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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index O > Category: Obscurity

Obscurity Quotes (28 quotes)

Il ne peut y avoir de langage plus universel et plus simple, plus exempt d’erreurs et d’obscurités, c'est-à-dire plus digne d'exprimer les rapports invariables des êtres naturels.
There cannot be a language more universal and more simple, more free from errors and obscurities, … more worthy to express the invariable relations of all natural things. [About mathematical analysis.]
From Théorie Analytique de la Chaleur (1822), xiv, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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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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Omnis perfectio in hac vita quandam imperfectionem sibi habet annexam: et omnis speculatio nostra quadam caligine non caret.
Every perfection in this life has some imperfection clinging to it; and no speculation is without a certain obscurity.
In De Imitatione Christi (1709), Book 1, Chap. 3, 6. As translated in Of the Imitation of Christ (1903), 8.
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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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Among your pupils, sooner or later, there must be one. who has a genius for geometry. He will be Sylvester’s special pupil—the one pupil who will derive from his master, knowledge and enthusiasm—and that one pupil will give more reputation to your institution than the ten thousand, who will complain of the obscurity of Sylvester, and for whom you will provide another class of teachers.
Letter (18 Sep 1875) recommending the appointment of J.J. Sylvester to Daniel C. Gilman. In Daniel C. Gilman Papers, Ms. 1, Special Collections Division, Milton S. Eisenhower Library, Johns Hopkins University. As quoted in Karen Hunger Parshall, 'America’s First School of Mathematical Research: James Joseph Sylvester at The Johns Hopkins University 1876—1883', Archive for History of Exact Sciences (1988), 38, No. 2, 167.
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Being also in accord with Goethe that discoveries are made by the age and not by the individual, I should consider the instances to be exceedingly rare of men who can be said to be living before their age, and to be the repository of knowledge quite foreign to the thought of the time. The rule is that a number of persons are employed at a particular piece of work, but one being a few steps in advance of the others is able to crown the edifice with his name, or, having the ability to generalise already known facts, may become in time to be regarded as their originator. Therefore it is that one name is remembered whilst those of coequals have long been buried in obscurity.
In Historical Notes on Bright's Disease, Addison's Disease, and Hodgkin's Disease', Guy's Hospital Reports (1877), 22, 259-260.
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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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Confined to its true domain, mathematical reasoning is admirably adapted to perform the universal office of sound logic: to induce in order to deduce, in order to construct. … It contents itself to furnish, in the most favorable domain, a model of clearness, of precision, and consistency, the close contemplation of which is alone able to prepare the mind to render other conceptions also as perfect as their nature permits. Its general reaction, more negative than positive, must consist, above all, in inspiring us everywhere with an invincible aversion for vagueness, inconsistency, and obscurity, which may always be really avoided in any reasoning whatsoever, if we make sufficient effort.
In Synthèse Subjective (1856), 98. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202-203. From the original French, “Bornée à son vrai domaine, la raison mathématique y peut admirablement remplir l’office universel de la saine logique: induire pour déduire, afin de construire. … Elle se contente de former, dans le domaine le plus favorable, un type de clarté, de précision, et de consistance, dont la contemplation familière peut seule disposer l’esprit à rendre les autres conceptions aussi parfaites que le comporte leur nature. Sa réaction générale, plus négative que positive, doit surtout consister à nous inspirer partout une invincible répugnance pour le vague, l’incohérence, et l’obscurité, que nous pouvons réellement éviter envers des pensées quelconques, si nous y faisons assez d’efforts.”
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Geologists have usually had recourse for the explanation of these changes to the supposition of sundry violent and extraordinary catastrophes, cataclysms, or general revolutions having occurred in the physical state of the earth's surface.
As the idea imparted by the term Cataclysm, Catastrophe, or Revolution, is extremely vague, and may comprehend any thing you choose to imagine, it answers for the time very well as an explanation; that is, it stops further inquiry. But it also has had the disadvantage of effectually stopping the advance of science, by involving it in obscurity and confusion.
Considerations on Volcanoes (1825), iv.
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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 devote all my efforts to bring light into the immense obscurity that today reigns in Analysis. It so lacks any plan or system, that one is really astonished that so many people devote themselves to it—and, still worse, it is absolutely devoid of any rigour.
In Oeuvres (1826), Vol. 2, 263. As translated and cited in Ernst Hairer and Gerhard Wanner Analysis by Its History (2008), 188. From the original French, “Je consacrerai toutes mes forces à répandre de la lumière sur l’immense obscurité qui règne aujourd’hui dans l’Analyse. Elle est tellement dépourvue de tout plan et de tout système, qu’on s’étonne seulement qu’il y ait tant de gens qui s’y livrent—et ce qui pis est, elle manque absolument de rigueur.”
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I trust ... I have succeeded in convincing you that modern chemistry is not, as it has so long appeared, an ever-growing accumulation of isolated facts, as impossible for a single intellect to co-ordinate as for a single memory to grasp.
The intricate formulae that hang upon these walls, and the boundless variety of phenomena they illustrate, are beginning to be for us as a labyrinth once impassable, but to which we have at length discovered the clue. A sense of mastery and power succeeds in our minds to the sort of weary despair with which we at first contemplated their formidable array. For now, by the aid of a few general principles, we find ourselves able to unravel the complexities of these formulae, to marshal the compounds which they represent in orderly series; nay, even to multiply their numbers at our will, and in a great measure to forecast their nature ere we have called them into existence. It is the great movement of modern chemistry that we have thus, for an hour, seen passing before us. It is a movement as of light spreading itself over a waste of obscurity, as of law diffusing order throughout a wilderness of confusion, and there is surely in its contemplation something of the pleasure which attends the spectacle of a beautiful daybreak, something of the grandeur belonging to the conception of a world created out of chaos.
Concluding remark for paper presented at the Friday Discourse of the the Royal Institution (7 Apr 1865). 'On the Combining Power of Atoms', Proceedings of the Royal Institution (1865), 4, No. 42, 416.
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I worked for many years in almost total obscurity doing what I thought was interesting.
In interview with Associated Press, as quoted in Sean Trembath, 'Chemist Henry Taube Was Saskatchewan's First Nobel Laureate', Saskatoon StarPhoenix (5 Jan 2017)
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In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain.
In Geometric Researches on the Theory of Parallels (1840), as translated by George Bruce Halstead (new ed. 1914) 11.
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It must happen that in some cases the author is not understood, or is very imperfectly understood; and the question is what is to be done. After giving a reasonable amount of attention to the passage, let the student pass on, reserving the obscurity for future efforts. … The natural tendency of solitary students, I believe, is not to hurry away prematurely from a hard passage, but to hang far too long over it; the just pride that does not like to acknowledge defeat, and the strong will that cannot endure to be thwarted, both urge to a continuance of effort even when success seems hopeless. It is only by experience we gain the conviction that when the mind is thoroughly fatigued it has neither the power to continue with advantage its course in .an assigned direction, nor elasticity to strike out a new path; but that, on the other hand, after being withdrawn for a time from the pursuit, it may return and gain the desired end.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 68.
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Kirchhoff’s whole tendency, and its true counterpart, the form of his presentation, was different [from Maxwell’s “dramatic bulk”]. … He is characterized by the extreme precision of his hypotheses, minute execution, a quiet rather than epic development with utmost rigor, never concealing a difficulty, always dispelling the faintest obscurity. … he resembled Beethoven, the thinker in tones. — He who doubts that mathematical compositions can be beautiful, let him read his memoir on Absorption and Emission … or the chapter of his mechanics devoted to Hydrodynamics.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 30, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 187. From the original German, “Kirchhoff … seine ganze Richtung war eine andere, und ebenso auch deren treues Abbild, die Form seiner Darstellung. … Ihn charakterisirt die schärfste Präcisirung der Hypothesen, feine Durchfeilung, ruhige mehr epische Fortentwicklung mit eiserner Consequenz ohne Verschweigung irgend einer Schwierigkeit, unter Aufhellung des leisesten Schattens. … er glich dem Denker in Tönen: Beethoven. – Wer in Zweifel zieht, dass mathematische Werke künstlerisch schön sein können, der lese seine Abhandlung über Absorption und Emission oder den der Hydrodynamik gewidmeten Abschnitt seiner Mechanik.” The memoir reference is Gesammelte Abhandlungen (1882), 571-598.
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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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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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Our posturing, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.
…...
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The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there… If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little….
In Elements de la géométrie de l'infini (1727), Preface, ciii. Quoted as a footnote to Michael S. Mahoney, 'Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century', collected in David C. Lindberg and Robert S. Westman (eds.), Reappraisals of the Scientific Revolution (1990), 489-490, footnote 46
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The reputation of science which ought to be the most lasting, as synonymous with truth, is often the least so. One discovery supersedes another; and the progress of light throws the past into obscurity. What is become of the Blacks, the Lavoisiers, the Priestleys, in chemistry? … When any set of men think theirs the only science worth studying, and themselves the only infallible persons in it, it is a sign how frail the traces are of past excellence in it.
Characteristics: In the Manner of Rochefoucault's Maxims (1837), 148-149.
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The science of metaphysics promises more than it performs. The study of … metaphysics begins with a torrent of tropes, and a copious current of words, yet loses itself at last, in obscurity and conjecture, like the Niger in his barren deserts of sand.
Reflection 342, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 162.
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The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.
In Essai sur les machines en général (1783), conclusion, as translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840 (1990), Vol. 1, 32.
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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 could not be a language more universal and more simple, more exempt from errors and obscurities, that is to say, more worthy of expressing the invariable relations of natural objects. Considered from this point of view, it is coextensive with nature itself; it defines all the sensible relations, measures the times, the spaces, the forces, the temperatures; this difficult science is formed slowly, but it retains all the principles it has once acquired. It grows and becomes more certain without limit in the midst of so many errors of the human mind.
From Théorie Analytique de la Chaleur, Discours Préliminaire (Theory of Heat, Introduction), quoted as translated in F.R. Moulton, 'The Influence of Astronomy on Mathematics', Science (10 Mar 1911), N.S. Vol. 33, No. 845, 359.
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Tungsten, X-rays, and Coolidge form a trinity that has left an indelible impression upon our life and times. The key word in this triad is Coolidge, for his work brought the element tungsten from laboratory obscurity to the central role of the industrial stage and gave the X-ray a central role in the progress of medicine throughout the world.
In National Academy of Sciences, Biographical Memoirs, Vol. 53, 141.
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When one begins to speak of something it sounds plausible, but when we reflect on it we find it false. The initial impression a thing makes on my mind is very important. Taking an overall view of a thing the mind sees every side of it obscurely, which is often of more value than a clear idea of only one side of it.
Aphorism 47 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 50-51.
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While Newton seemed to draw off the veil from some of the mysteries of nature, he showed at the same time the imperfections of the mechanical philosophy; and thereby restored her ultimate secrets to that obscurity, in which they ever did and ever will remain.
The History Of Great Britain, Containing the Commonwealth and the Reigns of Charles II. and James II. (2nd ed. 1759), Vol. 2, 450.
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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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