calling the first class Idols of the Tribe; the second, Idols of the Cave; the third, Idols of the Market Place; the fourth, Idols of the Theatre
The Idols of the Tribe have their foundation in human nature itself, and in the tribe or race of men. For it is a false assertion that the sense of man is the measure of things. On the contrary, all perceptions as well of the sense as of the mind are according to the measure of the individual and not according to the measure of the universe. And the human understanding is like a false mirror, which, receiving rays irregularly, distorts and discolours the nature of things by mingling its own nature with it.
The Idols of the Cave are the idols of the individual man. For every one (besides the errors common to human nature in general) has a cave or den of his own, which refracts and discolours the light of nature; owing either to his own proper and peculiar nature; or to his education and conversation with others; or to the reading of books, and the authority of those whom he esteems and admires; or to the differences of impressions, accordingly as they take place in a mind preoccupied and predisposed or in a mind indifferent and settled; or the like.
There are also Idols formed by the intercourse and association of men with each other, which I call Idols of the Market-place, on account of the commerce and consort of men there. For it is by discourse that men associate; and words are imposed according to the apprehension of the vulgar, and therefore the ill and unfit choice of words wonderfully obstructs the understanding. Nor do the definitions or explanations where with in some things learned men are wont to guard and defend themselves, by any means set the matter right. But words plainly force and overrule the understanding, and throw all into confusion, and lead men away into numberless empty controversies and idle fancies.
Lastly, there are Idols which have immigrated into men’s minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theatre; because in my judgment all the received systems are but so many stage-plays, representing worlds of their own creation after an unreal and scenic fashion.
From Novum Organum (1620), Book 1, Aphorisms 39, 41-44. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 53-55.
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There can be no scientific foundation of religion, and belief must always remain the foundation of religion, while that of science is logical reasoning from facts, that is, sense perceptions; and all that we can say is, that the two, science and religion, are not necessarily incompatible, but are different and unrelated activities of the human mind.
In 'Religion and Modern Science', The Christian Register (16 Nov 1922), 101, 1089. The article is introduced as “the substance of an address to the Laymen’s League in All Soul’s Church (5 Nov 1922).
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There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
'The Study of the Natural Sciences: An Introductory Lecture to the Course of Experimental Chemistry in the University of Munich, for the Winter Session of 1852-53,' as translated and republished in The Medical Times and Gazette (22 Jan 1853), N.S. Vol. 6, 82.
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There is no foundation in geological facts, for the popular theory of the successive development of the animal and vegetable world, from the simplest to the most perfect forms.
Principles of Geology (1830-3), Vol. 1, 153.
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Therefore O students study mathematics and do not build without foundations.
…...
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This Academy [at Lagado] is not an entire single Building, but a Continuation of several Houses on both Sides of a Street; which growing waste, was purchased and applied to that Use.
I was received very kindly by the Warden, and went for many Days to the Academy. Every Room hath in it ' one or more Projectors; and I believe I could not be in fewer than five Hundred Rooms.
The first Man I saw was of a meagre Aspect, with sooty Hands and Face, his Hair and Beard long, ragged and singed in several Places. His Clothes, Shirt, and Skin were all of the same Colour. He had been Eight Years upon a Project for extracting Sun-Beams out of Cucumbers, which were to be put into Vials hermetically sealed, and let out to warm the Air in raw inclement Summers. He told me, he did not doubt in Eight Years more, that he should be able to supply the Governor's Gardens with Sunshine at a reasonable Rate; but he complained that his Stock was low, and interested me to give him something as an Encouragement to Ingenuity, especially since this had been a very dear Season for Cucumbers. I made him a small Present, for my Lord had furnished me with Money on purpose, because he knew their Practice of begging from all who go to see them.
I saw another at work to calcine Ice into Gunpowder; who likewise shewed me a Treatise he had written concerning the Malleability of Fire, which he intended to publish.
There was a most ingenious Architect who had contrived a new Method for building Houses, by beginning at the Roof, and working downwards to the Foundation; which he justified to me by the life Practice of those two prudent Insects the Bee and the Spider.
In another Apartment I was highly pleased with a Projector, who had found a device of plowing the Ground with Hogs, to save the Charges of Plows, Cattle, and Labour. The Method is this: In an Acre of Ground you bury at six Inches Distance, and eight deep, a quantity of Acorns, Dates, Chestnuts, and other Masts or Vegetables whereof these Animals are fondest; then you drive six Hundred or more of them into the Field, where in a few Days they will root up the whole Ground in search of their Food, and make it fit for sowing, at the same time manuring it with their Dung. It is true, upon Experiment they found the Charge and Trouble very great, and they had little or no Crop. However, it is not doubted that this Invention may be capable of great Improvement.
I had hitherto seen only one Side of the Academy, the other being appropriated to the Advancers of speculative Learning.
Some were condensing Air into a dry tangible Substance, by extracting the Nitre, and letting the acqueous or fluid Particles percolate: Others softening Marble for Pillows and Pin-cushions. Another was, by a certain Composition of Gums, Minerals, and Vegetables outwardly applied, to prevent the Growth of Wool upon two young lambs; and he hoped in a reasonable Time to propagate the Breed of naked Sheep all over the Kingdom.
Gulliver's Travels (1726, Penguin ed. 1967), Part III, Chap. 5, 223.
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This is the reason why all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning. This situation makes it difficult to use our empirical knowledge, however comprehensive, in looking for the fundamental concepts and relations of physics, and it forces us to apply free speculation to a much greater extent than is presently assumed by most physicists.
…...
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This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
In The Philosophy of the Inductive Sciences Part 1, Bk. 2, chap. 4, sect. 8 (1868).
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To feed applied science by starving basic science is like economising on the foundations of a building so that it may be built higher. It is only a matter of time before the whole edifice crumbles.
In article, 'Lest the Edifice of Science Crumble', New Scientist (4 Sep 1986), 111, No. 1574, 16.
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To her [Florence Nightingale] chiefly I owed the awakening to the fact that sanitation is the supreme goal of medicine its foundation and its crown.
In Pioneer Work in Opening the Medical Profession to Women (1895), 176.
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Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.
In History of European Thought in the Nineteenth Century (1903), 630.
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Under the... new hypothesis [of Continental Drift] certain geological concepts come to acquire a new significance amounting in a few cases to a complete inversion of principles, and the inquirer will find it necessary to re-orient his ideas. For the first time he will get glimpses... of a pulsating restless earth, all parts of which are in greater or less degree of movement in respect to the axis of rotation, having been so, moreover, throughout geological time. He will have to leave behind him—perhaps reluctantly—the dumbfounding spectacle of the present continental masses, firmly anchored to a plastic foundation yet remaining fixed in space; set thousands of kilometres apart, it may be, yet behaving in almost identical fashion from epoch to epoch and stage to stage like soldiers, at drill; widely stretched in some quarters at various times and astoundingly compressed in others, yet retaining their general shapes, positions and orientations; remote from one another through history, yet showing in their fossil remains common or allied forms of terrestrial life; possessed during certain epochs of climates that may have ranged from glacial to torrid or pluvial to arid, though contrary to meteorological principles when their existing geographical positions are considered -to mention but a few such paradoxes!
Our Wandering Continents: An Hypothesis of Continental Drifting (1937), 3.
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War and the steam engine joined forces and forged what was to become one of the most delicate of concepts. Sadi Carnot … formed the opinion that one cause of France’s defeat had been her industrial inferiority. … Carnot saw steam power as a universal motor. … Carnot was a visionary and sharp analyst of what was needed to improve the steam engine. … Carnot’s work … laid the foundations of [thermodynamics].
In The Second Law (1984), 1-2.
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We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.
In article he wrote, 'Space-Time', for Encyclopaedia Britannica (14th ed., 1929), Vol. 21, 106.
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We consider species to be like a brick in the foundation of a building. You can probably lose one or two or a dozen bricks and still have a standing house. But by the time you’ve lost twenty percent of species, you’re going to destabilize the entire structure. That’s the way ecosystems work.
The Christian Science Monitor (26 May 1989)
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We do not listen with the best regard to the verses of a man who is only a poet, nor to his problems if he is only an algebraist; but if a man is at once acquainted with the geometric foundation of things and with their festal splendor, his poetry is exact and his arithmetic musical.
In 'Works and Days', Society and Solitude (1883), Chap. 7, 171.
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We have in the spinal cord the antetype (Vorbild) and the foundation for the entire structure of the brain.
Handbuch der Anatonne des Menschen nnt besonderer Riicksicht auf Physiologie und praktische Medicin (1851), Vol. 2, 682. Trans. Edwin Clarke and L. S. Jacyna, Nineteenth Century Origins of Neuroscentific Concepts (1987), 52.
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We may lay it down that a happy person never phantasises, only an unsatisfied one... The motive forces of phantasies are unsatisfied wishes, and every single phantasy is the fulfilment of a wish, a correction of unsatisfying reality. These motivating wishes vary according to the sex, character and circumstances of the person who is having the phantasy; but they fall naturally into two main groups. They are either ambitious wishes, which serve to elevate the subject's personality; or they are erotic ones. It was shocking when Nietzsche said this, but today it is commonplace; our historical position—and no end to it is in sight—is that of having to philosophise without 'foundations'.
Creative Writers and Day-Dreaming (1906), In James Strachey (ed.), The Standard Edition of the Complete Psychcological Works of Sigmund Freud (1959), Vol 9, 146-7.
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When the state is shaken to its foundations by internal or external events, when commerce, industry and all trades shall be at a stand, and perhaps on the brink of ruin; when the property and fortune of all are shaken or changed, and the inhabitants of towns look forward with dread and apprehension to the future, then the agriculturalist holds in his hand the key to the money chest of the rich, and the savings-box of the poor; for political events have not the slightest influence on the natural law, which forces man to take into his system, daily, a certain number of ounces of carbon and nitrogen.
Reflecting on events of 1848.
Familiar Letters on Chemistry (1851), 3rd edn., 483.
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With respect to those who may ask why Nature does not produce new beings? We may enquire of them in turn, upon what foundation they suppose this fact? What it is that authorizes them to believe this sterility in Nature? Know they if, in the various combinations which she is every instant forming, Nature be not occupied in producing new beings, without the cognizance of these observers? Who has informed them that this Nature is not actually assembling, in her immense elaboratory, the elements suitable to bring to light, generations entirely new, that will have nothing in common with those of the species at present existing? What absurdity then, or what want of just inference would there be, to imagine that the man, the horse, the fish, the bird will be no more? Are these animals so indispensably requisite to Nature, that without them she cannot continue her eternal course? Does not all change around us? Do we not ourselves change? ... Nature contains no one constant form.
The System of Nature (1770), trans. Samuel Wilkinson (1820), Vol. 1, 94-95.
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With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
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With the unlocking of the atom, mankind crossed one of the great watersheds of history. We have entered uncharted lands. The maps of strategy and diplomacy by which we guided ourselves until yesterday no longer reveal the way. Fusion and fission revolutionized the whole foundation of human affairs.
In a speech to the General Federation of Women’s Clubs, Philadelphia, Pennsylvania, May 24, 1955.
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World-wide practice of Conservation and the fair and continued access by all nations to the resources they need are the two indispensable foundations of continuous plenty and of permanent peace.
…...
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You may perceive something of the distinction which I think necessary to keep in view between art and science, between the artist and the man of knowledge, or the philosopher. The man of knowledge, the philosopher, is he who studies and acquires knowledge in order to improve his own mind; and with a desire of extending the department of knowledge to which he turns his attention, or to render it useful to the world, by discoveries, or by inventions, which may be the foundation of new arts, or of improvements in those already established. Excited by one or more of these motives, the philosopher employs himself in acquiring knowledge and in communicating it. The artist only executes and practises what the philosopher or man of invention has discovered or contrived, while the business of the trader is to retail the productions of the artist, exchange some of them for others, and transport them to distant places for that purpose.
From the first of a series of lectures on chemistry, collected in John Robison (ed.), Lectures on the Elements of Chemistry: Delivered in the University of Edinburgh (1807), Vol. 1, 3.
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Rosalind Franklin quote: In my view, all that is necessary for faith is the belief that by doing our best we shall come nearer
Your theories are those which you and many other people find easiest and pleasantest to believe, but, so far as I can see, they have no foundation other than they lead to a pleasant view of life … I agree that faith is essential to success in life … but I do not accept your definition of faith, i.e. belief in life after death. In my view, all that is necessary for faith is the belief that by doing our best we shall come nearer to success and that success in our aims (the improvement of the lot of mankind, present and future) is worth attaining … I maintain that faith in this world is perfectly possible without faith in another world.
Letter to her father, Ellis Franklin (undated, summer 1940? while she was an undergraduate at Cambridge). Excerpted in Brenda Maddox, The Dark Lady of DNA (2002), 61.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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