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Home > Category Index for Science Quotations > Category Index F > Category: Field

Field Quotes (364 quotes)

Agri non omnes frugiferi sunt.
Not all fields are fruitful.
From Tusculanae Disputationes (Tusculan Disputations) (45 BC), book 2, chap. 5, line 13. As translated in epigraph in Hagen Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (2009), 1368. Cicero uses this as a metaphor, to illustrate that all men are not equally susceptible of improvement.
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Ce qui est admirable, ce n'est pas que le champ des étoiles soit si vaste, c'est que l'homme l'ait mesuré.
The wonder is, not that the field of the stars is so vast, but that man has measured it.
The Garden of Epicurus (1894) translated by Alfred Allinson, in The Works of Anatole France in an English Translation (1920), 16.
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Changements arrivées dans le globe: Quand on a vu de ses yeux une montagne s’avancer dans une plaine, c’est-à-dire un immense rocher de cette montagne se détacher et couvrir des champs, un château tout entier enfoncé dans la terre, un fleuve englouti qui sort ensuite de son abîme, des marques indubitables qu’un vaste amas d’eau inondait autrefois un pays habité aujourd’hui, et cent vestiges d’autres révolutions, on est alors plus disposé à croire les grands changements qui ont altéré la face du monde, que ne l’est une dame de Paris qui sait seulement que la place où est bâtie sa maison était autrefois un champ labourable. Mais une dame de Naples, qui a vu sous terre les ruines d’Herculanum, est encore moins asservie au préjugé qui nous fait croire que tout a toujours été comme il est aujourd’hui.
Changes That Have Occurred in the Globe: When we have seen with our own eyes a mountain progressing into a plain; that is to say, an immense boulder separating from this mountain and covering the fields; an entire castle broken into pieces over the ground; a river swallowed up which then bursts out from its abyss; clear marks of a vast amount of water having once flooded regions now inhabited, and a hundred vestiges of other transformations, then we are much more willing to believe that great changes altered the face of the earth, than a Parisian lady who knows only that the place where her house was built was once a cultivated field. However, a lady from Naples who has seen the buried ruins of Herculaneum, is much less subject to the bias which leads us to believe that everything has always been as it is today.
From article 'Changements arrivées dans le globe', in Dictionnaire philosophique (1764), collected in Œuvres Complètes de Voltaire (1878), Vol. 2, 427-428. Translated by Ian Ellis.
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Dans les champs de l’observation le hasard ne favorise que les esprits préparés.
In the field of observation, chance favours only the prepared mind.
Inaugural Address as newly appointed Professor and Dean (Sep 1854) at the opening of the new Faculté des Sciences at Lille (7 Dec 1854). In René Vallery-Radot, The Life of Pasteur, translated by Mrs. R. L. Devonshire (1919), 76.
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Ut ager quamvis fertilis sine cultura fructuosus esse non potest, sic sine doctrina animus.
A mind without instruction can no more bear fruit than can a field, however fertile, without cultivation.
In Hannis Taylor and Mary Lillie Taylor Hunt, Cicero: a Sketch of His Life and Works (2nd Ed., 1918), 597.
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[Recalling Professor Ira Remsen's remarks (1895) to a group of his graduate students about to go out with their degrees into the world beyond the university:]
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier's first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.
Quoted in Frederick Hutton Getman, The Life of Ira Remsen (1980), 73.
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A century ago astronomers, geologists, chemists, physicists, each had an island of his own, separate and distinct from that of every other student of Nature; the whole field of research was then an archipelago of unconnected units. To-day all the provinces of study have risen together to form a continent without either a ferry or a bridge.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 182-183.
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A country grows in history not only because of the heroism of its troops on the field of battle, it grows also when it turns to justice and to right for the conservation of its interests.
…...
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A discovery must be, by definition, at variance with existing knowledge. During my lifetime, I made two. Both were rejected offhand by the popes of the field. Had I predicted these discoveries in my applications, and had those authorities been my judges, it is evident what their decisions would have been.
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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A fair number of people who go on to major in astronomy have decided on it certainly by the time they leave junior high, if not during junior high. I think it’s somewhat unusual that way. I think most children pick their field quite a bit later, but astronomy seems to catch early, and if it does, it sticks.
From interview by Rebecca Wright, 'Oral History Transcript' (15 Sep 2000), on NASA website.
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A field is the most just possession for men. For what nature requires it carefully bears: barley, oil, wine, figs, honey. Silver-plate and purple will do for the tragedians, not for life.
Philemon
Fragment 105 K-A quoted by Stobaeus 4. 15a. 15. In Matthew Leigh, Comedy and the Rise of Rome (2005), 112.
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A good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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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 mind exclusively bent upon the idea of utility necessarily narrows the range of the imagination. For it is the imagination which pictures to the inner eye of the investigator the indefinitely extending sphere of the possible,—that region of hypothesis and explanation, of underlying cause and controlling law. The area of suggestion and experiment is thus pushed beyond the actual field of vision.
In 'The Paradox of Research', The North American Review (Sep 1908), 188, No. 634, 425.
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A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 140-141.
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A scientifically unimportant discovery is one which, however true and however interesting for other reasons, has no consequences for a system of theory with which scientists in that field are concerned.
The Structure of Social Action (1937), Vol. 1, 7.
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A time will come, when fields will be manured with a solution of glass (silicate of potash), with the ashes of burnt straw, and with the salts of phosphoric acid, prepared in chemical manufactories, exactly as at present medicines are given for fever and goitre.
Agricultural Chemistry (1847), 4th edn., 186.
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A wonderful exhilaration comes from holding in the mind the deepest questions we can ask. Such questions animate all scientists. Many students of science were first attracted to the field as children by popular accounts of important unsolved problems. They have been waiting ever since to begin working on a mystery. [With co-author Arthur Zajonc]
In George Greenstein and Arthur Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (2006), xii.
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After the birth of printing books became widespread. Hence everyone throughout Europe devoted himself to the study of literature... Every year, especially since 1563, the number of writings published in every field is greater than all those produced in the past thousand years. Through them there has today been created a new theology and a new jurisprudence; the Paracelsians have created medicine anew and the Copernicans have created astronomy anew. I really believe that at last the world is alive, indeed seething, and that the stimuli of these remarkable conjunctions did not act in vain.
De Stella Nova, On the New Star (1606), Johannes Kepler Gesammelte Werke (1937- ), Vol. 1, 330-2. Quoted in N. Jardine, The Birth of History and Philosophy of Science: Kepler's A Defence of Tycho Against Ursus With Essays on its Provenance and Significance (1984), 277-8.
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All of us who are concerned for peace and triumph of reason and justice must be keenly aware how small an influence reason and honest good will exert upon events in the political field.
…...
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All the summer long is the swallow a most instructive pattern of unwearied industry and affection; for, from morning to night, while there is a family to be supported, she spends the whole day in skimming close to the ground, and exerting the most sudden turns and quick evolutions. Avenues, and long walks under hedges, and pasture-fields, and mown meadows where cattle graze, are her delight, especially if there are trees interspersed; because in such spots insects most abound. When a fly is taken a smart snap from her bill is heard, resembling the noise at the shutting of a watch case; but the motion of the mandibles are too quick for the eye.
In Letter to Daines Barrington (29 Jan 1774), in In The Natural History and Antiquities of Selborne (1789), 169-170.
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Almost always the men who achieve these fundamental inventions of a new paradigm have been either very young or very new to the field whose paradigm they change.
The Structure of Scientific Revolutions (1962), 89-90.
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Among the studies to which the [Rockefeller] Foundation is giving support is a series in a relatively new field, which may be called molecular biology, in which delicate modern techniques are being used to investigate ever more minute details of certain life processes.
In 'Molecular Biology', Annual Report of the Rockefeller Foundation (1938), 203-4. Reprinted in a letter to Science (6 Nov 1970), 170, 582.
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An article in Bioscience in November 1987 by Julie Ann Miller claimed the cortex was a “quarter-meter square.” That is napkin-sized, about ten inches by ten inches. Scientific American magazine in September 1992 upped the ante considerably with an estimate of 1½ square meters; that’s a square of brain forty inches on each side, getting close to the card-table estimate. A psychologist at the University of Toronto figured it would cover the floor of his living room (I haven’t seen his living room), but the prize winning estimate so far is from the British magazine New Scientist’s poster of the brain published in 1993 which claimed that the cerebral cortex, if flattened out, would cover a tennis court. How can there be such disagreement? How can so many experts not know how big the cortex is? I don’t know, but I’m on the hunt for an expert who will say the cortex, when fully spread out, will cover a football field. A Canadian football field.
In The Burning House: Unlocking the Mysteries of the Brain (1994, 1995), 11.
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An expert is a man who has made all the mistakes, which can be made, in a very narrow field.
recalled on his death, November 18, 1962.
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An expert is a person who has made all the mistakes that can be made in a very narrow field.
As quoted by Edward Teller, in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 62.
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Any chemist reading this book can see, in some detail, how I have spent most of my mature life. They can become familiar with the quality of my mind and imagination. They can make judgements about my research abilities. They can tell how well I have documented my claims of experimental results. Any scientist can redo my experiments to see if they still work—and this has happened! I know of no other field in which contributions to world culture are so clearly on exhibit, so cumulative, and so subject to verification.
From Design to Discovery (1990), 119-20.
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Apart from its healthful mental training as a branch of ordinary education, geology as an open-air pursuit affords an admirable training in habits of observation, furnishes a delightful relief from the cares and routine of everyday life, takes us into the open fields and the free fresh face of nature, leads us into all manner of sequestered nooks, whither hardly any other occupation or interest would be likely to send us, sets before us problems of the highest interest regarding the history of the ground beneath our feet, and thus gives a new charm to scenery which may be already replete with attractions.
Outlines of Field-Geology (1900), 251-2.
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As a result of the phenomenally rapid change and growth of physics, the men and women who did their great work one or two generations ago may be our distant predecessors in terms of the state of the field, but they are our close neighbors in terms of time and tastes. This may be an unprecedented state of affairs among professionals; one can perhaps be forgiven if one characterizes it epigrammatically with a disastrously mixed metaphor; in the sciences, we are now uniquely privileged to sit side-by-side with the giants on whose shoulders we stand.
In 'On the Recent Past of Physics', American Journal of Physics (1961), 29, 807.
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As every circumstance relating to so capital a discovery as this (the greatest, perhaps, that has been made in the whole compass of philosophy, since the time of Sir Isaac Newton) cannot but give pleasure to all my readers, I shall endeavour to gratify them with the communication of a few particulars which I have from the best authority. The Doctor [Benjamin Franklin], after having published his method of verifying his hypothesis concerning the sameness of electricity with the matter lightning, was waiting for the erection of a spire in Philadelphia to carry his views into execution; not imagining that a pointed rod, of a moderate height, could answer the purpose; when it occurred to him, that, by means of a common kite, he could have a readier and better access to the regions of thunder than by any spire whatever. Preparing, therefore, a large silk handkerchief, and two cross sticks, of a proper length, on which to extend it, he took the opportunity of the first approaching thunder storm to take a walk into a field, in which there was a shed convenient for his purpose. But dreading the ridicule which too commonly attends unsuccessful attempts in science, he communicated his intended experiment to no body but his son, who assisted him in raising the kite.
The kite being raised, a considerable time elapsed before there was any appearance of its being electrified. One very promising cloud passed over it without any effect; when, at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he inmmediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute, and when the rain had wetted the string, he collected electric fire very copiously. This happened in June 1752, a month after the electricians in France had verified the same theory, but before he had heard of any thing that they had done.
The History and Present State of Electricity, with Original Experiments (1767, 3rd ed. 1775), Vol. 1, 216-7.
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As in the domains of practical life so likewise in science there has come about a division of labor. The individual can no longer control the whole field of mathematics: it is only possible for him to master separate parts of it in such a manner as to enable him to extend the boundaries of knowledge by creative research.
In Die reine Mathematik in den Jahren 1884-99, 10. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 94.
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As science is more and more subject to grave misuse as well as to use for human benefit it has also become the scientist's responsibility to become aware of the social relations and applications of his subject, and to exert his influence in such a direction as will result in the best applications of the findings in his own and related fields. Thus he must help in educating the public, in the broad sense, and this means first educating himself, not only in science but in regard to the great issues confronting mankind today.
Message to University Students Studying Science', Kagaku Asahi 11, no. 6 (1951), 28-29. Quoted in Elof Axel Carlson, Genes, Radiation, and Society: The Life and Work of H. J. Muller (1981), 371.
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As soon as we touch the complex processes that go on in a living thing, be it plant or animal, we are at once forced to use the methods of this science [chemistry]. No longer will the microscope, the kymograph, the scalpel avail for the complete solution of the problem. For the further analysis of these phenomena which are in flux and flow, the investigator must associate himself with those who have labored in fields where molecules and atoms, rather than multicellular tissues or even unicellular organisms, are the units of study.
'Experimental and Chemical Studies of the Blood with an Appeal for More Extended Chemical Training for the Biological and Medical Investigator', Science (6 Aug 1915), 42, 176.
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Astronomers and physicists, dealing habitually with objects and quantities far beyond the reach of the senses, even with the aid of the most powerful aids that ingenuity has been able to devise, tend almost inevitably to fall into the ways of thinking of men dealing with objects and quantities that do not exist at all, e.g., theologians and metaphysicians. Thus their speculations tend almost inevitably to depart from the field of true science, which is that of precise observation, and to become mere soaring in the empyrean. The process works backward, too. That is to say, their reports of what they pretend actually to see are often very unreliable. It is thus no wonder that, of all men of science, they are the most given to flirting with theology. Nor is it remarkable that, in the popular belief, most astronomers end by losing their minds.
Minority Report: H. L. Mencken’s Notebooks (1956), Sample 74, 60.
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Astronomy is one of the sublimest fields of human investigation. The mind that grasps its facts and principles receives something of the enlargement and grandeur belonging to the science itself. It is a quickener of devotion.
In Thoughts Selected From the Writings of Horace Mann (1872), 41.
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Astronomy may be revolutionized more than any other field of science by observations from above the atmosphere. Study of the planets, the Sun, the stars, and the rarified matter in space should all be profoundly influenced by measurements from balloons, rockets, probes and satellites. ... In a new adventure of discovery no one can foretell what will be found, and it is probably safe to predict that the most important new discovery that will be made with flying telescopes will be quite unexpected and unforeseen. (1961)
Opening and closing of 'Flying Telescopes', Bulletin of the Atomic Scientists (May 1961), Vol. 17, No. 5, 191 and 194.
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At last such field studies have been put on a sound basis which should result in the hunting of information rather than specimens.
Concluding line of review (of Hiram Bingham’s 1932 book, Gorillas in a Native Habitat), in journal, Ecology (1933), 14, No. 3, 320. Note that the quote is authored by the reviewer, W.C. Allee, and any source attributing it directly to Bingham himself is incorrect.
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At present we begin to feel impatient, and to wish for a new state of chemical elements. For a time the desire was to add to the metals, now we wish to diminish their number. They increase upon us continually, and threaten to enclose within their ranks the bounds of our fair fields of chemical science. The rocks of the mountain and the soil of the plain, the sands of the sea and the salts that are in it, have given way to the powers we have been able to apply to them, but only to be replaced by metals.
In his 16th Lecture of 1818, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 256-257.
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Away from their laboratories, physicist and chemist are but disarmed soldiers on a battlefield.
Hors de leurs laboratoires, le physicien et le chimiste sont des soldats sans armes sur le champ de bataille.
In article 'The Budget of Science', Revue des Cours Scientifiques (1 Feb 1868) and published as a pamphlet, Some Reflections on Science in France. Original French quote in René Vallery-Radot, La Vie de Pasteur (1900), 215. As translated in René Vallery-Radot and Mrs R. L. Devonshire (trans.) The Life of Pasteur (1902), 199. Also translated as “Outside their laboratories, the physicist and chemist are soldiers without arms on the field of battle.”
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Besides electrical engineering theory of the transmission of messages, there is a larger field [cybernetics] which includes not only the study of language but the study of messages as a means of controlling machinery and society, the development of computing machines and other such automata, certain reflections upon psychology and the nervous system, and a tentative new theory of scientific method.
In Cybernetics (1948).
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Better to hunt in fields, for health unbought, Than fee the doctor for a nauseous draught, The wise, for cure, on exercise depend; God never made his work for man to mend.
'To my Honoured Kinsman, John Dryden', The English Poets (1901), Vol. 2, 491.
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Biology today is moving in the direction of chemistry. Much of what is understood in the field is based on the structure of molecules and the properties of molecules in relation to their structure. If you have that basis, then biology isn’t just a collection of disconnected facts.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 737.
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Boundaries which mark off one field of science from another are purely artificial, are set up only for temporary convenience. Let chemists and physicists dig deep enough, and they reach common ground.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 183.
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But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.
In Editor’s Preface to Augustus De Morgan and Thomas J. McCormack (ed.), Elementary Illustrations of the Differential and Integral Calculus (1899), v.
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But of this I can assure you that there is not a movement of any body of Men however small whether on Horse-back or on foot, nor an operation or March of any description nor any Service in the field that is not formed upon some mathematical principle, and in the performance of which the knowledge and practical application of the mathematicks will be found not only useful but necessary. The application of the Mathematicks to Gunnery, Fortification, Tactics, the survey and knowledge of formal Castrenantion etc. cannot be acquired without study.
Duke of Wellington to his son Douro (1826). Quoted in A Selection of the Private Correspondence of the First Duke of Wellington (1952), 44.
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But psychology is a more tricky field, in which even outstanding authorities have been known to run in circles, ‘describing things which everyone knows in language which no one understands.’
From The Scientific Analysis of Personality (1965), 18.
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By asking questions and quickly reading some books, [Melvin Calvin] felt comfortable in many fields of endeavor.
Co-author with Andrew A. Benson, 'Melvin Calvin', Biographical Memoirs of the US National Academy of Science.
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By its very nature the uterus is a field for growing the seeds, that is to say the ova, sown upon it. Here the eggs are fostered, and here the parts of the living [fetus], when they have further unfolded, become manifest and are made strong. Yet although it has been cast off by the mother and sown, the egg is weak and powerless and so requires the energy of the semen of the male to initiate growth. Hence in accordance with the laws of Nature, and like the other orders of living things, women produce eggs which, when received into the chamber of the uterus and fecundated by the semen of the male, unfold into a new life.
'On the Developmental Process', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 861.
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By profession a biologist, [Thomas Henry Huxley] covered in fact the whole field of the exact sciences, and then bulged through its four fences. Absolutely nothing was uninteresting to him. His curiosity ranged from music to theology and from philosophy to history. He didn't simply know something about everything; he knew a great deal about everything.
'Thomas Henry Huxley.' In the Baltimore Evening Sun (4 May 1925). Reprinted in A Second Mencken Chrestomathy: A New Selection from the Writings of America's Legendary Editor, Critic, and Wit (2006), 157.
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Concerning alchemy it is more difficult to discover the actual state of things, in that the historians who specialise in this field seem sometimes to be under the wrath of God themselves; for, like those who write of the Bacon-Shakespeare controversy or on Spanish politics, they seem to become tinctured with the kind of lunacy they set out to describe.
The Origins of Modern Science (1949), 115.
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Consider the lilies of the field, how they grow; they toil not, neither do they spin.
Bible
(circa 325 A.D.)
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Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”
In article 'Mathematics', Encyclopedia Britannica (1911, 11th ed.), Vol. 17, 880. In the 2006 DVD edition of the encyclopedia, the definition of mathematics is given as “The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects.” [Premiss is a variant form of “premise”. —Webmaster]
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Direct observation of the testimony of the earth … is a matter of the laboratory, of the field naturalist, of indefatigable digging among the ancient archives of the earth’s history. If Mr. Bryan, with an open heart and mind, would drop all his books and all the disputations among the doctors and study first hand the simple archives of Nature, all his doubts would disappear; he would not lose his religion; he would become an evolutionist.
'Evolution and Religion', New York Times (5 Mar 1922), 91. Written in response to an article a few days earlier in which William Jennings Bryan challenged the theory of evolution as lacking proof.
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Do experimental work but keep in mind that other investigators in the same field will consider your discoveries as less than one fourth as important as they seem to you.
In Victor Shelford, The Ecology of North America (1963), v.
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During my pre-college years I went on many trips with my father into the oil fields to visit their operations. … I puttered around the machine, electronics, and automobile shops while he carried on his business. Both of my parents are inveterate do-it-yourselfers, almost no task being beneath their dignity or beyond their ingenuity. Having picked up a keen interest in electronics from my father, I used to fix radios and later television sets for fun and spending money. I built my own hi-fi set and enjoyed helping friends with their amateur radio transmitters, but lost interest as soon as they worked.
Remarks on how his high school interests foreshadowed his career as a radio astronomer. From autobiography in Stig Lundqvist (ed.) Nobel Lectures, Physics 1971-1980 (1992).
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During the century after Newton, it was still possible for a man of unusual attainments to master all fields of scientific knowledge. But by 1800, this had become entirely impracticable.
The Intelligent Man's Guide to Science (1960), 19.
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During the time that [Karl] Landsteiner gave me an education in the field of imununology, I discovered that he and I were thinking about the serologic problem in very different ways. He would ask, What do these experiments force us to believe about the nature of the world? I would ask, What is the most. simple and general picture of the world that we can formulate that is not ruled by these experiments? I realized that medical and biological investigators were not attacking their problems the same way that theoretical physicists do, the way I had been in the habit of doing.
‘Molecular Disease’, Pfizer Spectrum (1958), 6:9, 234.
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Earth and sky, woods and fields, lakes and rivers, the mountain and the sea, are excellent schoolmasters, and teach some of us more than we can ever learn from books.
The Use of Life (1895), 70 or (2005), 66.
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Every discovery opens a new field for investigation of facts, shows us the imperfection of our theories. It has justly been said, that the greater the circle of light, the greater the boundary of darkness by which it is surrounded.
Humphry Davy and John Davy, 'Consolations in Travel--Dialogue V--The Chemical Philosopher', The Collected Works of Sir Humphry Davy (1840), Vol. 9, 362.
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Every leaf and twig was this morning covered with a sparkling ice armor; even the grasses in exposed fields were hung with innumerable diamond pendants, which jingled merrily when brushed by the foot of the traveler. It was literally the wreck of jewels and the crash of gems.
(21 Jan 1838). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: I: 1837-1846 (1906), 224.
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Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.
In 'Ten Lessons I Wish I Had Been Taught', Indiscrete Thoughts (2008), 196.
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Every man takes the limits of his own field of vision for the limits of the world.
In Arthur Schopenhauer and T. Bailey Saunders (ed., trans.), 'Further Psychological Observations', Studies in Pessimism: A Series of Essays (1891), 69.
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Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer. This was true of electron theory—perhaps some readers will remember a book called The Electrical Theory of the Universe by de Tunzelman. It is true of general relativity theory with its belief that we can formulate a mathematical scheme that will extrapolate to all past and future time and the unfathomed depths of space. It has been true of wave mechanics, with its first enthusiastic claim a brief ten years ago that no problem had successfully resisted its attack provided the attack was properly made, and now the disillusionment of age when confronted by the problems of the proton and the neutron. When will we learn that logic, mathematics, physical theory, are all only inventions for formulating in compact and manageable form what we already know, like all inventions do not achieve complete success in accomplishing what they were designed to do, much less complete success in fields beyond the scope of the original design, and that our only justification for hoping to penetrate at all into the unknown with these inventions is our past experience that sometimes we have been fortunate enough to be able to push on a short distance by acquired momentum.
The Nature of Physical Theory (1936), 136.
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Expertise in one field does not carry over into other fields. But experts often think so. The narrower their field of knowledge the more likely they are to think so.
In Time Enough for Love: The Lives of Lazarus Long (1973), 367.
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Fields of learning are surrounded ultimately only by illusory boundaries—like the “rooms” in a hall of mirrors.
It is when the illusion is penetrated that progress takes place. … Likewise science cannot be regarded as a thing apart, to be studied, admired or ignored. It is a vital part of our culture, our culture is part of it, it permeates our thinking, and its continued separateness from what is fondly called “the humanities” is a preposterous practical joke on all thinking men.
In Modern Science and the Nature of Life (1957).
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Firm support has been found for the assertion that electricity occurs at thousands of points where we at most conjectured that it was present. Innumerable electrical particles oscillate in every flame and light source. We can in fact assume that every heat source is filled with electrons which will continue to oscillate ceaselessly and indefinitely. All these electrons leave their impression on the emitted rays. We can hope that experimental study of the radiation phenomena, which are exposed to various influences, but in particular to the effect of magnetism, will provide us with useful data concerning a new field, that of atomistic astronomy, as Lodge called it, populated with atoms and electrons instead of planets and worlds.
'Light Radiation in a Magnetic Field', Nobel Lecture, 2 May 1903. In Nobel Lectures: Physics 1901-1921 (1967), 40.
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Food analysis is a veritable toddler among scientific fields.
Newspaper
From editorial, 'Vegging Out,' New York Times (14 Apr 1993), A20, reporting a scientist found people on a diet heavy in vegetables produces genistein, which blocks angiogenesis, with possible implications in cancer control.
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Food is at present obtained almost entirely from the energy of the sunlight. The radiation from the sun produces from the carbonic acid in the air more or less complicated carbon compounds which serve us in plants and vegetables. We use the latent chemical energy of these to keep our bodies warm, we convert it into muscular effort. We employ it in the complicated process of digestion to repair and replace the wasted cells of our bodies. … If the gigantic sources of power become available, food would be produced without recourse to sunlight. Vast cellars, in which artificial radiation is generated, may replace the cornfields and potato patches of the world.
From 'Fifty Years Hence', Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57, No. 3, 396-397.
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For it being the nature of the mind of man (to the extreme prejudice of knowledge) to delight in the spacious liberty of generalities, as in a champion region, and not in the enclosures of particularity; the Mathematics were the goodliest fields to satisfy that appetite.
In De Augmentis, Bk. 8; Advancement of Learning, Bk. 2.
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For out of old feldes, as men seith,
Cometh al this newe corn fro yere to yere;
And out of olde bokes, in good feith,
Cometh al this newe science that men lere.
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Fortunately I experienced Max Wertheimer's teaching in Berlin and collaborated for over a decade with Wolfgang Köhler. I need not emphasize my debts to these outstanding personalities. The fundamental ideas of Gestalt theory are the foundation of all our investigations in the field of the will, of affection, and of the personality.
From A Dynamic Theory of Personality. Selected papers (1935), 240.
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From that night on, the electron—up to that time largely the plaything of the scientist—had clearly entered the field as a potent agent in the supplying of man's commercial and industrial needs… The electronic amplifier tube now underlies the whole art of communications, and this in turn is at least in part what has made possible its application to a dozen other arts. It was a great day for both science and industry when they became wedded through the development of the electronic amplifier tube.
The Autobiography of Robert A. Millikan (1951), 136.
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Geology got into the hands of the theoreticians who were conditioned by the social and political history of their day more than by observations in the field. … We have allowed ourselves to be brainwashed into avoiding any interpretation of the past that involves extreme and what might be termed “catastrophic” processes. However, it seems to me that the stratigraphical record is full of examples of processes that are far from “normal” in the usual sense of the word. In particular we must conclude that sedimentation in the past has often been very rapid indeed and very spasmodic. This may be called the “Phenomenon of the Catastrophic Nature of the Stratigraphic Record.”
In The Nature of the Stratigraphical Record (3rd ed., 1993), 70.
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Half a century ago Oswald (1910) distinguished classicists and romanticists among the scientific investigators: the former being inclined to design schemes and to use consistently the deductions from working hypotheses; the latter being more fit for intuitive discoveries of functional relations between phenomena and therefore more able to open up new fields of study. Examples of both character types are Werner and Hutton. Werner was a real classicist. At the end of the eighteenth century he postulated the theory of “neptunism,” according to which all rocks including granites, were deposited in primeval seas. It was an artificial scheme, but, as a classification system, it worked quite satisfactorily at the time. Hutton, his contemporary and opponent, was more a romanticist. His concept of “plutonism” supposed continually recurrent circuits of matter, which like gigantic paddle wheels raise material from various depths of the earth and carry it off again. This is a very flexible system which opens the mind to accept the possible occurrence in the course of time of a great variety of interrelated plutonic and tectonic processes.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 456-7.
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He who gives a portion of his time and talent to the investigation of mathematical truth will come to all other questions with a decided advantage over his opponents. He will be in argument what the ancient Romans were in the field: to them the day of battle was a day of comparative recreation, because they were ever accustomed to exercise with arms much heavier than they fought; and reviews differed from a real battle in two respects: they encountered more fatigue, but the victory was bloodless.
Reflection 352, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 159.
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History … celebrates the battlefields that kill us, but keeps silent on the crop fields that sustain us. It knows the bastards of kings, she doesn’t know the origin of wheat. This is the way of human folly.
From the original French, “L’histoire … célèbre les champs de bataille qui nous tuent, elle garde le silence sur les champs de culture qui nous font vivre; elle sait les bâtards des rois, elle ne sait pas l'origine du froment. Ainsi le veut la sottise humaine,” in Les Merveilles de l'Instinct Chez les Insectes: Morceaux Choisis (The Wonders of Instinct in Insects: Selected Pieces) (1913), 242. English version by Webmaster using Google to translate literally and indicate the context is lamenting that history has not preserved the origins of food cultivation. The translation usually seen is “History celebrates the battlefields whereon we meet our death but scorns to speak of the ploughed fields whereby we live. It knows the names of the kings’ bastards, but cannot tell us the origin of wheat,” for example, in Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 88.
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Honest pioneer work in the field of science has always been, and will continue to be, life’s pilot. On all sides, life is surrounded by hostility. This puts us under an obligation.
Function of the Orgasm
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Houston, that may have seemed like a very long final phase. The autotargeting was taking us right into a... crater, with a large number of big boulders and rocks ... and it required... flying manually over the rock field to find a reasonably good area.
…...
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How peacefully he sleep!
Yet may his ever-questing spirit, freed at length
from all the frettings of this little world,
Wander at will among the uncharted stars.
Fairfield his name. Perchance celestial fields
disclosing long sought secrets of the past
Spread 'neath his enraptured gaze
And beasts and men that to his earthly sight
were merely bits of stone shall live again to
gladden those eager eyes.
o let us picture him—enthusiast—scientist—friend—
Seeker of truth and light through all eternity!
New York Sun (13 Nov 1935). Reprinted in 'Henry Fairfield Osborn', Supplement to Natural History (Feb 1936), 37:2, 135. Bound in Kofoid Collection of Pamphlets on Biography, University of California.
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Hypothesis is the most important mental technique of the investigator, and its main function is to suggest new experiments or new observations. Indeed, most experiments and many observations are carried out with the deliberate object of testing an hypothesis. Another function is to help one see the significance of an object or event that otherwise would mean nothing. For instance, a mind prepared by the hypothesis of evolution would make many more significant observations on a field excursion than one not so prepared. Hypotheses should be used as tools to uncover new facts rather than as ends in themselves.
The Art of Scientific Investigation (1953), 46.
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I admitted, that the world had existed millions of years. I am astonished at the ignorance of the masses on these subjects. Hugh Miller has it right when he says that 'the battle of evidences must now be fought on the field of the natural sciences.'
Letter to Burke A. Hinsdale, president of Hiram College (10 Jan 1859), commenting on the audience at Garfield's debate with William Denton. Quoted in John Clark Ridpath, The Life and Work of James A. Garfield (1881), 80.
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I also suspect that many workers in this field [molecular biology] and related fields have been strongly motivated by the desire, rarely actually expressed, to refute vitalism.
British Medical Bulletin (1965). In Maurice B. Strauss, Familiar Medical Quotations (1968), 653.
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I am a woman who came from the cotton fields of the South. From there I was promoted to the washtub. From there I was promoted to the cook kitchen. And from there I promoted myself into the business of manufacturing hair goods and preparations….I have built my own factory on my own ground.
From speech (Jul 1912) to the National Negro Business League Convention. Quoted in New York Times (2000), as cited in The Big Book of Business Quotations (2003), 2.
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I am perhaps more proud of having helped to redeem the character of the cave-man than of any other single achievement of mine in the field of anthropology.
Quoted in Closing Address by Dr. Henry Sloane Coffin, president of the Union Theological Seminary, New York, at the Memorial Service for Osborn at St. Bartholomew's Church, N.Y. (18 Dec 1935). In 'Henry Fairfield Osborn', Supplement to Natural History (Feb 1936), 37:2, 134. Bound in Kofoid Collection of Pamphlets on Biography, University of California.
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I am the most travelled of all my contemporaries; I have extended my field of enquiry wider than anybody else, I have seen more countries and climes, and have heard more speeches of learned men. No one has surpassed me in the composition of lines, according to demonstration, not even the Egyptian knotters of ropes, or geometers.
In Alan L. Mackay, A Dictionary of Scientific Quotations (1992, 1994), 71.
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I built the solenoid and with great expectations late one evening I pressed the switch which sent a current of 40 amperes through the coil. The result was spectacular—a deafening explosion, the apparatus disappeared, all windows were blown in or out, a wall caved in, and thus ended my pioneering experiment on liquid hydrogen cooled coils! [Recalling the result of his experiment, on 31 Mar 1930, to maximize the magnetic field by cooling the coils of an electromagnet in liquid hydrogen to reduce their resistance.]
'Magnets I have Known', Lecture Notes in Physics (1983), 177, 542-548. Quoted from his memoirs in M.J.M. Leask, 'Obituary: Professor Nicholas Kurti', The Independent (27 Nov 1998).
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I cannot let the year run out without sending you a sign of my continued existence and to extend my sincere wishes for the well-being of you and your dear ones in the New Year. We will not be able to send New Year greetings much longer; but even when we have passed away and have long since decomposed, the bonds that united us in life will remain and we shall be remembered as a not too common example of two men, who truly without envy and jealousy, contended and struggled in the same field, yet nevertheless remained always closely bound in friendship.
Letter from Liebig to Wohler (31 Dec 1871). Quoted in Ralph Oesper, The Human Side of Scientists (1975), 206.
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I cannot see of what use these slides can be to a field man. I don't believe in looking at a mountain through a microscope.
In Archibald Geikie, Memoir of Sir Andrew Crombie Ramsey (1895), 343.
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I cannot think of a single field in biology or medicine in which we can claim genuine understanding, and it seems to me the more we learn about living creatures, especially ourselves, the stranger life becomes.
In 'On Science and Certainty', Discover Magazine (Oct 1980).
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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
The Fractal Geometry of Nature (1977, 1983), Introduction, xiii.
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I consider it important, indeed urgently necessary, for intellectual workers to get together, both to protect their own economic status and, also, generally speaking, to secure their influence in the political field.
…...
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I did enjoy the [CCNY geology] field trips. We went upstate and clambered over formations of synclines and anticlines. We had to diagram them, and figure out their mirror images. If you had an anticline here, you should be able to predict a complementing syncline bulging out somewhere else. Very satisfying when I got it right. Geology allowed me to display my brilliance to my non-college friends. “You know, the Hudson really isn't a river.” “What are you talking about? … Everybody knows the Hudson River's a river.” I would explain that the Hudson was a “drowned” river, up to about Poughkeepsie. The Ice Age had depressed the riverbed to a depth that allowed the Atlantic Ocean to flood inland. Consequently, the lower Hudson was really a saltwater estuary.[Powell graduated with a B.S. degree in Geology.]
My American Journey (1996), 30-31.
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I don’t need hobbies. I mean, why should I run after a ball on a field after I have kicked papers around from nine to five?
From 'Asking Nature', collected in Lewis Wolpert and Alison Richards (eds.), Passionate Minds: The Inner World of Scientists (1997), 197.
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I fear that the character of my knowledge is from year to year becoming more distinct and scientific; that, in exchange for vistas wide as heaven’s scope, I am being narrowed down to the field of the microscope. I see details, not wholes nor the shadow of the whole. I count some parts, and say, “I know.”
(19 Aug 1851). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: II: 1850-September 15, 1851 (1906), 406.
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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 had no books as a child. I had real machines, and I went out to work in the fields. I was driving farm machinery at five, and fixing it at age seven or eight. It’s no accident that I worked on Hubble 50 to 60 years later. My books were nature; it was very important to how I related to the Earth, and the Earth from space. No doubt when I go into space, I go back into the cool soil of Earth. I’m always thinking of it. Nature was my book. Other people come from that tradition - Emerson, Thoreau, and especially Whitman. Look at what they said in their philosophy - go out and have a direct relationship with nature.
When asked by Discover magazine what books helped inspire his passion as an astronaut.
'The 1998 Discover Science Gift Guide: Fantastic Voyages Children's Books That Mattered', Discover (Dec 1998).
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I happen to have discovered a direct relation between magnetism and light, also electricity and light, and the field it opens is so large and I think rich.
Letter to Christian Schönbein (13 Nov 1845), The Letters of Faraday and Schoenbein, 1836-1862 (1899), 148.
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I have attempted to form a judgment as to the conditions for evolution based on the statistical consequences of Mendelian heredity. The most general conclusion is that evolution depends on a certain balance among its factors. There must be a gene mutation, but an excessive rate gives an array of freaks, not evolution; there must be selection, but too severe a process destroys the field of variability, and thus the basis for further advance; prevalence of local inbreeding within a species has extremely important evolutionary consequences, but too close inbreeding leads merely to extinction. A certain amount of crossbreeding is favorable but not too much. In this dependence on balance the species is like a living organism. At all levels of organization life depends on the maintenance of a certain balance among its factors.
In Proceedings of the Sixth International Congress of Genetics: Ithaca, New York, 1932 (1932) Vol. 1, 365.
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I have long been interested in landscape history, and when younger and more robust I used to do much tramping of the English landscape in search of ancient field systems, drove roads, indications of prehistoric settlement. Towns and cities, too, which always retain the ghost of their earlier incarnations beneath today's concrete and glass.
From 'An Interview With Penelope Lively', in a Reading Guide to the book The Photograph on the publisher's Penguin website.
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I have never looked upon ease and happiness as ends in themselves–this critical basis I call the ideal of a pigsty. The ideals that have lighted my way, and time after time have given me new courage to face life cheerfully, have been Kindness, Beauty, and Truth. Without the sense of kinship with men of like mind, without the occupation with the objective world, the eternally unattainable in the field of art and scientific endeavors, life would have seemed empty to me. The trite objects of human efforts–possessions, outward success, luxury–have always seemed to me contemptible.
In 'What I Believe,' Forum and Century (1930).
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I have not yet lost a feeling of wonder, and of delight, that this delicate motion should reside in all the things around us, revealing itself only to him who looks for it. I remember, in the winter of our first experiments, just seven years ago, looking on snow with new eyes. There the snow lay around my doorstep—great heaps of protons quietly precessing in the earth's magnetic field. To see the world for a moment as something rich and strange is the private reward of many a discovery.
Opening remark, Nobel Lecture (11 Dec 1952).
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I know of the boons that machinery has conferred on men, all tyrants have boons to confer, but service to the dynasty of steam and steel is a hard service and gives little leisure to fancy to flit from field to field.
In 'Romance of Modern Stage', National Review (1911). Quoted in Edward Hale Bierstadt, Dunsany the Dramatist (1917), 119.
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I like to tell students that the jobs I took [at NASA] after my Ph.D. were not in existence only a few years before. New opportunities can open up for you in this ever changing field.
From interview, 'Happy 90th Birthday, Nancy', on NASA website (30 May 2017).
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I must admit that when I chose the name, “vitamine,” I was well aware that these substances might later prove not to be of an amine nature. However, it was necessary for me to choose a name that would sound well and serve as a catchword, since I had already at that time no doubt about the importance and the future popularity of the new field.
The Vitamines translated by Harry Ennis Dubin (1922), 26, footnote.
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I recognize that many physicists are smarter than I am—most of them theoretical physicists. A lot of smart people have gone into theoretical physics, therefore the field is extremely competitive. I console myself with the thought that although they may be smarter and may be deeper thinkers than I am, I have broader interests than they have.
…...
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I return to the newborn world, and the soft-soil fields,
What their first birthing lifted to the shores
Of light, and trusted to the wayward winds.
First the Earth gave the shimmer of greenery
And grasses to deck the hills; then over the meadows
The flowering fields are bright with the color of springtime,
And for all the trees that shoot into the air.
On the Nature of Things, trans. Anthony M. Esolen (1995) Book 5, lines 777-84, 181.
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I start with the seedling, and I don't want to leave it. I don't feel I really know the story if I don't watch the plant all the way along. So I know every plant in the field. I know them intimately, and I find it a real pleasure to know them.
In Jay B. McDaniel, 'Christian Spirituality as Openness to Fellow Creatures', Environmental Ethics (1986) 8(1), 34. Quoted in Charles Birch, Biology and the Riddle of Life (1999), 56.
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I think of myself as a journalist who writes mainly about math and science, and a few other fields of interest.
In Kendrick Frazier, 'A Mind at Play: An Interview with Martin Gardner', Skeptical Inquirer (Mar/Apr 1998), 22, No. 2, 36.
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I think that I cannot preserve my health and spirits, unless I spend four hours a day at least—and it is commonly more than that—sauntering through the woods and over the hills and fields, absolutely free from all worldly engagements.
In 'Walking', The Atlantic (Jun 1862), 9, No. 56, 657-674. Collected in Walking (1841, 1914), 9.
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I think that the formation of [DNA's] structure by Watson and Crick may turn out to be the greatest developments in the field of molecular genetics in recent years.
‘Discussion des rapports de M Pauling’, Rep. Institut International de Chemie Solvay: Conference on Proteins, 6-14 April 1953 (1953), 113.
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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 wish people would more generally bring back the seeds of pleasing foreign plants and introduce them broadcast, sowing them by our waysides and in our fields, or in whatever situation is most likely to suit them. It is true, this would puzzle botanists, but there is no reason why botanists should not be puzzled. A botanist is a person whose aim is to uproot, kill and exterminate every plant that is at all remarkable for rarity or any special virtue, and the rarer it is the more bitterly he will hunt it down.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 281.
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If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that it would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity of age.
In A Mathematician's Apology (1940, 2012), 70.
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If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
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If I have put the case of science at all correctly, the reader will have recognised that modern science does much more than demand that it shall be left in undisturbed possession of what the theologian and metaphysician please to term its “legitimate field.” It claims that the whole range of phenomena, mental as well as physical—the entire universe—is its field. It asserts that the scientific method is the sole gateway to the whole region of knowledge.
From The Grammar of Science (1892), 29-30.
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If it is impossible to judge merit and guilt in the field of natural science, then it is not possible in any field, and historical research becomes an idle, empty activity.
Reden und Abhandlungen (1874). Trans. W. H. Brock.
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If my efforts have led to greater success than usual, this is due, I believe, to the fact that during my wanderings in the field of medicine, I have strayed onto paths where the gold was still lying by the wayside. It takes a little luck to be able to distinguish gold from dross, but that is all.
'Robert Koch', Journal of Outdoor Life (1908), 5, 164-9.
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If to be the Author of new things, be a crime; how will the first Civilizers of Men, and makers of Laws, and Founders of Governments escape? Whatever now delights us in the Works of Nature, that excells the rudeness of the first Creation, is New. Whatever we see in Cities, or Houses, above the first wildness of Fields, and meaness of Cottages, and nakedness of Men, had its time, when this imputation of Novelty, might as well have bin laid to its charge. It is not therefore an offence, to profess the introduction of New things, unless that which is introduc'd prove pernicious in itself; or cannot be brought in, without the extirpation of others, that are better.
The History of the Royal Society (1667), 322.
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If we assist the highest forms of education–in whatever field–we secure the widest influence in enlarging the boundaries of human knowledge.
In 'Some Random Reminiscences of Men and Events', collected in The World’s Work (1909), Vol. 17, 11104.
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If we define 'thought collective' as a community of persons mutually exchanging ideas or maintaining intellectual interaction, we will find by implication that it also provides the special 'carrier' for the historical development of any field of thought, as well as for the given stock of knowledge and level of culture. This we have designated thought style.
Genesis and the Development of a Scientific Fact (1935), 39.
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If we survey the mathematical works of Sylvester, we recognize indeed a considerable abundance, but in contradistinction to Cayley—not a versatility toward separate fields, but, with few exceptions—a confinement to arithmetic-algebraic branches. …
The concept of Function of a continuous variable, the fundamental concept of modern mathematics, plays no role, is indeed scarcely mentioned in the entire work of Sylvester—Sylvester was combinatorist [combinatoriker].
In Mathematische Annalen (1898), Bd.50, 134-135. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 173.
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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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If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds. To him who is a discoverer in this field the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities.
From 'On the Method of Theoretical Physics', in Essays in Science (1934, 2004), 12.
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If you were plowing a field, which would you rather use? Two strong oxen or 1024 chickens?
[Comparing the power of supercomputers versus parallel computing.]
Attributed. Seen as a quote in several books, but without citation. For example, in Craig Larman, Applying UML and Patterns (2002), 475. If you know a primary source, please contact webmaster.
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If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don’t listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.
In Herbert Spencer Lecture at Oxford (10 Jun 1933), 'On the Methods of Theoretical Physics'. Printed inPhilosophy of Science (Apr 1934), 1, No. 2, 163.
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In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”
In 'Einstein's Impact on Theoretical Physics', collected in Jong-Ping Hsu, Leonard Hsu (eds.), JingShin Theoretical Physics Symposium in Honor of Professor Ta-You Wu (1998), 70. Reprinted from Physics Today (Jun 1980), 49. The article was adapted from a talk given at the Second Marcel Grossman meeting, held in Trieste, Italy (Jul 1979), in honor of the 100th anniversary of the birth of Albert Einstein.
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In a lot of scientists, the ratio of wonder to skepticism declines in time. That may be connected with the fact that in some fields—mathematics, physics, some others—the great discoveries are almost entirely made by youngsters.
Quoted in interview with magazine staff, Psychology Today (Jan 1996).
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In a word, I consider hospitals only as the entrance to scientific medicine; they are the first field of observation which a physician enters; but the true sanctuary of medical science is a laboratory; only there can he seek explanations of life in the normal and pathological states by means of experimental analysis.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 146.
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In any field find the strangest thing and then explore it.
Quoted in James Gleick, Genius: the Life and Science of Richard Feynman (1993), 93.
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In August, 1896, I exposed the sodium flame to large magnetic forces by placing it between the poles of a strong electromagnet. Again I studied the radiation of the flame by means of Rowland's mirror, the observations being made in the direction perpendicular to the lines of force. Each line, which in the absence of the effect of the magnetic forces was very sharply defined, was now broadened. This indicated that not only the original oscillations, but also others with greater and again others with smaller periods of oscillation were being radiated by the flame. The change was however very small. In an easily produced magnetic field it corresponded to a thirtieth of the distance between the two sodium lines, say two tenths of an Angstrom, a unit of measure whose name will always recall to physicists the meritorious work done by the father of my esteemed colleague.
'Light Radiation in a Magnetic Field', Nobel Lecture, 2 May 1903. In Nobel Lectures: Physics 1901-1921 (1967), 34-5.
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In discussing the state of the atmosphere following a nuclear exchange, we point especially to the effects of the many fires that would be ignited by the thousands of nuclear explosions in cities, forests, agricultural fields, and oil and gas fields. As a result of these fires, the loading of the atmosphere with strongly light absorbing particles in the submicron size range (1 micron = 10-6 m) would increase so much that at noon solar radiation at the ground would be reduced by at least a factor of two and possibly a factor of greater than one hundred.
Paul J. Crutzen -and John W. Birks (1946-, American chemist), 'The Atmosphere after a Nuclear War: Twilight at Noon', Ambio, 1982, 11, 115.
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In fields of air he writes his name,
And treads the chambers of the sky;
He reads the stars, and grasps the flame
That quivers in the realms on high.
In poem 'Art', collected in Samuel Kettell (ed.), Specimens of American Poetry, with Critical and Biographical Notices (1829), Vol. 3, 198.
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In India we have clear evidence that administrative statistics had reached a high state of organization before 300 B.C. In the Arthasastra of Kautilya … the duties of the Gopa, the village accountant, [include] “by setting up boundaries to villages, by numbering plots of grounds as cultivated, uncultivated, plains, wet lands, gardens, vegetable gardens, fences (váta), forests altars, temples of gods, irrigation works, cremation grounds, feeding houses (sattra), places where water is freely supplied to travellers (prapá), places of pilgrimage, pasture grounds and roads, and thereby fixing the boundaries of various villages, of fields, of forests, and of roads, he shall register gifts, sales, charities, and remission of taxes regarding fields.”
Editorial, introducing the new statistics journal of the Indian Statistical Institute, Sankhayā (1933), 1, No. 1. Also reprinted in Sankhyā: The Indian Journal of Statistics (Feb 2003), 65, No. 1, viii.
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In its earliest development knowledge is self-sown. Impressions force themselves upon men’s senses whether they will or not, and often against their will. The amount of interest in which these impressions awaken is determined by the coarser pains and pleasures which they carry in their train or by mere curiosity; and reason deals with the materials supplied to it as far as that interest carries it, and no further. Such common knowledge is rather brought than sought; and such ratiocination is little more than the working of a blind intellectual instinct. It is only when the mind passes beyond this condition that it begins to evolve science. When simple curiosity passes into the love of knowledge as such, and the gratification of the æsthetic sense of the beauty of completeness and accuracy seems more desirable that the easy indolence of ignorance; when the finding out of the causes of things becomes a source of joy, and he is accounted happy who is successful in the search, common knowledge passes into what our forefathers called natural history, whence there is but a step to that which used to be termed natural philosophy, and now passes by the name of physical science.
In this final state of knowledge the phenomena of nature are regarded as one continuous series of causes and effects; and the ultimate object of science is to trace out that series, from the term which is nearest to us, to that which is at the farthest limit accessible to our means of investigation.
The course of nature as it is, as it has been, and as it will be, is the object of scientific inquiry; whatever lies beyond, above, or below this is outside science. But the philosopher need not despair at the limitation on his field of labor; in relation to the human mind Nature is boundless; and, though nowhere inaccessible, she is everywhere unfathomable.
The Crayfish: an Introduction to the Study of Zoölogy (1880), 2-3. Excerpted in Popular Science (Apr 1880), 16, 789-790.
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In mathematics as in other fields, to find one self lost in wonder at some manifestation is frequently the half of a new discovery.
In Werke, Bd. 8 (1897), 233.
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In my first publication I might have claimed that I had come to the conclusion, as a result of serious study of the literature and deep thought, that valuable antibacterial substances were made by moulds and that I set out to investigate the problem. That would have been untrue and I preferred to tell the truth that penicillin started as a chance observation. My only merit is that I did not neglect the observation and that I pursued the subject as a bacteriologist. My publication in 1929 was the starting-point of the work of others who developed penicillin especially in the chemical field.
'Penicillin', Nobel Lecture, 11 Dec 1945. In Nobel Lectures: Physiology or Medicine 1942-1962 (1964), 83.
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In my own field, x-ray crystallography, we used to work out the structure of minerals by various dodges which we never bothered to write down, we just used them. Then Linus Pauling came along to the laboratory, saw what we were doing and wrote out what we now call Pauling's Rules. We had all been using Pauling's Rules for about three or four years before Pauling told us what the rules were.
In The Extension of Man (1972), 116.
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In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
In 'Die Theorie der algebraischen Zahlkorper', Vorwort, Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 4.
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In the distant future I see open fields for far more important researches. Psychology will be based on a new foundation, that of the necessary acquirement of each mental power and capacity by gradation. Light will be thrown on the origin of man and his history.
On The Origin of Species by Means of Natural Selection (1859, 1882), 428 .
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In the field of thinking, the whole history of science from geocentrism to the Copernican revolution, from the false absolutes of Aristotle’s physics to the relativity of Galileo’s principle of inertia and to Einstein’s theory of relativity, shows that it has taken centuries to liberate us from the systematic errors, from the illusions caused by the immediate point of view as opposed to “decentered” systematic thinking.
As quoted in D. E. Berlyne, Structure and Direction in Thinking (1965), 232.
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In the field one has to face a chaos of facts, some of which are so small that they seem insignificant; others loom so large that they are hard to encompass with one synthetic glance. But in this crude form they are not scientific facts at all; they are absolutely elusive, and can be fixed only by interpretation, by seeing them sub specie aeternitatis, by grasping what is essential in them and fixing this. Only laws and gerneralizations are scientific facts, and field work consists only and exclusively in the interpretation of the chaotic social reality, in subordinating it to general rules.
Baloma (1954), 238.
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In the fields of observation chance favors only the prepared mind.
In a lecture at the University of Lille, December 7, 1854.
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In the future I see open fields for more important researches. Psychology will be securely based on the foundation already laid by Mr. Herbert Spencer, that of the necessary acquirement of each mental power and capacity by graduation.
Origin of Species
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In the medical field [scientific ignorance] could lead to horrendous results. People who don’t understand the difference between a controlled experiment and claims by some quack may die as a result of not taking medical science seriously. One of the most damaging examples of pseudoscience is false memory syndrome. I’m on the board of a foundation exposing this problem.
As quoted by Lawrence Toppman, 'Mastermind', The Charlotte Observer (20 Jun 1993), 6E. As quoted and cited in Dana Richards, 'Martin Gardner: A “Documentary”', collected in Elwyn R. Berlekamp and Tom Rodgers (ed.) The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner (1999), 11.
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In the training and in the exercise of medicine a remoteness abides between the field of neurology and that of mental health, psychiatry. It is sometimes blamed to prejudice on the part of the one side or the other. It is both more grave and less grave than that. It has a reasonable basis. It is rooted in the energy-mind problem. Physiology has not enough to offer about the brain in relation to the mind to lend the psychiatrist much help.
In 'The Brain Collaborates With Psyche', Man On His Nature: The Gifford Lectures, Edinburgh 1937-8 (1940), 283.
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In these strenuous times, we are likely to become morbid and look constantly on the dark side of life, and spend entirely too much time considering and brooding over what we can't do, rather than what we can do, and instead of growing morose and despondent over opportunities either real or imaginary that are shut from us, let us rejoice at the many unexplored fields in which there is unlimited fame and fortune to the successful explorer and upon which there is no color line; simply the survival of the fittest.
In article urging African-Americans to engage in plant breeding to develop improved species.'A New Industry for Colored Men and Women', Colored American (Jan 1908, 14, 33. Cited in Linda O. McMurry, George Washington Carver, Scientist and Symbol (1982), 109.
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In this age of specialization men who thoroughly know one field are often incompetent to discuss another. … The old problems, such as the relation of science and religion, are still with us, and I believe present as difficult dilemmas as ever, but they are not often publicly discussed because of the limitations of specialization.
Opening statement, in transcript of talk to the Caltech Lunch Forum (2 May 1956), 'The Relation of Science and Religion', collected in Richard Phillips Feynman and Jeffrey Robbins (ed.), The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman (1999, 2005), 245-246.
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In trying to evaluate Hopkins' unique contribution to biochemistry it may perhaps be said that he alone amongst his contemporaries succeeded in formulating the subject. Among others whose several achievements in their own fields may have surpassed his, no one has ever attempted to unify and correlate biochemical knowledge so as to form a comprehensible picture of the cell and its relation to life, reproduction and function.
'Sir F. G. Hopkins' Teaching and Scientific Influence'. In J. Needham and E. Baldwin (eds.), Hopkins and Biochemistry, 1861-1947 (1949), 36.
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Inspiration in the field of science by no means plays any greater role, as academic conceit fancies, than it does in the field of mastering problems of practical life by a modern entrepreneur. On the other hand, and this also is often misconstrued, inspiration plays no less a role in science than it does in the realm of art.
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
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It appears, according to the reported facts, that the electric conflict is not restricted to the conducting wire, but that it has a rather extended sphere of activity around it … the nature of the circular action is such that movements that it produces take place in directions precisely contrary to the two extremities of a given diameter. Furthermore, it seems that the circular movement, combined with the progressive movement in the direction of the length of the conjunctive wire, should form a mode of action which is exerted as a helix around this wire as an axis.
Recherches sur l’identité des forces chimiques et électriques (1813), 248. In James R. Hofmann, André-Marie Ampère (1996), 231.
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It has been just so in all my inventions. The first step is an intuition—and comes with a burst, then difficulties arise. This thing that gives out and then that—“Bugs”as such little faults and difficulties are called show themselves and months of anxious watching, study and labor are requisite before commercial success—or failure—is certainly reached.
[Describing his invention of a storage battery that involved 10,296 experiments. Note Edison's use of the term “Bug” in the engineering research field for a mechanical defect greatly predates the use of the term as applied by Admiral Grace Murray Hopper to a computing defect upon finding a moth in the electronic mainframe.]
Letter to Theodore Puskas (18 Nov 1878). In The Yale Book of Quotations (2006), 226.
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It is a wrong business when the younger cultivators of science put out of sight and deprecate what their predecessors have done; but obviously that is the tendency of Huxley and his friends … It is very true that Huxley was bitter against the Bishop of Oxford, but I was not present at the debate. Perhaps the Bishop was not prudent to venture into a field where no eloquence can supersede the need for precise knowledge. The young naturalists declared themselves in favour of Darwin’s views which tendency I saw already at Leeds two years ago. I am sorry for it, for I reckon Darwin’s book to be an utterly unphilosophical one.
Letter to James D, Forbes (24 Jul 1860). Trinity College Cambridge, Whewell Manuscripts.
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It is arguable whether the human race have been gainers by the march of science beyond the steam engine. Electricity opens a field of infinite conveniences to ever greater numbers, but they may well have to pay dearly for them. But anyhow in my thought I stop short of the internal combustion engine which has made the world so much smaller. Still more must we fear the consequences of entrusting a human race so little different from their predecessors of the so-called barbarous ages such awful agencies as the atomic bomb. Give me the horse.
Address to the Royal College of Surgeons (10 Jul 1951). Collected in Stemming the Tide: Speeches 1951 and 1952 (1953), 91.
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It is characteristic of our age to endeavour to replace virtues by technology. That is to say, wherever possible we strive to use methods of physical or social engineering to achieve goals which our ancestors thought attainable only by the training of character. Thus, we try so far as possible to make contraception take the place of chastity, and anaesthetics to take the place of fortitude; we replace resignation by insurance policies and munificence by the Welfare State. It would be idle romanticism to deny that such techniques and institutions are often less painful and more efficient methods of achieving the goods and preventing the evils which unaided virtue once sought to achieve and avoid. But it would be an equal and opposite folly to hope that the take-over of virtue by technology may one day be complete, so that the necessity for the laborious acquisition of the capacity for rational choice by individuals can be replaced by the painless application of the fruits of scientific discovery over the whole field of human intercourse and enterprise.
'Mental Health in Plato's Republic', in The Anatomy of the Soul: Historical Essays in the Philosophy of Mind (1973), 26.
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It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way. Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.
In 'The Mathematician', Works of the Mind (1947), 1, No. 1. Collected in James Roy Newman (ed.), The World of Mathematics (1956), Vol. 4, 2053.
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It is in the exploration of this vast deep-sea region that the finest field for submarine discovery yet remains.
In The Natural History of the European Seas (1859), 27.
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It is interesting to note how many fundamental terms which the social sciences are trying to adopt from physics have as a matter of historical fact originated in the social field. Take, for instance, the notion of cause. The Greek aitia or the Latin causa was originally a purely legal term. It was taken over into physics, developed there, and in the 18th century brought back as a foreign-born kind for the adoration of the social sciences. The same is true of the concept of law of nature. Originally a strict anthropomorphic conception, it was gradually depersonalized or dehumanized in the natural sciences and then taken over by the social sciences in an effort to eliminate final causes or purposes from the study of human affairs. It is therefore not anomalous to find similar transformations in the history of such fundamental concepts of statistics as average and probability. The concept of average was developed in the Rhodian laws as to the distribution of losses in maritime risks. After astronomers began to use it in correcting their observations, it spread to other physical sciences; and the prestige which it thus acquired has given it vogue in the social field. The term probability, as its etymology indicates, originates in practical and legal considerations of probing and proving.
The Statistical View of Nature (1936), 327-8.
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It is ironical that, in the very field in which Science has claimed superiority to Theology, for example—in the abandoning of dogma and the granting of absolute freedom to criticism—the positions are now reversed. Science will not tolerate criticism of special relativity, while Theology talks freely about the death of God, religionless Christianity, and so on.
In 'Preface', Science at the Crossroads (1972), 13.
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It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.
As quoted, without source by Eugene Wigner in 'John von Neumann (1903-1957)', Year Book of the American Philosophical Society: Biographical Memoirs (1958), 153. Collected in Eugene P. Wigner, The Collected Works of Eugene Paul Wigner: Historical, Philosophical, and Socio-Political Papers. Historical and Biographical Reflections and Syntheses (2013), 130.
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It is most interesting to observe into how small a field the whole of the mysteries of nature thus ultimately resolve themselves. The inorganic has one final comprehensive law, GRAVITATION. The organic, the other great department of mundane things, rests in like manner on one law, and that is,—DEVELOPMENT. Nor may even these be after all twain, but only branches of one still more comprehensive law, the expression of that unity which man's wit can scarcely separate from Deity itself.
Vestiges of the Natural History of Creation (1844), 360.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is now widely realized that nearly all the “classical” problems of molecular biology have either been solved or will be solved in the next decade. The entry of large numbers of American and other biochemists into the field will ensure that all the chemical details of replication and transcription will be elucidated. Because of this, I have long felt that the future of molecular biology lies in the extension of research to other fields of biology, notably development and the nervous system.
Letter to Max Perua, 5 June 1963. Quoted in William B. Wood (ed.), The Nematode Caenorhabditis Elegans (1988), x-xi.
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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 the invaluable merit of the great Basle mathematician Leonhard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1884), 12. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 153. Seen incorrectly attributed to Thomas Reid in N. Rose, Mathematical and Maxims and Minims (1988).
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It is the task of science, as a collective human undertaking, to describe from the external side, (on which alone agreement is possible), such statistical regularity as there is in a world “in which every event has a unique aspect, and to indicate where possible the limits of such description. It is not part of its task to make imaginative interpretation of the internal aspect of reality—what it is like, for example, to be a lion, an ant or an ant hill, a liver cell, or a hydrogen ion. The only qualification is in the field of introspective psychology in which each human being is both observer and observed, and regularities may be established by comparing notes. Science is thus a limited venture. It must act as if all phenomena were deterministic at least in the sense of determinable probabilities. It cannot properly explain the behaviour of an amoeba as due partly to surface and other physical forces and partly to what the amoeba wants to do, with out danger of something like 100 per cent duplication. It must stick to the former. It cannot introduce such principles as creative activity into its interpretation of evolution for similar reasons. The point of view indicated by a consideration of the hierarchy of physical and biological organisms, now being bridged by the concept of the gene, is one in which science deliberately accepts a rigorous limitation of its activities to the description of the external aspects of events. In carrying out this program, the scientist should not, however, deceive himself or others into thinking that he is giving an account of all of reality. The unique inner creative aspect of every event necessarily escapes him.
In 'Gene and Organism', American Naturalist, (1953), 87, 17.
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It is unnatural in a large field to have only one shaft of wheat, and in the infinite Universe only one living world.
Attributed. Variations of the idea are also seen. Webmaster has been unable to find and check a primary source. See 'Hunting the Wild Quote' at www.roger-pearse.com/weblog/?p=3894.
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It may very properly be asked whether the attempt to define distinct species, of a more or less permanent nature, such as we are accustomed to deal with amongst the higher plants and animals, is not altogether illusory amongst such lowly organised forms of life as the bacteria. No biologist nowadays believes in the absolute fixity of species … but there are two circumstances which here render the problem of specificity even more difficult of solution. The bacteriologist is deprived of the test of mutual fertility or sterility, so valuable in determining specific limits amongst organisms in which sexual reproduction prevails. Further, the extreme rapidity with which generation succeeds generation amongst bacteria offers to the forces of variation and natural selection a field for their operation wholly unparalleled amongst higher forms of life.
'The Evolution of the Streptococci', The Lancet, 1906, 2, 1415-6.
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It may well be doubted whether, in all the range of Science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results: for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light … “And if our fate be death, give light and let us die” This is the cry that, through all the ages, is going up from perplexed Humanity, and Science has little else to offer, that will really meet the demands of its votaries, than the conclusions of Pure Mathematics.
Opening of 'Introduction', A New Theory of Parallels (1890), xv. As a non-fiction work, the author’s name on the title page of this book was Charles Lutwidge Dodgson. Being better known for his works of fiction as Lewis Carroll, all quotes relating to this one person, published under either name, are gathered on this single web page under his pen name.
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It may well be doubted whether, in all the range of science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results; for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light!
Written without pseudonym as Charles L. Dodgson. Opening remarks in Introduction to A New Theory of Parallels (1888, 1890), xv.
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It seems plain and self-evident, yet it needs to be said: the isolated knowledge obtained by a group of specialists in a narrow field has in itself no value whatsoever, but only in its synthesis with all the rest of knowledge and only inasmuch as it really contributes in this synthesis toward answering the demand, ‘Who are we?’
…...
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It was basic research in the photoelectric field—in the photoelectric effect that would one day lead to solar panels. It was basic research in physics that would eventually produce the CAT scan. The calculations of today's GPS satellites are based on the equations that Einstein put to paper more than a century ago.
Speech to the National Academy of Sciences Annual Meeting (27 Apr 2009).
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It was not just the Church that resisted the heliocentrism of Copernicus. Many prominent figures, in the decades following the 1543 publication of De Revolutionibus, regarded the Copernican model of the universe as a mathematical artifice which, though it yielded astronomical predictions of superior accuracy, could not be considered a true representation of physical reality: 'If Nicolaus Copernicus, the distinguished and incomparable master, in this work had not been deprived of exquisite and faultless instruments, he would have left us this science far more well-established. For he, if anybody, was outstanding and had the most perfect understanding of the geometrical and arithmetical requisites for building up this discipline. Nor was he in any respect inferior to Ptolemy; on the contrary, he surpassed him greatly in certain fields, particularly as far as the device of fitness and compendious harmony in hypotheses is concerned. And his apparently absurd opinion that the Earth revolves does not obstruct this estimate, because a circular motion designed to go on uniformly about another point than the very center of the circle, as actually found in the Ptolemaic hypotheses of all the planets except that of the Sun, offends against the very basic principles of our discipline in a far more absurd and intolerable way than does the attributing to the Earth one motion or another which, being a natural motion, turns out to be imperceptible. There does not at all arise from this assumption so many unsuitable consequences as most people think.'
from Letter to Christopher Rothman, 20 Jan 1587
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It would be difficult and perhaps foolhardy to analyze the chances of further progress in almost every part of mathematics one is stopped by unsurmountable difficulties, improvements in the details seem to be the only possibilities which are left… All these difficulties seem to announce that the power of our analysis is almost exhausted, even as the power of ordinary algebra with regard to transcendental geometry in the time of Leibniz and Newton, and that there is a need of combinations opening a new field to the calculation of transcendental quantities and to the solution of the equations including them.
From Rapport historique sur les progrès des sciences mathématiques depuis 1789, et sur leur état actuel (1810), 131. As translated in George Sarton, The Study of the History of Mathematics (1936), 13. In the original French: “Il seroit difficile et peut-être téméraire d’analyser les chances que l’avenir offre à l’avancement des mathématiques: dans presque toutes les parties, on est arrêté par des difficultés insurmontables; des perfectionnements de détail semblent la seule chose qui reste à faire… Toutes ces difficultés semblent annoncer que la puissance de notre analyse est à-peu-près épuisée, comme celle de l’algèbre ordinaire l’étoit par rapport à la géométrie transcendante au temps de Leibnitz et de Newton, et qu’il faut des combinaisons qui ouvrent un nouveau champ au calcul des transcendantes et à la résolution des équations qui les contiennent.” Sarton states this comes from “the report on mathematical progress prepared for the French Academy of Sciences at Napoleon’s request”.
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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It... [can] be easily shown:
1. That all present mountains did not exist from the beginning of things.
2. That there is no growing of mountains.
3. That the rocks or mountains have nothing in common with the bones of animals except a certain resemblance in hardness, since they agree in neither matter nor manner of production, nor in composition, nor in function, if one may be permitted to affirm aught about a subject otherwise so little known as are the functions of things.
4. That the extension of crests of mountains, or chains, as some prefer to call them, along the lines of certain definite zones of the earth, accords with neither reason nor experience.
5. That mountains can be overthrown, and fields carried over from one side of a high road across to the other; that peaks of mountains can be raised and lowered, that the earth can be opened and closed again, and that other things of this kind occur which those who in their reading of history wish to escape the name of credulous, consider myths.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 232-4.
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It’s funny how worms can turn leaves into silk.
But funnier far is the cow:
She changes a field of green grass into milk
And not a professor knows how.
In Dorothy Caruso, Enrico Caruso: His Life and Death (1963), 42. Written for Michael Pupin, who made a similar statement in prose: “Look at those animals and remember the greatest scientists in the world have never discovered how to make grass into milk.”
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Knowledge is indivisible. When people grow wise in one direction, they are sure to make it easier for themselves to grow wise in other directions as well. On the other hand, when they split up knowledge, concentrate on their own field, and scorn and ignore other fields, they grow less wise–even in their own field.
In The Roving Mind (1983), 116.
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Let me describe briefly how a black hole might be created. Imagine a star with a mass 10 times that of the sun. During most of its lifetime of about a billion years the star will generate heat at its center by converting hydrogen into helium. The energy released will create sufficient pressure to support the star against its own gravity, giving rise to an object with a radius about five times the radius of the sun. The escape velocity from the surface of such a star would be about 1,000 kilometers per second. That is to say, an object fired vertically upward from the surface of the star with a velocity of less than 1,000 kilometers per second would be dragged back by the gravitational field of the star and would return to the surface, whereas an object with a velocity greater than that would escape to infinity.
When the star had exhausted its nuclear fuel, there would be nothing to maintain the outward pressure, and the star would begin to collapse because of its own gravity. As the star shrank, the gravitational field at the surface would become stronger and the escape velocity would increase. By the time the radius had got down to 10 kilometers the escape velocity would have increased to 100,000 kilometers per second, the velocity of light. After that time any light emitted from the star would not be able to escape to infinity but would be dragged back by the gravitational field. According to the special theory of relativity nothing can travel faster than light, so that if light cannot escape, nothing else can either. The result would be a black hole: a region of space-time from which it is not possible to escape to infinity.
'The Quantum Mechanics of Black Holes', Scientific American, 1977, 236, 34-40.
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Let us sum up the three possible explanations of the decision to drop the bomb and its timing. The first that it was a clever and highly successful move in the field of power politics, is almost certainly correct; the second, that the timing was coincidental, convicts the American government of a hardly credible tactlessness [towards the Soviet Union]; and the third, the Roman holiday theory [a spectacular event to justify the cost of the Manhattan Project], convicts them of an equally incredible irresponsibility.
In The Political and Military Consequences of Atomic Energy (1948), 126. As cited by Maurice W. Kirby and Jonathan Rosenhead, 'Patrick Blackett (1897)' in Arjang A. Assad (ed.) and Saul I. Gass (ed.),Profiles in Operations Research: Pioneers and Innovators (2011), 17. Blackett regarded the dropping of the atomic bombs on Japan as unnecessary because a Japanese surrender was inevitable.
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Looking through the telescope, one saw a circle of deep blue and the little round planet swimming in the field. It seemed such a little thing, so bright and small and still, faintly marked with transverse stripes, and slightly flattened from the perfect round. But so little it was, so silvery warm—a pin’s-head of light! It was as if it quivered, but really this was the telescope vibrating with the activity of the clockwork that kept the planet in view.
As I watched, the planet seemed to grow larger and smaller and to advance and recede, but that was simply that my eye was tired. Forty millions of miles it was from us—more than forty millions of miles of void. Few people realise the immensity of vacancy in which the dust of the material universe swims.
The War of the Worlds (1898), editted by Frank D. McConnell (1977), 128.
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Man is not only part of a field, but a part and member of his group. When people are together, as when they are at work, then the most unnatural behavior, which only appears in late stages or abnormal cases, would be to behave as separate Egos. Under normal circumstances they work in common, each a meaningfully functioning part of the whole.
Lecture at the Kantgesellschaft (Kant Society), Berlin (17 Dec 1924), 'Über Gestalttheorie', as taken down in shorthand. Translated by N. Nairn-Allison in Social Research (1944), 11, 91.
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Many animals even now spring out of the soil,
Coalescing from the rains and the heat of the sun.
Small wonder, then, if more and bigger creatures,
Full-formed, arose from the new young earth and sky.
The breed, for instance, of the dappled birds
Shucked off their eggshells in the springtime, as
Crickets in summer will slip their slight cocoons
All by themselves, and search for food and life.
Earth gave you, then, the first of mortal kinds,
For all the fields were soaked with warmth and moisture.
On the Nature of Things, trans. Anthony M. Esolen (1995), Book 5, lines 794-803, 181.
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Mars tugs at the human imagination like no other planet. With a force mightier than gravity, it attracts the eye to its shimmering red presence in the clear night sky. It is like a glowing ember in a field of ethereal lights, projecting energy and promise. It inspires visions of an approachable world. The mind vaults to thoughts of what might have been (if Mars were a litter closer to the warming Sun) and of what could be (if humans were one day to plant colonies there). Mysterious Mars, alluring Mars, fourth planet from the Sun: so far away and yet, on a cosmic scale, so very near.
…...
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Mathematics and music, the most sharply contrasted fields of scientific activity which can be found, and yet related, supporting each other, as if to show forth the secret connection which ties together all the activities of our mind, and which leads us to surmise that the manifestations of the artist’s genius are but the unconscious expressions of a mysteriously acting rationality.
In Vorträge und Reden (1884, 1896), Vol 1, 122. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 191. From the original German, “Mathematik und Musik, der schärfste Gegensatz geistiger Thätigkeit, den man auffinden kann, und doch verbunden, sich unterstützend, als wollten sie die geheime Consequenz nachweisen, die sich durch alle Thätigkeiten unseres Geistes hinzieht, und die auch in den Offenbarungen des künstlerischen Genius uns unbewusste Aeusserungen geheimnissvoll wirkender Vernunftmässigkeit ahnen lässt.”
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Mathematics has often been characterized as the most conservative of all sciences. This is true in the sense of the immediate dependence of new upon old results. All the marvellous new advancements presuppose the old as indispensable steps in the ladder. … Inaccessibility of special fields of mathematics, except by the regular way of logically antecedent acquirements, renders the study discouraging or hateful to weak or indolent minds.
In Number and its Algebra (1896), 136.
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Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined
In CRC Concise Encyclopedia of Mathematics (1998, 2nd ed. 2002 ), 1862.
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Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 82.
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Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.
The Principles of Quantum Mechanics (1930, 1981), Preface, viii.
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MATHEMATICS … the general term for the various applications of mathematical thought, the traditional field of which is number and quantity. It has been usual to define mathematics as “the science of discrete and continuous magnitude.”
Opening statement in article 'Mathematics', Encyclopedia Britannica (1911, 11th ed.), Vol. 17, 878. Whitehead then indicated this was an inadequate definition, which he then discussed at length and tried to give an improved definition later in the article. See the quote beginning “Definition of Mathematics…” on the Alfred North Whitehead Quotes page on this website.
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May the road rise to meet you. May the wind always be at your back. May the sun shine warm upon your face, the rains fall soft upon your fields and, until we meet again, may God hold you in the palm of his hand.
…...
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Melvin Calvin was a fearless scientist, totally unafraid to venture into new fields such as hot atom chemistry, carcinogenesis, chemical evolution and the origin of life, organic geochemistry, immunochemistry, petroleum production from plants, farming, Moon rock analysis, and development of novel synthetic biomembrane models for plant photosystems.
Co-author with Andrew A. Benson, 'Melvin Calvin', Biographical Memoirs of the US National Academy of Science.
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Most advances in science come when a person for one reason or another is forced to change fields.
Viewing a new field with fresh eyes, and bringing prior knowledge, results in creativity.
Quoted in Roger Von Oech, A Whack on the Side of the Head (1982), 71. (Berger is credited in the Introduction in a listed of people providing ideas and suggestions.) In Cheryl Farr, Jim Rhode, Newsletters, Patients and You (1985), 142.
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My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology
In Scientific American (Sep 1958). As cited in '50, 100 & 150 years ago', Scientific American (Sep 2008), 299, No. 3, 14.
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Nevertheless, scientific method is not the same as the scientific spirit. The scientific spirit does not rest content with applying that which is already known, but is a restless spirit, ever pressing forward towards the regions of the unknown, and endeavouring to lay under contribution for the special purpose in hand the knowledge acquired in all portions of the wide field of exact science. Lastly, it acts as a check, as well as a stimulus, sifting the value of the evidence, and rejecting that which is worthless, and restraining too eager flights of the imagination and too hasty conclusions.
'The Scientific Spirit in Medicine: Inaugural Sessional Address to the Abernethian Society', St. Bartholomew's Hospital Journal, 1912, 20, 19.
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No aphorism is more frequently repeated in connection with field trials, than that we must ask Nature few questions, or, ideally, one question, at a time. The writer is convinced that this view is wholly mistaken. Nature, he suggests, will best respond to a logical and carefully thought out questionnaire; indeed, if we ask her a single question, she will often refuse to answer until some other topic has been discussed.
'The Arrangement of Field Experiments', The Journal of the Ministry of Agriculture, 1926, 33, 511.
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No Geologist worth anything is permanently bound to a desk or laboratory, but the charming notion that true science can only be based on unbiased observation of nature in the raw is mythology. Creative work, in geology and anywhere else, is interaction and synthesis: half-baked ideas from a bar room, rocks in the field, chains of thought from lonely walks, numbers squeezed from rocks in a laboratory, numbers from a calculator riveted to a desk, fancy equipment usually malfunctioning on expensive ships, cheap equipment in the human cranium, arguments before a road cut.
An Urchin in the Storm (1988), 98.
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No occupation is more worthy of an intelligent and enlightened mind, than the study of Nature and natural objects; and whether we labour to investigate the structure and function of the human system, whether we direct our attention to the classification and habits of the animal kingdom, or prosecute our researches in the more pleasing and varied field of vegetable life, we shall constantly find some new object to attract our attention, some fresh beauties to excite our imagination, and some previously undiscovered source of gratification and delight.
In A Practical Treatise on the Cultivation of the Dahlia (1838), 1-2.
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No organization engaged in any specific field of work ever invents any important developers in that field, or adopts any important development in that field until forced to do so by outside competition.
Aphorism listed Frederick Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932) (1999), 54, being Transactions of the American Philosophical Society, Held at Philadelphia For Promoting Useful Knowledge, Vol. 86, Pt. 6.
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No other animals have ever lighted fires as far as we can tell. In field archeology, a charcoal deposit found in such a location that it could not have been made by a forest fire is taken as conclusive evidence of man. A circular dark disk in the soil five or six feet in diameter is such a find. … With … modern radioactive dating methods, we can trace man’s history.
In 'Man’s Place in the Physical Universe', Bulletin of the Atomic Scientists (Sep 1965), 21, No. 7, 15.
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No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. …because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory… The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity.
In 'Conclusion', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 326.
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Nothing is less predictable than the development of an active scientific field.
From interview with Henry Spall, as in an abridged version of Earthquake Information Bulletin (Jan-Feb 1980), 12, No. 1, that is on the USGS website.
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Now it came to me: … the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation. … This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.
In Paul Arthur Schilpp, 'Autobiographical Notes', Albert Einstein: Philosopher-Scientist (1949), 65-67.
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Now that we locate them [genes] in the chromosomes are we justified in regarding them as material units; as chemical bodies of a higher order than molecules? Frankly, these are questions with which the working geneticist has not much concern himself, except now and then to speculate as to the nature of the postulated elements. There is no consensus of opinion amongst geneticists as to what the genes are—whether they are real or purely fictitious—because at the level at which the genetic experiments lie, it does not make the slightest difference whether the gene is a hypothetical unit, or whether the gene is a material particle. In either case the unit is associated with a specific chromosome, and can be localized there by purely genetic analysis. Hence, if the gene is a material unit, it is a piece of chromosome; if it is a fictitious unit, it must be referred to a definite location in a chromosome—the same place as on the other hypothesis. Therefore, it makes no difference in the actual work in genetics which point of view is taken. Between the characters that are used by the geneticist and the genes that his theory postulates lies the whole field of embryonic development.
'The Relation of Genetics to Physiology and Medicine', Nobel Lecture (4 Jun 1934). In Nobel Lectures, Physiology or Medicine 1922-1941 (1965), 315.
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Now the serpent was more subtle than any beast of the field.
Bible
(circa 725 B.C.)
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Nowadays the field naturalist—who is usually at all points superior to the mere closet naturalist—follows a profession as full of hazard and interest as that of the explorer or of the big-game hunter in the remote wilderness.
African Game Trails (1910), 414-415.
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October 9, 1863
Always, however great the height of the balloon, when I have seen the horizon it has roughly appeared to be on the level of the car though of course the dip of the horizon is a very appreciable quantity or the same height as the eye. From this one might infer that, could the earth be seen without a cloud or anything to obscure it, and the boundary line of the plane approximately the same height as the eye, the general appearance would be that of a slight concavity; but I have never seen any part of the surface of the earth other than as a plane.
Towns and cities, when viewed from the balloon are like models in motion. I shall always remember the ascent of 9th October, 1863, when we passed over London about sunset. At the time when we were 7,000 feet high, and directly over London Bridge, the scene around was one that cannot probably be equalled in the world. We were still so low as not to have lost sight of the details of the spectacle which presented itself to our eyes; and with one glance the homes of 3,000,000 people could be seen, and so distinct was the view, that every large building was easily distinguishable. In fact, the whole of London was visible, and some parts most clearly. All round, the suburbs were also very distinct, with their lines of detached villas, imbedded as it were in a mass of shrubs; beyond, the country was like a garden, its fields, well marked, becoming smaller and smaller as the eye wandered farther and farther away.
Again looking down, there was the Thames, throughout its whole length, without the slightest mist, dotted over its winding course with innumerable ships and steamboats, like moving toys. Gravesend was visible, also the mouth of the Thames, and the coast around as far as Norfolk. The southern shore of the mouth of the Thames was not so clear, but the sea beyond was seen for many miles; when at a higher elevation, I looked for the coast of France, but was unable to see it. On looking round, the eye was arrested by the garden-like appearance of the county of Kent, till again London claimed yet more careful attention.
Smoke, thin and blue, was curling from it, and slowly moving away in beautiful curves, from all except one part, south of the Thames, where it was less blue and seemed more dense, till the cause became evident; it was mixed with mist rising from the ground, the southern limit of which was bounded by an even line, doubtless indicating the meeting of the subsoils of gravel and clay. The whole scene was surmounted by a canopy of blue, everywhere free from cloud, except near the horizon, where a band of cumulus and stratus extended all round, forming a fitting boundary to such a glorious view.
As seen from the earth, the sunset this evening was described as fine, the air being clear and the shadows well defined; but, as we rose to view it and its effects, the golden hues increased in intensity; their richness decreased as the distance from the sun increased, both right and left; but still as far as 90º from the sun, rose-coloured clouds extended. The remainder of the circle was completed, for the most part, by pure white cumulus of well-rounded and symmetrical forms.
I have seen London by night. I have crossed it during the day at the height of four miles. I have often admired the splendour of sky scenery, but never have I seen anything which surpassed this spectacle. The roar of the town heard at this elevation was a deep, rich, continuous sound the voice of labour. At four miles above London, all was hushed; no sound reached our ears.
Travels in the Air (1871), 99-100.
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Of all the conceptions of the human mind from unicorns to gargoyles to the hydrogen bomb perhaps the most fantastic is the black hole: a hole in space with a definite edge over which anything can fall and nothing can escape; a hole with a gravitational field so strong that even light is caught and held in its grip; a hole that curves space and warps time.
In Cosmology + I: Readings from Scientific American (1977), 63.
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Of the nucleosides from deoxyribonucleic acids, all that was known with any certainty [in the 1940s] was that they were 2-deoxy-­D-ribosides of the bases adenine, guanine, thymine and cytosine and it was assumed that they were structurally analogous to the ribonucleosides. The chemistry of the nucleotides—the phosphates of the nucleosides—was in a correspondingly primitive state. It may well be asked why the chemistry of these groups of compounds was not further advanced, particularly since we recognize today that they occupy a central place in the history of the living cell. True, their full significance was for a long time unrecognized and emerged only slowly as biochemical research got into its stride but I think a more important reason is to be found in the physical properties of compounds of the nucleotide group. As water-soluble polar compounds with no proper melting points they were extremely difficult to handle by the classic techniques of organic chemistry, and were accordingly very discouraging substances to early workers. It is surely no accident that the major advances in the field have coincided with the appearance of new experimental techniques such as paper and ion-exchange chromatography, paper electrophoresis, and countercurrent distribution, peculiarly appropriate to the compounds of this group.
In 'Synthesis in the Study of Nucleotides', Nobel Lecture, 11 December 1957. In Nobel Lectures: Chemistry 1942-1962 (1964), 524.
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On the afternoon of October 19, 1899, I climbed a tall cherry tree and, armed with a saw which I still have, and a hatchet, started to trim the dead limbs from the cherry tree. It was one of the quiet, colorful afternoons of sheer beauty which we have in October in New England, and as I looked towards the fields at the east, I imagined how wonderful it would be to make some device which had even the possibility of ascending to Mars. I was a different boy when I descended the tree from when I ascended for existence at last seemed very purposive.
In The Papers of Robert H. Goddard: 1898-1924 (1970), 9.
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Once the hatch was opened, I turned the lock handle and bright rays of sunlight burst through it. I opened the hatch and dust from the station flew in like little sparklets, looking like tiny snowflakes on a frosty day. Space, like a giant vacuum cleaner, began to suck everything out. Flying out together with the dust were some little washers and nuts that dad got stuck somewhere; a pencil flew by.
My first impression when I opened the hatch was of a huge Earth and of the sense of unreality concerning everything that was going on. Space is very beautiful. There was the dark velvet of the sky, the blue halo of the Earth and fast-moving lakes, rivers, fields and clouds clusters. It was dead silence all around, nothing whatever to indicate the velocity of the flight… no wind whistling in your ears, no pressure on you. The panorama was very serene and majestic.
…...
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One day at Fenner's (the university cricket ground at Cambridge), just before the last war, G. H. Hardy and I were talking about Einstein. Hardy had met him several times, and I had recently returned from visiting him. Hardy was saying that in his lifetime there had only been two men in the world, in all the fields of human achievement, science, literature, politics, anything you like, who qualified for the Bradman class. For those not familiar with cricket, or with Hardy's personal idiom, I ought to mention that “the Bradman class” denoted the highest kind of excellence: it would include Shakespeare, Tolstoi, Newton, Archimedes, and maybe a dozen others. Well, said Hardy, there had only been two additions in his lifetime. One was Lenin and the other Einstein.
Variety of Men (1966), 87.
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One major problem with any science is that people who don't know the conceptual history of their field go round re-inventing the elliptical wheel.
Telephone conversation with Susan Abrams 1983.
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One of my guiding principles is don’t do anything that other people are doing. Always do something a little different if you can. The concept is that if you do it a little differently there is a greater potential for reward than if you the same thing that other people are doing. I think that this kind of goal for one’s work, having obviously the maximum risk, would have the maximum reward no matter what the field may be.
In transcript of a video history interview with Seymour Cray by David K. Allison at the National Museum of American History, Smithsonian Institution, (9 May 1995), 29.
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One of my inventions was a large thermometer made of an iron rod, … The expansion and contraction of this rod was multiplied by a series of levers … so that the slightest change in the length of the rod was instantly shown on a dial about three feet wide multiplied about thirty-two thousand times. The zero-point was gained by packing the rod in wet snow. The scale was so large that … the temperature read while we were ploughing in the field below the house.
From The Story of My Boyhood and Youth (1913), 258-259. One of the inventions made while growing up on his father’s farm, before he left the year after he was 21.
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Our most successful theories in physics are those that explicitly leave room for the unknown, while confining this room sufficiently to make the theory empirically disprovable. It does not matter whether this room is created by allowing for arbitrary forces as Newtonian dynamics does, or by allowing for arbitrary equations of state for matter, as General Relativity does, or for arbitrary motions of charges and dipoles, as Maxwell's electrodynamics does. To exclude the unknown wholly as a “unified field theory” or a “world equation” purports to do is pointless and of no scientific significance.
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Our time is distinguished by wonderful achievements in the fields of scientific understanding and the technical application of those insights. Who would not be cheered by this? But let us not forget that human knowledge and skills alone cannot lead humanity to a happy and dignified life. Humanity has every reason to place the proclaimers of high moral standards and values above the discoverers of objective truth. What humanity owes to personalities like Buddha, Moses, and Jesus ranks for me higher than all the achievements of the inquiring constructive mind.
(Sep 1937). In Helen Dukas and Banesh Hoffman (ed.), Albert Einstein, the Human Side by (1979).
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Pathology, probably more than any other branch of science, suffers from heroes and hero-worship. Rudolf Virchow has been its archangel and William Welch its John the Baptist, while Paracelsus and Cohnheim have been relegated to the roles of Lucifer and Beelzebub. … Actually, there are no heroes in Pathology—all of the great thoughts permitting advance have been borrowed from other fields, and the renaissance of pathology stems not from pathology itself but from the philosophers Kant and Goethe.
Quoted from an address to a second year class, in Levin L. Waters, obituary for Harry S. N. Greene, M.D., in Yale Journal of Biology and Medicine (Feb-Apr 1971), 43:4-5, 207.
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Physiology and psychology cover, between them, the field of vital phenomena; they deal with the facts of life at large, and in particular with the facts of human life.
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Physiology is the experimental science par excellence of all sciences; that in which there is least to be learnt by mere observation, and that which affords the greatest field for the exercise of those faculties which characterize the experimental philosopher.
In 'Educational Value of Natural History Sciences', Lay Sermons, Addresses, and Reviews (1870), 90.
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Poets need be in no degree jealous of the geologists. The stony science, with buried creations for its domains, and half an eternity charged with its annals, possesses its realms of dim and shadowy fields, in which troops of fancies already walk like disembodied ghosts in the old fields of Elysium, and which bid fair to be quite dark and uncertain enough for all the purposes of poesy for centuries to come.
Lecture Third, collected in Popular Geology: A Series of Lectures Read Before the Philosophical Institution of Edinburgh, with Descriptive Sketches from a Geologist's Portfolio (1859), 127.
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Problems in human engineering will receive during the coming years the same genius and attention which the nineteenth century gave to the more material forms of engineering.
We have laid good foundations for industrial prosperity, now we want to assure the happiness and growth of the workers through vocational education, vocational guidance, and wisely managed employment departments. A great field for industrial experimentation and statemanship is opening up.
Letter printed in Engineering Magazine (Jan 1917), cover. Quoted in an article by Meyer Bloomfield, 'Relation of Foremen to the Working Force', reproduced in Daniel Bloomfield, Selected Articles on Employment Management (1919), 301.
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Quantum field theory, which was born just fifty years ago from the marriage of quantum mechanics with relativity, is a beautiful but not very robust child.
In Nobel Lecture (8 Dec 1989), 'Conceptual Foundations of the Unified Theory of Weak and Electromagnetic Interactions.'
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Research is industrial prospecting. The oil prospectors use every scientific means to find new paying wells. Oil is found by each one of a number of methods. My own group of men are prospecting in a different field, using every possible scientific means. We believe there are still things left to be discovered. We have only stumbled upon a few barrels of physical laws from the great pool of knowledge. Some day we are going to hit a gusher.
'Industrial Prospecting', an address to the Founder Societies of Engineers (20 May 1935). In National Research Council, Reprint and Circular Series of the National Research Council (1933), No. 107, 1.
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