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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Narrow Quotes (85 quotes)

…indeed what reason may not go to Schoole to the wisdome of Bees, Aunts, and Spiders? what wise hand teacheth them to doe what reason cannot teach us? Ruder heads stand amazed at those prodigious pieces of nature, Whales, Elephants, Dromidaries and Camels; these I confesse, are the Colossus and Majestick pieces of her hand; but in these narrow Engines there is more curious Mathematicks, and the civilitie of these little Citizens more neatly sets forth the wisedome of their Maker.
In Religio Medici and Other Writings (1909), 17.
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’Tis evident, that as common Air when reduc’d to half Its wonted extent, obtained near about twice as forcible a Spring as it had before; so this thus- comprest Air being further thrust into half this narrow room, obtained thereby a Spring about as strong again as that It last had, and consequently four times as strong as that of the common Air. And there is no cause to doubt, that If we had been here furnisht with a greater quantity of Quicksilver and a very long Tube, we might by a further compression of the included Air have made It counter-balance “the pressure” of a far taller and heavier Cylinder of Mercury. For no man perhaps yet knows how near to an infinite compression the Air may be capable of, If the compressing force be competently increast.
A Defense of the Doctrine Touching the Spring and Weight of the Air (1662), 62.
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[1665-08-16] ...Hence to the Exchange, which I have not been a great while. But Lord, how sad a sight it is to see the streets empty of people, and very few upon the Change - jealous of every door that one sees shut up, lest it should be the plague - and about us, two shops in three, if not more, generally shut up. ... It was dark before I could get home; and so land at church-yard stairs, where to my great trouble I met a dead Corps, of the plague, in the narrow ally, just bringing down a little pair of stairs - but I thank God I was not much disturbed at it. However, I shall beware of being late abroad again.
Diary of Samuel Pepys (16 Aug 1665)
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[A plant] does not change itself gradually, but remains unaffected during all succeeding generations. It only throws off new forms, which are sharply contrasted with the parent, and which are from the very beginning as perfect and as constant, as narrowly defined, and as pure of type as might be expected of any species.
In Species and Varieties: Their Origin and Mutation (1905), 28-9.
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[F. Werner, while a student in Princeton,] came to me and expressed his bewilderment with the fact that we make a rather narrow selection when choosing the data on which we test our theories. “How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?” It has to be admitted that we have no definite evidence that there is no such theory.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 535.
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[On Typhoid Fever] How often have I seen in past days, in the single narrow chamber of the day-labourer’s cottage, the father in the coffin, the mother in the sick-bed in muttering delirium, and nothing to relieve the desolation of the children but the devotion of some poor neighbour, who in too many cases paid the penalty of her kindness in becoming herself the victim of the same disorder.
As quoted by John Tyndall in Lecture (19 Oct 1876) to Glasgow Science Lectures Association. Printed in 'Address Delivered Before The British Association Assembled at Belfast', The Fortnightly Review (1 Nov 1876), 26 N.S., No. 119, 572.
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A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.
Science and the Common Understanding (1954), 53-4.
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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 research journal serves that narrow borderland which separates the known from the unknown.
Editorial, Vol. 1, Part 1, in the new statistics journal of the Indian Statistical Institute, Sankhayā (1933), as quoted and cited by MacTutor webpage for Mahalanobis. Also reprinted in Sankhyā: The Indian Journal of Statistics (Feb 2003), 65, No. 1, xii.
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Alas, your dear friend and servant is totally blind. Henceforth this heaven, this universe, which by wonderful observations I had enlarged by a hundred and a thousand times beyond the conception of former ages, is shrunk for me into the narrow space which I myself fill in it. So it pleases God; it shall therefore please me also.
In Letter, as quoted in Sir Oliver Lodge, Pioneers of Science (1905), 133.
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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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As soon as any one belongs to a narrow creed in science, every unprejudiced and true perception is gone.
Conversation (18 May 1824), with Johann Peter Eckermanns, in Conversations with Goethe (1850), 170.
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As yet, if a man has no feeling for art he is considered narrow-minded, but if he has no feeling for science this is considered quite normal. This is a fundamental weakness.
In Kermit Lansner, Second-Rate Brains: A Factual, Perceptive Report by Top Scientists, Educators, Journalists, and Their Urgent Recommendations (1958), 31. Note: Dr. I.I. Rabi was chairman of President Eisenhower's Science Advisory Committee.
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Catastrophe Theory is—quite likely—the first coherent attempt (since Aristotelian logic) to give a theory on analogy. When narrow-minded scientists object to Catastrophe Theory that it gives no more than analogies, or metaphors, they do not realise that they are stating the proper aim of Catastrophe Theory, which is to classify all possible types of analogous situations.
From 'La Théorie des catastrophes État présent et perspective', as quoted in Erick Christopher Zeeman, (ed.), Catastrophe Theory: Selected Papers, 1972-1977 (1977), 637, as cited in Martin Krampe (ed.), Classics of Semiotics (1987), 214.
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Chemistry is an art that has furnished the world with a great number of useful facts, and has thereby contributed to the improvement of many arts; but these facts lie scattered in many different books, involved in obscure terms, mixed with many falsehoods, and joined to a great deal of false philosophy; so that it is not great wonder that chemistry has not been so much studied as might have been expected with regard to so useful a branch of knowledge, and that many professors are themselves but very superficially acquainted with it. But it was particularly to be expected, that, since it has been taught in universities, the difficulties in this study should have been in some measure removed, that the art should have been put into form, and a system of it attempted—the scattered facts collected and arranged in a proper order. But this has not yet been done; chemistry has not yet been taught but upon a very narrow plan. The teachers of it have still confined themselves to the purposes of pharmacy and medicine, and that comprehends a small branch of chemistry; and even that, by being a single branch, could not by itself be tolerably explained.
John Thomson, An Account of the Life, Lectures and Writings of William Cullen, M.D. (1832), Vol. 1, 40.
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Creatures that by a rule in nature teach
The act of order to a peopled kingdom.
They have a king and officers of sorts;
Where some, like magistrates, correct at home,
Others, like merchants, venture trade abroad,
Others, like soldiers, armed in their stings,
Make boot upon the summer's velvet buds;
Which pillage they with merry march bring home
To the tent-royal of their emperor.
Who, busied in his majesty, surveys
The singing masons building roofs of gold;
The civil citizens kneading up the honey;
The poor mechanic porters crowding
Their heavy burdens at his narrow gate;
The sad-eyed justice, with his surly hum,
Delivering o'er to executors pale
The lazy yawning drone.
Henry V (1599), I, ii.
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Every complete set of chromosomes contains the full code; so there are, as a rule, two copies of the latter in the fertilized egg cell, which forms the earliest stage of the future individual. In calling the structure of the chromosome fibres a code-script we mean that the all-penetrating mind, once conceived by Laplace, to which every causal connection lay immediately open, could tell from their structure whether the egg would develop, under suitable conditions, into a black cock or into a speckled hen, into a fly or a maize plant, a rhododendron, a beetle, a mouse or a woman. To which we may add, that the appearances of the egg cells are very often remarkably similar; and even when they are not, as in the case of the comparatively gigantic eggs of birds and reptiles, the difference is not so much in the relevant structures as in the nutritive material which in these cases is added for obvious reasons.
But the term code-script is, of course, too narrow. The chromosome structures are at the same time instrumental in bringing about the development they foreshadow. They are law-code and executive power?or, to use another simile, they are architect's plan and builder’s craft-in one.
In What is Life? : The Physical Aspect of the Living Cell (1944), 20-21.
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Every progress that a church makes in the construction of its dogmas leads to a further taming of the free spirit; every new dogma … narrows the circle of free thought. … Science, on the other hand, liberates with every step of its development, it opens up new paths to thought … In other words, it allows the individual to be truly free.
Translated from the original German, “Jeder Fortschritt, den eine Kirche in dem Aufbau ihrer Dogmen macht, führt zu einer weiter gehenden Bändigung des freien Geistes; jedes neue Dogma … verengt den Kreis des freien Denkens. … Die Naturwissenschaft umgekehrt befreit mit jedem Schritte ihrer Entwicklung, sie eröffnet dem Gedanken neue Bahnen … Sie gestattet, mit anderen Worten, dem Einzelnen in vollem Masse wahr zu sein.” In Speech to the 24th meeting of the German Naturalists and Physicians at Rostock 'Ueber die Aufgaben der Naturwissenschaften in dem neuen nationalen Leben Deutschlands', (On the tasks of the natural sciences in the new national life of Germany), published in Chemisches Zentralblatt (11 Oct 1871), No. 41, 654-655. English version by Webmaster using Google translate.
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Every serious scientific worker is painfully conscious of this involuntary relegation to an ever-narrowing sphere of knowledge, which threatens to deprive the investigator of his broad horizon and degrades him to the level of a mechanic.
In Ideas and Opinions (1954), 69.
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Experimental physicists … walk a narrow path with pitfalls on either side. If we spend all our time developing equipment, we risk the appellation of “plumber,” and if we merely use the tools developed by others, we risk the censure of our peers for being parasitic.
In Nobel Lecture (11 Dec 1968), 'Recent Developments in Particle Physics', collected in Nobel Lectures: Physics 1963-1970 (1972), 241.
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Far from being the basis of the good society, the family, with its narrow privacy and tawdry secrets, is the source of all our discontents.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
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Faraday, who had no narrow views in regard to education, deplored the future of our youth in the competition of the world, because, as he said with sadness, “our school-boys, when they come out of school, are ignorant of their ignorance at the end of all that education.”
In Inaugural Presidential Address (9 Sep 1885) to the British Association for the Advancement of Science, Aberdeen, Scotland, 'Relations of Science to the Public Weal', Report to the Fifty-Fifth Meeting of the British Association (1886), 11.
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He was so narrow-minded he could see through a keyhole with two eyes.
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He who lacks a sense of the past is condemned to live in the narrow darkness of his own generation
Quoted, and described as “an old Armenian saying”, in Differential Equations: With Applications and Historical Notes (1972), ix.
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How narrow is the vision that exalts the busyness of the ant above the singing of the grasshopper.
In Kahlil Gibran: The Collected Works (2007), 203.
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I am nothing more than a single narrow gasping lung, floating over the mists and summits.
In Everest: Expedition to the Ultimate (1979), 180.
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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 once lodged in Hanover in a room whose window gave on to a narrow Street which formed a communicating link between two bigger streets. It was very pleasant to see how people's faces changed when they entered the little Street, where they thought they were less observed; how here one pissed, there another fixed her garter, one gave way to private laughter and another shook his head. Girls thought with a smile of the night before and adjusted their ribbons for conquests in the big Street ahead.
Aphorism 19 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 34.
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I think science has enjoyed an extraordinary success because it has such a limited and narrow realm in which to focus its efforts. Namely, the physical universe.
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If the doors of perception were cleansed, everything would appear as it is, infinite. For man has closed himself up, till he sees all things thro’ narrow chinks of his cavern.
In The Marriage of Heaven and Hell: And A Song of Liberty (1793, 1911), 62.
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If we imagine an observer to approach our planet from outer space, and, pushing aside the belts of red-brown clouds which obscure our atmosphere, to gaze for a whole day on the surface of the earth as it rotates beneath him, the feature, beyond all others most likely to arrest his attention would be the wedge-like outlines of the continents as they narrow away to the South.
The Face of the Earth (1904), Vol. 1, 1.
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Imagine a school-boy who has outgrown his clothes. Imagine the repairs made on the vestments where the enlarged frame had burst the narrow limits of the enclosure. Imagine the additions made where the projecting limbs had fairly and far emerged beyond the confines of the garment. Imagine the boy still growing, and the clothes, mended allover, now more than ever in want of mending—such is chemistry, and such is nomenclature.
Chemical Recreations (1834), 206, footnote.
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In defining an element let us not take an external boundary, Let us say, e.g., the smallest ponderable quantity of yttrium is an assemblage of ultimate atoms almost infinitely more like each other than they are to the atoms of any other approximating element. It does not necessarily follow that the atoms shall all be absolutely alike among themselves. The atomic weight which we ascribe to yttrium, therefore, merely represents a mean value around which the actual weights of the individual atoms of the “element” range within certain limits. But if my conjecture is tenable, could we separate atom from atom, we should find them varying within narrow limits on each side of the mean.
Address to Annual General Meeting of the Chemical Society (28 Mar 1888), printed in Journal of the Chemical Society (1888), 491.
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It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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It is profitable nevertheless to permit ourselves to talk about 'meaningless' terms in the narrow sense if the preconditions to which all profitable operations are subject are so intuitive and so universally accepted as to form an almost unconscious part of the background of the public using the term. Physicists of the present day do constitute a homogenous public of this character; it is in the air that certain sorts of operation are valueless for achieving certain sorts of result. If one wants to know how many planets there are one counts them but does not ask a philosopher what is the perfect number.
Reflections of a Physicist (1950), 6.
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It is with narrow-souled people as with narrow-necked bottles, the less they have in them, the more noise they make in pouring out.
Anonymous
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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 Oliver Wendell Holmes, Sr., who likened the bigot to the pupil of the human eye: the more light you expose it to the narrower it grows.
Ashley Montagu (ed.), Science and Creationism (1984), Introduction, 8.
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Its [science’s] effectiveness is almost inevitable because it narrows the possibility of refutation and failure. Science begins by saying it can only answer this type of question and ends by saying these are the only questions that can be asked. Once the implications and shallowness of this trick are fully realised, science will be humbled and we shall be free to celebrate ourselves once again.
From Understanding the Present: An Alternative History of Science (2004), 249.
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Man tries to make for himself in the fashion that suits him best a simplified and intelligible picture of the world; he then tries to some extent to substitute this cosmos of his for the world of experience, and thus to overcome it. This is what the painter, the poet, the speculative philosopher, and the natural scientist do, each in his own fashion. Each makes this cosmos and its construction the pivot of his emotional life, in order to find in this way the peace and security which he cannot find in the narrow whirlpool of personal experience.
Address at The Physical Society, Berlin (1918) for Max Planck’s 60th birthday, 'Principles of Research', collected in Essays in Science (1934, 2004) 3.
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Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer’s gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness of life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud cell, and is forever ready to burst forth into new forms of vegetable and animal existence.
From Commemoration Day Address (22 Feb 1877) at Johns Hopkins University, Baltimore, collected in The Collected Mathematical Papers: (1870-1883) (1909), 77-78.
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Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?
As quoted by Charles Melbourne Focken in Dimensional Methods and Their Applications (1953), 17.
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Men are noisy, narrow-band devices, but their nervous systems have very many parallel and simultaneously active channels. Relative to men, computing machines are very fast and very accurate, but they are constrained to perform only one or a few elementary operations at a time. Men are flexible, capable of “programming themselves contingently” on the basis of newly received information. Computing machines are single-minded, constrained by their “pre-programming.”
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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Modern civilization depends on science … James Smithson was well aware that knowledge should not be viewed as existing in isolated parts, but as a whole, each portion of which throws light on all the other, and that the tendency of all is to improve the human mind, and give it new sources of power and enjoyment … narrow minds think nothing of importance but their own favorite pursuit, but liberal views exclude no branch of science or literature, for they all contribute to sweeten, to adorn, and to embellish life … science is the pursuit above all which impresses us with the capacity of man for intellectual and moral progress and awakens the human intellect to aspiration for a higher condition of humanity.
[Joseph Henry was the first Secretary of the Smithsonian Institution, named after its benefactor, James Smithson.]
The first clause is inscribed on the National Museum of American History, Washington, D.C. In Library of Congress, Respectfully Quoted: A Dictionary of Quotations (1989), 313. From 'On the Smithsonian Institution', (Aug 1853), Proceedings of the Third Session of the American Association for the Advancement of Education (1854), 101.
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Oersted would never have made his great discovery of the action of galvanic currents on magnets had he stopped in his researches to consider in what manner they could possibly be turned to practical account; and so we would not now be able to boast of the wonders done by the electric telegraphs. Indeed, no great law in Natural Philosophy has ever been discovered for its practical implications, but the instances are innumerable of investigations apparently quite useless in this narrow sense of the word which have led to the most valuable results.
From Silvanus Phillips Thompson, 'Introductory Lecture to the Course on Natural Philosophy', The Life of Lord Kelvin (1910), Vol. 1, Appendix to Chap. 5, 249.
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On becoming very intimate with Fitz-Roy, I heard that I had run a very narrow risk of being rejected, on account of the shape of my nose! He was an ardent disciple of Lavater, and was convinced that he could judge a man's character by the outline of his features. He doubted whether anyone with my nose could possess sufficient energy and determination for the voyage. I think he was well-satisfied that my nose had spoken falsely.
In Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin: Including an Autobiographical Chapter (1896), 50.
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On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
Considerations on the Doctrine of Phlogiston (1796), 57-8.
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One could not be a successful scientist without realizing that, in contrast to the popular conception supported by newspapers and mothers of scientists, a goodly number of scientists are not only narrow-minded and dull, but also just stupid.
The Double Helix: A Personal Account of the Discovery of the Structure of DNA (1968, 1998), 14.
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One Science only will one Genius fit;
So vast is Art, so narrow Human Wit.
An Essay on Criticism (1709), 6.
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One-story intellects, two-story intellects, three-story intellects with skylights. All fact-collectors, who have no aim beyond their facts, are one-story men. Two-story men compare, reason, generalize, using the labors of the fact-collectors as well as their own. Three-story men idealize, imagine, predict; their best illumination comes from above, through the skylight. There are minds with large ground-floors, that can store an infinite amount of knowledge; some librarians, for instance, who know enough of books to help other people, without being able to make much other use of their knowledge, have intellects of this class. Your great working lawyer has two spacious stories; his mind is clear, because his mental floors are large, and he has room to arrange his thoughts so that lie can get at them,—facts below, principles above, and all in ordered series; poets are often narrow below, incapable of clear statement, and with small power of consecutive reasoning, but full of light, if sometimes rather bare of furniture, in the attics.
The Poet at the Breakfast Table (1883), 50.
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Out of all possible universes, the only one which can exist, in the sense that it can be known, is simply the one which satisfies the narrow conditions necessary for the development of intelligent life.
From In the Centre of Immensities: Creation (1979), as cited in Bill Swainson, The Encarta Book of Quotations (2000), 579.
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Outside our consciousness there lies the cold and alien world of actual things. Between the two stretches the narrow borderland of the senses. No communication between the two worlds is possible excepting across the narrow strip. For a proper understanding of ourselves and of the world, it is of the highest importance that this borderland should be thoroughly explored.
Keynote Address, a tribute to Helmholtz, at the Imperial Palace, Berlin (Aug 1891). Cited in Davis Baird, R.I.G. Hughes and Alfred Nordmann, Heinrich Hertz: Classical Physicist, Modern Philosopher (1998), 157.
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Poore soule, in this thy flesh what do'st thou know?
Thou know'st thy selfe so little, as thou know'st not.
How thou did'st die, nor how thou wast begot.
Thou neither know'st how thou at first camest in,
Nor how thou took'st the poyson of mans sin.
Nor dost thou, (though thou know'st, that thou art so)
By what way thou art made immortall, know.
Thou art too narrow, wretch, to comprehend
Even thy selfe; yea though thou wouldst but bend
To know thy body. Have not all soules thought
For many ages, that our body'is wrought
Of Ayre, and Fire, and other Elements?
And now they thinke of new ingredients,
And one soule thinkes one, and another way
Another thinkes, and 'tis an even lay.
Knowst thou but how the stone doth enter in
The bladder's Cave, and never breake the skin?
Knowst thou how blood, which to the hart doth flow,
Doth from one ventricle to th'other go?
And for the putrid stuffe, which thou dost spit,
Knowst thou how thy lungs have attracted it?
There are no passages, so that there is
(For aught thou knowst) piercing of substances.
And of those many opinions which men raise
Of Nailes and Haires, dost thou know which to praise?
What hope have we to know our selves, when wee
Know not the least things, which for our use bee?
Of the Progresse of the Soule. The Second Anniversarie, I. 254-280. The Works of John Donne (Wordsworth edition 1994), 196-7.
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Probably our atomic weights merely represent a mean value around which the actual atomic weights of the atoms vary within certain narrow limits... when we say, the atomic weight of, for instance, calcium is 40, we really express the fact that, while the majority of calcium atoms have an actual atomic weight of 40, there are not but a few which are represented by 39 or 41, a less number by 38 or 42, and so on.
Presidential Address, 2 September 1886, Section B, Chemical Science. Reports of the British Association for the Advancement of Science (1886), 569.
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Psychologists must cease to be content with the sterile and narrow conception of their science as the science of consciousness, and must boldly assert its claim to be the positive science of mind in all its aspects and modes of functining, or, as I would prefer to say, the positive science of conduct or behavior.
An Introduction to Social Psychology (1928), 13.
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Religion and science ... constitute deep-rooted and ancient efforts to find richer experience and deeper meaning than are found in the ordinary biological and social satisfactions. As pointed out by Whitehead, religion and science have similar origins and are evolving toward similar goals. Both started from crude observations and fanciful concepts, meaningful only within a narrow range of conditions for the people who formulated them of their limited tribal experience. But progressively, continuously, and almost simultaneously, religious and scientific concepts are ridding themselves of their coarse and local components, reaching higher and higher levels of abstraction and purity. Both the myths of religion and the laws of science, it is now becoming apparent, are not so much descriptions of facts as symbolic expressions of cosmic truths.
'On Being Human,' A God Within, Scribner (1972).
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Suppose a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake. Suppose then another similar cause to have excited another equal series of waves, which arrive at the same time, with the first. Neither series of waves will destroy the other, but their effects will be combined: if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations; but if the elevations of one series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions. And the surface of the water must remain smooth; at least I can discover no alternative, either from theory or from experiment.
A Reply to the Animadversions of the Edinburgh Reviewers on Some Papers Published in the Philosophical Transactions (1804), 17-8.
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Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.
Symmetry (1952), 5.
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The earth’s atmosphere is an imperfect window on the universe. Electromagnetic waves in the optical part of the spectrum (that is, waves longer than X rays and shorter than radio waves) penetrate to the surface of the earth only in a few narrow spectral bands. The widest of the transmitted bands corresponds roughly to the colors of visible light; waves in the flanking ultraviolet and infrared regions of the optical spectrum are almost totally absorbed by the atmosphere. In addition, atmospheric turbulence blurs the images of celestial objects, even when they are viewed through the most powerful ground-based telescopes.
in an article promoting the construction of the Hubble Space Telescope
Scientific American (July 1977)
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The increasing technicality of the terminology employed is also a serious difficulty. It has become necessary to learn an extensive vocabulary before a book in even a limited department of science can be consulted with much profit. This change, of course, has its advantages for the initiated, in securing precision and concisement of statement; but it tends to narrow the field in which an investigator can labour, and it cannot fail to become, in the future, a serious impediment to wide inductive generalisations.
Year Book of Science (1892), preface, from review in Chemical News and Journal of Physical Science (14 Apr 1892), 65, 190.
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The investigation of causal relations between economic phenomena presents many problems of peculiar difficulty, and offers many opportunities for fallacious conclusions. Since the statistician can seldom or never make experiments for himself, he has to accept the data of daily experience, and discuss as best he can the relations of a whole group of changes; he cannot, like the physicist, narrow down the issue to the effect of one variation at a time. The problems of statistics are in this sense far more complex than the problems of physics.
Udny Yule
In 'On the Theory of Correlation', Journal of the Royal Statistical Society (Dec 1897), 60, 812, as cited in Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900 (1986), 348.
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The last few meters up to the summit no longer seem so hard. On reaching the top, I sit down and let my legs dangle into space. I don’t have to climb anymore. I pull my camera from my rucksack and, in my down mittens, fumble a long time with the batteries before I have it working properly. Then I film Peter. Now, after the hours of torment, which indeed I didn’t recognize as torment, now, when the monotonous motion of plodding upwards is at an end, and I have nothing more to do than breathe, a great peace floods my whole being. I breathe like someone who has run the race of his life and knows that he may now rest forever. I keep looking all around, because the first time I didn’t see anything of the panorama I had expected from Everest, neither indeed did I notice how the wind was continually chasing snow across the summit. In my state of spiritual abstraction, I no longer belong to myself and to my eyesight. I am nothing more than a single, narrow, gasping lung, floating over the mists and the summits.
In Everest: Expedition to the Ultimate (1979), 180.
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The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work.
In Presidential Address British Association for the Advancement of Science, Section A, (1890), Nature, 42, 467.
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The most learned are often the most narrow-minded.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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The mythology of science asserts that with many different scientists all asking their own questions and evaluating the answers independently, whatever personal bias creeps into their individual answers is cancelled out when the large picture is put together. This might conceivably be so if scientists were women and men from all sorts of different cultural and social backgrounds who came to science with very different ideologies and interests. But since, in fact, they have been predominantly university-trained white males from privileged social backgrounds, the bias has been narrow and the product often reveals more about the investigator than about the subject being researched.
'Have Only Men Evolved?' Women Look at Biology Looking At Women, eds. Ruth Hubbard, Mary Sue Henifin, and Barbara Fried (1979).
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The narrow sectarian cannot read astronomy with impunity. The creeds of his church shrivel like dried leaves at the door of the observatory.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 474.
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The narrow slit through which the scientist, if he wants to be successful, must view nature constructs, if this goes on for a long time, his entire character; and, more often than not, he ends up becoming what the German language so appropriately calls a Fachidiot (professional idiot).
Heraclitean Fire: Sketches from a Life before Nature (1978), 33.
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The neutral zone of selective advantage in the neighbourhood of zero is thus so narrow that changes in the environment, and in the genetic constitution of species, must cause this zone to be crossed and perhaps recrossed relatively rapidly in the course of evolutionary change, so that many possible gene substitutions may have a fluctuating history of advance and regression before the final balance of selective advantage is determined.
'The Distribution of Gene Ratios for Rare Mutations', Proceedings of the Royal Society of Edinburgh, 1930, 50, 219.
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The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics “knows nothing of causation” could only be taken to express the whole truth, if by the term “causation” is understood “efficient causation.” The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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The principles of medical management are essentially the same for individuals of all ages, albeit the same problem is handled differently in different patients. ... [just as] the principles of driving an automobile are uniform, but one drives in one manner on the New Jersey Turnpike and in another manner on a narrow, winding road in the Rocky Mountains.
Quoted in Joseph Earle Moore, The Neurologic and Psychiatric Aspects of the Disorders of Aging (1956), 247.
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The rigid career path of a professor at a modern university is that One Must Build the Big Research Group, recruit doctoral students more vigorously than the head football coach, bombard the federal agencies with grant applications more numerous than the pollen falling from the heavens in spring, and leave the paper writing and the research to the postdocs, research associates, and students who do all the bench work and all the computer programming. A professor is chained to his previous topics by his Big Group, his network of contacts built up laboriously over decades, and the impossibility of large funding except in areas where the grantee has grown the group from a corner of the building to an entire floor. The senior tenure-track faculty at a research university–the “silverbacks” in anthropological jargon–are bound by invisible chains stronger than the strongest steel to a narrow range of what the Prevailing Consensus agrees are Very Important Problems. The aspiring scientist is confronted with the reality that his mentors are all business managers.
In his Foreword to Cornelius Lanczos, Discourse on Fourier Series, ix-x.
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The roads of science are narrow, so that they who travel them, must wither follow or meet one another…
In Samuel Johnson and W. Jackson Bate (Ed.), ',The Rambler, No. 121, Tuesday, 14 May 1751.' The Selected Essays from the Rambler, Adventurer, and Idler (1968), 172.
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There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.
In Pascal’s Pensées (1958), 3.
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There is an influence which is getting strong and stronger day by day, which shows itself more and more in all departments of human activity, and influence most fruitful and beneficial—the influence of the artist. It was a happy day for the mass of humanity when the artist felt the desire of becoming a physician, an electrician, an engineer or mechanician or—whatnot—a mathematician or a financier; for it was he who wrought all these wonders and grandeur we are witnessing. It was he who abolished that small, pedantic, narrow-grooved school teaching which made of an aspiring student a galley-slave, and he who allowed freedom in the choice of subject of study according to one's pleasure and inclination, and so facilitated development.
'Roentgen Rays or Streams', Electrical Review (12 Aug 1896). Reprinted in The Nikola Tesla Treasury (2007), 307. By Nikola Tesla
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There is one thing against which a scientist will have to guard himself: narrow patriotism.
Quoted in India Today (Apr 2008), 33, No 16, as cited on webpage of Dhirubhai Ambani Institute of Information and Communication Technology.
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This beast is best felt. Shake, rattle, and roll. We are thrown left and right against our straps in spasmodic little jerks. It is steering like crazy, like a nervous lady driving a wide car down a narrow alley, and I just hope it knows where it’s going, because for the first ten seconds we are perilously close to that umbilical tower.
…...
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To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
His handwritten note in the margin, beside the eighth proposition, in his copy of Diophantus' Arithmetica, Book 2. It is known as Fermat’s Last Theorem. (A proof remained elusive until 1994.) In Précis des Oeuvres Mathématiques de P. Fermat et de l'Arithmetique de Diophante (1853), 53-54. As translated by Vera Sandford in David Eugene Smith, A Source Book in Mathematics (1929), 212.
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To judge in this [utilitarian] way demonstrates … how small, narrow and indolent our minds are; it shows a disposition always to calculate the reward before the work, a cold heart and a lack of feeling for everything that is great and honours mankind. Unfortunately one cannot deny that such a mode of thinking is common in our age, and I am convinced that this is closely connected with the catastrophes which have befallen many countries in recent times; do not mistake me, I do not talk of the general lack of concern for science, but of the source from which all this has come, of the tendency to look out everywhere for one’s advantage and to relate everything to one’s physical well being, of indifference towards great ideas, of aversion to any effort which derives from pure enthusiasm.
Epigraph before title page, T. W. Körner, The Pleasures of Counting (1996).
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We are living in an age of awesome agricultural enterprise that needs to be interpreted. We find our simple faith in science dominated by the Religion of PhDeism under the reign of Data; so narrow in people and often so meaningless in context as to be worthless to the scientific farmer.
Letter to Joshua Lederberg (19 Apr 1970), Joshua Lederberg papers, National Library of Medicine (online). Hildebrand was a response to a Lederberg's letter published in the Washington Post (18 Apr 1970) about 'Ecology Has All Requisites of an Authentic Religion.' Note that Sam Murchid claimed this term PhDeism in another context in his diaries (as seen in diaries of 1964 and others).
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We receive it as a fact, that some minds are so constituted as absolutely to require for their nurture the severe logic of the abstract sciences; that rigorous sequence of ideas which leads from the premises to the conclusion, by a path, arduous and narrow, it may be, and which the youthful reason may find it hard to mount, but where it cannot stray; and on which, if it move at all, it must move onward and upward… . Even for intellects of a different character, whose natural aptitude is for moral evidence and those relations of ideas which are perceived and appreciated by taste, the study of the exact sciences may be recommended as the best protection against the errors into which they are most likely to fall. Although the study of language is in many respects no mean exercise in logic, yet it must be admitted that an eminently practical mind is hardly to be formed without mathematical training.
In Orations and Speeches (1870), Vol. 8, 510.
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When the child outgrows the narrow circle of family life … then comes the period of the school, whose object is to initiate him into the technicalities of intercommunication with his fellow-men, and to familiarize him with the ideas that underlie his civilization, and which he must use as tools of thought if he would observe and understand the phases of human life around him; for these … are invisible to the human being who has not the aid of elementary ideas with which to see them.
In Psychologic Foundations of Education: An Attempt to Show the Genesis of the Higher Faculties of the Mind (1907), 265.
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When we think how narrow and devious this path of nature is, how dimly we can trace it, for all our lamps of science, and how from the darkness which girds it round great and terrible possibilities loom ever shadowly upwards, it is a bold and a confident man who will put a limit to the strange by-oaths into which the human spirit may wander.
Lot No. 249 (1892)
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Without theory, practice is but routine born of habit. Theory alone can bring forth and develop the spirit of invention. ... [Do not] share the opinion of those narrow minds who disdain everything in science which has not an immediate application. ... A theoretical discovery has but the merit of its existence: it awakens hope, and that is all. But let it be cultivated, let it grow, and you will see what it will become.
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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Years ago I used to worry about the degree to which I specialized. Vision is limited enough, yet I was not really working on vision, for I hardly made contact with visual sensations, except as signals, nor with the nervous pathways, nor the structure of the eye, except the retina. Actually my studies involved only the rods and cones of the retina, and in them only the visual pigments. A sadly limited peripheral business, fit for escapists. But it is as though this were a very narrow window through which at a distance, one can only see a crack of light. As one comes closer the view grows wider and wider, until finally looking through the same narrow window one is looking at the universe. It is like the pupil of the eye, an opening only two to three millimetres across in daylight, but yielding a wide angle of view, and manoeuvrable enough to be turned in all directions. I think this is always the way it goes in science, because science is all one. It hardly matters where one enters, provided one can come closer, and then one does not see less and less, but more and more, because one is not dealing with an opaque object, but with a window.
In Scientific American, 1960s, attributed.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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