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Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
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Begin Quotes (260 quotes)

Socrates: Very good; let us begin then, Protarchus, by asking whether all this which they call the universe is left to the guidance of unreason and chance medley, or, on the contrary, as our fathers have declared, ordered and governed by a marvellous intelligence and wisdom.
Protarchus: Wide asunder are the two assertions, illustrious Socrates, for that which you were just now saying to me appears to be blasphemy, but the other assertion, that mind orders all things, is worthy of the aspect of the world…
Plato
From 'Philebus', collected in The Dialogues of Plato (1875), Vol. 4, 70.
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Ueber den Glauben lässt sich wissenschaftlich nicht rechten, denn die Wissenschaft und der Glaube schliessen sich aus. Nicht so, dass der eine die andere unmöglich machte oder umgekehrt, sondern so, dass, soweit die Wissenschaft reicht, kein Glaube existirt und der Glaube erst da anfangen darf, wo die Wissenschaft aufhört. Es lässt „sich nicht läugnen, dass, wenn diese Grenze eingehalten wird, der Glaube wirklich reale Objekte haben kann. Die Aufgabe der Wissenschaft ist es daher nicht, die Gegenstände des Glaubens anzugreifen, sondern nur die Grenzen zu stecken, welche die Erkenntniss erreichen kann, und innerhalb derselben das einheitliche Selbstbewusstsein zu begründen.
There is no scientific justification for faith, for science and faith are mutually exclusive. Not that one made the other impossible, or vice versa, but that, as far as science goes, there is no faith, and faith can only begin where science ends. It can not be denied that, if this limit is adhered to, faith can really have real objects. The task of science, therefore, is not to attack the objects of faith, but merely to set the limits which knowledge can attain and to establish within it the unified self-esteem.
Original German from 'Der Mensch' (1849), collected in Gesammelte abhandlungen zur wissenschaftlichen medicin (1856), 6. Webmaster used Google translate for the English version. This longer quote unites the shorter quotes from within it shown separately on the Rudolf Virchow quotations page, with alternative translations, which begin: “There can be no scientific dispute…”, “Belief has no place…”, and “The task of science…”.
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A body of work such as Pasteur’s is inconceivable in our time: no man would be given a chance to create a whole science. Nowadays a path is scarcely opened up when the crowd begins to pour in.
Pensées d’un Biologiste (1939). Translated in The Substance of Man (1962), Chap. 6.
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A fear of intellectual inadequacy, of powerlessness before the tireless electronic wizards, has given rise to dozens of science-fiction fantasies of computer takeovers. ... Other scientists too are apprehensive. D. Raj Reddy, a computer scientist at Pittsburgh’s Carnegie-Mellon University, fears that universally available microcomputers could turn into formidable weapons. Among other things, says Reddy, sophisticated computers in the wrong hands could begin subverting a society by tampering with people’s relationships with their own computers—instructing the other computers to cut off telephone, bank and other services, for example.
Magazine
An early prediction of DDoS (Distributed Denial of Service), viruses and worms like Stuxnet. As stated, without further citation, in 'The Age of Miracle Chips', Time (20 Feb 1978), 44. The article introduces a special section on 'The Computer Society.' Please contact Webmaster if you know a primary source.
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A few days afterwards, I went to him [the same actuary referred to in another quote] and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly. I told him that the law was involved in this circumstance. Take the table of the expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come. “You don’t mean that this always happens?”—“Try it.” He did try, again and again; and found it as I said. “This is, indeed, a curious thing; this is a discovery!” I might have sent him about trumpeting the law of life: but I contented myself with informing him that the same thing would happen with any table whatsoever in which the first column goes up and the second goes down.
In Budget of Paradoxes (1872), 172.
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A man’s indebtedness … is not virtue; his repayment is. Virtue begins when he dedicates himself actively to the job of gratitude.
In The Chrysanthemum and the Sword (1946, 2006), 114.
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A man’s worst difficulties begin when he is able to do as he likes.
Address at the formal opening of the Johns Hopkins University, Baltimore (12 Sep 1876), collected in 'University Education', American Addresses: With a Lecture on the Study of Biology (1877), 100.
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A million years is a short time—the shortest worth messing with for most problems. You begin tuning your mind to a time scale that is the planet’s time scale. For me, it is almost unconscious now and is a kind of companionship with the earth.
In Basin and Range (1981), 134.
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A popular cliche in philosophy says that science is pure analysis or reductionism, like taking the rainbow to pieces; and art is pure synthesis, putting the rainbow together. This is not so. All imagination begins by analyzing nature.
In The Ascent of Man (1973).
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A sick man talks obsessively about his illness; a healthy man never talks about his health; for as Pirandello points out, we take happiness for granted, and only begin to question life when we are unhappy.
In Introduction to the New Existentialism (1966), 15.
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A wonderful exhilaration comes from holding in the mind the deepest questions we can ask. Such questions animate all scientists. Many students of science were first attracted to the field as children by popular accounts of important unsolved problems. They have been waiting ever since to begin working on a mystery. [With co-author Arthur Zajonc]
In George Greenstein and Arthur Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (2006), xii.
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A work of genius is something like the pie in the nursery song, in which the four and twenty blackbirds are baked. When the pie is opened, the birds begin to sing. Hereupon three fourths of the company run away in a fright; and then after a time, feeling ashamed, they would fain excuse themselves by declaring, the pie stank so, they could not sit near it. Those who stay behind, the men of taste and epicures, say one to another, We came here to eat. What business have birds, after they have been baked, to be alive and singing? This will never do. We must put a stop to so dangerous an innovation: for who will send a pie to an oven, if the birds come to life there? We must stand up to defend the rights of all the ovens in England. Let us have dead birds..dead birds for our money. So each sticks his fork into a bird, and hacks and mangles it a while, and then holds it up and cries, Who will dare assert that there is any music in this bird’s song?
Co-author with his brother Augustus William Hare Guesses At Truth, By Two Brothers: Second Edition: With Large Additions (1848), Second Series, 86. (The volume is introduced as “more than three fourths new.” This quote is identified as by Julius; Augustus had died in 1833.)
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Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life.
The Expanding Universe (1933), 56-57.
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Accountants and second-rate business school jargon are in the ascendant. Costs, which rise rapidly, and are easily ascertained and comprehensible, now weigh more heavily in the scales than the unquantifiable and unpredictable values and future material progress. Perhaps science will only regain its lost primacy as peoples and government begin to recognize that sound scientific work is the only secure basis for the construction of policies to ensure the survival of Mankind without irreversible damage to Planet Earth.
In New Scientist, March 3, 1990.
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Albert Einstein called the intuitive or metaphoric mind a sacred gift. He added that the rational mind is a faithful servant. It it paradoxical that in the context of modern life we have begun to worship the servant and defile the divine.
In The Metaphoric Mind: A Celebration of Creative Consciousness (1976), 26. Note that these words are the author’s own free interpretation Einstein’s views. He is not directly quoting Einstein’s words. No verbatim version appears in Einstein writings. A variant of Samples’ words has become misattributed as an Einstein quote: “The intuitive mind is a sacred gift and the rational mind is a faithful servant; we have created a society that honors the servant and has forgotten the gift.”
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All great truths begin as blasphemies.
Spoken by the character the Grand Duchess in the play Annajanska, collected in Heartbreak House, Great Catherine, and Playlets of the War (1919), 262.
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All human knowledge begins with intuitions, proceeds from thence to concepts, and ends with ideas.
Critique of Pure Reason (1781, 1787), B 730. As translated by Norman Kemp Smith in Immanuel Kant's Critique of Pure Reason (1929), 569. Also translated in an epigraph as “All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas,” in David Hilbert and E.J. Townsend (trans.), 'Introduction', Foundations of Geometry (1902), 1, citing Kant, Kritik der reinen Vernunft, Elementarlehre, Part 2, Sec. 2.
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All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate. And, since the law of continuity requires that when the essential attributes of one being approximate those of another all the properties of the one must likewise gradually approximate those of the other, it is necessary that all the orders of natural beings form but a single chain, in which the various classes, like so many rings, are so closely linked one to another that it is impossible for the senses or the imagination to determine precisely the point at which one ends and the next begins?all the species which, so to say, lie near the borderlands being equivocal, at endowed with characters which might equally well be assigned to either of the neighboring species. Thus there is nothing monstrous in the existence zoophytes, or plant-animals, as Budaeus calls them; on the contrary, it is wholly in keeping with the order of nature that they should exist. And so great is the force of the principle of continuity, to my thinking, that not only should I not be surprised to hear that such beings had been discovered?creatures which in some of their properties, such as nutrition or reproduction, might pass equally well for animals or for plants, and which thus overturn the current laws based upon the supposition of a perfect and absolute separation of the different orders of coexistent beings which fill the universe;?not only, I say, should I not be surprised to hear that they had been discovered, but, in fact, I am convinced that there must be such creatures, and that natural history will perhaps some day become acquainted with them, when it has further studied that infinity of living things whose small size conceals them for ordinary observation and which are hidden in the bowels of the earth and the depth of the sea.
Lettre Prétendue de M. De Leibnitz, à M. Hermann dont M. Koenig a Cité le Fragment (1753), cxi-cxii, trans. in A. O. Lovejoy, Great Chain of Being: A Study of the History of an Idea (1936), 144-5.
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All the remedies for all the types of conflicts are alike in that they begin by finding the facts rather than by starting a fight.
As quoted, M.Guy Mellon in Presidential Address, Purdue University. Printed in Proceedings of the Indiana Academy of Science (1943), 52, 12.
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All the sciences are, in some measure, linked with each other, and before the one is ended, the other begins.
In History of the Earth and Animated Nature (1774, 1847), Vol. 1, 65.
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All things began in Order, so shall they end, and so shall they begin again, according to the Ordainer of Order, and the mystical mathematicks of the City of Heaven.
In 'Garden of Cyrus', Religio Medici and Other Writings (1909), 229.
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Alphonse of Castile is reported to have said that if he had had the making of the universe he would have done it much better. And I think so too. Instead of making a man go through the degradation of faculties and death, he should continually improve with age, and then be translated from this world to a superior planet, where he should begin life with the knowledge gained here, and so on. That would be to my mind, as an old man, a more satisfactory way of conducting affairs
Address, in 'Report to the Chemical Society's Jubilee', Nature (26 Mar 1891), 43, 493.
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Although the ocean’s surface seems at first to be completely homogeneous, after half a month we began to differentiate various seas and even different parts of oceans by their characteristic shades. We were astonished to discover that, during an flight, you have to learn anew not only to look, but also to see. At first the finest nuances of color elude you, but gradually your vision sharpens and your color perception becomes richer, and the planet spreads out before you with all its indescribable beauty.
…...
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Among the older records, we find chapter after chapter of which we can read the characters, and make out their meaning: and as we approach the period of man’s creation, our book becomes more clear, and nature seems to speak to us in language so like our own, that we easily comprehend it. But just as we begin to enter on the history of physical changes going on before our eyes, and in which we ourselves bear a part, our chronicle seems to fail us—a leaf has been torn out from nature's record, and the succession of events is almost hidden from our eyes.
Letter 1 to William Wordsworth. Quoted in the appendix to W. Wordsworth, A Complete Guide to the Lakes, Comprising Minute Direction for the Tourist, with Mr Wordsworth's Description of the Scenery of the County and Three Letters upon the Geology of the Lake District (1842), 14.
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And this is the ultimate lesson that our knowledge of the mode of transmission of typhus has taught us: Man carries on his skin a parasite, the louse. Civilization rids him of it. Should man regress, should he allow himself to resemble a primitive beast, the louse begins to multiply again and treats man as he deserves, as a brute beast. This conclusion would have endeared itself to the warm heart of Alfred Nobel. My contribution to it makes me feel less unworthy of the honour which you have conferred upon me in his name.
'Investigations on Typhus', Nobel Lecture, 1928. In Nobel Lectures: Physiology or Medicine 1922-1941 (1965), 187.
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Another error is a conceit that … the best has still prevailed and suppressed the rest: so as, if a man should begin the labor of a new search, he were but like to light upon somewhat formerly rejected, and by rejection brought into oblivion; as if the multitude, or the wisest for the multitude’s sake, were not ready to give passage rather to that which is popular and superficial, than to that which is substantial and profound: for the truth is, that time seemeth to be of the nature of a river or stream, which carrieth down to us that which is light and blown up, and sinketh and drowneth that which is weighty and solid.
Advancement of Learning, Book 1. Collected in The Works of Francis Bacon (1826), Vol 1, 36.
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Anthropology has reached that point of development where the careful investigation of facts shakes our firm belief in the far-reaching theories that have been built up. The complexity of each phenomenon dawns on our minds, and makes us desirous of proceeding more cautiously. Heretofore we have seen the features common to all human thought. Now we begin to see their differences. We recognize that these are no less important than their similarities, and the value of detailed studies becomes apparent. Our aim has not changed, but our method must change. We are still searching for the laws that govern the growth of human culture, of human thought; but we recognize the fact that before we seek for what is common to all culture, we must analyze each culture by careful and exact methods, as the geologist analyzes the succession and order of deposits, as the biologist examines the forms of living matter. We see that the growth of human culture manifests itself in the growth of each special culture. Thus we have come to understand that before we can build up the theory of the growth of all human culture, we must know the growth of cultures that we find here and there among the most primitive tribes of the Arctic, of the deserts of Australia, and of the impenetrable forests of South America; and the progress of the civilization of antiquity and of our own times. We must, so far as we can, reconstruct the actual history of mankind, before we can hope to discover the laws underlying that history.
The Jesup North Pacific Expedition: Memoir of the American Museum of Natural History (1898), Vol. 1, 4.
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Archeus, the Workman and Governour of generation, doth cloath himself presently with a bodily cloathing: For in things soulified he walketh thorow all the Dens and retiring places of his Seed, and begins to transform the matter, according to the perfect act of his own Image.
Oriatrike: Or, Physick Refined, trans. John Chandler (1662), 35.
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Arithmetic, as we shall see by and by, is overdone, in a certain sense, in our schools; just so far as the teaching is based upon the concrete, so far is it profitable; but when the book-makers begin to make it too abstract, as they very often do, it becomes a torture to both teacher and learners, or, at best, a branch of imaginary knowledge unconnected with real life.
From 'Introduction', Mathematical Teaching and its Modern Methods (1886), 10.
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As an exercise of the reasoning faculty, pure mathematics is an admirable exercise, because it consists of reasoning alone, and does not encumber the student with an exercise of judgment: and it is well to begin with learning one thing at a time, and to defer a combination of mental exercises to a later period.
In Annotations to Bacon’s Essays (1873), Essay 1, 493.
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As evolutionary time is measured, we have only just turned up and have hardly had time to catch breath, still marveling at our thumbs, still learning to use the brand-new gift of language. Being so young, we can be excused all sorts of folly and can permit ourselves the hope that someday, as a species, we will begin to grow up.
From 'Introduction' written by Lewis Thomas for Horace Freeland Judson, The Search for Solutions (1980, 1987), xvii.
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As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer. But Euclid for children is barbarous.
Electro-Magnetic Theory (1893), Vol. 1, 148. In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 130.
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At present we begin to feel impatient, and to wish for a new state of chemical elements. For a time the desire was to add to the metals, now we wish to diminish their number. They increase upon us continually, and threaten to enclose within their ranks the bounds of our fair fields of chemical science. The rocks of the mountain and the soil of the plain, the sands of the sea and the salts that are in it, have given way to the powers we have been able to apply to them, but only to be replaced by metals.
In his 16th Lecture of 1818, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 256-257.
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Bacon himself was very ignorant of all that had been done by mathematics; and, strange to say, he especially objected to astronomy being handed over to the mathematicians. Leverrier and Adams, calculating an unknown planet into a visible existence by enormous heaps of algebra, furnish the last comment of note on this specimen of the goodness of Bacon’s view… . Mathematics was beginning to be the great instrument of exact inquiry: Bacon threw the science aside, from ignorance, just at the time when his enormous sagacity, applied to knowledge, would have made him see the part it was to play. If Newton had taken Bacon for his master, not he, but somebody else, would have been Newton.
In Budget of Paradoxes (1872), 53-54.
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Basic research may seem very expensive. I am a well-paid scientist. My hourly wage is equal to that of a plumber, but sometimes my research remains barren of results for weeks, months or years and my conscience begins to bother me for wasting the taxpayer’s money. But in reviewing my life’s work, I have to think that the expense was not wasted.
Basic research, to which we owe everything, is relatively very cheap when compared with other outlays of modern society. The other day I made a rough calculation which led me to the conclusion that if one were to add up all the money ever spent by man on basic research, one would find it to be just about equal to the money spent by the Pentagon this past year.
In The Crazy Ape (1971).
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Belief begins where science leaves off and ends where science begins.
In Fielding Hudson Garrison, An Introduction to the History of Medicine (1929), 14.
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Bigotry and science can have no communication with each other, for science begins where bigotry and absolute certainty end.
Ashley Montagu (ed.), Science and Creationism (1984), Introduction, 8-9.
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Biologically the species is the accumulation of the experiments of all its successful individuals since the beginning.
repr. In The Works of H.G. Wells, vol. 9 (1925). A Modern Utopia, ch. 3, sect. 4 (1905).
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Bradley is one of the few basketball players who have ever been appreciatively cheered by a disinterested away-from-home crowd while warming up. This curious event occurred last March, just before Princeton eliminated the Virginia Military Institute, the year’s Southern Conference champion, from the NCAA championships. The game was played in Philadelphia and was the last of a tripleheader. The people there were worn out, because most of them were emotionally committed to either Villanova or Temple-two local teams that had just been involved in enervating battles with Providence and Connecticut, respectively, scrambling for a chance at the rest of the country. A group of Princeton players shooting basketballs miscellaneously in preparation for still another game hardly promised to be a high point of the evening, but Bradley, whose routine in the warmup time is a gradual crescendo of activity, is more interesting to watch before a game than most players are in play. In Philadelphia that night, what he did was, for him, anything but unusual. As he does before all games, he began by shooting set shots close to the basket, gradually moving back until he was shooting long sets from 20 feet out, and nearly all of them dropped into the net with an almost mechanical rhythm of accuracy. Then he began a series of expandingly difficult jump shots, and one jumper after another went cleanly through the basket with so few exceptions that the crowd began to murmur. Then he started to perform whirling reverse moves before another cadence of almost steadily accurate jump shots, and the murmur increased. Then he began to sweep hook shots into the air. He moved in a semicircle around the court. First with his right hand, then with his left, he tried seven of these long, graceful shots-the most difficult ones in the orthodoxy of basketball-and ambidextrously made them all. The game had not even begun, but the presumably unimpressible Philadelphians were applauding like an audience at an opera.
A Sense of Where You Are: Bill Bradley at Princeton
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But if you have seen the soil of India with your own eyes and meditate on its nature - if you consider the rounded stones found in the earth however deeply you dig, stones that are huge near the mountains and where the rivers have a violent current; stones that are of smaller size at greater distance from the mountains, and where the streams flow more slowly; stones that appear pulverised in the shape of sand where the streams begin to stagnate near their mouths and near the sea - if you consider all this, you could scarcely help thinking that India has once been a sea which by degrees has been filled up by the alluvium of the streams.
Alberuni's India, trans. E. C. Sachau (1888), Vol. 1, 198.
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But in nothing are swifts more singular than in their early retreat. They retire, as to the main body of them, by the tenth of August, and sometimes a few days sooner: and every straggler invariably withdraws by the twentieth, while their congeners, all of them, stay till the beginning of October; many of them all through that month, and some occasionally to the beginning of November. This early retreat is mysterious and wonderful, since that time is often the sweetest season in the year. But, what is more extraordinary, they begin to retire still earlier in the most southerly parts of Andalusia, where they can be no ways influenced by any defect of heat; or, as one might suppose, defect of food. Are they regulated in their motions with us by failure of food, or by a propensity to moulting, or by a disposition to rest after so rapid a life, or by what? This is one of those incidents in natural history that not only baffles our searches, but almost eludes our guesses!
In Letter to Daines Barrington, (28 Sep 1774), in The Natural History and Antiquities of Selborne (1789), 278.
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But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.
In Editor’s Preface to Augustus De Morgan and Thomas J. McCormack (ed.), Elementary Illustrations of the Differential and Integral Calculus (1899), v.
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But who can say that the vapour engine has not a kind of consciousness? Where does consciousness begin, and where end? Who can draw the line? Who can draw any line? Is not everything interwoven with everything? Is not machinery linked with animal life in an infinite variety of ways?
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By the act of generation nothing more is done than to ferment the sperm of ye female by the sperm of ye male that it may thereby become fit nourishment for ye Embryo: ffor ye nourishment of all animals is prepared by ferment & the ferment is taken from animals of the same kind, & makes the nourishment subtile & spiritual. In adult animals the nourishmt is fermented by the choler and pancreatic juice both wch come from the blood. The Embryo not being able to ferment its own nourishment wch comes from the mothers blood has it fermented by the sperm wch comes from ye fathers blood, & by this nourishment it swells, drops off from ye Ovarium & begins to grow with a life distinct from that of ye mother.
From 'Quæst 25' in Draft version of The Queries manuscript, Add. MS. 3970, folio 235 held by the University of Cambridge Library. As quoted and cited in R.W. Home, 'Force, Electricity, and Living Matter', from Margaret J. Osler and Paul Lawrence Farber (eds.), Religion, Science, and Worldview: Essays in Honor of Richard S. Westfall (2002), 113.
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Chaos is the beginning, simplicity is the end.
Letter (1950) to Ocy Tjeng Sit, as quoted in Maurits Cornelis Escher and ‎J.W. Vermeulen (ed.), Escher on Escher: Exploring the Infinite (1989), which is requoted in Michele Emmer and ‎Doris Schattschneider, M.C. Escher’s Legacy: A Centennial Celebration (2007), 71.
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Chaos theory is a new theory invented by scientists panicked by the thought that the public were beginning to understand the old ones.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 273.
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Children are to be guided to make a beginning in all the arts and sciences without interference with their spontaneity, the instinct of imitation being so used as to give them order without constraining them.
In Friedrich Fröbel and Josephine Jarvis (trans.), 'American Preface', The Education of Man (1885), vi.
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Conservation is getting nowhere because it is incompatible with our Abrahamic concept of land. We abuse land because we regard it as a commodity belonging to us. When we see land as a community to which we belong, we may begin to use it with love and respect. There is no other way for land to survive the impact of mechanized man, nor for us to reap from it the esthetic harvest it is capable, under science, of contributing to culture. That land is a community is the basic concept of ecology, but that land is to be loved and respected is an extension of ethics. That land yields a cultural harvest is a fact long known, but latterly often forgotten.
A Sand County Almanac, and Sketches Here and There (1949), viii-ix.
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Considering that, among all those who up to this time made discoveries in the sciences, it was the mathematicians alone who had been able to arrive at demonstrations—that is to say, at proofs certain and evident—I did not doubt that I should begin with the same truths that they have investigated, although I had looked for no other advantage from them than to accustom my mind to nourish itself upon truths and not to be satisfied with false reasons.
In Discourse upon Method, Part 2, in Henry A. Torrey (ed., trans. )Philosophy of Descartes in Extracts from His Writings , (1892), 47-48.
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Despite the high long-term probability of extinction, every organism alive today, including every person reading this paper, is a link in an unbroken chain of parent-offspring relationships that extends back unbroken to the beginning of life on earth. Every living organism is a part of an enormously long success story—each of its direct ancestors has been sufficiently well adapted to its physical and biological environments to allow it to mature and reproduce successfully. Viewed thus, adaptation is not a trivial facet of natural history, but a biological attribute so central as to be inseparable from life itself.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 330.
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Discovery begins by finding the discoverer.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 169.
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Earth bound history has ended. Universal history has begun.
…...
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Euler could repeat the Aeneid from the beginning to the end, and he could even tell the first and last lines in every page of the edition which he used. In one of his works there is a learned memoir on a question in mechanics, of which, as he himself informs us, a verse of Aeneid gave him the first idea. [“The anchor drops, the rushing keel is staid.”]
In Letters of Euler (1872), Vol. 1, 24.
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Every discovery, every enlargement of the understanding, begins as an imaginative preconception of what the truth might be. The imaginative preconception—a “hypothesis”—arises by a process as easy or as difficult to understand as any other creative act of mind; it is a brainwave, an inspired guess, a product of a blaze of insight. It comes anyway from within and cannot be achieved by the exercise of any known calculus of discovery.
In Advice to a Young Scientist (1979), 84.
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Every science begins as philosophy and ends as art.
In The Story of Philosophy (1926, 1961), 2.
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Every science begins by accumulating observations, and presently generalizes these empirically; but only when it reaches the stage at which its empirical generalizations are included in a rational generalization does it become developed science.
In The Data of Ethics (1879), 61.
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Everything you’ve learned in school as “obvious” becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There’s not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines.
…...
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Evolution ... is really two theories, the vague theory and the precise theory. The vague theory has been abundantly proved.... The precise theory has never been proved at all. However, like relativity, it is accepted on faith.... On getting down to actual details, difficulties begin.
In Science is a Sacred Cow (1950), 101 & 103.
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Exercises in being obedient can not begin too early, and I have, during an almost daily observation of six years, discovered no harm from an early, consistent guiding of the germinating will, provided only this guiding be done with the greatest mildness and justice, as if the infant had already an insight into the benefits of obedience.
In W. Preyer and H.W. Brown (trans.), The Mind of the Child: The Senses and the Will: Observations Concerning the Mental Development of the Human Being in the First Years of Life (1888, 1890), Vol. 1, 345.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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For God's sake, stop researching for a while and begin to think.
The Crisis in the University (1949), 183.
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For it is owing to their wonder that men now both begin and at first began to philosophize; they wondered originally at the obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e.g. about the phenomena of the moon and those of the sun and the stars, and about the genesis of the universe. And a man who is puzzled and wonders thinks himself ignorant (whence even the lover of myth is in a sense a lover of wisdom, for myth is composed of wonders); therefore since they philosophized in order to escape from ignorance, evidently they were pursuing science in order to know, and not for any utilitarian end. And this is confirmed by the facts; for it was when almost all the necessities of life and the things that make for comfort and recreation were present, that such knowledge began to be sought. Evidently then we do not seek it for the sake of any advantage; but as the man is free, we say, who exists for himself and not for another, so we pursue this as the only free science, for it alone exists for itself.
Aristotle
Metaphysics, 982b, 12-27. In Jonathan Baines (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1554.
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For most of history, man has had to fight nature to survive; in this century he is beginning to realize that, in order to survive, he must protect it.
…...
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Four college students taking a class together, had done so well through the semester, and each had an “A”. They were so confident, the weekend before finals, they went out partying with friends. Consequently, on Monday, they overslept and missed the final. They explained to the professor that they had gone to a remote mountain cabin for the weekend to study, but, unfortunately, they had a flat tire on the way back, didn’t have a spare, and couldn’t get help for a long time. As a result, they missed the final. The professor kindly agreed they could make up the final the following day. When they arrived the next morning, he placed them each in separate rooms, handed each one a test booklet, and told them to begin. The the first problem was simple, worth 5 points. Turning the page they found the next question, written: “(For 95 points): Which tire?”
Anonymous
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Furnished as all Europe now is with Academies of Science, with nice instruments and the spirit of experiment, the progress of human knowledge will be rapid and discoveries made of which we have at present no conception. I begin to be almost sorry I was born so soon, since I cannot have the happiness of knowing what will be known a hundred years hence.
…...
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God is a child; and when he began to play, he cultivated mathematics. It is the most godly of man’s games.
Said by the fictional character, mathematics teacher, Professor Hirt, in Das Blinde Spiel (The Blind Game, 1954), 253. As translated in an epigraph, Stanley Gudder, A Mathematical Journey (1976), 269. From the original German, “Gott ist ein Kind, und als er zu spielen begann, trieb er Mathematik. Die Mathematik ist göttlichste Spielerei unter den Menschen”, as quoted in Herbert Meschkowski, Hundert Jahre Mengenlehre (1973), 119.
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Gradually the sunken land begins to rise again, and falls perhaps again, and rises again after that, more and more gently each time, till as it were the panting earth, worn out with the fierce passions of her fiery youth, has sobbed herself to sleep once more, and this new world of man is made.
'Thoughts in a Gravel Pit', a lecture delivered at the Mechanics' Institute, Odiham (1857). The Works of Charles Kingsley (1880), 282.
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History warns us … that it is the customary fate of new truths to begin as heresies and to end as superstitions; and, as matters now stand, it is hardly rash to anticipate that, in another twenty years, the new generation, educated under the influences of the present day, will be in danger of accepting the main doctrines of the “Origin of Species,” with as little reflection, and it may be with as little justification, as so many of our contemporaries, twenty years ago, rejected them.
'The Coming of Age of the Origin of Species' (1880). In Collected Essays, Vol. 2: Darwiniana (1893), 229.
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How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.
Max Planck, Walter Henry Johnston, The Universe in the Light of Modern Physics (1931), 58.
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I am entitled to say, if I like, that awareness exists in all the individual creatures on the planet—worms, sea urchins, gnats, whales, subhuman primates, superprimate humans, the lot. I can say this because we do not know what we are talking about: consciousness is so much a total mystery for our own species that we cannot begin to guess about its existence in others.
In Late Night Thoughts on Listening to Mahler's Ninth Symphony(1984), 223.
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I begin my work at about nine or ten o'clock in the evening and continue until four or five in the morning. Night is a more quiet time to work. It aids thought.
In Orison Swett Marden, 'Bell Telephone Talk: Hints on Success by Alexander G. Bell', How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 31.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I confess, that after I began … to discern how useful mathematicks may be made to physicks, I have often wished that I had employed about the speculative part of geometry, and the cultivation of the specious Algebra I had been taught very young, a good part of that time and industry, that I had spent about surveying and fortification (of which I remember I once wrote an entire treatise) and other parts of practick mathematicks.
In 'The Usefulness of Mathematiks to Natural Philosophy', Works (1772), Vol. 3, 426.
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I do not believe that science per se is an adequate source of happiness, nor do I think that my own scientific outlook has contributed very greatly to my own happiness, which I attribute to defecating twice a day with unfailing regularity. Science in itself appears to me neutral, that is to say, it increases men’s power whether for good or for evil. An appreciation of the ends of life is something which must be superadded to science if it is to bring happiness, but only the kind of society to which science is apt to give rise. I am afraid you may be disappointed that I am not more of an apostle of science, but as I grow older, and no doubt—as a result of the decay of my tissues, I begin to see the good life more and more as a matter of balance and to dread all over-emphasis upon anyone ingredient.
Letter to W. W. Norton, Publisher (27 Jan 1931). In The Autobiography of Bertrand Russell, 1914-1944 (1968), Vol. 2, 200.
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I have always loved to begin with the facts, to observe them, to walk in the light of experiment and demonstrate as much as possible, and to discuss the results.
Quoted in Francesco Rodolico, 'Arduino', In Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1970), Vol. 1, 234.
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I love to do research, I want to do research, I have to do research, and I hate to sit down and begin to do research—I always try to put it off just as long as I can.
In I Want to be a Mathematician: an Automathography (1985), 321.
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I must begin with a good body of facts and not from a principle (in which I always suspect some fallacy) and then as much deduction as you please.
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I sometimes ask myself how it came about that I was the one to develop the theory of relativity. The reason, I think, is that a normal adult never stops to think about the problem of space and time. These are things which he has thought of as a child. But my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had already grown up.
In Ronald W. Clark, Einstein: The Life and Times (1971), 10.
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I think there is something more important than believing: Action! The world is full of dreamers, there aren’t enough who will move ahead and begin to take concrete steps to actualize their vision.
…...
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I was interested in flying beginning at age 7, when a close family friend took me in his little airplane. And I remember looking at the wheel of the airplane as we rolled down the runway, because I wanted to remember the exact moment that I first went flying... the other thing growing up is that I was always interested in science.
…...
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I [do not know] when the end of science will come. ... What I do know is that our species is dumber than we normally admit to ourselves. This limit of our mental faculties, and not necessarily of science itself, ensures to me that we have only just begun to figure out the universe.
In Death by Black Hole: And Other Cosmic Quandaries (2007), 17.
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If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties.
The Advancement of Learning (1605) in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1887-1901), Vol. 3, 293.
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If a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again.
Translation in Francis Bacon, James Spedding (ed.) et al., Works of Francis Bacon (1858) Vol. 6, 498.
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If a Schirrus by long standing, increasing, and motion of the adjacent Parts is thus moved, that the neighbouring Vessels around its edges begin to inflame, it’s become malignant, and from its likeness to a Crab, is now called a Cancer, or Carcinoma.
Aphorism No. 492 in Boerhaave’s Aphorisms: Concerning The Knowledge and Cure of Diseases (1715), 113.
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If the world has begun with a single quantum, the notions of space and would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time. I think that such a beginning of the world is far enough from the present order of Nature to be not at all repugnant. It may be difficult to follow up the idea in detail as we are not yet able to count the quantum packets in every case. For example, it may be that an atomic nucleus must be counted as a unique quantum, the atomic number acting as a kind of quantum number. If the future development of quantum theory happens to turn in that direction, we could conceive the beginning of the universe in the form of a unique atom, the atomic weight of which is the total mass of the universe. This highly unstable atom would divide in smaller and smaller atoms by a kind of super-radioactive process.
In 'The Beginning of the World from the Point of View of Quantum Theory', Nature (1931), 127, 706.
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If there is an underlying oneness of all things, it does not matter where we begin, whether with stars, or laws of supply and demand, or frogs, or Napoleon Bonaparte. One measures a circle, beginning anywhere.
Lo! (1931, 1941), 8.
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If we put together all that we have learned from anthropology and ethnography about primitive men and primitive society, we perceive that the first task of life is to live. Men begin with acts, not with thoughts.
Folkways: A Study of the Sociological Importance of Usages, Manners, Customs, Mores and Morals (1907), 2.
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If you go far enough out you can see the Universe itself, all the billion light years summed up time only as a flash, just as lonely, as distant as a star on a June night if you go far enough out. And still, my friend, if you go far enough out you are only at the beginning of yourself.
…...
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If you want to hear, you must begin by listening.
Aphorism as given by the fictional character Dezhnev Senior, in Fantastic Voyage II: Destination Brain (1987), 238.
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In dreams begins responsibility.
In The Collected Poems of W. B. Yeats (2000), 81.
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In every enterprise … the mind is always reasoning, and, even when we seem to act without a motive, an instinctive logic still directs the mind. Only we are not aware of it, because we begin by reasoning before we know or say that we are reasoning, just as we begin by speaking before we observe that we are speaking, and just as we begin by seeing and hearing before we know what we see or what we hear.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 146.
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In Geometry, (which is the only Science that it hath pleased God hitherto to bestow on mankind,) men begin at settling the significations of their words; which settling of significations, they call Definitions; and place them in the beginning of their reckoning.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 4, 105.
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In its earliest development knowledge is self-sown. Impressions force themselves upon men’s senses whether they will or not, and often against their will. The amount of interest in which these impressions awaken is determined by the coarser pains and pleasures which they carry in their train or by mere curiosity; and reason deals with the materials supplied to it as far as that interest carries it, and no further. Such common knowledge is rather brought than sought; and such ratiocination is little more than the working of a blind intellectual instinct. It is only when the mind passes beyond this condition that it begins to evolve science. When simple curiosity passes into the love of knowledge as such, and the gratification of the æsthetic sense of the beauty of completeness and accuracy seems more desirable that the easy indolence of ignorance; when the finding out of the causes of things becomes a source of joy, and he is accounted happy who is successful in the search, common knowledge passes into what our forefathers called natural history, whence there is but a step to that which used to be termed natural philosophy, and now passes by the name of physical science.
In this final state of knowledge the phenomena of nature are regarded as one continuous series of causes and effects; and the ultimate object of science is to trace out that series, from the term which is nearest to us, to that which is at the farthest limit accessible to our means of investigation.
The course of nature as it is, as it has been, and as it will be, is the object of scientific inquiry; whatever lies beyond, above, or below this is outside science. But the philosopher need not despair at the limitation on his field of labor; in relation to the human mind Nature is boundless; and, though nowhere inaccessible, she is everywhere unfathomable.
The Crayfish: an Introduction to the Study of Zoölogy (1880), 2-3. Excerpted in Popular Science (Apr 1880), 16, 789-790.
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In man’s brain the impressions from outside are not merely registered; they produce concepts and ideas. They are the imprint of the external world upon the human brain. Therefore, it is not surprising that, after a long period of searching and erring, some of the concepts and ideas in human thinking should have come gradually closer to the fundamental laws of the world, that some of our thinking should reveal the true structure of atoms and the true movements of the stars. Nature, in the form of man, begins to recognize itself.
In Knowledge and Wonder (1962).
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In mathematics it [sophistry] had no place from the beginning: Mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly we find no parties among mathematicians, and hardly any disputes.
In Essays on the Intellectual Powers of Man, Essay 1, chap. 1.
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In my work I now have the comfortable feeling that I am so to speak on my own ground and territory and almost certainly not competing in an anxious race and that I shall not suddenly read in the literature that someone else had done it all long ago. It is really at this point that the pleasure of research begins, when one is, so to speak, alone with nature and no longer worries about human opinions, views and demands. To put it in a way that is more learned than clear: the philological aspect drops out and only the philosophical remains.
In Davis Baird, R.I.G. Hughes and Alfred Nordmann, Heinrich Hertz: Classical Physicist, Modern Philosopher (1998), 157.
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In Science, it is when we take some interest in the great discoverers and their lives that it becomes endurable, and only when we begin to trace the development of ideas that it becomes fascinating.
Quoted in Robert J. Scully, The Demon and the Quantum (2007), 5.
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In the beginning was the myth. God, in his search for self-expression, invested the souls of Hindus, Greeks, and Germans with poetic shapes and continues to invest each child’s soul with poetry every day.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 8
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In the next twenty centuries … humanity may begin to understand its most baffling mystery—where are we going? The earth is, in fact, traveling many thousands of miles per hour in the direction of the constellation Hercules—to some unknown destination in the cosmos. Man must understand his universe in order to understand his destiny. Mystery, however, is a very necessary ingredient in our lives. Mystery creates wonder and wonder is the basis for man’s desire to understand. Who knows what mysteries will be solved in our lifetime, and what new riddles will become the challenge of the new generation? Science has not mastered prophesy. We predict too much for the next year yet far too little for the next ten. Responding to challenges is one of democracy’s great strengths. Our successes in space can be used in the next decade in the solution of many of our planet’s problems.
In a speech to a Joint Meeting of the Two Houses of Congress to Receive the Apollo 11 Astronauts (16 Sep 1969), in the Congressional Record.
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In the years since man unlocked the power stored up within the atom, the world has made progress, halting, but effective, toward bringing that power under human control. The challenge may be our salvation. As we begin to master the destructive potentialities of modern science, we move toward a new era in which science can fulfill its creative promise and help bring into existence the happiest society the world has ever known.
From Address to the Centennial Convocation of the National Academy of Sciences (22 Oct 1963), 'A Century of Scientific Conquest.' Online at The American Presidency Project.
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In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.
In A Mathematician's Apology (1940, 2012), 76.
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In this country all a man need to do is to attain a little eminence and immediately he begins to talk. Usually his eminence is financial, and the greater this eminence the more he talks and the further his voice reaches. I don't blame the rich people for talking; many of them don’t know what else to do with themselves. The fault is with these who listen. If no one would listen no harm would he done. But the American people are willing to listen to any one who has attained prominence. The main fact is that we've heard a man's name a great many times; that makes us ready to accept whatever he says. … We listen to the one who talks the most and loudest.
As quoted in 'Electricity Will Keep The World From Freezing Up', New York Times (12 Nov 1911), SM4.
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It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability. That a scientific investigation pursued on account of its probability will generally lead to truth, rather than falsehood, is at the best only probable.
In A Treatise on Probability (1921), 322.
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It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.
A Scandal in Bohemia (1891) in Adventures of Sherlock Holmes (1892), 5.
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It is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.
On The Doctrine of Chances, with Later Reflections (1878), 61.
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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 is not I who seek to base Man's dignity upon his great toe, or insinuate that we are lost if an Ape has a hippocampus minor. On the contrary, I have done my best to sweep away this vanity. I have endeavoured to show that no absolute structural line of demarcation, wider than that between the animals which immediately succeed us in the scale, can be drawn between the animal world and ourselves; and I may add the expression of my belief that the attempt to draw a physical distinction is equally futile, and that even the highest facuities of feeling and of intellect begin to germinate in lower forms of life. At the same time, no one is more strongly convinced than I am of the vastness of the gulf between civilized man and the brutes; or is more certain that whether from them or not, he is assuredly not of them.
'On the Relations of Man to the Lower Animals' (1863). In Collected Essays (1894), Vol. 7. 152-3.
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It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
Letter to Farkas Wolfgang Bolyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It is the customary fate of new truths to begin as heresies and to end as superstitions.
From Lecture (19 Mar 1880) delivered at the Royal Institute 'The Coming of Age of The Origin of Species', printed in John Michels (ed.), Science (3 Jul 1880), 1, 15. Also seen paraphrased as, “Every truth starts life as a heresy and ends life as an orthodoxy.”
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It is therefore through the study of mathematics, and only by it, that one can form a fair and comprehensive idea of what science is. … Any scientific education which does not begin with such a study, necessarily is fundamentally flawed.
From Cours de Philosophie Positive (1830), Vol. 1, 132. Comte believed in a hierarchy of the sciences, ordered by degree of generality and simplicity of their ideas. Mathematics he placed first, followed by astronomy, physics, chemistry, biology, and sociology in the sixth and last place. This quote was included by T.H. Huxley, in 'The Scientific Aspects of Positivism', Fortnightly Review (1869), 11, 666-667, in which Huxley strongly disagreed with ranking the abstract discipline of mathematics at the top, since education should begin with the concrete based on investigation by observation, “from the easy to the difficult.” English translation by Webmaster using online resources, from the original French, “C’est donc par l’étude des mathématiques, et seulement par elle, que l’on peut se faire une idée juste et approfondie de ce que c’est qu’une science. … Toute éducation scientifique qui ne commence point par une telle étude pèche donc nécessairement par sa base.”
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It is very difficult to say nowadays where the suburbs of London come to an end and where the country begins. The railways, instead of enabling Londoners to live in the country have turned the countryside into a city.
In The Three Clerks (1857, 1904), 30-31.
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It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.
Proclus
In scholium to Book X of Euclid t. V, 417 as quoted and cited in Ettore Carruccio and Isabel Quigly (trans.), Mathematics And Logic in History And in Contemporary Thought (1964), 27.
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It was a great step in science when men became convinced that, in order to understand the nature of things, they must begin by asking, not whether a thing is good or bad, noxious or beneficial, but of what kind it is? And how much is there of it? Quality and Quantity were then first recognised as the primary features to be observed in scientific inquiry.
'Address to the Mathematical and Physical Sections of the British Association, Liverpool, 15 Sep 1870', The Scientific Papers of James Clerk Maxwell (1890 edition, reprint 2003), Vol. 2, 217.
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It would take a civilization far more advanced than ours, unbelievably advanced, to begin to manipulate negative energy to create gateways to the past. But if you could obtain large quantities of negative energy—and that's a big “IF”—then you could create a time machine that apparently obeys Einstein's equation and perhaps the laws of quantum theory.
Quoted by J.R. Minkel in 'Borrowed Time: Interview with Michio Kaku', Scientific American (23 Nov 2003).
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It [science] must be amoral by its very nature: the minute it begins separating facts into the two categories of good ones and bad ones it ceases to be science and becomes a mere nuisance, like theology.
From American Mercury (Sep 1927). Collected in A Mencken Chrestomathy (1949, 1956), 331.
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It's hard to imagine anything more difficult to study than human sexuality, on every level from the technical to the political. One has only to picture monitoring orgasm in the lab to begin to grasp the challenge of developing testing techniques that are thorough and precise, yet respectful.
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Its [science’s] effectiveness is almost inevitable because it narrows the possibility of refutation and failure. Science begins by saying it can only answer this type of question and ends by saying these are the only questions that can be asked. Once the implications and shallowness of this trick are fully realised, science will be humbled and we shall be free to celebrate ourselves once again.
From Understanding the Present: An Alternative History of Science (2004), 249.
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I’m on the verge of a major breakthrough, but I’m also at the point where physics ends and chemistry begins, so I’ll have to drop the whole thing,
In Michael Dudley Sturge , Statistical and Thermal Physics (2003), 139.
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Judging from our experience upon this planet, such a history, that begins with elementary particles, leads perhaps inevitably toward a strange and moving end: a creature that knows, a science-making animal, that turns back upon the process that generated him and attempts to understand it. Without his like, the universe could be, but not be known, and this is a poor thing. Surely this is a great part of our dignity as men, that we can know, and that through us matter can know itself; that beginning with protons and electrons, out of the womb of time and the vastnesses of space, we can begin to understand; that organized as in us, the hydrogen, the carbon, the nitrogen, the oxygen, those 16-21 elements, the water, the sunlight—all having become us, can begin to understand what they are, and how they came to be.
In 'The Origins of Life', Proceedings of the National Academy of Sciences of the United States of America (1964), 52, 609-110.
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Let me describe briefly how a black hole might be created. Imagine a star with a mass 10 times that of the sun. During most of its lifetime of about a billion years the star will generate heat at its center by converting hydrogen into helium. The energy released will create sufficient pressure to support the star against its own gravity, giving rise to an object with a radius about five times the radius of the sun. The escape velocity from the surface of such a star would be about 1,000 kilometers per second. That is to say, an object fired vertically upward from the surface of the star with a velocity of less than 1,000 kilometers per second would be dragged back by the gravitational field of the star and would return to the surface, whereas an object with a velocity greater than that would escape to infinity.
When the star had exhausted its nuclear fuel, there would be nothing to maintain the outward pressure, and the star would begin to collapse because of its own gravity. As the star shrank, the gravitational field at the surface would become stronger and the escape velocity would increase. By the time the radius had got down to 10 kilometers the escape velocity would have increased to 100,000 kilometers per second, the velocity of light. After that time any light emitted from the star would not be able to escape to infinity but would be dragged back by the gravitational field. According to the special theory of relativity nothing can travel faster than light, so that if light cannot escape, nothing else can either. The result would be a black hole: a region of space-time from which it is not possible to escape to infinity.
'The Quantum Mechanics of Black Holes', Scientific American, 1977, 236, 34-40.
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Let us follow the natural order and begin with the primary facts.
Aristotle
In Ingram Bywater (trans.), Aristotle, On the Art of Poetry (1909), 3.
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Let us make education brave and preventive. Politics is an afterwork, a poor patching. We are always a little late… We shall one day learn to supercede politics by education… We must begin higher up, namely in Education.
Culture (1860). Quoted in Bruce A. Kimball, The True Professional Ideal in America: A History (1996), 198.
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Like all things of the mind, science is a brittle thing: it becomes absurd when you look at it too closely. It is designed for few at a time, not as a mass profession. But now we have megascience: an immense apparatus discharging in a minute more bursts of knowledge than humanity is able to assimilate in a lifetime. Each of us has two eyes, two ears, and, I hope, one brain. We cannot even listen to two symphonies at the same time. How do we get out of the horrible cacophony that assails our minds day and night? We have to learn, as others did, that if science is a machine to make more science, a machine to grind out so-called facts of nature, not all facts are equally worth knowing. Students, in other words, will have to learn to forget most of what they have learned. This process of forgetting must begin after each exam, but never before. The Ph.D. is essentially a license to start unlearning.
Voices In the Labyrinth: Nature, Man, and Science (1979), 2.
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Like Molière’s M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole’s The Mathematical Analysis of Logic.
Co-authored with James R. Newman in Gödel's Proof (1986, 2005), 30.
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Malthus argued a century and a half ago that man, by using up all his available resources, would forever press on the limits of subsistence, thus condemning humanity to an indefinite future of misery and poverty. We can now begin to hope and, I believe, know that Malthus was expressing not a law of nature, but merely the limitation then of scientific and social wisdom. The truth or falsity of his prediction will depend now, with the tools we have, on our own actions, now and in the years to come.
From Address to the Centennial Convocation of the National Academy of Sciences (22 Oct 1963), 'A Century of Scientific Conquest'. Online at The American Presidency Project.
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Man is not born to solve the problem of the universe, but to find out where the problem begins and then restrain himself within the limits of the comprehensible.
The Homiletic Review, Vol. 83-84 (1922), Vol. 84, 290.
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Man … begins life as an ambiguous speck of matter which can in no way be distinguished from the original form of the lowest animal or plant. He next becomes a cell; his life is precisely that of the animalcule. Cells cluster round this primordial cell, and the man is so far advanced that he might be mistaken for an undeveloped oyster; he grows still more, and it is clear that he might even be a fish; he then passes into a stage which is common to all quadrupeds, and next assumes a form which can only belong to quadrupeds of the higher type. At last the hour of birth approaches; coiled within the dark womb he sits, the image of an ape; a caricature of the man that is to be. He is born, and for some time he walks only on all fours; he utters only inarticulate sounds; and even in his boyhood his fondness for climbing trees would seem to be a relic of the old arboreal life.
In The Martyrdom of Man (1876), 393.
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Many people are shrinking from the future and from participation in the movement toward a new, expanded reality. And, like homesick travelers abroad, they are focusing their anxieties on home. The reasons are not far to seek. We are at a turning point in human history... We could turn our attention to the problems that going to the moon certainly will not solve ... But I think this would be fatal to our future... A society that no longer moves forward does not merely stagnate; it begins to die.
…...
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Melvin [Calvin]’s marvellous technique for delivering a scientific lecture was unique. His mind must have roamed constantly, especially in planning lectures. His remarkable memory enabled him to formulate a lecture or manuscript with no breaks in the sequence of his thoughts. His lectures usually began hesitatingly, as if he had little idea of how to begin or what to say. This completely disarmed his audiences, who would try to guess what he might have to say. Soon enough, however, his ideas would coalesce, to be delivered like an approaching freight train, reaching a crescendo of information at breakneck speed and leaving his rapt audience nearly overwhelmed.
Co-author with Andrew A. Benson, 'Melvin Calvin', Biographical Memoirs of the US National Academy of Science.
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Most of us aren’t even sure where science leaves off and technology begins. Neither are the experts.
In Visions of Technology (1999), 22.
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My decision to begin research in radio astronomy was influenced both by my wartime experience with electronics and antennas and by one of my teachers, Jack Ratcliffe, who had given an excellent course on electromagnetic theory during my final undergraduate year.
From Autobiography in Wilhelm Odelberg (ed.), Les Prix Nobel en 1974/Nobel Lectures (1975)
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My mother, my dad and I left Cuba when I was two [January, 1959]. Castro had taken control by then, and life for many ordinary people had become very difficult. My dad had worked [as a personal bodyguard for the wife of Cuban president Batista], so he was a marked man. We moved to Miami, which is about as close to Cuba as you can get without being there. It’s a Cuba-centric society. I think a lot of Cubans moved to the US thinking everything would be perfect. Personally, I have to say that those early years were not particularly happy. A lot of people didn’t want us around, and I can remember seeing signs that said: “No children. No pets. No Cubans.” Things were not made easier by the fact that Dad had begun working for the US government. At the time he couldn’t really tell us what he was doing, because it was some sort of top-secret operation. He just said he wanted to fight against what was happening back at home. [Estefan’s father was one of the many Cuban exiles taking part in the ill-fated, anti-Castro Bay of Pigs invasion to overthrow dictator Fidel Castro.] One night, Dad disappered. I think he was so worried about telling my mother he was going that he just left her a note. There were rumours something was happening back home, but we didn’t really know where Dad had gone. It was a scary time for many Cubans. A lot of men were involved—lots of families were left without sons and fathers. By the time we found out what my dad had been doing, the attempted coup had taken place, on April 17, 1961. Intitially he’d been training in Central America, but after the coup attempt he was captured and spent the next wo years as a political prisoner in Cuba. That was probably the worst time for my mother and me. Not knowing what was going to happen to Dad. I was only a kid, but I had worked out where my dad was. My mother was trying to keep it a secret, so she used to tell me Dad was on a farm. Of course, I thought that she didn’t know what had really happened to him, so I used to keep up the pretence that Dad really was working on a farm. We used to do this whole pretending thing every day, trying to protect each other. Those two years had a terrible effect on my mother. She was very nervous, just going from church to church. Always carrying her rosary beads, praying her little heart out. She had her religion, and I had my music. Music was in our family. My mother was a singer, and on my father’s side there was a violinist and a pianist. My grandmother was a poet.
…...
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Never mind what two tons refers to. What is it? How has it entered in so definite a way into our exprerience? Two tons is the reading of the pointer when the elephant was placed on a weighing machine. Let us pass on. … And so we see that the poetry fades out of the problem, and by the time the serious application of exact science begins we are left only with pointer readings.
From Gifford Lecture, Edinburgh, (1927), 'Pointer Readings', collected in The Nature of the Physical World (1928), 252.
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Newton supposed that the case of the planet was similar to that of [a ball spun around on the end of an elastic string]; that it was always pulled in the direction of the sun, and that this attraction or pulling of the sun produced the revolution of the planet, in the same way that the traction or pulling of the elastic string produces the revolution of the ball. What there is between the sun and the planet that makes each of them pull the other, Newton did not know; nobody knows to this day; and all we are now able to assert positively is that the known motion of the planet is precisely what would be produced if it were fastened to the sun by an elastic string, having a certain law of elasticity. Now observe the nature of this discovery, the greatest in its consequences that has ever yet been made in physical science:—
I. It begins with an hypothesis, by supposing that there is an analogy between the motion of a planet and the motion of a ball at the end of a string.
II. Science becomes independent of the hypothesis, for we merely use it to investigate the properties of the motion, and do not trouble ourselves further about the cause of it.
'On Some of the Conditions of Mental Development,' a discourse delivered at the Royal Institution, 6 Mar 1868, in Leslie Stephen and Frederick Pollock (eds.), Lectures and Essays, by the Late William Kingdon Clifford (1886), 56.
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Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to this idea in its elf, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?
…...
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Nothing in the entire universe ever perishes, believe me, but things vary, and adopt a new form. The phrase “being born” is used for beginning to be something different from what one was before, while “dying” means ceasing to be the same. Though this thing may pass into that, and that into this, yet the sums of things remains unchanged.
…...
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Of course I know that “knickers” begins with a “k”. I’ve been to Oxford—it’s one of the first things they teach you.
As quoted in William Reville, 'The Science of Writing a Good Joke', The Irish Times (5 Jun 2000).
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On Breaking Habits. To begin knocking off the habit in the evening, then the afternoon as well and, finally, the morning too is better than to begin cutting it off in the morning and then go on to the afternoon and evening. I speak from experience as regards smoking and can say that when one comes to within an hour or two of smoke-time one begins to be impatient for it, whereas there will be no impatience after the time for knocking off has been confirmed as a habit.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 220.
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On one occasion, when he was giving a dinner to some friends at the university, he left the table to get them a bottle of wine; but, on his way to the cellar, he fell into reflection, forgot his errand and his company, went to his chamber, put on his surplice, and proceeded to the chapel. Sometimes he would go into the street half dressed, and on discovering his condition, run back in great haste, much abashed. Often, while strolling in his garden, he would suddenly stop, and then run rapidly to his room, and begin to write, standing, on the first piece of paper that presented itself. Intending to dine in the public hall, he would go out in a brown study, take the wrong turn, walk a while, and then return to his room, having totally forgotten the dinner. Once having dismounted from his horse to lead him up a hill, the horse slipped his head out of the bridle; but Newton, oblivious, never discovered it till, on reaching a tollgate at the top of the hill, he turned to remount and perceived that the bridle which he held in his hand had no horse attached to it. His secretary records that his forgetfulness of his dinner was an excellent thing for his old housekeeper, who “sometimes found both dinner and supper scarcely tasted of, which the old woman has very pleasantly and mumpingly gone away with”. On getting out of bed in the morning, he has been discovered to sit on his bedside for hours without dressing himself, utterly absorbed in thought.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 257.
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Once the forest has been removed and the swamp starts being drained, that organic matter begins to oxidise and give off continuing emissions. It’s sort of like the goose that keeps on giving.
From interview with Inter Press Service (IPS), with Stephen de Tarczynski, 'Environment—Indonesia: Deforestation Causing More Than Landslides' (9 Mar 2008).
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Once the hatch was opened, I turned the lock handle and bright rays of sunlight burst through it. I opened the hatch and dust from the station flew in like little sparklets, looking like tiny snowflakes on a frosty day. Space, like a giant vacuum cleaner, began to suck everything out. Flying out together with the dust were some little washers and nuts that dad got stuck somewhere; a pencil flew by.
My first impression when I opened the hatch was of a huge Earth and of the sense of unreality concerning everything that was going on. Space is very beautiful. There was the dark velvet of the sky, the blue halo of the Earth and fast-moving lakes, rivers, fields and clouds clusters. It was dead silence all around, nothing whatever to indicate the velocity of the flight… no wind whistling in your ears, no pressure on you. The panorama was very serene and majestic.
…...
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One cannot ignore half of life for the purposes of science, and then claim that the results of science give a full and adequate picture of the meaning of life. All discussions of “life” which begin with a description of man's place on a speck of matter in space, in an endless evolutionary scale, are bound to be half-measures, because they leave out most of the experiences which are important to use as human beings.
In Religion and the Rebel (1957), 309.
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One must be wary in attributing scientific discovery wholly to any one person. Almost every discovery has a long and precarious history. Someone finds a bit here, another a bit there. A third step succeeds later and thus onward till a genius pieces the bits together and makes the decisive contribution. Science, like the Mississippi, begins in a tiny rivulet in the distant forest. Gradually other streams swell its volume. And the roaring river that bursts the dikes is formed from countless sources.
In 'The Usefulness of Useless Knowledge', Harper’s (Jun/Nov 1939), No. 179, 549
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One must expect a war between U.S.A. and U.S.S.R. which will begin with the total destruction of London. I think the war will last 30 years, and leave a world without civilised people, from which everything will have to build afresh—a process taking (say) 500 years.
Stated just one month after the Hiroshima atomic explosion. Russell became one of the best-known antinuclear activists of his era.
Letter to Gamel Brenan (1 Sep 1945). In Nicholas Griffin (Ed.), The Selected Letters of Bertrand Russell (2002), 410.
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Over very long time scales, when the perturbing influences of both Jupiter and Saturn are taken into account, the seemingly regular orbits of asteroids that stray into the Kirkwood gaps turn chaotic. For millions of years … such an orbit seems predictable. Then the path grows increasingly eccentric until it begins to cross the orbit of Mars and then the Earth. Collisions or close encounters with those planets are inevitable.
In article 'Tales of Chaos: Tumbling Moons and Unstable Asteroids", New York Times (20 Jan 1987), C3.
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People who are unused to learning, learn little, and that slowly, while those more accustomed do much more and do it more easily. The same thing also happens in connection with research. Those who are altogether unfamiliar with this become blinded and bewildered as soon as their minds begin to work: they readily withdraw from the inquiry, in a state of mental fatigue and exhaustion, much like people who attempt to race without having been trained. He, on the other hand, who is accustomed to research, seeks and penetrates everywhere mentally, passing constantly from one topic to another; nor does he ever give up his investigation; he pursues it not merely for a matter of days, but throughout his whole life. Also by transferring his mind to other ideas which are yet not foreign to the questions at issue, he persists till he reaches the solution.
'On Paralysis'. Quoted in A. J. Brock, Greek Medicine: Being Extracts Illustrative of Medical Writers from Hippocrates to Galen (1929), 185.
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Philosophy begins in wonder. And, at the end, when philosophic thought has done its best, the wonder remains. There have been added, however, some grasp of the immensity of things, some purification of emotion by understanding.
In Modes of Thought: Six Lectures Delivered in Wellesley College, Massachusetts, and Two Lectures in the University of Chicago (1908, 1938), 168
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Science has so accustomed us to devising and accepting theories to account for the facts we observe, however fantastic, that our minds must begin their manufacture before we are aware of it.
Seven American Nights (1978). In the collection, David G. Hartwell (Ed.), The Dark Descent (1997), 653.
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Science is organized knowledge; and before knowledge can be organized, some of it must first be possessed. Every study, therefore, should have a purely experimental introduction; and only after an ample fund of observations has been accumulated, should reasoning begin.
In essay 'The Art of Education', The North British Review (May 1854), 137.
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Science only begins for man from the moment when his mind lays hold of matter—when he tries to subject the mass accumulated by experience to rational combinations.
In 'Introduction', Cosmos: Sketch of a Physical Description of the Universe (1849), Vol. 1, 64. Translation “under the superintendence of” Edward Sabine.
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Science should be taught the way mathematics is taught today. Science education should begin in kindergarten. In the first grade one would learn a little more, in the second grade, a little more, and so on. All students should get this basic science training.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 738.
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Science, by itself, cannot supply us with an ethic. It can show us how to achieve a given end, and it may show us that some ends cannot be achieved. But among ends that can be achieved our choice must be decided by other than purely scientific considerations. If a man were to say, “I hate the human race, and I think it would be a good thing if it were exterminated,” we could say, “Well, my dear sir, let us begin the process with you.” But this is hardly argument, and no amount of science could prove such a man mistaken.
'The Science to Save us from Science', New York Times Magazine (19 Mar 1950). Collected in M. Gardner (ed.), Great Essays in Science (1950), 396-397.
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Science, like the Mississippi, begins in a tiny rivulet in the distant forest.
In 'The Usefulness of Useless Knowledge', Harper’s (Jun/Nov 1939), No. 179, 549. Part of a longer quote beginning, “One must be wary in attributing scientific discovery…”, on the Abraham Flexner Quotes page of this website.
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Since the discovery of secret things and in the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort; therefore to the end that the noble substance of that great loadstone, our common mother (the earth), still quite unknown, and also the forces extraordinary and exalted of this globe may the better be understood, we have decided first to begin with the common stony and ferruginous matter, and magnetic bodies, and the parts of the earth that we may handle and may perceive with the senses; then to proceed with plain magnetic experiments, and to penetrate to the inner parts of the earth.
On the Loadstone and Magnetic Bodies and on the Great Magnet the Earth: A New Physiology, Demonstrated with many Arguments and Experiments (1600), trans. P. Fleury Mottelay (1893), Author’s Preface, xlvii.
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Society is not a mere sum of individuals. Rather, the system formed by their association represents a specific reality which has its own characteristics... The group thinks, feels, and acts quite differently from the way in which its members would were they isolated. If, then, we begin with the individual, we shall be able to understand nothing of what takes place in the group.
The Rules of Sociological Method (1895), 8th edition, trans. Sarah A. Solovay and John M. Mueller, ed. George E. G. Catlin (1938,1964 edition), 103-4.
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Sooner or later in every talk, [David] Brower describes the creation of the world. He invites his listeners to consider the six days of Genesis as a figure of speech for what has in fact been 4 billion years. On this scale, one day equals something like six hundred and sixty-six million years, and thus, all day Monday and until Tuesday noon, creation was busy getting the world going. Life began Tuesday noon, and the beautiful organic wholeness of it developed over the next four days. At 4 p.m. Saturday, the big reptiles came on. At three minutes before midnight on the last day, man appeared. At one-fourth of a second before midnight Christ arrived. At one-fortieth of a second before midnight, the Industrial Revolution began. We are surrounded with people who think that what we have been doing for that one-fortieth of a second can go on indefinitely. They are considered normal, but they are stark. raving mad.
In Encounters with the Archdruid (1971), 79-80.
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Spherical space is not very easy to imagine. We have to think of the properties of the surface of a sphere—the two-dimensional case—and try to conceive something similar applied to three-dimensional space. Stationing ourselves at a point let us draw a series of spheres of successively greater radii. The surface of a sphere of radius r should be proportional to r2; but in spherical space the areas of the more distant spheres begin to fall below the proper proportion. There is not so much room out there as we expected to find. Ultimately we reach a sphere of biggest possible area, and beyond it the areas begin to decrease. The last sphere of all shrinks to a point—our antipodes. Is there nothing beyond this? Is there a kind of boundary there? There is nothing beyond and yet there is no boundary. On the earth’s surface there is nothing beyond our own antipodes but there is no boundary there
In Space, Time and Gravitation: An Outline of the General Relativity Theory (1920, 1921), 158-159.
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Standing now in diffused light, with the wind at my back, I experience suddenly a feeling of completeness–not a feeling of having achieved something or of being stronger than everyone who was ever here before, not a feeling of having arrived at the ultimate point, not a feeling of supremacy. Just a breath of happiness deep inside my mind and my breast. The summit seemed suddenly to me to be a refuge, and I had not expected to find any refuge up here. Looking at the steep, sharp ridges below us, I have the impression that to have come later would have been too late. Everything we now say to one another, we only say out of embarrassment. I don’t think anymore. As I pull the tape recorder, trancelike, from my rucksack, and switch it on wanting to record a few appropriate phrases, tears again well into my eyes. “Now we are on the summit of Everest,” I begin, “it is so cold that we cannot take photographs…” I cannot go on, I am immediately shaken with sobs. I can neither talk nor think, feeling only how this momentous experience changes everything. To reach only a few meters below the summit would have required the same amount of effort, the same anxiety and burden of sorrow, but a feeling like this, an eruption of feeling, is only possible on the summit itself.
In Everest: Expedition to the Ultimate (1979), 180.
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Success is dangerous. One begins to copy oneself and to copy oneself is more dangerous than to copy others.
As quoted in The Artist (1978), 93, 5.
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Symbolism is useful because it makes things difficult. Now in the beginning everything is self-evident, and it is hard to see whether one self-evident proposition follows from another or not. Obviousness is always the enemy to correctness. Hence we must invent a new and difficult symbolism in which nothing is obvious. … Thus the whole of Arithmetic and Algebra has been shown to require three indefinable notions and five indemonstrable propositions.
In International Monthly (1901), 4, 85-86.
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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 advanced course in physics began with Rutherford’s lectures. I was the only woman student who attended them and the regulations required that women should sit by themselves in the front row. There had been a time when a chaperone was necessary but mercifully that day was past. At every lecture Rutherford would gaze at me pointedly, as I sat by myself under his very nose, and would begin in his stentorian voice: “Ladies and Gentlemen”. All the boys regularly greeted this witticism with thunderous applause, stamping with their feet in the traditional manner, and at every lecture I wished I could sink into the earth. To this day I instinctively take my place as far back as possible in a lecture room.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 118.
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The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
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The artist and the scientist—and the physician, in a sense, is both—is a man who is presumed to be interested primarily in his work, not in its emoluments. He can do genuinely good work, indeed, only to the extent that he is so interested. The moment he begins habitually to engage in enterprises that offer him only profit he ceases to be either an artist or a scientist, and becomes a mere journeyman artisan.
From Baltimore Evening Sun (12 May 1924). Collected in A Mencken Chrestomathy (1949, 1956), 297.
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The beginning of a revolution is in reality the end of a belief.
From the original French, “Les revolutions qui commencent sont en réalité des croyances qui finissent.” in Psychologie des Foules (1895), 130. English text in The Crowd: A Study of the Popular Mind (1897), Book 2, Chap. 4, 143. [Note: The original French uses plurals, and could be translated: “Revolutions that begin are actually beliefs that end.” —Webmaster]
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The beginning of morality is to see the world as it is.
…...
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The best part of working at a university is the students. They come in fresh, enthusiastic, open to ideas, unscarred by the battles of life. They don't realize it, but they're the recipients of the best our society can offer. If a mind is ever free to be creative, that's the time. They come in believing textbooks are authoritative but eventually they figure out that textbooks and professors don't know everything, and then they start to think on their own. Then, I begin learning from them.
As quoted in autobiography of Stephen Chu in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 120.
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The best scientist is open to experience and begins with romance— the idea that anything is possible.
…...
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The biologist can push it back to the original protist, and the chemist can push it back to the crystal, but none of them touch the real question of why or how the thing began at all. The astronomer goes back untold million of years and ends in gas and emptiness, and then the mathematician sweeps the whole cosmos into unreality and leaves one with mind as the only thing of which we have any immediate apprehension. Cogito ergo sum, ergo omnia esse videntur. All this bother, and we are no further than Descartes. Have you noticed that the astronomers and mathematicians are much the most cheerful people of the lot? I suppose that perpetually contemplating things on so vast a scale makes them feel either that it doesn’t matter a hoot anyway, or that anything so large and elaborate must have some sense in it somewhere.
As co-author with Robert Eustace, The Documents in the Case (1930), 72.
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The card-player begins by arranging his hand for maximum sense. Scientists do the same with the facts they gather.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 318.
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The contributions of physiological knowledge to an understanding of distribution are necessarily inferential. Distribution is a historical phenomenon, and the data ordinarily obtained by students of physiology are essentially instantaneous. However, every organism has a line of ancestors which extends back to the beginning of life on earth and which, during this immensity of time, has invariably been able to avoid, to adapt to, or to compensate for environmental changes.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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The day dawned grey and dreary
The sky made of silver
While the first snowflakes
Began to fall.
A lone bird chirped
In a tree bare of its leaves.
Standing on a lonely road
I stood watching as the world
Started changing.
And I embraced the winter
With memories of summer’s warmth
Still in my heart.
And soon the snowflakes
Began to dance about me
And I twirled around and around
As everything
Turned into a winter wonderland.
…...
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The discovery of the famous original [Rosetta Stone] enabled Napoleon’s experts to begin the reading of Egypt’s ancient literature. In like manner the seismologists, using the difficult but manageable Greek of modern physics, are beginning the task of making earthquakes tell the nature of the earth’s interior and translating into significant speech the hieroglyphics written by the seismograph.
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The distinctive Western character begins with the Greeks, who invented the habit of deductive reasoning and the science of geometry.
In 'Western Civilization', collected in In Praise of Idleness and Other Essays (1935), 161.
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The earth itself assures us it is a living entity. Deep below surface one can hear its slow pulse, feel its vibrant rhythm. The great breathing mountains expand and contract. The vast sage desert undulates with almost imperceptible tides like the oceans. From the very beginning, throughout all its cataclysmic upthrusts and deep sea submergences, the planet Earth seems to have maintained an ordered rhythm.
…...
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The Earth Speaks, clearly, distinctly, and, in many of the realms of Nature, loudly, to William Jennings Bryan, but he fails to hear a single sound. The earth speaks from the remotest periods in its wonderful life history in the Archaeozoic Age, when it reveals only a few tissues of its primitive plants. Fifty million years ago it begins to speak as “the waters bring forth abundantly the moving creatures that hath life.” In successive eons of time the various kinds of animals leave their remains in the rocks which compose the deeper layers of the earth, and when the rocks are laid bare by wind, frost, and storm we find wondrous lines of ascent invariably following the principles of creative evolution, whereby the simpler and more lowly forms always precede the higher and more specialized forms.
The earth speaks not of a succession of distinct creations but of a continuous ascent, in which, as the millions of years roll by, increasing perfection of structure and beauty of form are found; out of the water-breathing fish arises the air-breathing amphibian; out of the land-living amphibian arises the land-living, air-breathing reptile, these two kinds of creeping things resembling each other closely. The earth speaks loudly and clearly of the ascent of the bird from one kind of reptile and of the mammal from another kind of reptile.
This is not perhaps the way Bryan would have made the animals, but this is the way God made them!
The Earth Speaks to Bryan (1925), 5-6. Osborn wrote this book in response to the Scopes Monkey Trial, where William Jennings Bryan spoke against the theory of evolution. They had previously been engaged in the controversy about the theory for several years. The title refers to a Biblical verse from the Book of Job (12:8), “Speak to the earth and it shall teach thee.”
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The engineer is concerned to travel from the abstract to the concrete. He begins with an idea and ends with an object. He journeys from theory to practice. The scientist’s job is the precise opposite. He explores nature with his telescopes or microscopes, or much more sophisticated techniques, and feeds into a computer what he finds or sees in an attempt to define mathematically its significance and relationships. He travels from the real to the symbolic, from the concrete to the abstract. The scientist and the engineer are the mirror image of each other.
In The Development of Design (1981), 19-20.
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The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning.
In Thomas Hobbes and William Molesworth (ed.) Leviathan: Or the Matter, Form and Power of a Commonwealth Ecclesiastical and Civil (1839), Vol. 3, 24.
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The first thing the reasonable man must do is to be content with a very little knowledge and a very great deal of ignorance. The second thing he must do is to make the utmost possible use of the knowledge he has and not waste his energy crying for the moon. The third thing he must do is try and see clearly where his knowledge ends and his ignorance begins.
Scientific Method: An Inquiry into the Character and Validy of Natural Law (1923), 177.
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The generation of seeds ... is therefore marvelous and analogous to the other productions of living things. For first of all an umbilicus appears. ... Its extremity gradually expands and after gathering a colliquamentous ichor becomes analogous to an amnion. ... In the course of time the seed or fetus begins to become visible.
'On the Developmental Process', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 850.
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The good news is that Americans will, in increasing numbers, begin to value and protect the vast American Landscape. The bad news is that they may love it to death.
The American Land
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The great question. … is, shall we surrender to our surroundings, or shall we make our peace with nature and begin to make reparations for the damage we have done to our air, our land, our water? Restoring nature to its natural state is a cause beyond party and beyond factions. It has become a common cause of all the people of America.
State of the Union Address (22 Jan 1970).
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The Himalayas are the crowning achievement of the Indo-Australian plate. India in the Oligocene crashed head on into Tibet, hit so hard that it not only folded and buckled the plate boundaries but also plowed into the newly created Tibetan plateau and drove the Himalayas five and a half miles into the sky. The mountains are in some trouble. India has not stopped pushing them, and they are still going up. Their height and volume are already so great they are beginning to melt in their own self-generated radioactive heat. When the climbers in 1953 planted their flags on the highest mountain, they set them in snow over the skeletons of creatures that had lived in a warm clear ocean that India, moving north, blanked out. Possibly as much as 20,000 feet below the sea floor, the skeletal remains had turned into rock. This one fact is a treatise in itself on the movements of the surface of the earth.
If by some fiat, I had to restrict all this writing to one sentence; this is the one I would choose: the summit of Mount Everest is marine limestone.
Annals of the Former World
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The long-range trend toward federal regulation, which found its beginnings in the Interstate Commerce Act of 1887 and the Sherman Act of 1890, which was quickened by a large number of measures in the Progressive era, and which has found its consummation in our time, was thus at first the response of a predominantly individualistic public to the uncontrolled and starkly original collectivism of big business. In America the growth of the national state and its regulative power has never been accepted with complacency by any large part of the middle-class public, which has not relaxed its suspicion of authority, and which even now gives repeated evidence of its intense dislike of statism. In our time this growth has been possible only under the stress of great national emergencies, domestic or military, and even then only in the face of continuous resistance from a substantial part of the public. In the Progressive era it was possible only because of widespread and urgent fear of business consolidation and private business authority. Since it has become common in recent years for ideologists of the extreme right to portray the growth of statism as the result of a sinister conspiracy of collectivists inspired by foreign ideologies, it is perhaps worth emphasizing that the first important steps toward the modern organization of society were taken by arch-individualists—the tycoons of the Gilded Age—and that the primitive beginning of modern statism was largely the work of men who were trying to save what they could of the eminently native Yankee values of individualism and enterprise.
…...
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The material world begins to seem so trivial, so arbitrary, so ephemeral when contrasted with the timeless beauty of mathematics.
In The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities (1994), 160.
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The mathematics of the twenty-first century may be very different from our own; perhaps the schoolboy will begin algebra with the theory of substitution groups, as he might now but for inherited habits.
From Address before the New York Mathematical Society, Bulletin of the New York Mathematical Society (1893), 3, 107. As cited in G.A. Miller, 'Appreciative Remarks on the Theory of Groups', The American Mathematical Monthly (1903), 10, No. 4, 89. https://books.google.com/books?id=hkM0AQAAMAAJ 1903
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The maxim of science is simply that of common sense—simple cases first; begin with seeing how the main force acts when there is as little as possible to impede it, and when you thoroughly comprehend that, add to it in succession the separate effects of each of the incumbering and interfering agencies.
Collected in The Works of Walter Bagehot (1889), Vol. 5, 319-320.
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The microbial global brain—gifted with long-range transport, data trading, genetic variants … and the ability to reinvent genomes—began its operations some 91 trillion bacterial generations before the birth of the Internet. Ancient bacteria, if they functioned like those today, had mastered the art of worldwide information exchange. … The earliest microorganisms would have used planet-sweeping currents of wind and water to carry the scraps of genetic code…
In 'Creative Nets in the Precambrian Era', Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 18-19.
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The more you’re in this business, the more conservative you get. I’ve been in it long enough to be very conservative, to want to improve what we’ve got rather than begin by building what we haven’t.
Expressing being wary of unproved new ideas. Quoted in 'Reach For The Stars', Time (17 Feb 1958), 71, 25.
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The oil industry is a stunning example of how science, technology, and mass production can divert an entire group of companies from their main task. ... No oil company gets as excited about the customers in its own backyard as about the oil in the Sahara Desert. ... But the truth is, it seems to me, that the industry begins with the needs of the customer for its products. From that primal position its definition moves steadily back stream to areas of progressively lesser importance until it finally comes to rest at the search for oil.
In 'Marketing Myopia' originally published in Harvard Business Review (). Reprinted in Harvard Business Review Classics: Marketing Myopia (2008), 66-71.
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The only objections that have occurred to me are, 1st that you have loaded yourself with an unnecessary difficulty in adopting Natura non facit saltum so unreservedly. … And 2nd, it is not clear to me why, if continual physical conditions are of so little moment as you suppose, variation should occur at all. However, I must read the book two or three times more before I presume to begin picking holes.
Comments after reading Darwin's book, Origin of Species.]
Letter to Charles Darwin (23 Nov 1859). In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 214.
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The precise moment at which a great belief is doomed is easily recognizable; it is the moment when its value begins to be called into question.
From Psychologie des Foules (1895), 130. English text in The Crowd: A Study of the Popular Mind (1897), Book 2, Chap. 4, 143. Original French text: “Le jour précis où une grande croyance est marquée pour mourir est facile à reconnaître; c’est celui où sa valeur commence à être discutée.”
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The principles of Geology like those of geometry must begin at a point, through two or more of which the Geometrician draws a line and by thus proceeding from point to point, and from line to line, he constructs a map, and so proceeding from local to gen maps, and finally to a map of the world. Geometricians founded the science of Geography, on which is based that of Geology.
Abstract View of Geology, page proofs of unpublished work, Department of Geology, University of Oxford, 1.
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The process of tracing regularity in any complicated, and at first sight confused, set of appearances, is necessarily tentative; we begin by making any supposition, even a false one, to see what consequences will follow from it ; and by observing how these differ from the real phenomena, we learn what corrections to make in our assumption.
A System of Logic, Ratiocinative and Inductive (1858), 295.
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The real danger is not that computers will begin to think like men, but that men will begin to think like computers.
As quoted, without citation, in Howard W. Eves, Return to Mathematical Circles, (1988), 63.
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The realization that our small planet is only one of many worlds gives mankind the perspective it needs to realize sooner that our own world belongs to all of its creatures, that the Moon landing marks the end of our childhood as a race and the beginning of a newer and better civilization.
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The reason Dick's [Richard Feynman] physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans [Bethe] and Oppy [Oppenheimer] and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial.
Quoted in Michio Kaku and Jennifer Trainer Thompson, Beyond Einstein: the Cosmic Quest for the Theory of the Universe (1987, 1999), 56-57, citing Freeman Dyson, Disturbing the Universe (1979, 1981), 55-56.
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The reason I love the sea I cannot explain - it’s physical. When you dive you begin to feel like an angel. It’s a liberation of your weight.
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The science hangs like a gathering fog in a valley, a fog which begins nowhere and goes nowhere, an incidental, unmeaning inconvenience to passers-by.
repr. In The Works of H.G. Wells, vol. 9 (1925). A Modern Utopia, ch. 3, sect. 3 (1905)
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The science of mathematics performs more than it promises…. The study of the mathematics, like the Nile, begins in minuteness, but ends in magnificence.
Reflection 342, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 162.
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The science of metaphysics promises more than it performs. The study of … metaphysics begins with a torrent of tropes, and a copious current of words, yet loses itself at last, in obscurity and conjecture, like the Niger in his barren deserts of sand.
Reflection 342, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 162.
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The scientific method is a potentiation of common sense, exercised with a specially firm determination not to persist in error if any exertion of hand or mind can deliver us from it. Like other exploratory processes, it can be resolved into a dialogue between fact and fancy, the actual and the possible; between what could be true and what is in fact the case. The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about nature. It begins as a story about a Possible World—a story which we invent and criticise and modify as we go along, so that it ends by being, as nearly as we can make it, a story about real life.
Induction and Intuition in Scientific Thought (1969), 59.
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The starting point of Darwin’s theory of evolution is precisely the existence of those differences between individual members of a race or species which morphologists for the most part rightly neglect. The first condition necessary, in order that any process of Natural Selection may begin among a race, or species, is the existence of differences among its members; and the first step in an enquiry into the possible effect of a selective process upon any character of a race must be an estimate of the frequency with which individuals, exhibiting any given degree of abnormality with respect to that, character, occur. The unit, with which such an enquiry must deal, is not an individual but a race, or a statistically representative sample of a race; and the result must take the form of a numerical statement, showing the relative frequency with which the various kinds of individuals composing the race occur.
Biometrika: A Joumal for the Statistical Study of Biological Problems (1901), 1, 1-2.
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The stream of human knowledge is heading towards a non-mechanical reality. The universe begins to look more like a great thought than a great machine. Mind no longer appears to be an accidental intruder into the realm of matter. We are beginning to suspect that we ought rather to hail it as the creator and governor of this realm.
The Mysterious Universe (1930), 137.
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The term ecology comes from the Greek word oikos, and means ‘the household.’ Ecological responsibility, then, begins at home and expands to fill the entire planet.
The Green Lifestyle Handbook
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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 worst state of affairs is when science begins to concern itself with art.
Paul Klee
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There are many different styles of composition. I characterize them always as Mozart versus Beethoven. When Mozart began to write at that time he had the composition ready in his mind. He wrote the manuscript and it was ‘aus einem Guss’ (casted as one). And it was also written very beautiful. Beethoven was an indecisive and a tinkerer and wrote down before he had the composition ready and plastered parts over to change them. There was a certain place where he plastered over nine times and one did remove that carefully to see what happened and it turned out the last version was the same as the first one.
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There is much to be said for being a mathematician. To begin with, he has to be completely honest in his work, not from any superior morality, but because he simply cannot get away with a fake.
In 'The Mathematician’s Art of Work' (1967), collected in Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 195.
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There’s Nature and she’s going to come out the way She is. So therefore when we go to investigate we shouldn’t predecide what it is we’re looking for only to find out more about it. Now you ask: “Why do you try to find out more about it?” If you began your investigation to get an answer to some deep philosophical question, you may be wrong. It may be that you can’t get an answer to that particular question just by finding out more about the character of Nature. But that’s not my interest in science; my interest in science is to simply find out about the world and the more I find out the better it is, I like to find out...
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They say,
The solid earth whereon we tread
In tracts of fluent heat began,
And grew to seeming-random forms,
The seeming prey of cyclic storms,
Till at the last arose the Man. …
From poem, 'In Memoriam A.H.H.' written between 1833-50, and first published anonymously in 1850. Collected in Poetical Works of Alfred Tennyson (1860), Vol.2, 147.
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This is the element that distinguishes applied science from basic. Surprise is what makes the difference. When you are organized to apply knowledge, set up targets, produce a usable product, you require a high degree of certainty from the outset. All the facts on which you base protocols must be reasonably hard facts with unambiguous meaning. The challenge is to plan the work and organize the workers so that it will come out precisely as predicted. For this, you need centralized authority, elaborately detailed time schedules, and some sort of reward system based on speed and perfection. But most of all you need the intelligible basic facts to begin with, and these must come from basic research. There is no other source. In basic research, everything is just the opposite. What you need at the outset is a high degree of uncertainty; otherwise it isn’t likely to be an important problem. You start with an incomplete roster of facts, characterized by their ambiguity; often the problem consists of discovering the connections between unrelated pieces of information. You must plan experiments on the basis of probability, even bare possibility, rather than certainty.
The Planning of Science, The Lives of a Cell: Notes of a Biology Watcher, (1974) .
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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, however, seems to be certain: the ichor, that is, the material I have mentioned that finally becomes red, exists before the heart begins to beat, but the heart exists and even beats before the blood reddens.
'On the Formation of the Chick in the Egg' (1673), in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 957.
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Thought-economy is most highly developed in mathematics, that science which has reached the highest formal development, and on which natural science so frequently calls for assistance. Strange as it may seem, the strength of mathematics lies in the avoidance of all unnecessary thoughts, in the utmost economy of thought-operations. The symbols of order, which we call numbers, form already a system of wonderful simplicity and economy. When in the multiplication of a number with several digits we employ the multiplication table and thus make use of previously accomplished results rather than to repeat them each time, when by the use of tables of logarithms we avoid new numerical calculations by replacing them by others long since performed, when we employ determinants instead of carrying through from the beginning the solution of a system of equations, when we decompose new integral expressions into others that are familiar,—we see in all this but a faint reflection of the intellectual activity of a Lagrange or Cauchy, who with the keen discernment of a military commander marshalls a whole troop of completed operations in the execution of a new one.
In Populär-wissenschafliche Vorlesungen (1903), 224-225.
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Thus science must begin with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices.
In Conjectures and Refutations: the Growth of Scientific Knowledge (1963, 2002), 66.
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To introduce something altogether new would mean to begin all over, to become ignorant again, and to run the old, old risk of failing to learn.
Isaac Asimov, Patricia S. Warrick, Martin Harry Greenberg, Machines That Think: The Best Science Fiction Stories About Robots and Computers? (1984), 2.
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To set foot on the soil of the asteroids, to lift by hand a rock from the Moon, to observe Mars from a distance of several tens of kilometers, to land on its satellite or even on its surface, what can be more fantastic? From the moment of using rocket devices a new great era will begin in astronomy: the epoch of the more intensive study of the firmament.
(1896). As quoted in Firmin Joseph Krieger, Behind the Sputniks: A Survey of Soviet Space Science (1958), 23.
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To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
In Axiomatic Set Theory (1971), 9-15. In Thomas Tymoczko, New Directions in the Philosophy of Mathematics: an Anthology (), 11-12.
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Today there is a wide measure of agreement, which on the physical side of science approaches almost to unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a great machine. Mind no longer appears as an accidental intruder into the realm of matter; we are beginning to suspect that we ought rather to hail it as a creator and governor of the realm of matter. …
In The Mysterious Universe (1930, 1932), 181.
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Truth travels down from the heights of philosophy to the humblest walks of life, and up from the simplest perceptions of an awakened intellect to the discoveries which almost change the face of the world. At every stage of its progress it is genial, luminous, creative. When first struck out by some distinguished and fortunate genius, it may address itself only to a few minds of kindred power. It exists then only in the highest forms of science; it corrects former systems, and authorizes new generalizations. Discussion, controversy begins; more truth is elicited, more errors exploded, more doubts cleared up, more phenomena drawn into the circle, unexpected connexions of kindred sciences are traced, and in each step of the progress, the number rapidly grows of those who are prepared to comprehend and carry on some branches of the investigation,— till, in the lapse of time, every order of intellect has been kindled, from that of the sublime discoverer to the practical machinist; and every department of knowledge been enlarged, from the most abstruse and transcendental theory to the daily arts of life.
In An Address Delivered Before the Literary Societies of Amherst College (25 Aug 1835), 16-17.
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Understanding … must begin by saturating itself with facts and realities. … Besides, we only understand that which is already within us. To understand is to possess the thing understood, first by sympathy and then by intelligence. Instead of first dismembering and dissecting the object to be conceived, we should begin by laying hold of it in its ensemble. The procedure is the same, whether we study a watch or a plant, a work of art or a character.
(7 Apr 1886). In Mary A. Ward (trans.), Amiel’s Journal: The Journal Intime of Henri-Frédéric Amiel (1889), 119.
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