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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Obscure Quotes (66 quotes)

[My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who] devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.
Quoted in Max Davidson, 'Bill Bryson: Have faith, science can solve our problems', Daily Telegraph (26 Sep 2010)
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[P]olitical and social and scientific values … should be correlated in some relation of movement that could be expressed in mathematics, nor did one care in the least that all the world said it could not be done, or that one knew not enough mathematics even to figure a formula beyond the schoolboy s=(1/2)gt2. If Kepler and Newton could take liberties with the sun and moon, an obscure person ... could take liberties with Congress, and venture to multiply its attraction into the square of its time. He had only to find a value, even infinitesimal, for its attraction.
The Education of Henry Adams: An Autobiography? (1918), 376.
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L’Astronomie est utile, parce qu’elle nous élève au-dessus de nous-mêmes; elle est utile, parce qu’elle est grande; elle est utile, parce qu’elle est belle… C’est elle qui nous montre combien l’homme est petit par le corps et combien il est grand par l’esprit, puisque cette immensité éclatante où son corps n’est qu’un point obscur, son intelligence peut l’embrasser tout entière et en goûter la silencieuse harmonie.
Astronomy is useful because it raises us above ourselves; it is useful because it is grand[; it is useful because it is beautiful]… It shows us how small is man’s body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.
In La Valeur de la Science (1904), 276, translated by George Bruce Halsted, in The Value of Science (1907), 84. Webmaster added the meaning of “elle est utile, parce qu’elle est belle,” in brackets, which was absent in Halsted’s translation.
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A disease which new and obscure to you, Doctor, will be known only after death; and even then not without an autopsy will you examine it with exacting pains. But rare are those among the extremely busy clinicians who are willing or capable of doing this correctly.
In Atrocis, nee Descipti Prius, Morbi Historia as translated in Bulletin of the Medical Library Association (1944), 43, 217.
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A man has no reason to be ashamed of having an ape for his grandfather. If there were an ancestor whom I should feel shame in recalling it would rather be a man—a man of restless and versatile intellect—who … plunges into scientific questions with which he has no real acquaintance, only to obscure them by an aimless rhetoric, and distract the attention of his hearers from the real point at issue by eloquent digressions and skilled appeals to religious prejudice.
As recollected in a letter written by an undergraduate, John Richard Green, writing to his friend, afterwards Professor Boyd Dawkins. This was Huxley's rebuttal to Bishop Samuel Wilberforce who ridiculed Darwin's theory of evolution at a meeting of the British Association at Oxford (30 Jun 1860). After hearing Wilberforce's speech, and before rising himself, Huxley is said to have remarked, “The Lord has delivered him into my hands!” (No transcript was taken at the time, so the words are not verbatim. The version above is commonly seen, and was said by Huxley to be fair in substance, if not wholely accurate. The letter excerpt is in Leonard Huxley (ed.), Life and Letters of Thomas Henry Huxley (1916), Vol. 1, 199. Additional accounts of the debate are given in the book.
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John Ray quote: A multitude of words doth rather obscure than illustrate, they being a burden to the memory, and the first apt t
A multitude of words doth rather obscure than illustrate, they being a burden to the memory, and the first apt to be forgotten, before we come to the last. So that he that uses many words for the explaining of any subject, doth, like the cuttle-fish, hide himself, for the most part, in his own ink.
John Ray
The Wisdom of God Manifested in the Works of the Creation (1691).
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A practical botanist will distinguish, at the first glance, the plant of different quarters of the globe, and yet will be at a loss to tell by what mark he detects them. There is, I know not what look—sinister, dry, obscure, in African plants; superb and elevated in the Asiatic; smooth and cheerful in the American; stunted and indurated in the Alpine.
Quoted in William Whewell, History of the Inductive Sciences (1847), Vol. 3, 355-356, citing ‘Philosophia Botanica’ (1751), 171.
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All things are hidden, obscure and debatable if the cause of the phenomena is unknown, but everything is clear if its cause be known.
In Louis Pasteur and Harold Clarence Ernst (trans), The Germ Theory and Its Application to Medicine and Surgery, Chap. 2. Reprinted in Charles W. Eliot (ed.), The Harvard Classics: Scientific Papers: Physiology, Medicine, Surgery, Geology (1897, 1910), Vol. 38, 384. Cited as read before French Academy of Science (20 Apr 1878), published in Comptes Rendus de l’Académie des Sciences, 84, 1037-43.
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Appearances are a glimpse of the obscure.
Anaxagoras, fr. 21a. Trans. R. W. Sharples.
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At the bidding of a Peter the Hermit many millions of men swarmed to the East; the words of an hallucinated person … have created the force necessary to triumph over the Graeco-Roman world; an obscure monk like Luther set Europe ablaze and bathed in blood. The voice of a Galileo or a Newton will never have the least echo among the masses. The inventors of genius transform a civilization. The fanatics and the hallucinated create history.
From Les Premières Civilisations (1889), 171. English in The Psychology of Peoples (1898), Book 1, Chap. 1, 204, tweaked by Webmaster. Original French text: “A la voix d'un Pierre l'Ermite, plusieurs millions d'hommes se sont précipités sur l'Orient; les paroles d'un halluciné … ont créé la force nécessaire pour triompher du vieux monde gréco-romain; un moine obscur, comme Luther, a mis l'Europe à feu et à sang. Ce n’est pas parmi les foules que la voix d’un Galilée ou d’un Newton aura jamais le plus faible écho. Les inventeurs de génie transforment une civilisation. Les fanatiques et les hallucinés créent l’histoire.”
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But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
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But why, it has been asked, did you go there [the Antarctic]? Of what use to civilization can this lifeless continent be? ... [Earlier] expeditions contributed something to the accumulating knowledge of the Antarctic ... that helps us thrust back further the physical and spiritual shadows enfolding our terrestrial existence. Is it not true that one of the strongest and most continuously sustained impulses working in civilization is that which leads to discovery? As long as any part of the world remains obscure, the curiosity of man must draw him there, as the lodestone draws the mariner's needle, until he comprehends its secret.
In 'Hoover Presents Special Medal to Byrd...', New York Times (21 Jun 1930), 1.
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But, further, no animal can live upon a mixture of pure protein, fat and carbohydrate, and even when the necessary inorganic material is carefully supplied, the animal still cannot flourish. The animal body is adjusted to live either upon plant tissues or the tissues of other animals, and these contain countless substances other than the proteins, carbohydrates and fats... In diseases such as rickets, and particularly in scurvy, we have had for long years knowledge of a dietetic factor; but though we know how to benefit these conditions empirically, the real errors in the diet are to this day quite obscure. They are, however, certainly of the kind which comprises these minimal qualitative factors that I am considering.
'The Analyst and the Medical Man', The Analyst (1906), 31, 395-6.
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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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Embryology will often reveal to us the structure, in some degree obscured, of the prototype of each great class.
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Experts always tend to obscure the obvious.
In The Nature of the Stratigraphical Record (1973), 7.
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Finally, to the theme of the respiratory chain, it is especially noteworthy that David Kellin's chemically simple view of the respiratory chain appears now to have been right all along–and he deserves great credit for having been so reluctant to become involved when the energy-rich chemical intermediates began to be so fashionable. This reminds me of the aphorism: 'The obscure we see eventually, the completely apparent takes longer'.
'David Kellin's Respiratory Chain Concept and Its Chemiosmotic Consequences', Nobel Lecture (8 Dec 1978). In Nobel Lectures: Chemistry 1971-1980 (1993), 325.
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He who makes two blades of grass grow where one grew before is the benefactor of mankind, but he who obscurely worked to find the laws of such growth is the intellectual superior as well as the greater benefactor of mankind.
Presidential Address (28 Oct 1899) to the Physical Society of America Meeting, New York. Printed in American Journal of Science (Dec 1899). Reprinted in the The Johns Hopkins University Circular (Mar 1900), 19, No. 143, 17. Compare earlier remark by Jonathan Swift, beginning “whoever could make two ears of corn…” on the Jonathan Swift Quotes page of this website.
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However much the pits may be apparent, yet none, as far as can be comprehended by the senses, passes through the septum of the heart from the right ventricle into the left. I have not seen even the most obscure passages by which the septum of the ventricles is pervious, although they are mentioned by professors of anatomy since they are convinced that blood is carried from the right ventricle into the left. As a result—as I shall declare more openly elsewhere—I am in no little doubt regarding the function of the heart in this part.
In De Humani Corporis Fabrica Libri Septem [Seven Books on the Structure of the Human Body] (revised ed. 1555), 734. Quoted and trans. in Charles Donald O'Malley, Andreas Vesalius of Brussels, 1514-1564 (1964), 281.
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I have destroyed almost the whole race of frogs, which does not happen in that savage Batrachomyomachia of Homer. For in the anatomy of frogs, which, by favour of my very excellent colleague D. Carolo Fracassato, I had set on foot in order to become more certain about the membranous substance of the lungs, it happened to me to see such things that not undeservedly I can better make use of that [saying] of Homer for the present matter—
“I see with my eyes a work trusty and great.”
For in this (frog anatomy) owing to the simplicity of the structure, and the almost complete transparency of the vessels which admits the eye into the interior, things are more clearly shown so that they will bring the light to other more obscure matters.
De Pulmonibus (1661), trans. James Young, Proceedings of the Royal Society of Medicine (1929-30), 23, 7.
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I shall never forget my first encounter with gorillas. Sound preceded sight. Odor preceded sound in the form of an overwhelming, musky-barnyard, humanlike scent. The air was suddenly rent by a high-pitched series of screams followed by the rhythmic rondo of sharp pok-pok chestbeats from a great silverbacked male obscured behind what seemed an impenetrable wall of vegetation.
Describing her 1963 trip to Kabara in Gorillas in the Mist (1983), 3. (The screams and chest-beating were of alarm, not ferocity.)
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I wanted to preserve the spontaneity of thought in speech… [and to] guard the spontaneity of the argument. A spoken argument is informal and heuristic; it singles out the heart of the matter and shows in what way it is crucial and new; and it gives the direction and line of the solution so that, simplified as it is, still the logic is right. For me, this philosophic form of argument is the foundation of science, and nothing should be allowed to obscure it.
On his philosophy in presenting the TV series, from which the book followed. In 'Foreward', The Ascent of Man, (1973), 14-15.
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If the man of science chose to follow the example of historians and pulpit-orators, and to obscure strange and peculiar phenomena by employing a hollow pomp of big and sounding words, this would be his opportunity; for we have approached one of the greatest mysteries which surround the problem of animated nature and distinguish it above all other problems of science. To discover the relations of man and woman to the egg-cell would be almost equivalent of the egg-cell in the body of the mother, the transfer to it by means of the seed, of the physical and mental characteristics of the father, affect all the questions which the human mind has ever raised in regard to existence.
Quoted in Ernst Heinrich Philipp August Haeckel, The Evolution of Man (1897), vol 1, 148.
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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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In the vast cosmical changes, the universal life comes and goes in unknown quantities ... sowing an animalcule here, crumbling a star there, oscillating and winding, ... entangling, from the highest to the lowest, all activities in the obscurity of a dizzying mechanism, hanging the flight of an insect upon the movement of the earth... Enormous gearing, whose first motor is the gnat, and whose last wheel is the zodiac.
Victor Hugo and Charles E. Wilbour (trans.), Les Misérables (1862), 41.
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It is a very strange thing to reflect that but for the invention of Professor Haber the Germans could not have continued the War after their original stack of nitrates was exhausted. The invention of this single man has enabled them, utilising the interval in which their accumulations were used up, not only to maintain an almost unlimited supply of explosives for all purposes, but to provide amply for the needs of agriculture in chemical manures. It is a remarkable fact, and shows on what obscure and accidental incidents the fortunes of possible the whole world may turn in these days of scientific discovery.
[During World War I, Fritz Haber and Karl Bosch invented a large scale process to cause the direct combination of hydrogen and nitrogen gases to chemically synthesize ammonia, thus providing a replacement for sodium nitrate in the manufacture of explosives and fertilizers.]
Parliamentary debate (25 Apr 1918). In Winston Churchill, Richard Langworth (ed.), Churchill by Himself: The Definitive Collection of Quotations (2008), 469. by Winston Churchill, Richard Langworth
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It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
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It is well to observe the force and virtue and consequence of discoveries, and these are to be seen nowhere more conspicuously than in those three which were unknown to the ancients, and of which the origins, although recent, are obscure and inglorious; namely, printing, gunpowder, and the magnet. For these three have changed the whole face and state of things throughout the world; the first in literature, the second in warfare, the third in navigation; whence have followed innumerable changes, insomuch that no empire, no sect, no star seems to have exerted greater power and influence in human affairs than these mechanical discoveries.
From Novum Organum (1620), Book 1, Aphorism 129. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 114.
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Learning obscures as well as illustrates; it heaps up chaff when there is no more wheat.
In 'On the Interpretation of Scripture', Essays and Reviews (1860), 337.
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Lord Kelvin had, in a manner hardly and perhaps never equalled before, except by Archimedes, the power of theorizing on the darkest, most obscure, and most intimate secrets of Nature, and at the same time, and almost in the same breath, carrying out effectively and practically some engineering feat, or carrying to a successful issue some engineering invention. He was one of the leaders in the movement which has compelled all modern engineers worthy of the name to be themselves men not merely of practice, but of theory, to carry out engineering undertakings in the spirit of true scientific inquiry and with an eye fixed on the rapidly growing knowledge of the mechanics of Nature, which can only be acquired by the patient work of physicists and mathematicians in their laboratories and studies.
In Speech (May 1921) to the Institute of Civil Engineers, to award the newly created Kelvin Medal. As quoted in Sarah Knowles Bolton, 'Lord Kelvin', Famous Men of Science (1889, Revised Ed. 1926), 316-317.
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Magic and all that is ascribed to it is a deep presentiment of the powers of science. The shoes of swiftness, the sword of sharpness, the power of subduing the elements, of using the secret virtues of minerals, of understanding the voices of birds, are the obscure efforts of the mind in a right direction.
From 'History', collected in The Complete Works of Ralph Waldo Emerson (1903), 34.
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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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Mediocre men often have the most acquired knowledge. It is in the darker. It is in the darker regions of science that great men are recognized; they are marked by ideas which light up phenomena hitherto obscure and carry science forward.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (reprint 1999), 42.
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Never leave an unsolved difficulty behind. I mean, don’t go any further in that book till the difficulty is conquered. In this point, Mathematics differs entirely from most other subjects. Suppose you are reading an Italian book, and come to a hopelessly obscure sentence—don’t waste too much time on it, skip it, and go on; you will do very well without it. But if you skip a mathematical difficulty, it is sure to crop up again: you will find some other proof depending on it, and you will only get deeper and deeper into the mud.
From letter to Edith Rix with hints for studying (about Mar 1885), in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 241.
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Newton advanced, with one gigantic stride, from the regions of twilight into the noon day of science. A Boyle and a Hooke, who would otherwise have been deservedly the boast of their century, served but as obscure forerunners of Newton's glories.
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1845), 5.
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No branches of historical inquiry have suffered more from fanciful speculation than those which relate to the origin and attributes of the races of mankind. The differentiation of these races began in prehistoric darkness, and the more obscure a subject is, so much the more fascinating. Hypotheses are tempting, because though it may be impossible to verify them, it is, in the paucity of data, almost equally impossible to refute them.
Creighton Lecture delivered before the University of London on 22 Feb 1915. Race Sentiment as a Factor in History (1915), 3.
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No other part of science has contributed as much to the liberation of the human spirit as the Second Law of Thermodynamics. Yet, at the same time, few other parts of science are held to be so recondite. Mention of the Second Law raises visions of lumbering steam engines, intricate mathematics, and infinitely incomprehensible entropy. Not many would pass C.P. Snow’s test of general literacy, in which not knowing the Second Law is equivalent to not having read a work of Shakespeare.
In The Second Law (1984), Preface, vii.
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Not only in antiquity but in our own times also laws have been passed...to secure good conditions for workers; so it is right that the art of medicine should contribute its portion for the benefit and relief of those for whom the law has shown such foresight...[We] ought to show peculiar zeal...in taking precautions for their safety. I for one have done all that lay in my power, and have not thought it beneath me to step into workshops of the meaner sort now and again and study the obscure operations of mechanical arts.
De Morbis Artificum Diatriba (1713). Translation by W.C.Wright, in A.L.Birmingham Classics of Medicine Library (1983). Quoted in Edward J. Huth, T. J. Murray (eds.), Medicine in Quotations: Views of Health and Disease Through the Ages
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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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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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People who write obscurely are either unskilled in writing or up to mischief.
From 'Science and Literature', Pluto’s Republic (1984), 52.
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Promoting science isn’t just about providing resources—it’s about protecting free and open inquiry. It’s about ensuring that facts and evidence are never twisted or obscured by politics or ideology. It’s about listening to what our scientists have to say, even when it’s inconvenient—especially when it’s inconvenient.
From weekly Democratic address as President-Elect, online video (20 Dec 2008), announcing his selection of science and technology advisers. C-Span video 282995-102.
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Religion is so great a thing that it is right that those who will not take the trouble to seek it if it be obscure, should be deprived of it.
In Pensées (1670), Section 24, No. 10. As translated in Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', No. 574, collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 92. From the original French, “La religion est une chose si grande, qu’il est juste que ceux qui ne voudraient pas prendre la peine de la chercher, si elle est obscure, en soient privés,” in Ernest Havet (ed.), Pensées de Pascal (1892), 422.
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Science is the tool of the Western mind and with it more doors can be opened than with bare hands. It is part and parcel of our knowledge and obscures our insight only when it holds that the understanding given by it is the only kind there is.
Carl Jung
In Jung’s 'Commentary' as translated for the English edition of Richard Wilhelm, The Secret Of The Golden Flower: A Chinese Book of Life (1999, 2013), 82.
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Science keeps religion from sinking into the valley of crippling irrationalism and paralyzing obscurantism. Religion prevents science from falling into the marsh of obsolete materialism and moral nihilism.
In 'A Tough Mind and a Tender Heart', Strength To Love (1963), 3.
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Since the stomach gives no obvious external sign of its workings, investigators of gastric movements have hitherto been obliged to confine their studies to pathological subjects or to animals subjected to serious operative interference. Observations made under these necessarily abnormal conditions have yielded a literature which is full of conflicting statements and uncertain results. The only sure conclusion to be drawn from this material is that when the stomach receives food, obscure peristaltic contractions are set going, which in some way churn the food to a liquid chyme and force it into the intestines. How imperfectly this describes the real workings of the stomach will appear from the following account of the actions of the organ studied by a new method. The mixing of a small quantity of subnitrate of bismuth with the food allows not only the contractions of the gastric wall, but also the movements of the gastric contents to be seen with the Röntgen rays in the uninjured animal during normal digestion.
In 'The Movements of the Stomach Studied by Means of the Röntgen Rays,' American Journal of Physiology (1898), 1, 359-360.
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Some experience of popular lecturing had convinced me that the necessity of making things plain to uninstructed people, was one of the very best means of clearing up the obscure corners in one's own mind.
'Preface'. In Man's Place in Nature and Other Anthropological Essays. Collected Essays (1894), Vol. 7, Preface, ix.
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The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.
In Tobias Dantzig and Joseph Mazur (ed.), Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 99.
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The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a woman, who because of her sex and our prejudices encounters infinitely more obstacles that an man in familiarizing herself with complicated problems, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, without doubt she must have the noblest courage, quite extraordinary talents and superior genius.
in a letter to Sophie Germain (c.April 1807)
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The game of status seeking, organized around committees, is played in roughly the same fashion in Africa and in America and in the Soviet Union. Perhaps the aptitude for this game is a part of our genetic inheritance, like the aptitude for speech and for music. The game has had profound consequences for science. In science, as in the quest for a village water supply, big projects bring enhanced status; small projects do not. In the competition for status, big projects usually win, whether or not they are scientifically justified. As the committees of academic professionals compete for power and influence, big science becomes more and more preponderant over small science. The large and fashionable squeezes out the small and unfashionable. The space shuttle squeezes out the modest and scientifically more useful expendable launcher. The Great Observatory squeezes out the Explorer. The centralized adduction system squeezes out the village well. Fortunately, the American academic system is pluralistic and chaotic enough that first-rate small science can still be done in spite of the committees. In odd corners, in out-of the-way universities, and in obscure industrial laboratories, our Fulanis are still at work.
From a Danz lecture at University of Washington, 'Six Cautionary Tales for Scientists' (1988), collected in From Eros to Gaia (1992), Vol. 5, 19.
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The history of chemistry is properly divided into the mythologic, the obscure, and the certain. The first period exhibits it from its infancy, deformed by fictions, until the destruction of the library of Alexandria by the Arabs. —The second, though freed in some measure from these absurdities, yet is still clothed in numberless enigmas and allegorical expressions.— The third period commences at the middle of the seventeenth century, with the first establishment of societies and academies of science; of which the wise associates, in many places uniting their efforts, determined to pursue the study of Natural Philosophy by observation and experiments, and candidly to publish their attempts in a general account of their transactions.
In Essays, Physical and Chemical (1791), 4, translated from the original Latin.
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The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adhering to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depends upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.
Address to the University of Cambridge upon being elected Lucasian Professor of Mathematics (14 Mar 1664). In Mathematical Lectures (1734), xxviii.
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The mental process by which hypotheses are suggested is obscure. Ordinarily they flash into consciousness without premonition, and it would he easy to ascribe them to a mysterious intuition or creative faculty; but this would contravene one of the broadest generalizations of modern psychology. Just as in the domain of matter nothing is created from nothing, just as in the domain of life there is no spontaneous generation, so in the domain of mind there are no ideas which do not owe their existence to antecedent ideas which stand in the relation of parent to child.
In Address (11 Dec 1895) as President of the Geological Society, 'The Origin of Hypotheses, illustrated by the Discussion of a Topographical Problem', printed as Presidential Address of Grove Karl Gilbert (1896), 4. Also collected in Science (1896), 3, 2.
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The most useless investigation may prove to have the most startling practical importance: Wireless telegraphy might not yet have come if Clerk Maxwell had been drawn away from his obviously “useless” equations to do something of more practical importance. Large branches of chemistry would have remained obscure had Willard Gibbs not spent his time at mathematical calculations which only about two men of his generation could understand.
A.V. Hill
Quoted in Larry R. Squire (ed.), The History of Neuroscience in Autobiography (1996), Vol. 1, 350-351. The above is a highlight excerpted from a longer quote beginning “To prove to an indignant questioner ….” in this same collection for A. V. Hill.
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The prominent reason why a mathematician can be judged by none but mathematicians, is that he uses a peculiar language. The language of mathesis is special and untranslatable. In its simplest forms it can be translated, as, for instance, we say a right angle to mean a square corner. But you go a little higher in the science of mathematics, and it is impossible to dispense with a peculiar language. It would defy all the power of Mercury himself to explain to a person ignorant of the science what is meant by the single phrase “functional exponent.” How much more impossible, if we may say so, would it be to explain a whole treatise like Hamilton’s Quaternions, in such a wise as to make it possible to judge of its value! But to one who has learned this language, it is the most precise and clear of all modes of expression. It discloses the thought exactly as conceived by the writer, with more or less beauty of form, but never with obscurity. It may be prolix, as it often is among French writers; may delight in mere verbal metamorphoses, as in the Cambridge University of England; or adopt the briefest and clearest forms, as under the pens of the geometers of our Cambridge; but it always reveals to us precisely the writer’s thought.
In North American Review (Jul 1857), 85, 224-225.
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The student of medicine can no more hope to advance in the mastery of his subject with a loose and careless mind than the student of mathematics. If the laws of abstract truth require such rigid precision from those who study them, we cannot believe the laws of nature require less. On the contrary, they would seem to require more; for the facts are obscure, the means of inquiry imperfect, and in every exercise of the mind there are peculiar facilities to err.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 6.
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The student should read his author with the most sustained attention, in order to discover the meaning of every sentence. If the book is well written, it will endure and repay his close attention: the text ought to be fairly intelligible, even without illustrative examples. Often, far too often, a reader hurries over the text without any sincere and vigorous effort to understand it; and rushes to some example to clear up what ought not to have been obscure, if it had been adequately considered. The habit of scrupulously investigating the text seems to me important on several grounds. The close scrutiny of language is a very valuable exercise both for studious and practical life. In the higher departments of mathematics the habit is indispensable: in the long investigations which occur there it would be impossible to interpose illustrative examples at every stage, the student must therefore encounter and master, sentence by sentence, an extensive and complicated argument.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 67.
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There are many things akin to highest deity that are still obscure. Some may be too subtle for our powers of comprehension, others imperceptible to us because such exalted majesty conceals itself in the holiest part of its sanctuary, forbidding access to any power save that of the spirit. How many heavenly bodies revolve unseen by human eye!
From Quaestiones Naturales as translated in Charles Singer, From Magic to Science (1958), 57.
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There are three kinds of explanation in science: explanations which throw a light upon, or give a hint at a matter; explanations which do not explain anything; and explanations which obscure everything.
Aphorism 82 from Selected Aphorisms from the Lyceum (1797-1800). In Friedrich Schlegel, translated by Ernst Behler and Roman Struc, Dialogue on Poetry and Literary Aphorisms (trans. 1968), 138.
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There must be some bond of union between mass and the chemical elements; and as the mass of a substance is ultimately expressed (although not absolutely, but only relatively) in the atom, a functional dependence should exist and be discoverable between the individual properties of the elements and their atomic weights. But nothing, from mushrooms to a scientific dependence can be discovered without looking and trying. So I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and soon this convinced me that the properties of the elements are in periodic dependence upon their atomic weights; and although I had my doubts about some obscure points, yet I have never doubted the universality of this law, because it could not possibly be the result of chance.
Principles of Chemistry (1905), Vol. 2, 18.
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To prove to an indignant questioner on the spur of the moment that the work I do was useful seemed a thankless task and I gave it up. I turned to him with a smile and finished, “To tell you the truth we don’t do it because it is useful but because it’s amusing.” The answer was thought of and given in a moment: it came from deep down in my soul, and the results were as admirable from my point of view as unexpected. My audience was clearly on my side. Prolonged and hearty applause greeted my confession. My questioner retired shaking his head over my wickedness and the newspapers next day, with obvious approval, came out with headlines “Scientist Does It Because It’s Amusing!” And if that is not the best reason why a scientist should do his work, I want to know what is. Would it be any good to ask a mother what practical use her baby is? That, as I say, was the first evening I ever spent in the United States and from that moment I felt at home. I realised that all talk about science purely for its practical and wealth-producing results is as idle in this country as in England. Practical results will follow right enough. No real knowledge is sterile. The most useless investigation may prove to have the most startling practical importance: Wireless telegraphy might not yet have come if Clerk Maxwell had been drawn away from his obviously “useless” equations to do something of more practical importance. Large branches of chemistry would have remained obscure had Willard Gibbs not spent his time at mathematical calculations which only about two men of his generation could understand. With this faith in the ultimate usefulness of all real knowledge a man may proceed to devote himself to a study of first causes without apology, and without hope of immediate return.
A.V. Hill
From lecture to a scientific society in Philadelphia on “The Mechanism of the Muscle” given by invitation after he received a Nobel Prize for that work. The quote is Hill’s response to a post-talk audience question asking disapprovingly what practical use the speaker thought there was in his research. The above quoted answer, in brief, is—for the intellectual curiosity. As quoted about Hill by Bernard Katz in his own autobiographical chapter, 'Sir Bernard Katz', collected in Larry R. Squire (ed.), The History of Neuroscience in Autobiography (1996), Vol. 1, 350-351. Two excerpts from the above have been highlighted as standalone quotes here in this same quote collection for A. V. Hill. They begin “All talk about science…” and “The most useless investigation may prove…”.
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To suppose that so perfect a system as that of Euclid’s Elements was produced by one man, without any preceding model or materials, would be to suppose that Euclid was more than man. We ascribe to him as much as the weakness of human understanding will permit, if we suppose that the inventions in geometry, which had been made in a tract of preceding ages, were by him not only carried much further, but digested into so admirable a system, that his work obscured all that went before it, and made them be forgot and lost.
In Essay on the Powers of the Human Mind (1812), Vol. 2, 368.
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We live on an obscure hunk of rock and metal circling a humdrum sun, which is on the outskirts of a perfectly ordinary galaxy comprised of 400 billion other suns, which, in turn, is one of some hundred billion galaxies that make up the universe, which, current thinking suggests, is one of a huge number—perhaps an infinite number—of other closed-off universes. From that perspective, the idea that we’re at the center, that we have some cosmic importance, is ludicrous.
From interview with Linda Obst in her article 'Valentine to Science', in Interview (Feb 1996). Quoted and cited in Tom Head (ed.), Conversations with Carl Sagan (2006), ix, and cited on p.xix.
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What hopes filled me when I discovered that there were laws behind so many obscure phenomena!
In Speech (27 Dec 1892) at the Golden Jubilee celebration for Pasteur's 70th birthday. As translated in Nature (1893), 47, 205.
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What is the use of this history, what the use of all this minute research? I well know that it will not produce a fall in the price of pepper, a rise in that of crates of rotten cabbages, or other serious events of this kind, which cause fleets to be manned and set people face to face intent upon one another's extermination. The insect does not aim at so much glory. It confines itself to showing us life in the inexhaustible variety of its manifestations; it helps us to decipher in some small measure the obscurest book of all, the book of ourselves.
Introducing the natural history and his study of the insect Minotaurus typhoeus. In Jean-Henri Fabre and Alexander Teixeira de Mattos (trans.), The Life and Love of the Insect (1918), 128.
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Who could have believed that … the introduction into the human body of a small particle of matter from a cow’s udder might be the means of saving thousands of human lives? We learn from these and innumerable similar instances that the highest truths lie hid in the simplest facts; that, unlike human proclamations, nature’s teachings are not by sound of trumpet, but often in the stillest voice, by indirect hints and obscure suggestions.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 109.
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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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- 70 -
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- 50 -
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- 40 -
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- 20 -
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