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Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Expect Quotes (200 quotes)

Mathematical truth has validity independent of place, personality, or human authority. Mathematical relations are not established, nor can they be abrogated, by edict. The multiplication table is international and permanent, not a matter of convention nor of relying upon authority of state or church. The value of π is not amenable to human caprice. The finding of a mathematical theorem may have been a highly romantic episode in the personal life of the discoverer, but it cannot be expected of itself to reveal the race, sex, or temperament of this discoverer. With modern means of widespread communication even mathematical notation tends to be international despite all nationalistic tendencies in the use of words or of type.
Anonymous
In 'Light Thrown on the Nature of Mathematics by Certain Aspects of Its Development', Mathematics in General Education (1940), 256. This is the Report of the Committee on the Function of Mathematics in General Education of the Commission on Secondary School Curriculum, which was established by the Executive Board of the Progressive Education Association in 1932.
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Question: State the relations existing between the pressure, temperature, and density of a given gas. How is it proved that when a gas expands its temperature is diminished?
Answer: Now the answer to the first part of this question is, that the square root of the pressure increases, the square root of the density decreases, and the absolute temperature remains about the same; but as to the last part of the question about a gas expanding when its temperature is diminished, I expect I am intended to say I don't believe a word of it, for a bladder in front of a fire expands, but its temperature is not at all diminished.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 175, Question 1. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.
In 'On the Development of the Methods of Theoretical Physics in Recent Times', Populäre Schriften, Essay 14. Address (22 Sep 1899) to the Meeting of Natural Scientists at Munich. Collected in Brian McGuinness (ed.), Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, Selected Writings (1974), 79.
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A fossil hunter needs sharp eyes and a keen search image, a mental template that subconsciously evaluates everything he sees in his search for telltale clues. A kind of mental radar works even if he isn’t concentrating hard. A fossil mollusk expert has a mollusk search image. A fossil antelope expert has an antelope search image. … Yet even when one has a good internal radar, the search is incredibly more difficult than it sounds. Not only are fossils often the same color as the rocks among which they are found, so they blend in with the background; they are also usually broken into odd-shaped fragments. … In our business, we don’t expect to find a whole skull lying on the surface staring up at us. The typical find is a small piece of petrified bone. The fossil hunter’s search therefore has to have an infinite number of dimensions, matching every conceivable angle of every shape of fragment of every bone on the human body.
Describing the skill of his co-worker, Kamoya Kimeu, who discovered the Turkana Boy, the most complete specimen of Homo erectus, on a slope covered with black lava pebbles.
Richard Leakey and Roger Lewin, Origins Reconsidered: In Search of What Makes Us Human (1992), 26.
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A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 286.
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A large proportion of mankind, like pigeons and partridges, on reaching maturity, having passed through a period of playfulness or promiscuity, establish what they hope and expect will be a permanent and fertile mating relationship. This we call marriage.
Genetics And Man (1964), 298.
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A man is flying in a hot air balloon and realizes he is lost. He reduces height, spots a man down below and asks,“Excuse me, can you help me? I promised to return the balloon to its owner, but I don’t know where I am.”
The man below says: “You are in a hot air balloon, hovering approximately 350 feet above mean sea level and 30 feet above this field. You are between 40 and 42 degrees north latitude, and between 58 and 60 degrees west longitude.”
“You must be an engineer,” says the balloonist.
“I am,” replies the man.“How did you know?”
“Well,” says the balloonist, “everything you have told me is technically correct, but I have no idea what to make of your information, and the fact is I am still lost.”
The man below says, “You must be a manager.”
“I am,” replies the balloonist,“but how did you know?”
“Well,” says the engineer,“you don’t know where you are, or where you are going. You have made a promise which you have no idea how to keep, and you expect me to solve your problem.The fact is you are in the exact same position you were in before we met, but now it is somehow my fault.”
Anonymous
In Jon Fripp, Michael Fripp and Deborah Fripp, Speaking of Science (2000), 199.
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A man who writes a great deal and says little that is new writes himself into a daily declining reputation. When he wrote less he stood higher in people’s estimation, even though there was nothing in what he wrote. The reason is that then they still expected better things of him in the future, whereas now they can view the whole progression.
Aphorism 43 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 50.
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A plain, reasonable working man supposes, in the old way which is also the common-sense way, that if there are people who spend their lives in study, whom he feeds and keeps while they think for him—then no doubt these men are engaged in studying things men need to know; and he expects of science that it will solve for him the questions on which his welfare, and that of all men, depends. He expects science to tell him how he ought to live: how to treat his family, his neighbours and the men of other tribes, how to restrain his passions, what to believe in and what not to believe in, and much else. And what does our science say to him on these matters?
It triumphantly tells him: how many million miles it is from the earth to the sun; at what rate light travels through space; how many million vibrations of ether per second are caused by light, and how many vibrations of air by sound; it tells of the chemical components of the Milky Way, of a new element—helium—of micro-organisms and their excrements, of the points on the hand at which electricity collects, of X rays, and similar things.
“But I don't want any of those things,” says a plain and reasonable man—“I want to know how to live.”
In 'Modern Science', Essays and Letters (1903), 221-222.
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A strict materialist believes that everything depends on the motion of matter. He knows the form of the laws of motion though he does not know all their consequences when applied to systems of unknown complexity.
Now one thing in which the materialist (fortified with dynamical knowledge) believes is that if every motion great & small were accurately reversed, and the world left to itself again, everything would happen backwards the fresh water would collect out of the sea and run up the rivers and finally fly up to the clouds in drops which would extract heat from the air and evaporate and afterwards in condensing would shoot out rays of light to the sun and so on. Of course all living things would regrede from the grave to the cradle and we should have a memory of the future but not of the past.
The reason why we do not expect anything of this kind to take place at any time is our experience of irreversible processes, all of one kind, and this leads to the doctrine of a beginning & an end instead of cyclical progression for ever.
Letter to Mark Pattison (7 Apr 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 360-1.
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A theory is a supposition which we hope to be true, a hypothesis is a supposition which we expect to be useful; fictions belong to the realm of art; if made to intrude elsewhere, they become either make-believes or mistakes.
As quoted by William Ramsay, in 'Radium and Its Products', Harper’s Magazine (Dec 1904), 52. The first part, about suppositions, appears in a paper read by G. Johnson Stoney to the American Philosophical Society, Philadelphia (3 Apr 1903), printed in 'On the Dependence of What Apparently Takes Place in Nature Upon What Actually Occurs in the Universe of Real Existences', Proceedings of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge (Apr-May 1903) 42, No. 173, 107. If you know a primary source for the part on fictions and mistakes, please contact Webmaster.
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All palaetiological sciences, all speculations which attempt to ascend from the present to the remote past, by the chain of causation, do also, by an inevitable consequence, urge us to look for the beginning of the state of things which we thus contemplate; but in none of these cases have men been able, by the aid of science, to arrive at a beginning which is homogeneous with the known course of events. The first origin of language, of civilization, of law and government, cannot be clearly made out by reasoning and research; and just as little, we may expect, will a knowledge of the origin of the existing and extinct species of plants and animals, be the result of physiological and geological investigation.
In History of the Inductive Sciences (1837), Vol. 3, 581.
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Although the time of death is approaching me, I am not afraid of dying and going to Hell or (what would be considerably worse) going to the popularized version of Heaven. I expect death to be nothingness and, for removing me from all possible fears of death, I am thankful to atheism.
In John Altson, Patti Rae Miliotis, What Happened to Grandpa? (2009).
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Among those whom I could never pursuade to rank themselves with idlers, and who speak with indignation of my morning sleeps and nocturnal rambles, one passes the day in catching spiders, that he may count their eyes with a microscope; another exhibits the dust of a marigold separated from the flower with a dexterity worthy of Leuwenhoweck himself. Some turn the wheel of electricity; some suspend rings to a lodestone, and find that what they did yesterday, they can do again to-day.—Some register the changes of the wind, and die fully convinced that the wind is changeable.—There are men yet more profound, who have heard that two colorless liquors may produce a color by union, and that two cold bodies will grow hot of they are mingled: they mingle them, and produce the effect expected, say it is strange, and mingle them again.
In Tryon Edwards, A Dictionary of Thoughts (1908), 243.
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Any artist or novelist would understand—some of us do not produce their best when directed. We expect the artist, the novelist and the composer to lead solitary lives, often working at home. While a few of these creative individuals exist in institutions or universities, the idea of a majority of established novelists or painters working at the “National Institute for Painting and Fine Art” or a university “Department of Creative Composition” seems mildly amusing. By contrast, alarm greets the idea of a creative scientist working at home. A lone scientist is as unusual as a solitary termite and regarded as irresponsible or worse.
Homage to Gala: The Life of an Independent Scholar (2000), 2.
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Any country that wants to make full use of all its potential scientists and technologists … must not expect to get the women quite so simply as it gets the men. It seems to me that marriage and motherhood are at least as socially important as military service. Government regulations are framed to ensure (in the United Kingdom) that a man returning to work from military service is not penalized by his absence. Is it utopian, then, to suggest that any country that really wants a woman to return to a scientific career when her children no longer need her physical presence should make special arrangements to encourage her to do so?
In Impact of Science on Society (1970), 20 58. Commenting how for men who went to war, their jobs were held for them pending their return.
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Apparently the anti-evolutionist expects to see a monkey or an ass transformed into a man, though he must be familiar enough with the reverse process.
As quoted by E. Newton Harvey, in 'Edwin Grant Conklin: A Biographical Memoir', Biographical Memoirs of the National Academy of Sciences(1958), Vol. 31, 59.
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ARCHIMEDES. On hearing his name, shout “Eureka!” Or else: “Give me a fulcrum and I will move the world”. There is also Archimedes’ screw, but you are not expected to know what that is.
The Dictionary of Accepted Ideas (1881), trans. Jaques Barzun (1968), 15.
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Before his [Sir Astley Cooper’s] time, operations were too often frightful alternatives or hazardous compromises; and they were not seldom considered rather as the resource of despair than as a means of remedy; he always made them follow, as it were, in the natural course of treatment; he gave them a scientific character; and he moreover, succeeded, in a great degree, in divesting them of their terrors, by performing them unostentatiously, simply, confidently, and cheerfully, and thereby inspiring the patient with hope of relief, where previously resignation under misfortune had too often been all that could be expected from the sufferer.
In John Forbes (ed.), British and Foreign Medical Review (Jul 1840), 10, No. 19, 104. In Bransby Blake Cooper, The Life of Sir Astley Cooper (1843), Vol. 2, 37.
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Before the promulgation of the periodic law the chemical elements were mere fragmentary incidental facts in nature; there was no special reason to expect the discovery of new elements, and the new ones which were discovered from time to time appeared to be possessed of quite novel properties. The law of periodicity first enabled us to perceive undiscovered elements at a distance which formerly were inaccessible to chemical vision, and long ere they were discovered new elements appeared before our eyes possessed of a number of well-defined properties.
In Faraday Lecture, delivered before the Fellows of the Chemical Society in the Theatre of the Royal Institution (4 Jun 1889), printed in Professor Mendeléeff, 'The Periodic Law of the Chemical Elements', Transactions of the Chemical Society (1889), 55, 648.
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Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.
The Anatomy of Science (1926), 158-9.
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Chemical biodynamics, involving as it does, the fusion of many scientific disciplines, … [played a role] in the elucidation of the carbon cycle. It can be expected to take an increasingly important place in the understanding of the dynamics of living organisms on a molecular level.
In Nobel Lecture (11 Dec 1961), 'The Path of Carbon in Photosynthesis', Nobel Lectures: Chemistry 1942-1962 (1964).
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Chemistry is an art that has furnished the world with a great number of useful facts, and has thereby contributed to the improvement of many arts; but these facts lie scattered in many different books, involved in obscure terms, mixed with many falsehoods, and joined to a great deal of false philosophy; so that it is not great wonder that chemistry has not been so much studied as might have been expected with regard to so useful a branch of knowledge, and that many professors are themselves but very superficially acquainted with it. But it was particularly to be expected, that, since it has been taught in universities, the difficulties in this study should have been in some measure removed, that the art should have been put into form, and a system of it attempted—the scattered facts collected and arranged in a proper order. But this has not yet been done; chemistry has not yet been taught but upon a very narrow plan. The teachers of it have still confined themselves to the purposes of pharmacy and medicine, and that comprehends a small branch of chemistry; and even that, by being a single branch, could not by itself be tolerably explained.
John Thomson, An Account of the Life, Lectures and Writings of William Cullen, M.D. (1832), Vol. 1, 40.
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Christianity possesses the source of its justification within itself and does not expect science to constitute its primary apologetic. Science must bear witness to its own worth.
In Letter (1 Jun 1988) to Father George V. Coyne, Director of the Vatican Observatory. On vatican.va website.
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Civilized people can talk about anything. For them no subject is taboo…. In civilized societies there will be no intellectual bogeys at sight of which great grown-up babies are expected to hide their eyes
In Civilization: An Essay (1928), 138.
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Common sense is a fool when it expects fools to act with common sense.
In Letters of Horace Walpole, Earl of Orford, to Sir Horace Mann (31 Jul 1767), Vol. 1, 356.
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Do not expect to be hailed as a hero when you make your great discovery. More likely you will be a ratbag—maybe failed by your examiners. Your statistics, or your observations, or your literature study, or your something else will be patently deficient. Do not doubt that in our enlightened age the really important advances are and will be rejected more often than acclaimed. Nor should we doubt that in our own professional lifetime we too will repudiate with like pontifical finality the most significant insight ever to reach our desk.
Theories of the Earth and Universe (1988), 365.
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Do the day’s work. If it be to protect the rights of the weak, whoever objects, do it. If it be to help a powerful corporation better to serve the people, whatever the opposition, do that. Expect to be called a stand-patter, but don’t be a stand-patter. Expect to be called a demagogue, but don’t be a demagogue. Don’t hesitate to be as revolutionary as science. Don’t hesitate to be as reactionary as the multiplication table. Don’t expect to build up the weak by pulling down the strong. Don’t hurry to legislate. Give administration a chance to catch up with legislation.
Speech (7 Jan 1914), to the State Senate of Massachusetts upon election as its president. Collected in Coolidge, Have Faith in Massachusetts (1919, 2004), 7-8.
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Does it not seem as if Algebra had attained to the dignity of a fine art, in which the workman has a free hand to develop his conceptions, as in a musical theme or a subject for a painting? It has reached a point where every properly developed algebraical composition, like a skillful landscape, is expected to suggest the notion of an infinite distance lying beyond the limits of the canvas.
In 'Lectures on the Theory of Reciprocants', Lecture XXI, American Journal of Mathematics (Jul 1886), 9, No. 3, 136.
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During the time of the Deluge, whilst the Water was out upon, and covered the Terrestrial Globe, … all Fossils whatever that had before obtained any Solidity, were totally dissolved, and their constituent Corpuscles all disjoyned, their Cohesion perfectly ceasing … [A]nd, to be short, all Bodies whatsoever that were either upon the Earth, or that constituted the Mass of it, if not quite down to the Abyss, yet at least to the greatest depth we ever dig: I say all these were assumed up promiscuously into the Water, and sustained in it, in such a manner that the Water, and Bodies in it, together made up one common confused Mass. That at length all the Mass that was thus borne up in the Water, was again precipitated and subsided towards the bottom. That this subsidence happened generally, and as near as possibly could be expected in so great a Confusion, according to the laws of Gravity.
In An Essay Toward A Natural History of the Earth (1695), 74-75.
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Even those to whom Providence has allotted greater strength of understanding, can expect only to improve a single science. In every other part of learning, they must be content to follow opinions, which they are not able to examine; and, even in that which they claim as peculiarly their own, can seldom add more than some small particle of knowledge, to the hereditary stock devolved to them from ancient times, the collective labour of a thousand intellects.
In Samuel Johnson and W. Jackson Bate (Ed.), ',The Rambler, No. 121, Tuesday, 14 May 1751.' The Selected Essays from the Rambler, Adventurer, and Idler (1968), 172.
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Expect an early death - it will keep you busier.
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Experiment is the interpreter of nature. Experiments never deceive. It is our judgment which sometimes deceives itself because it expects results which experiment refuses. We must consult experiment, varying the circumstances, until we have deduced general rules, for experiment alone can furnish reliable rules.
In Introductory College Physics by Oswald Blackwood (1939).
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Finally in a large population, divided and subdivided into partially isolated local races of small size, there is a continually shifting differentiation among the latter (intensified by local differences in selection but occurring under uniform and static conditions) which inevitably brings about an indefinitely continuing, irreversible, adaptive, and much more rapid evolution of the species. Complete isolation in this case, and more slowly in the preceding, originates new species differing for the most part in nonadaptive parallel orthogenetic lines, in accordance with the conditions. It is suggested, in conclusion, that the differing statistical situations to be expected among natural species are adequate to account for the different sorts of evolutionary processes which have been described, and that, in particular, conditions in nature are often such as to bring about the state of poise among opposing tendencies on which an indefinitely continuing evolutionary process depends.
In 'Evolution In Mendelian Populations', Genetics, (1931), 16, 158.
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For the most part we humans live with the false impression of security and a feeling of being at home in a seemingly trustworthy physical and human environment. But when the expected course of everyday life is interrupted, we are like shipwrecked people on a miserable plank in the open sea, having forgotten where they came from and not knowing whither they are drifting. But once we fully accept this, life becomes easier and there is no longer any disappointment.
…...
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For these two years I have been gravitating towards your doctrines, and since the publication of your primula paper with accelerated velocity. By about this time next year I expect to have shot past you, and to find you pitching into me for being more Darwinian than yourself. However, you have set me going, and must just take the consequences, for I warn you I will stop at no point so long as clear reasoning will take me further.
Thomas Henry Huxley, Leonard Huxley, Life and Letters of Thomas Henry Huxley (1901), 211.
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For those of us who make only a brief study of chemistry, the benefits to be expected are of an indirect nature. Increased capacity for enjoyment, a livelier interest in the world in which we live, a more intelligent attitude toward the great questions of the day—these are the by-products of a well-balanced education, including chemistry in its proper relation to other studies.
In 'Introduction', General Chemistry: An Elementary Survey Emphasizing Industrial Applications of Fundamental Principles (1923), 4.
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From the physician, as emphatically the student of Nature, is expected not only an inquiry into cause, but an investigation of the whole empire of Nature and a determination of the applicability of every species of knowledge to the improvement of his art.
In 'An Inquiry, Analogical and Experimental, into the Different Electrical conditions of Arterial and Venous Blood', New Orleans Medical and Surgical Journal (1853-4), 10, 584-602 & 738-757. As cited in George B. Roth, 'Dr. John Gorrie—Inventor of Artificial Ice and Mechanical Refrigeration', The Scientific Monthly (May 1936) 42 No. 5, 464-469.
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Gauss [replied], when asked how soon he expected to reach certain mathematical conclusions, “that he had them long ago, all he was worrying about was how to reach them.”
In Louis Pasteur, Free Lance of Science (1950), 365. Also excerpted in 'Mechanisms of Discovery', collected in I.S. Gordon and S. Sorkin (eds.) The Armchair Science Reader (1959), 336.
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He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws.
In A Week on the Concord and Merrimack Rivers (1862), 381.
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He who plants a Walnut-Tree, expects not to eat of the fruit.
No. 2401 in Gnomologia: Adagies and Proverbs, Wise Sentences and Witty Sayings (1732), 99.
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Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law.
Gödel, Escher, Bach: An Eternal Golden Braid (1979), 152.
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I always tried to live up to Leo Szilard's commandment, “don't lie if you don't have to.” I had to. I filled up pages with words and plans I knew I would not follow. When I go home from my laboratory in the late afternoon, I often do not know what I am going to do the next day. I expect to think that up during the night. How could I tell them what I would do a year hence?
In 'Dionysians and Apollonians', Science (2 Jun 1972), 176, 966. Reprinted in Mary Ritchie Key, The Relationship of Verbal and Nonverbal Communication (1980), 318.
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I am very sorry, Pyrophilus, that to the many (elsewhere enumerated) difficulties which you may meet with, and must therefore surmount, in the serious and effectual prosecution of experimental philosophy I must add one discouragement more, which will perhaps is much surprise as dishearten you; and it is, that besides that you will find (as we elsewhere mention) many of the experiments published by authors, or related to you by the persons you converse with, false and unsuccessful (besides this, I say), you will meet with several observations and experiments which, though communicated for true by candid authors or undistrusted eye-witnesses, or perhaps recommended by your own experience, may, upon further trial, disappoint your expectation, either not at all succeeding constantly, or at least varying much from what you expected.
Opening paragraph of The First Essay Concerning the Unsuccessfulness of Experiments (1673), collected in The Works of the Honourable Robert Boyle in Six Volumes to Which is Prefixed the Life of the Author (1772), Vol. 1, 318-319.
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I believe that life can go on forever. It takes a million years to evolve a new species, ten million for a new genus, one hundred million for a class, a billion for a phylum—and that’s usually as far as your imagination goes. In a billion years, it seems, intelligent life might be as different from humans as humans are from insects. But what would happen in another ten billion years? It’s utterly impossible to conceive of ourselves changing as drastically as that, over and over again. All you can say is, on that kind of time scale the material form that life would take is completely open. To change from a human being to a cloud may seem a big order, but it’s the kind of change you’d expect over billions of years.
Quoted in Omni (1986), 8, 38.
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I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.
Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.
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I did not expect to find the electric cable in its primitive state, such as it was on leaving the manufactory. The long serpent, covered with the remains of shells, bristling with foraminiferae, was encrusted with a strong coating which served as a protection against all boring mollusks. It lay quietly sheltered from the motions of the sea, and under a favorable pressure for the transmission of the electric spark which passes from Europe to America in .32 of a second. Doubtless this cable will last for a great length of time, for they find that the gutta-percha covering is improved by the sea water.
[Referring to the Transatlantic telegraph cable laid in 1866, as viewed from the fictional submarine Nautilus.]
Twenty Thousand Leagues Under The Seas, (1874), 285. Translated from the original French edition, Vingt Mille Lieues Sous Les Mers (1870).
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I expect to think that I would rather be author of your book [The Origin of Species] than of any other on Nat. Hist. Science.
Letter to Darwin (12 Dec 1859). Quoted in Leonard Huxley, Life and Letters of Sir Joseph Dalton Hooker (1918), Vol. 1, 511.
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I fully expect that NASA will send me back to the Moon as they treated Senator [John] Glenn, and if they don’t do otherwise, why, then I’ll have to do it myself.
About looking forward to the day he turned 77. In interview with Associated Press, as quoted in Peter Bond, 'Obituary: Charles Conrad Jnr', The Independent (10 Jul 1999).
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I grow increasingly aware, and in more ways than expected that I am at the center of my own field; and whether it be folly or wisdom, it is a very pleasant feeling.
In Davis Baird, R.I.G. Hughes and Alfred Nordmann, Heinrich Hertz: Classical Physicist, Modern Philosopher (1998), 1.
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I have been driven to assume for some time, especially in relation to the gases, a sort of conducting power for magnetism. Mere space is Zero. One substance being made to occupy a given portion of space will cause more lines of force to pass through that space than before, and another substance will cause less to pass. The former I now call Paramagnetic & the latter are the diamagnetic. The former need not of necessity assume a polarity of particles such as iron has with magnetic, and the latter do not assume any such polarity either direct or reverse. I do not say more to you just now because my own thoughts are only in the act of formation, but this I may say: that the atmosphere has an extraordinary magnetic constitution, & I hope & expect to find in it the cause of the annual & diurnal variations, but keep this to yourself until I have time to see what harvest will spring from my growing ideas.
Letter to William Whewell, 22 Aug 1850. In L. Pearce Williams (ed.), The Selected Correspondence of Michael Faraday (1971), Vol. 2, 589.
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I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations. … For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it.
Although this preface would have been assumed by contemporary readers to be written by Copernicus, it was unsigned. It is now believed to have been written and added at press time by Andreas Osiander (who was then overseeing the printing of the book). It suggests the earth’s motion as described was merely a mathematical device, and not to be taken as absolute reality. Text as given in 'To the Reader on the Hypotheses in this Work', Copernicus: On the Revolutions of the Heavenly Spheres (1543), translated by ‎Alistair Matheson Duncan (1976), 22-3. By adding this preface, Osiander wished to stave off criticism by theologians. See also the Andreas Osiander Quotes page of this website.
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I have seen the science I worshipped, and the aircraft I loved, destroying the civilization I expected them to serve.
Quoted in 'Antiseptic Christianity', book review of Lindbergh, Of Flight and Life in Time magazine, (6 Sep 1948).
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I have spent much time in the study of the abstract sciences; but the paucity of persons with whom you can communicate on such subjects disgusted me with them. When I began to study man, I saw that these abstract sciences are not suited to him, and that in diving into them, I wandered farther from my real object than those who knew them not, and I forgave them for not having attended to these things. I expected then, however, that I should find some companions in the study of man, since it was so specifically a duty. I was in error. There are fewer students of man than of geometry.
Thoughts of Blaise Pascal (1846), 137.
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I have, also, a good deal of respect for the job they [physicists] did in the first months after Hiroshima. The world desperately needed information on this new problem in the daily life of the planet, and the physicists, after a slow start, did a good job of giving it to them. It hasn’t come out with a fraction of the efficiency that the teachers might have wished, but it was infinitely more effective than anyone would have dared expect.
In 'A Newsman Looks at Physicists', Physics Today (May 1948), 1, No. 1, 15.
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I hope that in due time the chemists will justify their proceedings by some large generalisations deduced from the infinity of results which they have collected. For me I am left hopelessly behind and I will acknowledge to you that through my bad memory organic chemistry is to me a sealed book. Some of those here, [August] Hoffman for instance, consider all this however as scaffolding, which will disappear when the structure is built. I hope the structure will be worthy of the labour. I should expect a better and a quicker result from the study of the powers of matter, but then I have a predilection that way and am probably prejudiced in judgment.
Letter to Christian Schönbein (9 Dec 1852), The Letters of Faraday and Schoenbein, 1836-1862 (1899), 209-210.
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I remember being with my grandmother and mother and my uncle came in and asked what I wanted to be when grew up. I said ‘A doctor,’ which took him aback. He was expecting me to say ‘nurse’ or ‘actress.’ And my mother and grandmother laughed like, ‘Kids say the darndest things.’ I grew up in a time when women were not expected to do anything interesting.
As quoted in Anna Azvolinsky, 'Fearless About Folding', The Scientist (Jan 2016).
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I said, that Superstition was the child of Fear, and Fear the child of Ignorance; and you might expect me to say antithetically, that Science was the child of Courage, and Courage the child of Knowledge.
Opening of 'Science', a lecture delivered at the Royal Institution, published in Fraser's Magazine (Jul 1866), 74, 15.
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I suppose I should be run after for a professorship if I had studied at Giessen, as it seems to be a settled point that no young man can be expected to know anything of chemistry unless he has studied with Liebig; while the truth is, that any one who goes there and does not afterwards correct the bad habits acquired there, in some other laboratory, is almost unfitted for doing things in Chemistry. No doubt Liebig is a remarkable man, who has done much for organic Chemistry, not to speak of his having quarreled with all the Chemists in Europe...
Letter to his brother, William Dwight Whitney (25 Apr 1846). In Edwin Tenney Brewster and Josiah Dwight Whitney, Life and Letters of Josiah Dwight Whitney (1909), 79-80.
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I think the next [21st] century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don’t know how the laws fit together, and what happens under extreme conditions. But I expect we will find a complete unified theory sometime this century. The is no limit to the complexity that we can build using those basic laws.
[Answer to question: Some say that while the twentieth century was the century of physics, we are now entering the century of biology. What do you think of this?]
'"Unified Theory" Is Getting Closer, Hawking Predicts', interview in San Jose Mercury News (23 Jan 2000), 29A. Answer quoted in Ashok Sengupta, Chaos, Nonlinearity, Complexity: The Dynamical Paradigm of Nature (2006), vii. Question included in Hans-Joachim Schellnhuber, Nicholas Stern and Mario Molina , Global Sustainability: a Nobel Cause (2010), 13. Cite from Brent Davis and Dennis J. Sumara, Complexity and Education: Inquiries Into Learning, Teaching, and Research (2006), 171.
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I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
In 'Reflections on my Eightieth Birthday', Portraits from Memory (1956), 54.
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I will insist particularly upon the following fact, which seems to me quite important and beyond the phenomena which one could expect to observe: The same [double sulfate of uranium and potassium] crystalline crusts, arranged the same way [as reported to the French academy on 24 Feb 1896] with respect to the photographic plates, in the same conditions and through the same screens, but sheltered from the excitation of incident rays and kept in darkness, still produce the same photographic images … [when kept from 26 Feb 1896] in the darkness of a bureau drawer. … I developed the photographic plates on the 1st of March, expecting to find the images very weak. Instead the silhouettes appeared with great intensity.
It is important to observe that it appears this phenomenon must not be attributed to the luminous radiation emitted by phosphorescence … One hypothesis which presents itself to the mind naturally enough would be to suppose that these rays, whose effects have a great similarity to the effects produced by the rays studied by M. Lenard and M. Röntgen, are invisible rays …
[Having eliminated phosphorescence as a cause, he has further revealed the effect of the as yet unknown radioactivity.]
Read at French Academy of Science (2 Mar 1896). In Comptes Rendus (1896), 122, 501. As translated by Carmen Giunta on the Classic Chemistry web site.
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If Einstein’s theory [of relativity] should prove to be correct, as I expect it will, he will be considered the Copernicus of the twentieth century.
As quoted in Philipp Frank and Shuichi Kusaka, Einstein, His Life and Times (1947), 101.
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If one small and odd lineage of fishes had not evolved fins capable of bearing weight on land (though evolved for different reasons in lakes and seas,) terrestrial vertebrates would never have arisen. If a large extraterrestrial object—the ultimate random bolt from the blue—had not triggered the extinction of dinosaurs 65 million years ago, mammals would still be small creatures, confined to the nooks and crannies of a dinosaur's world, and incapable of evolving the larger size that brains big enough for self-consciousness require. If a small and tenuous population of protohumans had not survived a hundred slings and arrows of outrageous fortune (and potential extinction) on the savannas of Africa, then Homo sapiens would never have emerged to spread throughout the globe. We are glorious accidents of an unpredictable process with no drive to complexity, not the expected results of evolutionary principles that yearn to produce a creature capable of understanding the mode of its own necessary construction.
Full House: The Spread of Excellence from Plato to Darwin (1996), 216.
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If we knew exactly what to expect throughout the Solar System, we would have no reason to explore it.
The Saturn Game (1981)
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If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.
In Novi Comm. Petr., Vol. 4, Preface.
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In all our academies we attempt far too much. ... In earlier times lectures were delivered upon chemistry and botany as branches of medicine, and the medical student learned enough of them. Now, however, chemistry and botany are become sciences of themselves, incapable of comprehension by a hasty survey, and each demanding the study of a whole life, yet we expect the medical student to understand them. He who is prudent, accordingly declines all distracting claims upon his time, and limits himself to a single branch and becomes expert in one thing.
Quoted in Johann Hermann Baas, Henry Ebenezer Handerson (trans.), Outlines of the History of Medicine and the Medical Profession (1889), 842-843.
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In mathematics, … and in natural philosophy since mathematics was applied to it, we see the noblest instance of the force of the human mind, and of the sublime heights to which it may rise by cultivation. An acquaintance with such sciences naturally leads us to think well of our faculties, and to indulge sanguine expectations concerning the improvement of other parts of knowledge. To this I may add, that, as mathematical and physical truths are perfectly uninteresting in their consequences, the understanding readily yields its assent to the evidence which is presented to it; and in this way may be expected to acquire the habit of trusting to its own conclusions, which will contribute to fortify it against the weaknesses of scepticism, in the more interesting inquiries after moral truth in which it may afterwards engage.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 3, 182.
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In other words then, if a machine is expected to be infallible, it cannot also be intelligent.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 124.
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In reality, all Arguments from Experience are founded on the Similarity which we discover among natural Objects, and by which we are induc'd to expect effects similar to those which we have found to follow from such Objects. And tho' none but a Fool or Madman will ever pretend to dispute the Authority of Experience, or to reject that great Guide of human Life, it may surely be allow'd a Philosopher to have so much Curiosity at least as to examine the Principle of human Nature, which gives this mighty Authority to Experience, and makes us draw Advantage from that Similarity which Nature has plac'd among different Objects. From Causes which appear similar we expect similar Effects. This is the Sum of our experimental Conclusions.
An Enquiry Concerning Human Understanding (1748), 63.
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In the beginning of the year 1800 the illustrious professor conceived the idea of forming a long column by piling up, in succession, a disc of copper, a disc of zinc, and a disc of wet cloth, with scrupulous attention to not changing this order. What could be expected beforehand from such a combination? Well, I do not hesitate to say, this apparently inert mass, this bizarre assembly, this pile of so many couples of unequal metals separated by a little liquid is, in the singularity of effect, the most marvellous instrument which men have yet invented, the telescope and the steam engine not excepted.
In François Arago, 'Bloge for Volta' (1831), Oeuvres Completes de François Arago (1854), Vol. 1, 219-20.
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In the discussion of the. energies involved in the deformation of nuclei, the concept of surface tension of nuclear matter has been used and its value had been estimated from simple considerations regarding nuclear forces. It must be remembered, however, that the surface tension of a charged droplet is diminished by its charge, and a rough estimate shows that the surface tension of nuclei, decreasing with increasing nuclear charge, may become zero for atomic numbers of the order of 100. It seems therefore possible that the uranium nucleus has only small stability of form, and may, after neutron capture, divide itself into two nuclei of roughly equal size (the precise ratio of sizes depending on liner structural features and perhaps partly on chance). These two nuclei will repel each other and should gain a total kinetic energy of c. 200 Mev., as calculated from nuclear radius and charge. This amount of energy may actually be expected to be available from the difference in packing fraction between uranium and the elements in the middle of the periodic system. The whole 'fission' process can thus be described in an essentially classical way, without having to consider quantum-mechanical 'tunnel effects', which would actually be extremely small, on account of the large masses involved.
[Co-author with Otto Robert Frisch]
Lise Meitner and O. R. Frisch, 'Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction', Nature (1939), 143, 239.
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In the modern world, science and society often interact in a perverse way. We live in a technological society, and technology causes political problems. The politicians and the public expect science to provide answers to the problems. Scientific experts are paid and encouraged to provide answers. The public does not have much use for a scientist who says, “Sorry, but we don’t know.” The public prefers to listen to scientists who give confident answers to questions and make confident predictions of what will happen as a result of human activities. So it happens that the experts who talk publicly about politically contentious questions tend to speak more clearly than they think. They make confident predictions about the future, and end up believing their own predictions. Their predictions become dogmas which they do not question. The public is led to believe that the fashionable scientific dogmas are true, and it may sometimes happen that they are wrong. That is why heretics who question the dogmas are needed.
Frederick S. Pardee Distinguished Lecture (Oct 2005), Boston University. Collected in 'Heretical Thoughts About Science and Society', A Many-Colored Glass: Reflections on the Place of Life in the Universe (2007), 43-44.
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Injustice or oppression in the next street...or any spot inhabited by men was a personal affront to Thomas Addis and his name, from its early alphabetical place, was conspicuous on lists of sponsors of scores of organizations fighting for democracy and against fascism. He worked on more committees than could reasonably have been expected of so busy a man... Tom Addis was happy to have a hand in bringing to the organization of society some of the logic of science and to further that understanding and to promote that democracy which are the only enduring foundations of human dignity.
Kevin V. Lemley and Linus Pauling, 'Thomas Addis: 1881-1949', Biographical Memoirs, National Academy of Sciences, 63, 27-29.
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Insanity: doing the same thing over and over again and expecting different results.
…...
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It did not cause anxiety that Maxwell’s equations did not apply to gravitation, since nobody expected to find any link between electricity and gravitation at that particular level. But now physics was faced with an entirely new situation. The same entity, light, was at once a wave and a particle. How could one possibly imagine its proper size and shape? To produce interference it must be spread out, but to bounce off electrons it must be minutely localized. This was a fundamental dilemma, and the stalemate in the wave-photon battle meant that it must remain an enigma to trouble the soul of every true physicist. It was intolerable that light should be two such contradictory things. It was against all the ideals and traditions of science to harbor such an unresolved dualism gnawing at its vital parts. Yet the evidence on either side could not be denied, and much water was to flow beneath the bridges before a way out of the quandary was to be found. The way out came as a result of a brilliant counterattack initiated by the wave theory, but to tell of this now would spoil the whole story. It is well that the reader should appreciate through personal experience the agony of the physicists of the period. They could but make the best of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays, and Fridays they must look on light as a wave; on Tuesdays, Thursdays, and Saturdays, as a particle. On Sundays they simply prayed.
The Strange Story of the Quantum (1947), 42.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is as if Cleopatra fell off her barge in 40 BC and hasn't hit the water yet.
[Illustrating how strange the behaviour of kaon particles, when first found in cosmic rays, which lived without predicted decay for a surprisingly long time—seemingly postponed a million billion times longer than early theory expected.]
Anonymous
In Frank Close, Michael Marten, Christine Sutton, The Particle Odyssey: a Journey to the Heart of the Matter (2004),75.
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It is by no means hopeless to expect to make a machine for really very difficult mathematical problems. But you would have to proceed step-by-step. I think electricity would be the best thing to rely on.
In Charles Sanders Peirce, Max Harold Fisch, Christian J. W. Kloesel Writings of Charles S. Peirce: 1884-1886 (1993), 422.
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It is certainly true in the United States that there is an uneasiness about certain aspects of science, particularly evolution, because it conflicts, in some people’s minds, with their sense of how we all came to be. But you know, if you are a believer in God, it’s hard to imagine that God would somehow put this incontrovertible evidence in front of us about our relationship to other living organisms and expect us to disbelieve it. I mean, that doesn't make sense at all.
From video of interview with Huffington post reporter at the 2014 Davos Annual Meeting, World Economic Forum (25 Jan 2014). On web page 'Dr. Francis Collins: “There Is An Uneasiness” About Evolution'
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It is clear that the degradation of the position of the scientist as an independent worker and thinker to that of a morally irresponsible stooge in a science-factory has ‘proceeded even more rapidly and devastatingly than I had expected. This subordination of those who ought to think to those who have the administrative power is ruinous for the morale of the scientist, and quite to the same extent it is ruinous to the quality of the subjective scientific output of the country.
In 'A Rebellious Scientist after Two Years', Bulletin of the Atomic Scientists, (1948), 4, 338.
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It is contrary to the usual order of things, that events so harmonious as those of the system of the world, should depend on such diversified agents as are supposed to exist in our artificial arrangements; and there is reason to anticipate a great reduction in the number of undecompounded bodies, and to expect that the analogies of nature will be found conformable to the refined operations of art. The more the phenomena of the universe are studied, the more distinct their connection appears, and the more simple their causes, the more magnificent their design, and the more wonderful the wisdom and power of their Author.
Elements of Chemical Philosophy (1812), in J. Davy (ed.), The Collected Works of Sir Humphry Davy(1839-40), Vol. 4, 42.
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It is easier to love humanity as a whole than to love one’s neighbor. There may even be a certain antagonism between love of humanity and love of neighbor; a low capacity for getting along with those near us often goes hand in hand with a high receptivity to the idea of the brotherhood of men. About a hundred years ago a Russian landowner by the name of Petrashevsky recorded a remarkable conclusion: “Finding nothing worthy of my attachment either among women or among men, I have vowed myself to the service of mankind.” He became a follower of Fourier, and installed a phalanstery on his estate. The end of the experiment was sad, but what one might perhaps have expected: the peasants—Petrashevsky’s neighbors-burned the phalanstery.
In 'Brotherhood', The Ordeal of Change (1963), 91.
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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 madness and a contradiction to expect that things which were never yet performed should be effected, except by means hitherto untried.
Novum Organum (1620), Part 1, Sec. 1, Aphorism 6. In The Works of Franics Bacon (1815), Vol. 4, 4.
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It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
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It is the constant attempt in this country [Canada] to make fundamental science responsive to the marketplace. Because technology needs science, it is tempting to require that scientific projects be justified in terms of the worth of the technology they can be expected to generate. The effect of applying this criterion is, however, to restrict science to developed fields where the links to technology are most evident. By continually looking for a short-term payoff we disqualify the sort of science that … attempts to answer fundamental questions, and, having answered them, suggests fundamentally new approaches in the realm of applications.
'A Scientist and the World He Lives In', Speech to the Empire Club of Canada (27 Nov 1986) in C. Frank Turner and Tim Dickson (eds.), The Empire Club of Canada Speeches 1986-1987 (1987), 149-161.
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It is unreasonable to expect science to produce a system of ethics—ethics are a kind of highway code for traffic among mankind—and the fact that in physics atoms which were yesterday assumed to be square are now assumed to be round is exploited with unjustified tendentiousness by all who are hungry for faith; so long as physics extends our dominion over nature, these changes ought to be a matter of complete indifference to you.
Letter to Oskar Pfister, 24 Feb 1928. Quoted in H. Meng and E. Freud (eds.), Psycho-Analysis and Faith: The Letters of Sigmund Freud and Oscar Pfister (1963), 123.
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It may be said “In research, if you know what you are doing, then you shouldn't be doing it.” In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.
In Numerical Methods for Scientists and Engineers (1973), 704.
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It will be noticed that the fundamental theorem proved above bears some remarkable resemblances to the second law of thermodynamics. Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase of a measurable quantity, in the one case the entropy of a physical system and in the other the fitness, measured by m, of a biological population. As in the physical world we can conceive the theoretical systems in which dissipative forces are wholly absent, and in which the entropy consequently remains constant, so we can conceive, though we need not expect to find, biological populations in which the genetic variance is absolutely zero, and in which fitness does not increase. Professor Eddington has recently remarked that “The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of nature.” It is not a little instructive that so similar a law should hold the supreme position among the biological sciences. While it is possible that both may ultimately be absorbed by some more general principle, for the present we should note that the laws as they stand present profound differences—-(1) The systems considered in thermodynamics are permanent; species on the contrary are liable to extinction, although biological improvement must be expected to occur up to the end of their existence. (2) Fitness, although measured by a uniform method, is qualitatively different for every different organism, whereas entropy, like temperature, is taken to have the same meaning for all physical systems. (3) Fitness may be increased or decreased by changes in the environment, without reacting quantitatively upon that environment. (4) Entropy changes are exceptional in the physical world in being irreversible, while irreversible evolutionary changes form no exception among biological phenomena. Finally, (5) entropy changes lead to a progressive disorganization of the physical world, at least from the human standpoint of the utilization of energy, while evolutionary changes are generally recognized as producing progressively higher organization in the organic world.
The Genetical Theory of Natural Selection (1930), 36.
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It would be an unsound fancy and self-contradictory to expect that things which have never yet been done can be done except by means which have never yet been tried.
From Novum Organum (1620), Book 1, Aphorism 6. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 48.
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Let us ... consider the ovum [egg] as a physical system. Its potentialities are prodigious and one's first impulse is to expect that such vast potentialities would find expression in complexity of structure. But what do we find? The substance is clouded with particles, but these can be centrifuged away leaving it optically structureless but still capable of development.... On the surface of the egg there is a fine membrane, below it fluid of high viscosity, next fluid of relatively low viscosity, and within this the nucleus, which in the resting stage is simply a bag of fluid enclosed in a delicate membrane.... The egg's simplicity is not that of a machine or a crystal, but that of a nebula. Gathered into it are units relatively simple but capable by their combinations of forming a vast number of dynamical systems...
As guest of honour, closing day address (Jun 1928), Sixth Colloid Symposium, Toronto, Canada, 'Living Matter', printed in Harry Boyer Weiser (ed.), Colloid Symposium Monograph (1928), Vol. 6, 15. Quoted in Joseph Needham, Chemical Embryology (1931), Vol. 1, 612-613.
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Life is not a miracle. It is a natural phenomenon, and can be expected to appear whenever there is a planet whose conditions duplicate those of the earth.
[Stating his belief that planets supporting life cannot be rare.]
Lecture at New York Academy of Medicine. Quoted in article, 'Life Begins,' Time (24 Nov 1952).
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Man, in his quest for knowledge and progress, is determined and cannot be deterred. The exploration of space will go ahead, whether we join in or not, and it is one of the great adventures of all time, and no nation which expects to be the leader of other nations can expect to stay behind in this race for space.
Address at Rice University in Houston (12 Sep 1962). On website of John F. Kennedy Presidential Library and Museum.
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Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.
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Men will never disappoint us if we observe two rules: (i) To find out what they are; (2) to expect them to be just that.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 175.
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My main point today is that usually one gets what one expects, but very rarely in the way one expected it. (1970)
Draft (22 May 1970) of speech he hoped to give upon his retirement. In Susan Hough, Richter's Scale: Measure of an Earthquake, Measure of a Man (2007), 309.
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No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
In A Mathematician's Apology (1941, reprint with Foreward by C.P. Snow 1992), 70-71.
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Nor can it be supposed that the diversity of chemical structure and process stops at the boundary of the species, and that within that boundary, which has no real finality, rigid uniformity reigns. Such a conception is at variance with any evolutionary conception of the nature and origin of species. The existence of chemical individuality follows of necessity from that of chemical specificity, but we should expect the differences between individuals to be still more subtle and difficult of detection. Indications of their existence are seen, even in man, in the various tints of skin, hair, and eyes, and in the quantitative differences in those portions of the end-products of metabolism which are endogenous and are not affected by diet, such as recent researches have revealed in increasing numbers. Even those idiosyncrasies with regard to drugs and articles of food which are summed up in the proverbial saying that what is one man's meat is another man's poison presumably have a chemical basis.
Inborn Errors of Metabolism. The Croonian Lectures delivered before the Royal College of Physicians of London, in June, 1908 (1909), 2-3.
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Occurrences that other men would have noted only with the most casual interest became for Whitney exciting opportunities to experiment. Once he became disturbed by a scientist's seemingly endless pursuit of irrelevant details in the course of an experiment, and criticized this as being as pointless as grabbing beans out of a pot, recording the numbers, and then analyzing the results. Later that day, after he had gone home, his simile began to intrigue him, and he asked himself whether it would really be pointless to count beans gathered in such a random manner. Another man might well have dismissed this as an idle fancy, but to Whitney an opportunity to conduct an experiment was not to be overlooked. Accordingly, he set a pot of beans beside his bed, and for several days each night before retiring he would take as many beans as he could grasp in one hand and make a note of how many were in the handful. After several days had passed he was intrigued to find that the results were not as unrewarding as he had expected. He found that each handful contained more beans than the one before, indicating that with practice he was learning to grasp more and more beans. “This might be called research in morphology, the science of animal structure,” he mused. “My hand was becoming webbed … so I said to myself: never label a real experiment useless, it may reveal something unthought of but worth knowing.”
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 358-359.
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Oh, how much is today hidden by science! Oh, how much it is expected to hide!
…...
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Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a schoolboy now can predict what a Faraday then could only guess at roughly. By Ohm's discovery a large part of the domain of electricity became annexed by Coulomb's discovery of the law of inverse squares, and completely annexed by Green's investigations. Poisson attacked the difficult problem of induced magnetisation, and his results, though differently expressed, are still the theory, as a most important first approximation. Ampere brought a multitude of phenomena into theory by his investigations of the mechanical forces between conductors supporting currents and magnets. Then there were the remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents. These were rather long in being brought from the crude experimental state to a compact system, expressing the real essence. Unfortunately, in my opinion, Faraday was not a mathematician. It can scarely be doubted that had he been one, he would have anticipated much later work. He would, for instance, knowing Ampere's theory, by his own results have readily been led to Neumann’s theory, and the connected work of Helmholtz and Thomson. But it is perhaps too much to expect a man to be both the prince of experimentalists and a competent mathematician.
From article 'Electro-magnetic Theory II', in The Electrician (16 Jan 1891), 26, No. 661, 331.
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On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
Considerations on the Doctrine of Phlogiston (1796), 57-8.
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One must believe that every living thing whatsoever must change insensibly in its organization and in its form... One must therefore never expect to find among living species all those which are found in the fossil state, and yet one may not assume that any species has really been lost or rendered extinct.
Système des Animaux sans Vertébres, (1801) trans. D. R. Newth, in Annals of Science (1952), 5, 253-4.
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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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One of the things that makes the history of science so endlessly fascinating is to follow the slow education of our species in the sort of beauty to expect in nature.
In Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature (1992), 158.
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One wonders whether the rare ability to be completely attentive to, and to profit by, Nature’s slightest deviation from the conduct expected of her is not the secret of the best research minds and one that explains why some men turn to most remarkably good advantage seemingly trivial accidents. Behind such attention lies an unremitting sensitivity.
In The Furtherance of Medical Research (1941), 98.
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Our children will enjoy in their homes electrical energy too cheap to meter. ... Transmutation of the elements, unlimited power, ability to investigate the working of living cells by tracer atoms, the secret of photosynthesis about to be uncovered, these and a host of other results, all in about fifteen short years. It is not too much to expect that our children will know of great periodic famines in the world only as matters of history, will travel effortlessly over the seas and under the and through the air with a minimum of danger and at great speeds, and will experience a life span far longer than ours, as disease yields and man comes to understand what causes him to age.
Speech at the 20th anniversary of the National Association of Science Writers, New York City (16 Sep 1954), asquoted in 'Abundant Power From Atom Seen', New York Times (17 Sep 1954) 5.
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Perfect concordance among reformers is not to be expected; and men who are honestly struggling towards the light cannot hope to attain at one bound to the complete truth. There is always a danger lest the fascination of a new discovery should lead us too far. Men of science, being human, are apt, like lovers, to exaggerate the perfections and be a little blind to the faults of the object of their choice.
'The Anniversary Address of the President', Quarterly Journal of the Geological Society of London, 1885, 41, 55.
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Perhaps the most impressive illustration of all is to suppose that you could label the molecules in a tumbler of water. ... threw it anywhere you please on the earth, and went away from the earth for a few million years while all the water on the earth, the oceans, rivers, lakes and clouds had had time to mix up perfectly. Now supposing that perfect mixing had taken place, you come back to earth and draw a similar tumbler of water from the nearest tap, how many of those marked molecules would you expect to find in it? Well, the answer is 2000. There are 2000 times more molecules in a tumbler of water than there are tumblers of water in the whole earth.
In Lecture (1936) on 'Forty Years of Atomic Theory', collected in Needham and Pagel (eds.) in Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 99-100.
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Persons possessing great intellect and a capacity for excelling in the creative arts and also in the sciences are generally likely to have heavier brains than the ordinary individual. Arguing from this we might expect to find a corresponding lightness in the brain of the criminal, but this is not always the case ... Many criminals show not a single anomaly in their physical or mental make-up, while many persons with marked evidences of morphological aberration have never exhibited the criminal tendency.
Every attempt to prove crime to be due to a constitution peculiar only to criminals has failed signally. It is because most criminals are drawn from the ranks of the low, the degraded, the outcast, that investigators were ever deceived into attempting to set up a 'type' of criminal. The social conditions which foster the great majority of crimes are more needful of study and improvement.
From study of known normal brains we have learned that there is a certain range of variation. No two brains are exactly alike, and the greatest source of error in the assertions of Benedict and Lombroso has been the finding of this or that variation in a criminal’s brains, and maintaining such to be characteristic of the 'criminal constitution,' unmindful of the fact that like variations of structure may and do exist in the brains of normal, moral persons.
Address to the American Association for the Advancement of Science in Philadelphia (28 Dec 1904), as quoted in 'Americans of Future Will Have Best Brains', New York Times (29 Dec 1904), 6.
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Physical Science and Industrialism may be conceived as a pair of dancers, both of whom know their steps and have an ear for the rhythm of the music. If the partner who has been leading chooses to change parts and to follow instead, there is perhaps no reason to expect that he will dance less correctly than before.
From 'Introduction: The Geneses of Civilizations', A Study of History (1948), Vol. 1, 3, footnote.
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Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.
Science Good, Bad and Bogus (1981), 123.
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Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.
In 'Great Fakes Of Science', Science Good, Bad and Bogus (1983), 123. Excerpted in John Carey (ed.), Eyewitness to Science (1995), 451.
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Progress is made by trial and failure; the failures are generally a hundred times more numerous than the successes; yet they are usually left unchronicled. The reason is that the investigator feels that even though he has failed in achieving an expected result, some other more fortunate experimenter may succeed, and it is unwise to discourage his attempts.
From 'Radium and its Products', Harper’s Magazine (Dec 1904), 110, No. 655, 52.
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Sample recommendation letter:
Dear Search Committee Chair,
I am writing this letter for Mr. John Smith who has applied for a position in your department. I should start by saying that I cannot recommend him too highly.
In fact, there is no other student with whom I can adequately compare him, and I am sure that the amount of mathematics he knows will surprise you.
His dissertation is the sort of work you don’t expect to see these days.
It definitely demonstrates his complete capabilities.
In closing, let me say that you will be fortunate if you can get him to work for you.
Sincerely,
A. D. Visor (Prof.)
In A Mathematician Reads the Newspaper (1995), 43
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Science cannot stop while ethics catches up ... and nobody should expect scientists to do all the thinking for the country.
To the 116th meeting of the American Association for the Advancement of Science, New York City (26-31 Dec 1949), as quoted in Life magazine (9 Jan 1950), 28, No. 2, 17.
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Science gains from it [the pendulum] more than one can expect. With its huge dimensions, the apparatus presents qualities that one would try in vain to communicate by constructing it on a small [scale], no matter how carefully. Already the regularity of its motion promises the most conclusive results. One collects numbers that, compared with the predictions of theory, permit one to appreciate how far the true pendulum approximates or differs from the abstract system called 'the simple pendulum'.
In 'Demonstration Experimentale du Movement de Rotation de la Terre' (31 May 1851). In C.M. Gariel (ed.), J. Bertrand (ed.) and Harold Burstyn (trans.), Recueil des Travaux Scientifiques de Lion Foucault (1878), Vol. 2, 527.
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Science itself is badly in need of integration and unification. The tendency is more and more the other way ... Only the graduate student, poor beast of burden that he is, can be expected to know a little of each. As the number of physicists increases, each specialty becomes more self-sustaining and self-contained. Such Balkanization carries physics, and indeed, every science further away, from natural philosophy, which, intellectually, is the meaning and goal of science.
Science, The Center of Culture (1970), 92. Quoted by Victor F. Weisskopf, 'One Hundred Years of the Physical Review', in H. Henry Stroke, Physical Review: The First Hundred Years: a Selection of Seminal Papers and Commentaries, Vol. 1, 15.
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Simultaneous discovery is utterly commonplace, and it was only the rarity of scientists, not the inherent improbability of the phenomenon, that made it remarkable in the past. Scientists on the same road may be expected to arrive at the same destination, often not far apart.
From review '[Arthur] Koestler’s Theory of the Creative Act: “The Act of Creation”', in New Statesman (19 Jun 1964). According to Michael Scammell in his biography (Koestler: The Literary and Political Odyssey of a Twentieth-Century Skeptic (2009), 491 and 654), Medawar eviscerated the book as “amateurish” with “overstretched metaphors” and “fatuous epigrams” while Koestler’s psychological insights were “in the style of the nineteenth century.” The review, with follow-ups, were reprinted in Medawar’s The Art of the Soluble: Creativity and Originality in Science (1967), 85-98.
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Since natural selection demands only adequacy, elegance of design is not relevant; any combination of behavioural adjustment, physiological regulation, or anatomical accommodation that allows survival and reproduction may be favoured by selection. Since all animals are caught in a phylogenetic trap by the nature of past evolutionary adjustments, it is to be expected that a given environmental challenge will be met in a variety of ways by different animals. The delineation of the patterns of the accommodations of diverse types of organisms to the environment contributes much of the fascination of ecologically relevant physiology.
In 'The roles of physiology and behaviour in the maintenance of homeostasis in the desert environment.', Symposia of the Society for Experimental Biology (1964), 11.
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Since science's competence extends to observable and measurable phenomena, not to the inner being of things, and to the means, not to the ends of human life, it would be nonsense to expect that the progress of science will provide men with a new type of metaphysics, ethics, or religion.
'Science and Ontology', Bulletin of Atomic Scientists (1949), 5, 200.
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Sir Adolph Abrams, the physician, in a lecture entitled Amanuensis, described a case history as an amalgam of false memories, rumour, innuendo and downright lies, and on these we are expected to make a diagnosis.
Myre Sim
Quoted in book review by Myre Sim about 'Ending the Cycle of Abuse', The Canadian Journal of Psychiatry (May 1997), 42:4, 424-425. Webmaster believes the correct name should be Sir Adolphe Abrahams of Westminster Hospital.
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Some recent work by E. Fermi and L. Szilard, which has been communicated to me in manuscript, leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. Certain aspects of the situation seem to call for watchfulness and, if necessary, quick action on the part of the Administration. …
In the course of the last four months it has been made probable … that it may become possible to set up nuclear chain reactions in a large mass of uranium, by which vast amounts of power and large quantities of new radium-like elements would be generated. Now it appears almost certain that this could be achieved in the immediate future.
This new phenomenon would also lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may thus be constructed. A single bomb of this type, carried by boat or exploded in a port, might well destroy the whole port altogether with some of the surrounding territory. However, such bombs might well prove to be too heavy for transportation by air.
Letter to President Franklin P. Roosevelt, (2 Aug 1939, delivered 11 Oct 1939). In Otto Nathan and Heinz Norden (Eds.) Einstein on Peace (1960, reprinted 1981), 294-95.
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Sometimes you get a glimpse of a semicolon coming, a few lines farther on, and it is like climbing a steep path through woods and seeing a wooden bench just at a bend in the road ahead, a place where you can expect to sit for a moment, catching your breath.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1995), 129.
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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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Such an atmosphere is un-American, the most un-American thing we have to contend with today. It is the climate of a totalitarian country in which scientists are expected to change their theories to match changes in the police state's propaganda line.
[Stinging rebuke of J. Parnell Thomas, Chairman, House Committee on Un-American activities, who had attacked Dr. Condon (1 Mar 1948) as a weak link in American atomic security.]
Opening address (13 Sep 1953) at the annual meeting of the American Association for the Advancement of Science where Condon would be elected as the new AAAS president. Obituary, New York Times (27 Mar 1974), 46.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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Surely every medicine is an innovation, and he that will not apply new remedies must expect new evils for time is the greatest innovator.
From essay, 'Of Innovations' (1625). As collected and translated in The Works of Francis Bacon (1765), Vol. 1, 479.
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Taking a very gloomy view of the future of the human race, let us suppose that it can only expect to survive for two thousand millions years longer, a period about equal to the past age of the earth. Then, regarded as a being destined to live for three-score years and ten, humanity although it has been born in a house seventy years old, is itself only three days old. But only in the last few minutes has it become conscious that the whole world does not centre round its cradle and its trappings, and only in the last few ticks of the clock has any adequate conception of the size of the external world dawned upon it. For our clock does not tick seconds, but years; its minutes are the lives of men.
EOS: Or the Wider Aspects of Cosmology (1928), 12-3.
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That the great majority of those who leave school should have some idea of the kind of evidence required to substantiate given types of belief does not seem unreasonable. Nor is it absurd to expect that they should go forth with a lively interest in the ways in which knowledge is improved and a marked distaste for all conclusions reached in disharmony with the methods of scientific inquiry.
Address to Section L, Education, of the American Association for the Advancement of Science, at Boston (1909), 'Science as Subject-Matter and as Method'. Published in Science (28 Jan 1910), N.S. Vol. 31, No. 787, 126.
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The best class of scientific mind is the same as the best class of business mind. The great desideratum in either case is to know how much evidence is enough to warrant action. It is as unbusiness-like to want too much evidence before buying or selling as to be content with too little. The same kind of qualities are wanted in either case. The difference is that if the business man makes a mistake, he commonly has to suffer for it, whereas it is rarely that scientific blundering, so long as it is confined to theory, entails loss on the blunderer. On the contrary it very often brings him fame, money and a pension. Hence the business man, if he is a good one, will take greater care not to overdo or underdo things than the scientific man can reasonably be expected to take.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 217.
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The chemical differences among various species and genera of animals and plants are certainly as significant for the history of their origins as the differences in form. If we could define clearly the differences in molecular constitution and functions of different kinds of organisms, there would be possible a more illuminating and deeper understanding of question of the evolutionary reactions of organisms than could ever be expected from morphological considerations.
'Uber das Vorkommen von Haemoglobin in den Muskeln der Mollusken und die Verbreitung desselben in den lebenden Organismen', Pflügers Archiv für die gesamte Physiologie des Menschen und der Tiere, 1871, 4, 318-9. Trans. Joseph S. Fruton, Proteins, Enzymes, Genes: The Interplay of Chemistry and Biology (1999), 270.
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The discrepancy between what was expected and what has been observed has grown over the years, and we're straining harder and harder to fill the gap.
[Commenting on the 1984 article in Nature discrediting neutrinos as the explanation for the missing mass of the universe, leaving astrophysicists more baffled for a solution.]
In 'If Theory is Right, Most of Universe is Still “Missing”', New York Times (11 Sep 1984).
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The energy of a covalent bond is largely the energy of resonance of two electrons between two atoms. The examination of the form of the resonance integral shows that the resonance energy increases in magnitude with increase in the overlapping of the two atomic orbitals involved in the formation of the bond, the word ‘overlapping” signifying the extent to which regions in space in which the two orbital wave functions have large values coincide... Consequently it is expected that of two orbitals in an atom the one which can overlap more with an orbital of another atom will form the stronger bond with that atom, and, moreover, the bond formed by a given orbital will tend to lie in that direction in which the orbital is concentrated.
Nature of the Chemical Bond and the Structure of Molecules and Crystals (1939), 76.
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The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from transformation of these atoms is talking moonshine. … We hope in the next few years to get some idea of what these atoms are, how they are made, and the way they are worked.
Address at Leicester (11 Sep 1933). Cited as 'Atom Powered World Absurd, Scientists Told: Lord Rutherford Scoffs at Theory of Harnessing Energy in Laboratories', New York Herald Tribune (12 Sep 1933), in Jacqueline D. Spears and Dean Zollman, The Fascination of Physics, (1985), 508.
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The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.
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The fact that stares one in the face is that people of the greatest sincerity and of all levels of intelligence differ and have always differed in their religious beliefs. Since at most one faith can be true, it follows that human beings are extremely liable to believe firmly and honestly in something untrue in the field of revealed religion. One would have expected this obvious fact to lead to some humility, to some thought that however deep one's faith, one may conceivably be mistaken. Nothing is further from the believer, any believer, than this elementary humility. All in his power … must have his faith rammed down their throats. In many cases children are indeed indoctrinated with the disgraceful thought that they belong to the one group with superior knowledge who alone have a private wire to the office of the Almighty, all others being less fortunate than they themselves.
From 'Religion is a Good Thing', collected in R. Duncan and M. Wesson-Smith (eds.) Lying Truths: A Critical Scruting of Current Beliefs and Conventions (1979), 205. As quoted in Paul Davies, God and the New Physics (1984), 6-7.
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The frequent allegation that the selective processes in the human species are no longer 'natural' is due to persistence of the obsolete nineteenth-century concept of 'natural' selection. The error of this view is made clear when we ask its proponents such questions as, why should the 'surviving fittest' be able to withstand cold and inclement weather without the benefit of fire and clothing? Is it not ludicrous to expect selection to make us good at defending ourselves against wild beasts when wild beasts are getting to be so rare that it is a privilege to see one outside of a zoo? Is it necessary to eliminate everyone who has poor teeth when our dentists stand ready to provide us with artificial ones? Is it a great virtue to be able to endure pain when anaesthetics are available?
[Co-author with American statistician Gordon Allen]
Theodosius Dobzhansky and Gordon Allen, 'Does Natural Selection Continue to Operate in Modern Mankind?', American Anthropologist, 1956, 58, 595.
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The future offers very little hope for those who expect that our new mechanical slaves will offer us a world in which we may rest from thinking. Help us they may, but at the cost of supreme demands upon our honesty and our intelligence. The world of the future will be an ever more demanding struggle against the limitations of our intelligence, not a comfortable hammock in which we can lie down to be waited upon by our robot slaves.
In God & Golem, Inc (1964), 73-74.
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The general knowledge of our author [Leonhard Euler] was more extensive than could well be expected, in one who had pursued, with such unremitting ardor, mathematics and astronomy as his favorite studies. He had made a very considerable progress in medical, botanical, and chemical science. What was still more extraordinary, he was an excellent scholar, and possessed in a high degree what is generally called erudition. He had attentively read the most eminent writers of ancient Rome; the civil and literary history of all ages and all nations was familiar to him; and foreigners, who were only acquainted with his works, were astonished to find in the conversation of a man, whose long life seemed solely occupied in mathematical and physical researches and discoveries, such an extensive acquaintance with the most interesting branches of literature. In this respect, no doubt, he was much indebted to an uncommon memory, which seemed to retain every idea that was conveyed to it, either from reading or from meditation.
In Philosophical and Mathematical Dictionary (1815), 493-494.
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The greatest spiritual revolutionary Western history, Saint Francis, proposed what he thought was an alternative Christian view of nature and man’s relation to it: he tried to substitute the idea of the equality of creatures, including man, for the idea of man’s limitless rule of creation. He failed. Both our present science and our present technology are so tinctured with orthodox Christian arrogance toward nature that no solution for our ecologic crisis can be expected from them alone. Since the roots of our trouble are so largely religious, the remedy must also be essentially religious, whether we call it that or not. We must rethink and refeel our nature and destiny. The profoundly religious, but heretical, sense of the primitive Franciscans for the spiritual autonomy of all parts of nature may point a direction. I propose Francis as a patron saint for ecologists.
In The Historical Roots of our Ecologic Crisis (1967), 1207.
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The greatest value of a picture is when it forces us to notice what we never expected to see.
In Exploratory Data Analysis (1977), vi. Cited in epigraph, Chandrika Kamath, Scientific Data Mining: A Practical Perspective (2009), 209 .
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The history of science teaches only too plainly the lesson that no single method is absolutely to be relied upon, that sources of error lurk where they are least expected, and that they may escape the notice of the most experienced and conscientious worker.
Transactions of the Sections', Reports of the British Association for the Advancement of Science (1883), 438.
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The hype, skepticism and bewilderment associated with the Internet—concerns about new forms of crime, adjustments in social mores, and redefinition of business practices— mirror the hopes, fears, and misunderstandings inspired by the telegraph. Indeed, they are only to be expected. They are the direct consequences of human nature, rather than technology.
Given a new invention, there will always be some people who see only its potential to do good, while others see new opportunities to commit crime or make money. We can expect the same reactions to whatever new inventions appear in the twenty-first century.
Such reactions are amplified by what might be termed chronocentricity—the egotism that one’s own generation is poised on the very cusp of history. Today, we are repeatedly told that we are in the midst of a communications revolution. But the electric telegraph was, in many ways, far more disconcerting for the inhabitants of the time than today’s advances are for us. If any generation has the right to claim that it bore the full bewildering, world-shrinking brunt of such a revolution, it is not us—it is our nineteenth- century forebears.
In The Victorian Internet (1998).
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The Internet is like a herd of performing elephants with diarrhea—massive, difficult to redirect, awe-inspiring, entertaining and a source of mind-boggling amounts of excrement when you least expect it.
Posted to a mailing list (1992), and circulated from there by some newsgroups. As authenticated in 'Quotable Spaf' on his faculty webpage at purdue.com
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The last few meters up to the summit no longer seem so hard. On reaching the top, I sit down and let my legs dangle into space. I don’t have to climb anymore. I pull my camera from my rucksack and, in my down mittens, fumble a long time with the batteries before I have it working properly. Then I film Peter. Now, after the hours of torment, which indeed I didn’t recognize as torment, now, when the monotonous motion of plodding upwards is at an end, and I have nothing more to do than breathe, a great peace floods my whole being. I breathe like someone who has run the race of his life and knows that he may now rest forever. I keep looking all around, because the first time I didn’t see anything of the panorama I had expected from Everest, neither indeed did I notice how the wind was continually chasing snow across the summit. In my state of spiritual abstraction, I no longer belong to myself and to my eyesight. I am nothing more than a single, narrow, gasping lung, floating over the mists and the summits.
…...
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The only man who behaved sensibly was my tailor; he took my measurement anew every time he saw me, while all the rest went on with their old measurements and expected them to fit me.
…...
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The question whether atoms exist or not... belongs rather to metaphysics. In chemistry we have only to decide whether the assumption of atoms is an hypothesis adapted to the explanation of chemical phenomena... whether a further development of the atomic hypothesis promises to advance our knowledge of the mechanism of chemical phenomena... I rather expect that we shall some day find, for what we now call atoms, a mathematico-mechanical explanation, which will render an account of atomic weight, of atomicity, and of numerous other properties of the so-called atoms.
Laboratory (1867), 1, 303.
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The role of hypothesis in research can be discussed more effectively if we consider first some examples of discoveries which originated from hypotheses. One of the best illustrations of such a discovery is provided by the story of Christopher Columbus’ voyage; it has many of the features of a classic discovery in science. (a) He was obsessed with an idea—that since the world is round he could reach the Orient by sailing West, (b) the idea was by no means original, but evidently he had obtained some additional evidence from a sailor blown off his course who claimed to have reached land in the west and returned, (c) he met great difficulties in getting someone to provide the money to enable him to test his idea as well as in the actual carrying out of the experimental voyage, (d) when finally he succeeded he did not find the expected new route, but instead found a whole new world, (e) despite all evidence to the contrary he clung to the bitter end to his hypothesis and believed that he had found the route to the Orient, (f) he got little credit or reward during his lifetime and neither he nor others realised the full implications of his discovery, (g) since his time evidence has been brought forward showing that he was by no means the first European to reach America.
The Art of Scientific Investigation (1950), 41.
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The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is, correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria—that is, in relation to how much it describes, it must be rather simple.
From 'Method in the Physical Sciences', in John von Neumann and L. Leary (ed.), The Unity of Knowledge (1955), 158. Reprinted in John Von Neumann, F. Bródy (ed.) and Tibor Vámos (ed.), The Neumann Compendium (2000), 628.
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The sciences throw an inexpressible grace over our compositions, even where they are not immediately concerned; as their effects are discernible where we least expect to find them.
'A Dialogue Concerning Oratory', The Works of Tacitus By Cornelius Tacitus (1854), Vol. 2, 439.
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The scientific man does not aim at an immediate result. He does not expect that his advanced ideas will be readily taken up. His work is like that of the planter—for the future. His duty is to lay the foundation for those who are to come, and point the way.
'The Problem of Increasing Human Energy', The Century (Jun 1900), 211. Collected in The Century (1900), Vol. 60, 211
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The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. ... it was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.
Introduction to a paper on magnetic monopoles, 'Quantised singularities in the electromagnetic field', Proceedings of the Royal Society of Lonndon (1931), A, 133 60. In Helge Kragh, Dirac: a Scientific Biography (1990), 208.
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The success of Apollo was mainly due to the fact that the project was conceived and honestly presented to the public as an international sporting event and not as a contribution to science. The order of priorities in Apollo was accurately reflected by the first item to be unloaded after each landing on the Moon's surface, the television camera. The landing, the coming and going of the astronauts, the exploring of the moon's surface, the gathering of Moon rocks and the earthward departure, all were expertly choreographed with the cameras placed in the right positions to make a dramatic show on television. This was to me the great surprise of the Apollo missions. There was nothing surprising in the fact that astronauts could walk on the Moon and bring home Moon rocks. There were no big scientific surprises in the chemistry of the Moon rocks or in the results of magnetic and seismic observations that the astronauts carried out. The big surprise was the quality of the public entertainment that the missions provided. I had never expected that we would see in real time astronauts hopping around in lunar gravity and driving their Rover down the Lincoln- Lee scarp to claim a lunar speed record of eleven miles per hour. Intensive television coverage was the driving force of Apollo. Von Braun had not imagined the possibilities of television when he decided that one kilohertz would be an adequate communication bandwidth for his Mars Project.
From a Danz lecture at University of Washington, 'Sixty Years of Space Science 1958-2018' (1988), collected in From Eros to Gaia (1992), Vol. 5, 52.
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The three of us have worked on the development of the small and totally harmless fruit fly, Drosophila. This animal has been extremely cooperative in our hands - and has revealed to us some of its innermost secrets and tricks for developing from a single celled egg to a complex living being of great beauty and harmony. ... None of us expected that our work would be so successful or that our findings would ever have relevance to medicine.
Nobel Banquet Speech, 10 Dec 1995
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The traveler was active; he went strenuously in search of people, of adventure, of experience. The tourist is passive; he expects interesting things to happen to him. He goes “sight-seeing.”
The Image: A Guide to Pseudo-Events in America (1961, 2012), 85. https://books.google.com/books?isbn=0307819167 Daniel J. Boorstin - 2012
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The various elements had different places before they were arranged so as to form the universe. At first, they were all without reason and measure. But when the world began to get into order, fire and water and earth and air had only certain faint traces of themselves, and were altogether such as everything might be expected in the absence of God; this, I say, was their nature at that time, and God fashioned them by form and number.
Plato
In Plato and B. Jowett (trans.), The Dialogues of Plato: Republic (3rd ed., 1892), Vol. 3, 473.
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The various systems of doctrine that have held dominion over man have been demonstrated to be true beyond all question by rationalists of such power—to name only a few—as Aquinas and Calvin and Hegel and Marx. Guided by these master hands the intellect has shown itself more deadly than cholera or bubonic plague and far more cruel. The incompatibility with one another of all the great systems of doctrine might surely be have expected to provoke some curiosity about their nature.
In 'Has the Intellect A Function?', The Collected Papers of Wilfred Trotter, FRS (1941), 167.
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Therefore, these [geotectonic] models cannot be expected to assume that the deeper parts of the earth’s crust were put together and built in a simpler way. The myth about the increasing simplicity with depth results from a general pre-scientific trend according to which the unknown or little known has to be considered simpler than the known. Many examples of this myth occur in the history of geology as, for instance, the development of views on the nature of the seafloor from the past to the present.
In 'Stockwerktektonik und Madelle van Esteinsdifferentiation', in Geotektonisches Symposium zu Ehren von Hans Stille, als Festschrift zur Vollendung seines 80, Lebensjahres (1956), 17, trans. Albert V. and Marguerite Carozzi.
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This leads us to ask for the reasons which call for this new theory of transmutation. The beginning of things must needs lie in obscurity, beyond the bounds of proof, though within those of conjecture or of analogical inference. Why not hold fast to the customary view, that all species were directly, instead of indirectly, created after their respective kinds, as we now behold them,--and that in a manner which, passing our comprehension, we intuitively refer to the supernatural? Why this continual striving after “the unattained and dim,”—these anxious endeavors, especially of late years, by naturalists and philosophers of various schools and different tendencies, to penetrate what one of them calls “the mystery of mysteries,” the origin of species? To this, in general, sufficient answer may be found in the activity of the human intellect, “the delirious yet divine desire to know,” stimulated as it has been by its own success in unveiling the laws and processes of inorganic Nature,—in the fact that the principal triumphs of our age in physical science have consisted in tracing connections where none were known before, in reducing heterogeneous phenomena to a common cause or origin, in a manner quite analogous to that of the reduction of supposed independently originated species to a common ultimate origin,—thus, and in various other ways, largely and legitimately extending the domain of secondary causes. Surely the scientific mind of an age which contemplates the solar system as evolved from a common, revolving, fluid mass,— which, through experimental research, has come to regard light, heat, electricity, magnetism, chemical affinity, and mechanical power as varieties or derivative and convertible forms of one force, instead of independent species,—which has brought the so-called elementary kinds of matter, such as the metals, into kindred groups, and raised the question, whether the members of each group may not be mere varieties of one species,—and which speculates steadily in the direction of the ultimate unity of matter, of a sort of prototype or simple element which may be to the ordinary species of matter what the protozoa or component cells of an organism are to the higher sorts of animals and plants,—the mind of such an age cannot be expected to let the old belief about species pass unquestioned.
Asa Gray
'Darwin on the Origin of Species', The Atlantic Monthly (Jul 1860), 112-3. Also in 'Natural Selection Not Inconsistent With Natural Theology', Darwiniana: Essays and Reviews Pertaining to Darwinism (1876), 94-95.
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Those of us who were familiar with the state of inorganic chemistry in universities twenty to thirty years ago will recall that at that time it was widely regarded as a dull and uninteresting part of the undergraduate course. Usually, it was taught almost entirely in the early years of the course and then chiefly as a collection of largely unconnected facts. On the whole, students concluded that, apart from some relationships dependent upon the Periodic table, there was no system in inorganic chemistry comparable with that to be found in organic chemistry, and none of the rigour and logic which characterised physical chemistry. It was widely believed that the opportunities for research in inorganic chemistry were few, and that in any case the problems were dull and uninspiring; as a result, relatively few people specialized in the subject... So long as inorganic chemistry is regarded as, in years gone by, as consisting simply of the preparations and analysis of elements and compounds, its lack of appeal is only to be expected. The stage is now past and for the purpose of our discussion we shall define inorganic chemistry today as the integrated study of the formation, composition, structure and reactions of the chemical elements and compounds, excepting most of those of carbon.
Inaugural Lecture delivered at University College, London (1 Mar 1956). In The Renaissance of Inorganic Chemistry (1956), 4-5.
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Though genius isn't something that can be produced arbitrarily, it is freely willed—like wit, love, and faith, which one day will have to become arts and sciences. You should demand genius from everyone, but not expect it. A Kantian would call this the categorical imperative of genius.
Critical Fragment 16 in Friedrich Schlegel's Lucinde and the Fragments (1971), 144.
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To expect a personality to survive the disintegration of the brain is like expecting a cricket club to survive when all of its members are dead.
…...
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To expect defeat is nine-tenths of defeat itself.
…...
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To expect that the intricacies of science will be pierced by a careless glance, or the eminences of fame ascended without labour, is to expect a peculiar privilege, a power denied to the rest of mankind; but to suppose that the maze is inscrutable to diligence, or the heights inaccessible to perseverance, is to submit tamely to the tyranny of fancy, and enchain the mind in voluntary shackles.
'The Need For General Knowledge,' Rambler No. 137 (9 Jul 1751). In Samuel Johnson, Donald Greene (ed.), Samuel Johnson (1984), 223.
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To expect the unexpected shows a thoroughly modern intellect.
In Lily Splane, Quantum Consciousness (2004), 309
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To learn… the ordinary arrangement of the different strata of minerals in the earth, to know from their habitual colocations and proximities, where we find one mineral; whether another, for which we are seeking, may be expected to be in its neighborhood, is useful.
In The Writings of Thomas Jefferson (1854), Vol. 7, 443.
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Truth is born into this world only with pangs and tribulations, and every fresh truth is received unwillingly. To expect the world to receive a new truth, or even an old truth, without challenging it, is to look for one of those miracles which do not occur.
In 'Alfred Russel Wallace: An interview by W. B. Northrop', The Outlook (1913), 105, 622.
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Unless you expect the unexpected you will never find it, for it is hard to discover and hard to attain.
As quoted in Peter Pešic, Labyrinth: A Search for the Hidden Meaning of Science (2001), 2.
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Very old and wide-spread is the opinion that forests have an important impact on rainfall. ... If forests enhance the amount and frequency of precipitation simply by being there, deforestation as part of agricultural expansion everywhere, must necessarily result in less rainfall and more frequent droughts. This view is most poignantly expressed by the saying: Man walks the earth and desert follows his steps! ... It is not surprising that under such circumstances the issue of a link between forests and climate has ... been addressed by governments. Lately, the Italian government has been paying special attention to reforestation in Italy and its expected improvement of the climate. ... It must be prevented that periods of heavy rainfall alternate with droughts. ...In the Unites States deforestation plays an important role as well and is seen as the cause for a reduction in rainfall. ... committee chairman of the American Association for Advancement of Science demands decisive steps to extend woodland in order to counteract the increasing drought. ... some serious concerns. In 1873, in Vienna, the congress for agriculture and forestry discussed the problem in detail; and when the Prussian house of representatives ordered a special commission to examine a proposed law pertaining to the preservation and implementation of forests for safeguarding, it pointed out that the steady decrease in the water levels of Prussian rivers was one of the most serious consequences of deforestation only to be rectified by reforestation programs. It is worth mentioning that ... the same concerns were raised in Russia as well and governmental circles reconsidered the issue of deforestation.
as quoted in Eduard Brückner - The Sources and Consequences of Climate Change and Climate Variability in Historical Times editted by N. Stehr and H. von Storch (2000)
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We are as yet got little farther than to the surface of things: yet ought we not to be discouraged; though we can never hope to attain to the complete knowledge of the texture, or constituent frame and nature of bodies, yet may we reasonably expect by this method of experiments, to make farther and farther advances abundantly sufficient to reward our pains.
In 'Preface', Statical Essays: Containing Hæmastatics (1769), Vol. 2, ii.
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We cannot expect in the immediate future that all women who seek it will achieve full equality of opportunity. But if women are to start moving towards that goal, we must believe in ourselves or no one else will believe in us; we must match our aspirations with the competence, courage and determination to succeed.
From a speech given to students in Stockholm, Sweden, Oct 1977 as quoted in The Decade of Women (1980) by Suzanne Levine and Harriet Lyons
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We expect that the study of lunar geology will help to answer some longstanding questions about the early evolution of the earth. The moon and the earth are essentially a two-planet system, and the two bodies are probably closely related in origin. In this connection the moon is of special interest because its surface has not been subjected to the erosion by running water that has helped to shape the earth's surface.
In Scientific American (Sep 1964). As cited in '50, 100 & 150 Years Ago', Scientific American (Dec 2014), 311, No. 6, 98.
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We have a right to expect that the best trained, the best educated men on the Pacific slope, the Rocky Mountains, and great plains States will take the lead in the preservation and right use of forests, in securing the right use of waters, and in seeing that our land policy is not twisted from its original purpose, but is perpetuated by amendment, by change when such change is necessary in the life of that purpose, the purpose being to turn the public domain into farms each to be the property of the man who actually tills it and makes his home in it.
Address at Leland Stanford, Jr., University, Palo Alto, California, 12 May 1903. Addresses and Presidential Messages of Theodore Roosevelt, 1902-1904 (1904), 198.
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We have seen that a proton of energy corresponding to 30,000 volts can effect the transformation of lithium into two fast α-particles, which together have an energy equivalent of more than 16 million volts. Considering the individual process, the output of energy in the transmutation is more than 500 times greater than the energy carried by the proton. There is thus a great gain of energy in the single transmutation, but we must not forget that on an average more than 1000 million protons of equal energy must be fired into the lithium before one happens to hit and enter the lithium nucleus. It is clear in this case that on the whole the energy derived from transmutation of the atom is small compared with the energy of the bombarding particles. There thus seems to be little prospect that we can hope to obtain a new source of power by these processes. It has sometimes been suggested, from analogy with ordinary explosives, that the transmutation of one atom might cause the transmutation of a neighbouring nucleus, so that the explosion would spread throughout all the material. If this were true, we should long ago have had a gigantic explosion in our laboratories with no one remaining to tell the tale. The absence of these accidents indicates, as we should expect, that the explosion is confined to the individual nucleus and does not spread to the neighbouring nuclei, which may be regarded as relatively far removed from the centre of the explosion.
The Transmutation of the Atom (1933), 23-4
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We in the modern world expect that tomorrow will be better than today.
In Day the Universe Changed (1985), 19.
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We might expect that as we come close upon living nature the characters of our old records would grow legible and clear; but just when we begin to enter on the history of the 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 book, and the succession of events is almost hidden from our eyes. [On gaps in the Pleistocene fossil record.]
As quoted by Hugh Miller in Lecture First, collected in Popular Geology: A Series of Lectures Read Before the Philosophical Institution of Edinburgh, with Descriptive Sketches from a Geologist's Portfolio (1859), 82-83.
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We might expect … in the summer of the “great year,” which we are now considering, that there would be a great predominance of tree-ferns and plants allied to the palms and arborescent grasses in the isles of the wide ocean, while the dicotyledenous plants and other forms now most common in temperate regions would almost disappear from the earth. Then might these genera of animals return, of which the memorials are preserved in the ancient rocks of our continents. The huge iguanodon might reappear in the woods, and the ichthyosaur in the sea, while the pterodactyle might flit again through umbrageous groves of tree-ferns. Coral reefs might be prolonged beyond the arctic circle, where the whale and narwal [sic] now abound. Turtles might deposit their eggs in the sand of the sea beach, where now the walrus sleeps, and where the seal is drifted on the ice-floe.
In Principles of Geology (1830-3), Vol. 1, 123.
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We must therefore bear the undoubtedly bad effect s of the weak surviving and propagating their kind; but there appears to be at least one check in steady action, namely that the weaker and inferior members of society do not marry so freely as the sound; and this check might be indefinitely increased by the weak in body or mind refraining from marriage, though this is more to be hoped for than expected.
…...
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We of an older generation can get along with what we have, though with growing hardship; but in your full manhood and womanhood you will want what nature once so bountifully supplied and man so thoughtlessly destroyed; and because of that want you will reproach us, not for what we have used, but for what we have wasted...So any nation which in its youth lives only for the day, reaps without sowing, and consumes without husbanding, must expect the penalty of the prodigal whose labor could with difficulty find him the bare means of life.
'Arbor Day: A Message to the School-Children of the United States', 15 Apr 1907. In Presidential Addresses and State Papers (1910), Vol. 11, 1207-8.
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We often frame our understanding of what the [Hubble] space telescope will do in terms of what we expect to find, and actually it would be terribly anticlimactic if in fact we find what we expect to find. … The most important discoveries will provide answers to questions that we do not yet know how to ask and will concern objects we have not yet imagined.
As quoted in Timothy Ferris, 'The Space Telescope: A Sign of Intelligent Life', New York Times (29 Apr 1990), A1.
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We want them to use the education to be leaders in their community with an understanding of ecology and conservation for the wild outdoors far beyond their legislators back home. We expect these people to he a grain of sand on the beach of future leadership.
…...
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Well, in the first place, it leads to great anxiety as to whether it’s going to be correct or not … I expect that’s the dominating feeling. It gets to be rather a fever…
At age 60, when asked about his feelings on discovering the Dirac equation.
"Interview with T. Kuhn (7 May 1963), Niels Bohr Library, American Intitute of Physics, New York. In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 110.
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What friends do with us and for us is a real part of our life; for it strengthens and advances our personality. The assault of our enemies is not part of our life ; it is only part of our experience ; we throw it off and guard ourselves against it as against frost, storm, rain, hail, or any other of the external evils which may be expected to happen.
In The Maxims and Reflections of Goethe (1906), 201.
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What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today’s mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it’s not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers?
Mathematics is all of these, and none. Mostly, it’s just different. It’s not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.
Opening paragraphs of 'Preface', From Here to Infinity (1996), vii.
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What is peculiar and new to the [19th] century, differentiating it from all its predecessors, is its technology. It was not merely the introduction of some great isolated inventions. It is impossible not to feel that something more than that was involved. … The process of change was slow, unconscious, and unexpected. In the nineteeth century, the process became quick, conscious, and expected. … The whole change has arisen from the new scientific information. Science, conceived not so much in its principles as in its results, is an obvious storehouse of ideas for utilisation. … Also, it is a great mistake to think that the bare scientific idea is the required invention, so that it has only to be picked up and used. An intense period of imaginative design lies between. One element in the new method is just the discovery of how to set about bridging the gap between the scientific ideas, and the ultimate product. It is a process of disciplined attack upon one difficulty after another This discipline of knowledge applies beyond technology to pure science, and beyond science to general scholarship. It represents the change from amateurs to professionals. … But the full self-conscious realisation of the power of professionalism in knowledge in all its departments, and of the way to produce the professionals, and of the importance of knowledge to the advance of technology, and of the methods by which abstract knowledge can be connected with technology, and of the boundless possibilities of technological advance,—the realisation of all these things was first completely attained in the nineteeth century.
In Science and the Modern World (1925, 1997), 96.
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Whatever the skill of any country may be in the sciences, it is from its excellence in polite learning alone that it must expect a character from posterity.
Essays, on Miscellaneous Subjects (1818), 198.
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When we see a natural style, we are astonished and delighted; for we expected to see an author, and we find a man.
In Pensées (1670), Section 7, No. 28. As translated in Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', No. 29, collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 16. Translated as “When we encounter a natural style we are always surprised and delighted, for we thought to see an author and found a man,” in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966), 277. From the original French, “Quand on voit le style naturel, on est tout étonné et ravi, car on s’attendait de voir un auteur, et on trouve un homme,” in Ernest Havet (ed.), Pensées de Pascal (1892), 222.
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Where there is an observatory and a telescope, we expect that any eyes will see new worlds at once.
In A Week on the Concord and Merrimack Rivers (1862), 382-383.
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Whilst you put up a public house at one end of your street and a provident dispensary at the other, how can you expect your people to be healthy?
As quoted in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xxvi. [Note: a “public house” is better known as a pub or bar.]
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You are not expected to complete the work in your lifetime. Nor must you refuse to do your unique part.
Talmud
…...
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[A plant] does not change itself gradually, but remains unaffected during all succeeding generations. It only throws off new forms, which are sharply contrasted with the parent, and which are from the very beginning as perfect and as constant, as narrowly defined, and as pure of type as might be expected of any species.
In Species and Varieties: Their Origin and Mutation (1905), 28-9.
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[Alchemists] finde out men so covetous of so much happiness, whom they easily perswade that they shall finde greater Riches in Hydargyrie [mercury], than Nature affords in Gold. Such, whom although they have twice or thrice already been deluded, yet they have still a new Device wherewith to deceive um again; there being no greater Madness…. So that the smells of Coles, Sulphur, Dung, Poyson, and Piss, are to them a greater pleasure than the taste of Honey; till their Farms, Goods, and Patrimonies being wasted, and converted into Ashes and Smoak, when they expect the rewards of their Labours, births of Gold, Youth, and Immortality, after all their Time and Expences; at length, old, ragged, famisht, with the continual use of Quicksilver [mercury] paralytick, onely rich in misery, … a laughing-stock to the people: … compell’d to live in the lowest degree of poverty, and … at length compell’d thereto by Penury, they fall to Ill Courses, as Counterfeiting of Money.
In The Vanity of the Arts and Sciences (1530), translation (1676), 313.
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[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher’s assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds.
In editorial in Focus, a Journal of the Mathematical Association of America (1986), quoted in obituary by Eric Pace, New York Times (11 Jun 1992).
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[The octopus has] an amazing skin, because there are up to 20 million of these chromatophore pigment cells and to control 20 million of anything is going to take a lot of processing power. ... These animals have extraordinarily large, complicated brains to make all this work. ... And what does this mean about the universe and other intelligent life? The building blocks are potentially there and complexity will arise. Evolution is the force that's pushing that. I would expect, personally, a lot of diversity and a lot of complicated structures. It may not look like us, but my personal view is that there is intelligent life out there.
From transcript of PBS TV program Nova episode 'Origins: Where are the Aliens?' (2004).
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[W]e might expect intelligent life and technological communities to have emerged in the universe billions of years ago. Given that human society is only a few thousand years old, and that human technological society is mere centuries old, the nature of a community with millions or even billions of years of technological and social progress cannot even be imagined. ... What would we make of a billion-year-old technological community?
In Are We Alone?(1995), 48.
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“Expect surprises!” should be the watchword of all scientists who try to look beyond the fashions of the day.
In Internal Factors in Evolution (1965), 13.
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“I’m not so sure he’s wrong about automobiles,” he said, “With all their speed forward they may be a step backward for civilization—that is, spiritual civilization … But automobiles have come, and they bring a greater change in our life than most of us expect. They are here, and almost all outward things are going to be different because of what they bring. They are going to alter war, and they are going to alter peace.”
Spoken by character Eugene, in the novel, The Magnificent Ambersons (1918), 275
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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