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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 P > Category: Precede

Precede Quotes (23 quotes)

Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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A mathematical science is any body of propositions which is capable of an abstract formulation and arrangement in such a way that every proposition of the set after a certain one is a formal logical consequence of some or all the preceding propositions. Mathematics consists of all such mathematical sciences.
In Lectures on Fundamental Concepts of Algebra and Geometry (1911), 222.
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Anyone who thinks we can continue to have world wars but make them nice polite affairs by outlawing this weapon or that should meditate upon the outlawing of the cross-bow by Papal authority. Setting up the machinery for international law and order must surely precede disarmament. The Wild West did not abandon its shooting irons till after sheriffs and courts were established.
Speech, American Library Assiciation Conference (3 Jul 1947), as quoted by Lawrence E. Davies in 'Army's Atomic Bid Viewed in Making', New York Times (4 Jul 1947), 11.
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Cellular pathology is not an end if one cannot see any alteration in the cell. Chemistry brings the clarification of living processes nearer than does anatomy. Each anatomical change must have been preceded by a chemical one.
Attributed in H. Coper and H. Herken, Deutsche Medizini Wochenschrift (18 Oct 1963), 88, No. 42, 2035, in the original German, “Nach der Überlieferung durch His soll Virchow geäußert haben: ‘Die Zellular-pathologie ist nicht am Ende, wenn man an einer Zelle keine Veränderungen mehr sehen kann. Die Chemie steht der Erklärung der Lebensvorgänge näher als die Anatomie. Jede anatomische Verände-rung setzt notwendig eine chemische voraus.’” As translated in Angel Pentschew,'Morphology and morphogenesis of lead encephalopathy', Acta Neuropathologica (Sep 1965) 5, No. 2, 133-160, as cited in I. Arthur Michaelson and Mitchell W. Sauerhoff, 'Animal Models of Human Disease: Severe and Mild Lead Encephalopathy in the Neonatal Rat', Environmental Health Perspectives (May 1974), 7, 204 & 223 footnote. Note: Although given in quotation marks in the original German text, the subject quote is almost definitely NOT verbatim, but only a paraphrase of Virchow’s teachings. The German text introduces the subject quote with, “Nach der Überlieferung durch His soll Virchow geäußert haben:…” which means, “According to tradition Virchow is said to have expressed:…” (using Google translate). However, it is useful as a succinct statement to the effect of what Virchow might say to summarize his doctrine.
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Focusing on the science-technology relationship may strike some as strange, because conventional wisdom views this relationship as an unproblematic given. … Technology is seen as being, at best, applied science … the conventional view perceives science as clearly preceding and founding technology. … Recent studies in the history of technology have begun to challenge this assumed dependency of technology on science. … But the conventional view of science is persistent.
In 'Technology and Science', Stephen V. Monsma (ed.), Responsible Technology: A Christian Perspective (1986), 78-79.
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Geometry may sometimes appear to take the lead of analysis, but in fact precedes it only as a servant goes before his master to clear the path and light him on his way. The interval between the two is as wide as between empiricism and science, as between the understanding and the reason, or as between the finite and the infinite.
From 'Astronomical Prolusions', Philosophical Magazine (Jan 1866), 31, No. 206, 54, collected in Collected Mathematical Papers of James Joseph Sylvester (1908), Vol. 2, 521.
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In all science, error precedes the truth, and it is better it should go first than last.
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In the sciences hypothesis always precedes law, which is to say, there is always a lot of tall guessing before a new fact is established. The guessers are often quite as important as the factfinders; in truth, it would not be difficult to argue that they are more important.
From Baltimore Evening Sun (6 Apr 1931). Collected in A Mencken Chrestomathy (1949, 1956), 329.
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It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously. I also cannot imagine some will or goal outside the human sphere has been cited as a statement that precedes the last three sentences here, but this might have originated in a paraphrase, a transcription error, or a misquotation; it does not appear in any editions of the essay which have thus far been checked.
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Just as the arts of tanning and dyeing were practiced long before the scientific principles upon which they depend were known, so also the practice of Chemical Engineering preceded any analysis or exposition of the principles upon which such practice is based.
In William H. Walker, Warren K. Lewis and William H. MacAdams, The Principles of Chemical Engineering (1923), Preface to 1st. edition, v.
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Not seldom did he [Sir William Thomson], in his writings, set down some mathematical statement with the prefacing remark “it is obvious that” to the perplexity of mathematical readers, to whom the statement was anything but obvious from such mathematics as preceded it on the page. To him it was obvious for physical reasons that might not suggest themselves at all to the mathematician, however competent.
As given in Life of Lord Kelvin (1910), Vol. 2, 1136. [Note: William Thomson, later became Lord Kelvin —Webmaster]
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Nothing drives progress like the imagination. The idea precedes the deed. The only exceptions are accidents and natural selection.
In The Marketing Imagination (1983, 1986), 127.
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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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Reach high, for stars lie hidden in your soul. Dream deep, for every dream precedes the goal.
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Remember this, the rule for giving an extempore lecture is—let the the mind rest from the subject entirely for an interval preceding the lecture, after the notes are prepared; the thoughts will ferment without your knowing it, and enter into new combinations; but if you keep the mind active upon the subject up to the moment, the subject will not ferment but stupefy.
In Letter (10 Jul 1854) to William Rowan Hamilton, collected in Robert Perceval Graves, Life of Sir William Rowan Hamilton (1882-89), Vol. 3, 487.
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The best education will not immunize a person against corruption by power. The best education does not automatically make people compassionate. We know this more clearly than any preceding generation. Our time has seen the best-educated society, situated in the heart of the most civilized part of the world, give birth to the most murderously vengeful government in history.
In Before the Sabbath (1979), 40-41.
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The conditions that direct the order of the whole of the living world around us, are marked by their persistence in improving the birthright of successive generations. They determine, at much cost of individual comfort, that each plant and animal shall, on the general average, be endowed at its birth with more suitable natural faculties than those of its representative in the preceding generation.
In 'The Observed Order of Events', Inquiries Into Human Faculty and Its Development (1882), 229.
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The Law of Causation, the recognition of which is the main pillar of inductive science, is but the familiar truth that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it.
In 'On the Law of Universal Causation', A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation, (1846), 197.
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The study of the theory of a physical science should be preceded by some general experimental acquaintance therewith, in order to secure the inimitable advantage of a personal acquaintance with something real and living.
Opening sentence of Electromagnetic Theory (1892), Vol. 2, 1.
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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 can hardly overestimate the significance of the fact that the scientific and religious propensities were one before they became two different activities. Their fundamental unity precedes their separateness.
Epigraph, without citation, in Michael Dowd, Thank God for Evolution: How the Marriage of Science and Religion Will Transform Your Life and Our World (2008), 108.
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We may safely say, that the whole form of modern mathematical thinking was created by Euler. It is only with the greatest difficulty that one is able to follow the writings of any author immediately preceding Euler, because it was not yet known how to let the formulas speak for themselves. This art Euler was the first one to teach.
As quoted in W. Ahrens Scherz und Ernst in der Mathematik (1904), 251. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 183.
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When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with the pencil on paper, he experiences a feeling of pride, of satisfaction. And justly so, for the fountain of all thought has been opened to him, the difference between the ideal and the real, potentia et actu, has become clear to him; henceforth the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.
In Sprüche in Reimen. Sprüche in Prosa. Ethisches (1850), Vol. 3, 214. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 67. From the original German, “Wenn der knabe zu begreifen anfängt, daß einem sichtbaren Punkte ein unsichtbarer vorhergehen müsse, daß der nächste Weg zwischen zwei Punkten schon als Linie gedacht werde, ehe sie mit dem Bleistift aufs Papier gezogen wird, so fühlt er einen gewissen Stolz, ein Behagen. Und nicht mit Unrecht; denn ihm ist die Quelle alles Denkens aufgeschlossen, Idee und Verwirklichtes, potentia et actu, ist ihm klargeworden; der Philosoph entdeckt ihm nichts Neues; dem Geometer war von seiner Seite der Grund alles Denkens aufgegangen.” The Latin phrase, “potentia et actu” means “potentiality and actuality”.
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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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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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- 10 -
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