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Today in Science History - Quickie Quiz
Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.”
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Know Quotes (536 quotes)

...the scientific cast of mind examines the world critically, as if many alternative worlds might exist, as if other things might be here which are not. Then we are forced to ask why what we see is present and not something else. Why are the Sun and moon and the planets spheres? Why not pyramids, or cubes, or dodecahedra? Why not irregular, jumbly shapes? Why so symmetrical, worlds? If you spend any time spinning hypotheses, checking to see whether they make sense, whether they conform to what else we know. Thinking of tests you can pose to substantiate or deflate hypotheses, you will find yourself doing science.
…...
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3. The Third Law of Ecology: Nature knows best.
In The Closing Circle: Nature, Man, and Technology (2014).
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Bei solchen chemischen Untersuchungen, die man zersetzende oder zergliedernde nennt, kommt es zunächst darauf an, zu ermitteln, mit welchen Stoffen man es zu thun hat, oder um chemisch zu reden, welche Stoffe in einem bestimmten Gemenge oder Gemisch enthalten sind. Hierzu bedient man sich sogenannter gegenwirkender Mittel, d. h. Stoffe, die bestimmte Eigenschaften und Eigenthümlichkeiten besitzen und die man aus Ueberlieferung oder eigner Erfahrung genau kennt, so daß die Veränderungen, welche sie bewirken oder erleiden, gleichsam die Sprache sind, mit der sie reden und dadurch dem Forscher anzeigen, daß der und der bestimmte Stoff in der fraglichen Mischung enthalten sei.
In the case of chemical investigations known as decompositions or analyses, it is first important to determine exactly what ingredients you are dealing with, or chemically speaking, what substances are contained in a given mixture or composite. For this purpose we use reagents, i.e., substances that possess certain properties and characteristics, which we well know from references or personal experience, such that the changes which they bring about or undergo, so to say the language that they speak thereby inform the researcher that this or that specific substance is present in the mixture in question.
From Zur Farben-Chemie Musterbilder für Freunde des Schönen und zum Gebrauch für Zeichner, Maler, Verzierer und Zeugdrucker [On Colour Chemistry...] (1850), Introduction. Translation tweaked by Webmaster from version in Herbert and W. Roesky and Klaud Möckel, translated from the original German by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 1.
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Ce grand ouvrage, toujours plus merveilleux à mesure qu’il est plus connu, nous donne une si grande idée de son ouvrier, que nous en sentons notre esprit accablé d’admiration et de respect.
[The Universe] This great work, always more amazing in proportion as it is better known, raises in us so grand an idea of its Maker, that we find our mind overwhelmed with feelings of wonder and adoration.
Original French and translation in Craufurd Tait Ramage (ed.) Beautiful Thoughts from French and Italian Authors (1866), 119-120.
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Ein Fachmann ist ein Mann, der einige der gröbsten Fehler kennt, die man in dem betreffenden Fach machen kann, und der sie deshalb zu vermeiden versteht.
An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them.
From the original German, “Ein Fachmann ist ein Mann, der einige der gröbsten Fehler kennt, die man in dem betreffenden Fach machen kann, und der sie deshalb zu vermeiden versteht”, in Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik (The Part and the Whole: Conversations in the Atomic Physics) (1969, 2001), 247. Excerpt in magazine article, 'Kein Chaos, aus dem nicht wieder Ordnung würde,' Die Zeit (22 August 1969), 34. English version in Werner Heisenberg and Arnold J. Pomerans (trans.), Physics and Beyond: Encounters and Conversations (1971), 210.
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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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Ich weiss viel. Ich weiss zu viel. Ich bin ein Quantengreis
I know a great deal. I know too much. I am a quantum ancient.
As quoted by Isidor Rabi in interview with Jeremy Bernstein for article, 'Physicist' The New Yorker (1970). Collected in Jeremy Bernstein, 'Rabi: The Modern Age', Experiencing Science (1978), 102. Both the original German and the translation come from Rabi.
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Je suis médecin. Je tiens boutique de mensonges. Je soulage, je console. Peut-on consoler et soulager sans mentir? … Les femmes et les médecins savent seuls combien le mensonge est nécessaire et bienfaisant aux hommes.
I am a physician. I keep a drug-shop of lies. I give relief, consolation. Can one console and relieve without lying? … Only women and doctors know how necessary and how helpful lies are to men.
From the fictional Dr. Trublet in Histoire Comique (1900), 171-172. As translated in Lewis P. Shanks, Anatole France (1919), 165.
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L’oeuvre de Pasteur est admirable; elle montre son génie, mais it faut avoir vécu dans son intimité pour connaître toute la bonté de son coeur.
The work of Pasteur is admirable; it shows his genius, but it must have been experienced intimately to know all the goodness of his heart.
Epigraph in René Vallery-Radot, La Vie de Pasteur (1900), title page. English by Google translation, tweaked by Webmaster. Pierre Paul Émile Roux had indeed known Pasteur well, as one of his closest collaborators.
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Nada me inspira más veneración y asombro que un anciano que sabe cambiar de opinión.
Nothing inspires more reverence and awe in me than an old man who knows how to change his mind.
In Pensamientos Escogidos (1924), 58.
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Socrates: Shall we set down astronomy among the objects of study? Glaucon: I think so, to know something about the seasons, the months and the years is of use for military purposes, as well as for agriculture and for navigation. Socrates: It amuses me to see how afraid you are, lest the common herd of people should accuse you of recommending useless studies.
Socrates
As quoted by Plato. In Richard Garnett, Léon Vallée, Alois Brandl (eds.), The Universal Anthology: A Collection of the Best Literature (1899), Vol. 4, 111.
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Wer fremde Sprachen nicht kennt, weiss nichts von seiner eigenen
He who is ignorant of foreign languages knows not his own.
Original German in Über Kunst und Alterthum (1821), 30. Quoted, in translation, in Samuel Arthur Bent, Short Sayings of Great Men: With Historical and Explanatory Notes (1882). Also seen as, “He who knows but one language knows none.”
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[Et peut-être la posterité me saura gré de lui avoir fait connaître que les Anciens n’ont pas tout su.]
And perhaps, posterity will thank me for having shown that the ancients did not know everything.
'Relation of New Discoveries in the Science of Numbers', in Letter (Aug 1659) to Pierre de Carcavi, an amateur mathematician, collected in OEuvres de Fermat: Correspondance (1894), 436. Translation, used as an epigraph, in D.M. Burton, Elementary Number Theory (1976, 1989), 107.
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[Interviewer: If the building you are in now started to shake and you knew an earthquake was occurring, what would you do?]
I would walk - not run - to the nearest seismograph.
From interview in the Earthquake Information Bulletin (Jul-Aug 1971), 3, No. 4, as abridged in article on USGS website.
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A celebrity is a person who is known for his well-knownness.
In The Image: A Guide to Pseudo-Events in America (1961), 57.
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A historical fact is rather like the flamingo that Alice in Wonderland tried to use as a croquet mallet. As soon as she got its neck nicely straightened out and was ready to hit the ball, it would turn and look at her with a puzzled expression, and any biographer knows that what is called a “fact” has a way of doing the same.
From 'Getting at the Truth', The Saturday Review (19 Sep 1953), 36, No. 38, 11. Excerpted in Meta Riley Emberger and Marian Ross Hall, Scientific Writing (1955), 399.
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A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
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A little learning is a dangerous thing;—not if you know how little it is.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), lxvi.
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A little science is something that they must have. I should like my nephews to know what air is, and water; why we breathe, and why wood burns; the nutritive elements essential to plant life, and the constituents of the soil. And it is no vague and imperfect knowledge from hearsay I would have them gain of these fundamental truths, on which depend agriculture and the industrial arts and our health itself; I would have them know these things thoroughly from their own observation and experience. Books here are insufficient, and can serve merely as aids to scientific experiment.
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A man who speaks out honestly and fearlessly that which he knows, and that which he believes, will always enlist the good will and the respect, however much he may fail in winning the assent, of his fellow men.
Reflection #295, Thomas Henry Huxley and Henrietta A. Huxley (ed.), Aphorisms and Reflections from the Works of T.H. Huxley (1907).
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A metaphysician is one who, when you remark that twice two makes four, demands to know what you mean by twice, what by two, what by makes, and what by four. For asking such questions metaphysicians are supported in oriental luxury in the universities, and respected as educated and intelligent men.
A previously unpublished epigram, added in A Mencken Chrestomathy (1949, 1956), 13-14.
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A paranoid man is a man who knows a little about what’s going on.
…...
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A professor … may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered. This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. … The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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A scientist lives with all of reality. There is nothing better. To know reality is to accept it and eventually to love it.
…...
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A topologist is one who doesn’t know the difference between a doughnut and a coffee cup.
In General Topology (1955), 88, footnote.
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A troubling question for those of us committed to the widest application of intelligence in the study and solution of the problems of men is whether a general understanding of the social sciences will be possible much longer. Many significant areas of these disciplines have already been removed by the advances of the past two decades beyond the reach of anyone who does not know mathematics; and the man of letters is increasingly finding, to his dismay, that the study of mankind proper is passing from his hands to those of technicians and specialists. The aesthetic effect is admittedly bad: we have given up the belletristic “essay on man” for the barbarisms of a technical vocabulary, or at best the forbidding elegance of mathematical syntax.
Opening paragraph of 'The Study of Man: Sociology Learns the Language of Mathematics' in Commentary (1 Sep 1952). Reprinted in James Roy Newman, The World of Mathematics (1956), Vol. 2, 1294.
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A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment.
In 'Chance', Science et Méthode (1908). Quoted in Richard Kautz, Chaos: The Science of Predictable Random Motion (2011), 167 as translated in Science and Method by F. Maitland (1918).
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A week or so after I learned that I was to receive the Miller Award, our president, Marty Morton, phoned and asked me if I would utter a few words of scientific wisdom as a part of the ceremony. Unfortunately for me, and perhaps for you, I agreed to do so. In retrospect I fear that my response was a serious error, because I do not feel wise. I do not know whether to attribute my response to foolhardiness, to conceit, to an inordinate susceptibility to flattery, to stupidity, or to some combination of these unfortunate attributes all of which I have been told are recognizable in my personality. Personally, I tend to favor stupidity, because that is a condition over which I have little control.
Bartholomew, April 1993, unpublished remarks when receiving the Miller Award from the Cooper Ornithological Society.
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About 85 per cent of my “thinking” time was spent getting into a position to think, to make a decision, to learn something I needed to know. Much more time went into finding or obtaining information than into digesting it. Hours went into the plotting of graphs... When the graphs were finished, the relations were obvious at once, but the plotting had to be done in order to make them so.
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence…. The two propositions: “The earth turns round” and “it is more convenient to suppose the earth turns round” have the same meaning; there is nothing more in the one than in the other.
From La Science et l’Hypothèse (1908), 141, as translated by George Bruce Halsted in Science and Hypothesis (1905), 85-86. From the original French, “L’espace absolu, c’est-à-dire le repère auquel il faudrait rapporter la terre pour savoir si réellement elle tourne, n’a aucune existence objective. … Ces deux propositions: ‘la terre tourne’, et: ‘il est plus commode de supposer que la terre tourne’, ont un seul et même sens; il n’y a rien de plus dans l’une que dans l’autre.”
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Abstruse mathematical researches … are … often abused for having no obvious physical application. The fact is that the most useful parts of science have been investigated for the sake of truth, and not for their usefulness. A new branch of mathematics, which has sprung up in the last twenty years, was denounced by the Astronomer Royal before the University of Cambridge as doomed to be forgotten, on account of its uselessness. Now it turns out that the reason why we cannot go further in our investigations of molecular action is that we do not know enough of this branch of mathematics.
In 'Conditions of Mental Development', Lectures and Essays (1901), Vol. 1, 115.
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Aerodynamically the bumblebee shouldn’t be able to fly, but the bumblebee doesn’t know that so it goes on flying anyway.
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Agnosticism is of the essence of science, whether ancient or modern. It simply means that a man shall not say he knows or believes that for which he has no grounds for professing to believe.
In Life and Letters of Thomas Henry Huxley (1913), Vol. 3, 98, footnote 2.
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All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics ... It has survived all tests and there is no reason to believe that there is any flaw in it.... We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.
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All the unhappiness of men arises from one single fact, that they cannot stay quietly in their own chamber.
In Pensées (1670), Section 4, No. 2. As translated in Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', No. 139, collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 52. Also seen translated as, “The sole cause of man’s unhappiness is that he does not know how to stay quietly in his room.” From the original French, “Tout le malheur des hommes vient d’une seule chose, qui est de ne savoir pas demeurer en repos, dans une chambre,” in Ernest Havet (ed.), Pensées de Pascal (1892), 152.
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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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All you really need to know for the moment is that the universe is a lot more complicated than you might think, even if you start from a position of thinking it’s pretty damn complicated in the first place.
In Mostly Harmless (1992), 195.
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An essential [of an inventor] is a logical mind that sees analogies. No! No! not mathematical. No man of a mathematical habit of mind ever invented anything that amounted to much. He hasn’t the imagination to do it. He sticks too close to the rules, and to the things he is mathematically sure he knows, to create anything new.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
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Any fool can know. The point is to understand.
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Anyone who sits on top of the largest hydrogen-oxygen fueled system in the world; knowing they’re going to light the bottom, and doesn’t get a little worried, does not fully understand the situation.
Response to question whether he was worried about embarking on the first space shuttle flight. As quoted on the nmspacemuseum.org website of the New Mexico Museum of Space History.
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Anyone who tries to make a distinction between education and entertainment doesn’t know the first thing about either.
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Archaeology is the peeping Tom of the sciences. It is the sandbox of men who care not where they are going; they merely want to know where everyone else has been.
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Arithmetic tells you how many you lose or win if you know how many you had before you lost or won.
From 'Arithmetic', Harvest Poems, 1910-1960 (1960), 115.
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As far as we know in the universe, man is unique. He happens to represent the highest form of organization of matter and energy that has ever appeared.
In The Meaning of Evolution (Rev.Ed. 1967), 345.
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As soon as I hear the phrase “everybody knows,” I start to wonder. I start asking, “Does everybody know this? And how do they know it?”
As quoted in interview about earthquake predictions for magazine article in Joshua Fischman, 'Falling Into the Gap', Discover (Oct 1992), 13, No. 10, 58. The article writer appears to be quoting, but throughout the article has used no double quote marks. The article is also online.
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As to how far in advance of the first flight the man should know he’s going. I’m not in agreement with the argument that says word should be delayed until the last possible moment to save the pilot from developing a bad case of the jitters. If we don’t have the confidence to keep from getting clutched at that time, we have no business going at all. If I’m the guy going, I’ll be glad to get the dope as soon as possible. As for keeping this a big secret from us and having us all suited up and then saying to one man “you go” and stuffing him in and putting the lid on that thing and away he goes, well, we’re all big boys now.
As he wrote in an article for Life (14 Sep 1959), 38. In fact, he was the first to fly in Earth orbit on 20 Feb 1962, though Alan Shepard was picked for the earlier first suborbital flight.
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Bacteria represent the world’s greatest success story. They are today and have always been the modal organisms on earth; they cannot be nuked to oblivion and will outlive us all. This time is their time, not the ‘age of mammals’ as our textbooks chauvinistically proclaim. But their price for such success is permanent relegation to a microworld, and they cannot know the joy and pain of consciousness. We live in a universe of trade-offs; complexity and persistence do not work well as partners.
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Behold a universe so immense that I am lost in it. I no longer know where I am. I am just nothing at all. Our world is terrifying in its insignificance.
In Etretiens sur la Pluralité des Mondes (Conversations with a Lady on the Plurality of Worlds) (1686) as cited in Edward Harrison, Cosmology: The Science of the Universe (2000), 162.
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Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611. [The French phrase, à peu près means “approximately”. —Webmaster]
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Beyond lonely Pluto, dark and shadowless, lies the glittering realm of interstellar space, the silent ocean that rolls on and on, past stars and galaxies alike, to the ends of the Universe. What do men know of this vast infinity, this shoreless ocean? Is it hostile or friendly–or merely indifferent?
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Biology as a discipline would benefit enormously if we could bring together the scientists working at the opposite ends of the biological spectrum. Students of organisms who know natural history have abundant questions to offer the students of molecules and cells. And molecular and cellular biologists with their armory of techniques and special insights have much to offer students of organisms and ecology.
In 'The role of natural history in contemporary biology', BioScience (1986), 36, 328-329.
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Bridges would not be safer if only people who knew the proper definition of a real number were allowed to design them.
In 'Topological Theory of Defects', Review of Modern Physics (Jul 1979), 51, No. 3. 591–648. This is seen widely on the web (? mis-)attributed to H.L. Mencken, for which Webmaster has so far been unable to find any validation whatsoever.
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But does Man have any “right” to spread through the universe? Man is what he is, a wild animal with the will to survive, and (so far) the ability, against all competition. Unless one accepts that, anything one says about morals, war, politics, you name it, is nonsense. Correct morals arise from knowing what man is, not what do-gooders and well-meaning old Aunt Nellies would like him to be. The Universe will let us know - later - whether or not Man has any “right” to expand through it.
Starship Troopers
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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 for us, it’s different. Look again at that dot. That’s here. That’s home. That’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every “superstar,” every “supreme leader,” every saint and sinner in the history of our species lived there - on a mote of dust suspended in a sunbeam.
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But that which will excite the greatest astonishment by far, and which indeed especially moved me to call the attention of all astronomers and philosophers, is this: namely, that I have observed four planets, neither known nor observed by any one of the astronomers before my time, which have their orbits round a certain bright star [Jupiter], one of those previously known, like Venus or Mercury round the sun, and are sometimes in front of it, sometimes behind it, though they never depart from it beyond certain limits. All of which facts were discovered and observed a few days ago by the help of a telescope devised by me, through God’s grace first enlightening my mind.
In pamphlet, The Sidereal Messenger (1610), reprinted in The Sidereal Messenger of Galileo Galilei: And a Part of the Preface to the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries (1880), 9.
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But the nature of our civilized minds is so detached from the senses, even in the vulgar, by abstractions corresponding to all the abstract terms our languages abound in, and so refined by the art of writing, and as it were spiritualized by the use of numbers, because even the vulgar know how to count and reckon, that it is naturally beyond our power to form the vast image of this mistress called ‘Sympathetic Nature.’
The New Science, bk. 2, para. 378 (1744, trans. 1984).
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Cauchy is mad, and there is no way of being on good terms with him, although at present he is the only man who knows how mathematics should be treated. What he does is excellent, but very confused…
In Oeuvres (1826), Vol. 2, 259. As quoted and cited in Ernst Hairer and Gerhard Wanner Analysis by Its History (2008), 188. From the original French, “Cauchy est fou, et avec lui il n’y a pas moyen de s’entendre, bien que pour le moment il soit celui qui sait comment les mathématiques doivent être traitées. Ce qu’il fait est excellent, mais très brouillé….”
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Circumstantial evidence can be overwhelming. We have never seen an atom, but we nevertheless know that it must exist.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 31.
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Compared to the breadth of knowledge yet to be known, what does your life actually matter?
Movie
Europa Report (2013)
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Consider the plight of a scientist of my age. I graduated from the University of California at Berkeley in 1940. In the 41 years since then the amount of biological information has increased 16 fold; during these 4 decades my capacity to absorb new information has declined at an accelerating rate and now is at least 50% less than when I was a graduate student. If one defines ignorance as the ratio of what is available to be known to what is known, there seems no alternative to the conclusion that my ignorance is at least 25 times as extensive as it was when I got my bachelor’s degree. Although I am sure that my unfortunate condition comes as no surprise to my students and younger colleagues, I personally find it somewhat depressing. My depression is tempered, however, by the fact that all biologists, young or old, developing or senescing, face the same melancholy situation because of an interlocking set of circumstances.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 228.
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Doctor Thomas …
Said, “Cancer’s a funny thing.
Nobody knows what the cause is,
Though some pretend they do;
It’s like some hidden assassin
Waiting to strike at you.
Childless women get it.
And men when they retire;
It’s as if there had to be some outlet
For their foiled creative fire.”
In 'Miss Gee', in Collected Shorter Poems, 1930-1944 (1950), 242.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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During the eight days I spent in space, I realized that mankind needs height primarily to better know our long-suffering Earth, to see what cannot be seen close up. Not just to love her beauty, but also to ensure that we do not bring even the slightest harm to the natural world
Pham Tuan
In Jack Hassard and Julie Weisberg , Environmental Science on the Net: The Global Thinking Project (1999), 40.
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Each and every loss becomes an instance of ultimate tragedy–something that once was, but shall never be known to us. The hump of the giant deer–as a nonfossilizable item of soft anatomy–should have fallen into the maw of erased history. But our ancestors provided a wondrous rescue, and we should rejoice mightily. Every new item can instruct us; every unexpected object possesses beauty for its own sake; every rescue from history’s great shredding machine is–and I don’t know how else to say this–a holy act of salvation for a bit of totality.
…...
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Education is learning what you didn't even know you didn't know.
In Democracy and its Discontents: Reflections on Everyday America (1974, 1975), 51.
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Even bees, the little alms-men of spring bowers,
Know there is richest juice in poison-flowers.
From poem, 'Isabella', collected in The Poetical Works of John Keats (1885), 186.
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Every day we are interacting with the economy, whether we want to or not, and whether we know it or not. To have a level of control over our lives, we need to understand the connections between money and events and ourselves.
As quoted in brochure for PBS TV financial news series, Adam Smith’s Money World.
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Every honest researcher I know admits he’s just a professional amateur. He’s doing whatever he’s doing for the first time. That makes him an amateur. He has sense enough to know that he’s going to have a lot of trouble, so that makes him a professional.
…...
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Every morning in Africa, a Gazelle wakes up. It knows it must run faster than the fastest lion or it will be killed. Every morning a Lion wakes up. It knows it must outrun the slowest Gazelle or it will starve to death. It doesn't matter whether you are a Lion or a Gazelle; when the sun comes up, you'd better be running.
Anonymous
As seen in The Economist (1985), 296, 37. Sometimes cited in other sources as an African proverb. For example, referred as from a poster of an old African proverb in Venise T. Berry, So Good (1996), 241.
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Everyone doing his best is not the answer. It is necessary that people know what to do.
In Quality, Productivity, and Competitive Position (1982), ii. A similar quote often attributed to Deming, but without citation, is “It is not enough to do your best; you must know what to do, and then do your best.”
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Everything material which is the subject of knowledge has number, order, or position; and these are her first outlines for a sketch of the universe. If our feeble hands cannot follow out the details, still her part has been drawn with an unerring pen, and her work cannot be gainsaid. So wide is the range of mathematical sciences, so indefinitely may it extend beyond our actual powers of manipulation that at some moments we are inclined to fall down with even more than reverence before her majestic presence. But so strictly limited are her promises and powers, about so much that we might wish to know does she offer no information whatever, that at other moments we are fain to call her results but a vain thing, and to reject them as a stone where we had asked for bread. If one aspect of the subject encourages our hopes, so does the other tend to chasten our desires, and he is perhaps the wisest, and in the long run the happiest, among his fellows, who has learned not only this science, but also the larger lesson which it directly teaches, namely, to temper our aspirations to that which is possible, to moderate our desires to that which is attainable, to restrict our hopes to that of which accomplishment, if not immediately practicable, is at least distinctly within the range of conception.
From Presidential Address (Aug 1878) to the British Association, Dublin, published in the Report of the 48th Meeting of the British Association for the Advancement of Science (1878), 31.
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Few intellectual tyrannies can be more recalcitrant than the truths that everybody knows and nearly no one can defend with any decent data (for who needs proof of anything so obvious). And few intellectual activities can be more salutary than attempts to find out whether these rocks of ages might crumble at the slightest tap of an informational hammer.
…...
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Finally, from what we now know about the cosmos, to think that all this was created for just one species among the tens of millions of species who live on one planet circling one of a couple of hundred billion stars that are located in one galaxy among hundreds of billions of galaxies, all of which are in one universe among perhaps an infinite number of universes all nestled within a grand cosmic multiverse, is provincially insular and anthropocentrically blinkered. Which is more likely? That the universe was designed just for us, or that we see the universe as having been designed just for us?
…...
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For all these years you were merely
A smear of light through our telescopes
On the clearest, coldest night; a hint
Of a glint, just a few pixels wide
On even your most perfectly-framed portraits.
But now, now we see you!
Swimming out of the dark - a great
Stone shark, your star-tanned skin pitted
And pocked, scarred after eons of drifting
Silently through the endless ocean of space.
Here on Earth our faces lit up as we saw
You clearly for the first time; eyes wide
With wonder we traced the strangely familiar
Grooves raked across your sides,
Wondering if Rosetta had doubled back to Mars
And raced past Phobos by mistake –
Then you were gone, falling back into the black,
Not to be seen by human eyes again for a thousand
Blue Moons or more. But we know you now,
We know you; you’ll never be just a speck of light again.
…...
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For many planet hunters, though, the ultimate goal is still greater (or actually, smaller) prey: terrestrial planets, like Earth, circling a star like the Sun. Astronomers already know that three such planets orbit at least one pulsar. But planet hunters will not rest until they are in sight of a small blue world, warm and wet, in whose azure skies and upon whose wind-whipped oceans shines a bright yellow star like our own.
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For the most part we humans live with the false impression of security and a feeling of being at home in a seemingly trustworthy physical and human environment. But when the expected course of everyday life is interrupted, we are like shipwrecked people on a miserable plank in the open sea, having forgotten where they came from and not knowing whither they are drifting. But once we fully accept this, life becomes easier and there is no longer any disappointment.
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Fortunately science, like that nature to which it belongs, is neither limited by time nor by space. It belongs to the world, and is of no country and of no age. The more we know, the more we feel our ignorance; the more we feel how much remains unknown; and in philosophy, the sentiment of the Macedonian hero can never apply,– there are always new worlds to conquer.
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Forty years ago the philosopher Alfred North Whitehead thought it self-evident that you would get a good government if you took power out of the hands of the acquisitive and gave it to the learned and the cultivated. At present, a child in kindergarten knows better than that.
In Before the Sabbath (1979), 40-41.
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Free men are aware of the imperfection inherent in human affairs, and they are willing to fight and die for that which is not perfect. They know that basic human problems can have no final solutions, that our freedom, justice, equality, etc. are far from absolute, and that the good life is compounded of half measures, compromises, lesser evils, and gropings toward the perfect. The rejection of approximations and the insistence on absolutes are the manifestation of a nihilism that loathes freedom, tolerance, and equity.
In The Temper of Our Time (1967), 103.
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Freeman’s gift? It’s cosmic. He is able to see more interconnections between more things than almost anybody. He sees the interrelationships, whether it’s in some microscopic physical process or in a big complicated machine like Orion. He has been, from the time he was in his teens, capable of understanding essentially anything that he’s interested in. He’s the most intelligent person I know.
As quoted in Kenneth Brower, 'The Danger of Cosmic Genius', The Atlantic (Dec 2010). Webmaster note: The Orion Project was a study of the possibility of nuclear powered propulsion of spacecraft.
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From our home on the Earth, we look out into the distances and strive to imagine the sort of world into which we were born. Today, we have reached far into space. Our immediate neighborhood we know rather intimately. But with increasing distance our knowledge fades … The search will continue. The urge is older than history. It is not satisfied and will not be suppressed.
In 'From Our Home On The Earth', The Land (1946), 5, 145. As cited on the webpage of the Edwin Powell Hubble Papers.
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Furnished as all Europe now is with Academies of Science, with nice instruments and the spirit of experiment, the progress of human knowledge will be rapid and discoveries made of which we have at present no conception. I begin to be almost sorry I was born so soon, since I cannot have the happiness of knowing what will be known a hundred years hence.
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Genetics has always turned out to be much more complicated than it seemed reasonable to imagine. Biology is not like physics. The more we know, the less it seems that there is one final explanation waiting to be discovered.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 275.
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Genius knows where the questions are hidden
City Aphorisms, Fourth Selection (1987).
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Gentlemen, as we study the universe we see everywhere the most tremendous manifestations of force. In our own experience we know of but one source of force, namely will. How then can we help regarding the forces we see in nature as due to the will of some omnipresent, omnipotent being? Gentlemen, there must be a GOD.
As quoted in W. E. Byerly (writing as a Professor Emeritus at Harvard University, but a former student at a Peirce lecture on celestial mechanics), 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 6.
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Gentlemen, everyone in this room knows the difference between a live horse and a dead horse. Pray, therefore, let us cease flogging the latter.
(in conversation)
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Geometry enlightens the intellect and sets one’s mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
In Ibn Khaldûn, Franz Rosenthal (trans.) and N.J. Dawood (ed.), The Muqaddimah: An Introduction to History (1967, 1969), Vol. 1, 378.
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Give me the liberty to know, to utter, and to argue freely according to conscience, above all liberties.
In Areopagitica: A speech of Mr John Milton for the Liberty of Unlicenced printing to the Parliament of England (23 Nov 1644), 35.
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Goethe said that he who cannot draw on 3,000 years of learning is living hand to mouth. It could just as well be said that individuals who do tap deeply into this rich cultural legacy are wealthy indeed. Yet the paradox is that much of this wisdom is buried in a sea of lesser books or like lost treasure beneath an ocean of online ignorance and trivia. That doesn’t mean that with a little bit of diligence you can’t tap into it. Yet many people, perhaps most, never take advantage of all this human experience. They aren’t obtaining knowledge beyond what they need to know for work or to get by. As a result, their view of our amazing world is diminished and their lives greatly circumscribed.
In An Embarrassment of Riches: Tapping Into the World's Greatest Legacy of Wealth (2013), 65.
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Governments derive their just powers from the consent of the governed. You have neither solicited nor received ours. We did not invite you. You do not know us, nor do you know our world. Cyberspace does not lie within your borders. Do not think that you can build it, as though it were a public construction project. You cannot. It is an act of nature and it grows itself through our collective actions.
In 'A Declaration of the Independence of Cyberspace' (8 Feb 1996). Published on Electronic Frontier Foundation website. Reproduced in Lawrence Lessig, Code: Version 2.0) (2008), 303.
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Guard well your spare moments. They are like uncut diamonds. Discard them and their value will never be known. Improve them and they will become the brightest gems in a useful life.
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He had read much, if one considers his long life; but his contemplation was much more than his reading. He was wont to say that if he had read as much as other men he should have known no more than other men.
From 'Thomas Hobbes', in Andrew Clark (ed.) Brief Lives (1898), Vol. 1, 349.
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He saw virus particles shaped like snakes, in negative images. They were white cobras tangled among themselves, like the hair of Medusa. They were the face of nature herself, the obscene goddess revealed naked. This life form thing was breathtakingly beautiful. As he stared at it, he found himself being pulled out of the human world into a world where moral boundaries blur and finally dissolve completely. He was lost in wonder and admiration, even though he knew that he was the prey.
The Hot Zone
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He who loves practice without theory is like a seafarer who boards ship without wheel or compass and knows not wither he travels.
From the original Italian: “Quelli che s’inamorā di pratica sāza sciētia, sō come ’l nochiere che ēstra navilio sanza timone o bussola che mai à certezza dove si uada.” Italian and English in Jean Paul Richter (trans), G. 8a, 'General Introduction to the Book on Painting', The Literary Works of Leonardo da Vinci (1883), Vol. 1, 18. Also seen translated as “He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast,” in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972), 224.
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He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer. I believe that it is impossible to do this, and to study geometry as it admits of being studied and am conscious it can be taught, without finding the reason invigorated, the invention quickened, the sentiment of the orderly and beautiful awakened and enhanced, and reverence for truth, the foundation of all integrity of character, converted into a fixed principle of the mental and moral constitution, according to the old and expressive adage “abeunt studia in mores”.
In 'A probationary Lecture on Geometry, in Collected Mathematical Papers (1908), Vol. 2, 9. [The Latin phrase, “abeunt studia in mores” translates as “studies pass on into character”. —Webmaster]
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Holding then to science with one hand—the left hand—we give the right hand to religion, and cry: ‘Open Thou mine eyes, that I may behold wondrous things, more wondrous than the shining worlds can tell.’ Obedient to the promise, religion does awaken faculties within us, does teach our eyes to the beholding of more wonderful things. Those great worlds blazing like suns die like feeble stars in the glory of the morning, in the presence of this new light. The soul knows that an infinite sea of love is all about it, throbbing through it, everlasting arms of affection lift it, and it bathes itself in the clear consciousness of a Father’s love.
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How strange is the lot of us mortals! Each of us is here for a brief sojourn; for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people–first of all for those upon whose smiles and well-being our own happiness is wholly dependent, and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving.
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Human language is in some ways similar to, but in other ways vastly different from, other kinds of animal communication. We simply have no idea about its evolutionary history, though many people have speculated about its possible origins. There is, for instance, the “bow-bow” theory, that language started from attempts to imitate animal sounds. Or the “ding-dong” theory, that it arose from natural sound-producing responses. Or the “pooh-pooh” theory, that it began with violent outcries and exclamations.
We have no way of knowing whether the kinds of men represented by the earliest fossils could talk or not…
Language does not leave fossils, at least not until it has become written.
Man in Nature (1961), 10.
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I am an adherent of the ideal of democracy, although I well know the weaknesses of the democratic form of government. Social equality and economic protection of the individual appeared to me always as the important communal aims of the state.
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I am born into an environment–I know not whence I came nor whither I go nor who I am. This is my situation as yours, every single one of you. The fact that everyone always was in this same situation, and always will be, tells me nothing. Our burning question as to the whence and whither–all we can ourselves observe about it is the present environment. That is why we are eager to find out about it as much as we can. That is science, learning, knowledge; it is the true source of every spiritual endeavour of man. We try to find out as much as we can about the spatial and temporal surroundings of the place in which we find ourselves put by birth.
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I am larger, better than I thought,
I did not know I held so much goodness.
From poem, 'Song of the Open Road', Leaves of Grass (1881), 123.
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I am very astonished that the scientific picture of the real world around me is deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously.
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I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.
In Teaching of Mathematics (1902), 14.
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I believe the best test of a model is how well can the modeller answer the questions, ‘What do you know now that you did not know before?’ and ‘How can you find out if it is true?’
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 177.
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I can hear the sizzle of newborn stars, and know anything of meaning, of the fierce magic emerging here. I am witness to flexible eternity, the evolving past, and I know we will live forever, as dust or breathe in the face of stars, in the shifting pattern of winds.
Joy Harjo
In Secrets from the Center of the World (1989), 56.
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I can’t think of any definition of the words mathematician or scientist that would apply to me. I think of myself as a journalist who knows just enough about mathematics to be able to take low-level math and make it clear and interesting to nonmathematicians. Let me say that I think not knowing too much about a subject is an asset for a journalist, not a liability. The great secret of my column is that I know so little about mathematics that I have to work hard to understand the subject myself. Maybe I can explain things more clearly than a professional mathematician can.
In Scot Morris, 'Interview: Martin Gardner', Omni, 4, No. 4 (Jan 1982), 68.
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I do not define time, space, place, and motion, as being well known to all.
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I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified. The comparative smallness of what we know today as gravitational effects is not a conclusive reason for ignoring the principle of general relativity in theoretical investigations of a fundamental character. In other words, I do not believe that it is justifiable to ask: What would physics look like without gravitation?
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I do not think it is possible really to understand the successes of science without understanding how hard it is—how easy it is to be led astray, how difficult it is to know at any time what is the next thing to be done.
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I do not think we can impose limits on research. Through hundreds of thousands of years, man’s intellectual curiosity has been essential to all the gains we have made. Although in recent times we have progressed from chance and hit-or-miss methods to consciously directed research, we still cannot know in advance what the results may be. It would be regressive and dangerous to trammel the free search for new forms of truth.
In Margaret Mead and Rhoda Bubendey Métraux (ed.), Margaret Mead, Some Personal Views (1979), 89.
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I don’t believe in evolution, like people believe in God … Science and technology are not advanced by people who believe, but by people who don’t know but are doing their best to find out.
In Terry Pratchett, Ian Stewart and Jack Cohen, The Science of Discworld (2014), 41.
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I don’t know anything about mathematics; can’t even do proportion. But I can hire all the good mathematicians I need for fifteen dollars a week.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
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I don’t know what you could say about a day in which you have seen four beautiful sunsets.
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I fear that the character of my knowledge is from year to year becoming more distinct and scientific; that, in exchange for vistas wide as heaven’s scope, I am being narrowed down to the field of the microscope. I see details, not wholes nor the shadow of the whole. I count some parts, and say, “I know.”
(19 Aug 1851). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: II: 1850-September 15, 1851 (1906), 406.
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I hate quotations. Tell me what you know.
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I have known silence: the cold earthy silence at the bottom of a newly dug well; the implacable stony silence of a deep cave; the hot, drugged midday silence when everything is hypnotised and stilled into silence by the eye of the sun;… I have heard summer cicadas cry so that the sound seems stitched into your bones. I have heard tree frogs in an orchestration as complicated as Bach singing in a forest lit by a million emerald fireflies. I have heard the Keas calling over grey glaciers that groaned to themselves like old people as they inched their way to the sea. I have heard the hoarse street vendor cries of the mating Fur seals as they sang to their sleek golden wives, the crisp staccato admonishment of the Rattlesnake, the cobweb squeak of the Bat and the belling roar of the Red deer knee-deep in purple heather.
Letter to Lee McGeorge (31 Jul 1978). Collected in Letters of Note: Volume 2: An Eclectic Collection of Correspondence (2016), 76.
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I have never seen a food writer mention this, but all shrimp imported into the United States must first be washed in chlorine bleach to kill bugs. What this does for the taste, I do not know, but I think we should be told.
In The End of the Line: How Overfishing Is Changing the World and What We Eat (2008), 301.
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I have recently read an article on handwriting and forgeries in which it is stated that ink eradicators do not remove ink: but merely bleach it, and that ink so bleached can be easily brought out by a process of fuming: known to all handwriting experts. Can you give me a description of this process, what chemicals are used: and how it is performed?
Showing his early interest in science, at age 16, while a student at Tulsa Central High School. From the first time Gardner’s writing appeared in print: a query printed in a magazine in Hugo Gernsback (ed.), 'Now It Is Now It Isn’t', Science and Invention (Apr 1930), 1119. As quoted and cited in Dana Richards, 'Martin Gardner: A “Documentary”', collected in Elwyn R. Berlekamp and ‎Tom Rodgers (ed.) The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner (1999), 3.
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I know no such thing as genius,—genius is nothing but labor and diligence.
Louis Klopsch, Many Thoughts of Many Minds (1896), 106.
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I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones.
In interview, Alfred Werner, Liberal Judaism (Apr-May 1949), 16. Einstein Archive 30-1104. As cited in Alice Calaprice, The New Quotable Einstein (2005), 173.
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I know of no area of human endeavor in which science has not had at least one important thing to say.
In 'With Science on Our Side', Washington Post (9 Jan 1994).
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I know of no department of natural science more likely to reward a man who goes into it thoroughly than anthropology. There is an immense deal to be done in the science pure and simple, and it is one of those branches of inquiry which brings one into contact with the great problems of humanity in every direction.
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I know of the boons that machinery has conferred on men, all tyrants have boons to confer, but service to the dynasty of steam and steel is a hard service and gives little leisure to fancy to flit from field to field.
In 'Romance of Modern Stage', National Review (1911). Quoted in Edward Hale Bierstadt, Dunsany the Dramatist (1917), 119.
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I like to find mavericks, students who don’t know what they’re looking for, who are sensitive and vulnerable and have unusual pasts. If you do enough work with these students you can often transform their level of contribution. After all, the real breakthroughs come from the mavericks.
As quoted in Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 143. Mead attributes her own pioneering approach to being educated at home by her grandmother, a retired schoolteacher, whom she said “was about 50 years ahead of her time—for instance, she taught me algebra before arithmetic.”
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I read somewhere that some people believe that the entire universe is a matrix of living thought. And I said, “Man, if that’s not a definition of God, I don’t know what is.”
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 33
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I think we all have a little voice inside us that will guide us. It may be God, I don’t know. But I think that if we shut out all the noise and clutter from our lives and listen to that voice, it will tell us the right thing to do.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 142
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I traveled among unknown men,
In lands beyond the sea;
Nor England! did I know till then
What love I bore to thee.
First verse of poem, 'I Travelled among Unknown Men', In Poems: In Two Volumes (1807), Vol. 1, 68.
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I want to know God’s thoughts; the rest are details.
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I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts; the rest are details.
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I want to turn women loose on the environmental crisis…. Nobody knows more about pollution when detergents back up in the sink.
In Unity, Freedom & Peace: A Blueprint for Tomorrow (1968), 87.
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I was born not knowing and have only had a little time to change that here and there.
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I would not be confident in everything I say about the argument: but one thing I would fight for to the end, both in word and in deed if I were able—that if we believe we should try to find out what is not known, we should be better and braver and less idle than if we believed that what we do not know is impossible to find out and that we need not even try.
Socrates
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I would think I knew nothing in physics if I could say only how things could be but, without demonstrating that they can’t be otherwise.
From the original French, “Pour la Physique, ie croyrois n’y rien sçauoir, si ie ne sçauois que dire comment les choses peuuent estre, sans demonstrer qu’elles ne peuuent estre autrement,” in letter (11 Mar 1640) to Père Marin Mersenne, collected in Lettres de Mr Descartes (1659), Vol. 2, 213. As translated by John Cottingham, et al., (trans.), in The Philosophical Writings of Descartes: Volume 3, The Correspondence (1991), 145.
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I [do not know] when the end of science will come. ... What I do know is that our species is dumber than we normally admit to ourselves. This limit of our mental faculties, and not necessarily of science itself, ensures to me that we have only just begun to figure out the universe.
In Death by Black Hole: And Other Cosmic Quandaries (2007), 17.
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If a child left school at ten, knowing nothing of detailed information, but knowing the pleasure that comes from agreeable music, from reading, from making things, from finding things out, it would be better off than a man who left university at twenty-two, full of facts but without any desire to enquire further into such dry domains.
In Mathematician's Delight (1943), 9.
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If a man devotes himself to the promotion of science, he is firstly opposed, and then he is informed that his ground is already occupied. At first men will allow no value to what we tell them, and then they behave as if they knew it all themselves.
In The Maxims and Reflections of Goethe (1906), 199.
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If I am given a sign [formula], and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?
In De Magistro (400s), Book 1, chap 10, 23. As quoted in Ettore Carruccio, Mathematics And Logic in History And in Contemporary Thought (1964), 152.
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If I had a screwdriver and a pair of pliers, anything that could be opened was in danger. I had this need to know what was inside.
Concerning his curiosity for electrical devices which began as a child. Quoted in Timothy L. O’Brien, 'Not Invented here: Are U.S. Innovators Losing Their Competitive Edge?', New York Times (13 Nov 2005), B6.
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If I had been taught from my youth all the truths of which I have since sought out demonstrations, and had thus learned them without labour, I should never, perhaps, have known any beyond these; at least, I should never have acquired the habit and the facility which I think I possess in always discovering new truths in proportion as I give myself to the search.
In Discours de la Méthode (1637). In English from John Veitch (trans.), A Discourse on Method (1912), 57.
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If Spirit is an abstraction, a conjecture, a Chimera: Matter is an abstraction, a conjecture, a Chimera; for We know as much, or rather as little of one as of the other.
In Letter (26 May 1817) to Thomas Jefferson.
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If the observation of the amount of heat the sun sends the earth is among the most important and difficult in astronomical physics, it may also be termed the fundamental problem of meteorology, nearly all whose phenomena would become predictable, if we knew both the original quantity and kind of this heat.
In Report of the Mount Whitney Expedition, quoted in Charles Greeley Abbot, Adventures in the World of Science (1958), 17. Also quoted and cited in David H. Devorkin, 'Charles Greeley Abbot', Biographical Memoirs (1998), 4.
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If the whole universe has no meaning, we should never have found out that it has no meaning: just as, if there were no light in the universe and therefore no creatures with eyes, we should never know it was dark. Dark would be without meaning.
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If we knew all the laws of Nature, we should need only one fact or the description of one actual phenomenon to infer all the particular results at that point. Now we know only a few laws, and our result is vitiated, not, of course, by any confusion or irregularity in Nature, but by our ignorance of essential elements in the calculation. Our notions of law and harmony are commonly confined to those instances which we detect, but the harmony which results from a far greater number of seemingly conflicting, but really concurring, laws which we have not detected, is still more wonderful. The particular laws are as our points of view, as to the traveler, a mountain outline varies with every step, and it has an infinite number of profiles, though absolutely but one form. Even when cleft or bored through, it is not comprehended in its entireness.
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If we knew what it was we were doing, it would not be called research, would it?
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If we knew what we were doing, it wouldn’t be called research, would it?
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If you can’t describe what you are doing as a process, you don’t know what you’re doing.
Widely quoted, without citation. If you know a primary source, please contact Webmaster.
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If you do not know how to ask the right question, you discover nothing.
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If you don’t know where you are going, any road will get you there.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 246
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If you take a plunge into the sea, you unconsciously close your pores against the cold. If you go out on a cold day, you consciously put on an overcoat. Science can give you reason why you should not make & put on an overcoat without knowing it just as you shut your pores.
Letter to E.C. Chapman (29 Jul 1891), Dan H. Laurence (ed.), Collected Letters (1965), Vol. 1, 303.
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If you want to grow old as a pilot, you’ve got to know when to push it, and when to back off.
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In an era in which the domain of intellect and politics were almost exclusively male, Theon [her father] was an unusually liberated person who taught an unusually gifted daughter [Hypatia] and encouraged her to achieve things that, as far as we know, no woman before her did or perhaps even dreamed of doing.
From 'Hypatia', in Louise S. Grinstein (ed.), Women of Mathematics, (1987), 74.
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In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away.
From the French, “Il semble que la perfection soit atteinte non quand il n'y a plus rien à ajouter, mais quand il n'y a plus rien à retrancher,” in Terre des Hommes (1939). As translated by Lewis Galantière, in Wind, Sand, and Stars (1939), 66.
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In degenerating programmes, however, theories are fabricated only in order to accommodate known facts.
In Radio Lecture (30 Jun 1973) broadcast by the Open University, collected in Imre Lakatos, John Worrall (ed.) and Gregory Currie (ed.), 'Introduction: Science and Pseudoscience', The Methodology of Scientific Research Programmes (1978, 1980), Vol. 1, 5.
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In fact, I’ve come to the conclusion that I never did know anything about it [electricity].
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In my understanding of God I start with certain firm beliefs. One is that the laws of nature are not broken. We do not, of course, know all these laws yet, but I believe that such laws exist. I do not, therefore, believe in the literal truth of some miracles which are featured in the Christian Scriptures, such as the Virgin Birth or water into wine. ... God works, I believe, within natural laws, and, according to natural laws, these things happen.
Essay 'Science Will Never Give Us the Answers to All Our Questions', collected in Henry Margenau, and Roy Abraham Varghese (eds.), Cosmos, Bios, Theos (1992), 66.
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In our way of life … with every decision we make, we always keep in mind the seventh generation of children to come. … When we walk upon Mother Earth, we always plant our feet carefully, because we know that the faces of future generations are looking up at us from beneath the ground. We never forget them.
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In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite.
As quoted, without citation, in Robert Jungk and James Cleugh (trans.), Brighter Than a Thousand Suns: A Personal History of the Atomic Scientists (1958), 22. The writing of poetry by Robert Oppenheimer was being remarked upon by Dirac, as he was talking with him.
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In some sense, there’s nothing as impractical as astronomy. You could take away the whole astronomical universe, and most people wouldn’t know the difference—except for the sun and maybe the moon.
In interview, Rushworth M. Kidder, 'Grounded in Space Science', Christian Science Monitor (22 Dec 1989).
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In teaching man, experimental science results in lessening his pride more and more by proving to him every day that primary causes, like the objective reality of things, will be hidden from him forever and that he can only know relations.
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In the end, science as we know it has two basic types of practitioners. One is the educated man who still has a controlled sense of wonder before the universal mystery, whether it hides in a snail’s eye or within the light that impinges on that delicate organ. The second kind of observer is the extreme reductionist who is so busy stripping things apart that the tremendous mystery has been reduced to a trifle, to intangibles not worth troubling one’s head about.
In 'Science and the Sense of the Holy,' The Star Thrower (1978), 190.
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In the next twenty centuries … humanity may begin to understand its most baffling mystery—where are we going? The earth is, in fact, traveling many thousands of miles per hour in the direction of the constellation Hercules—to some unknown destination in the cosmos. Man must understand his universe in order to understand his destiny. Mystery, however, is a very necessary ingredient in our lives. Mystery creates wonder and wonder is the basis for man’s desire to understand. Who knows what mysteries will be solved in our lifetime, and what new riddles will become the challenge of the new generation? Science has not mastered prophesy. We predict too much for the next year yet far too little for the next ten. Responding to challenges is one of democracy’s great strengths. Our successes in space can be used in the next decade in the solution of many of our planet’s problems.
In a speech to a Joint Meeting of the Two Houses of Congress to Receive the Apollo 11 Astronauts (16 Sep 1969), in the Congressional Record.
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In the past, you wouldn’t have had any problem in getting a countryman to explain the difference between a blackbird and a song thrush, but you might have that difficulty with a kid now. Equally, if you asked a chap about gorillas in the 19th-century, he wouldn’t have heard of the creatures, but today an urban boy knows all about them.
Explaining how the success of nature documentaries may result in children who know more about gorillas than the wildlife in their own gardens. As reported by Adam Lusher in 'Sir David Attenborough', Daily Mail (28 Feb 2014).
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Induction is the process of generalizing from our known and limited experience, and framing wider rules for the future than we have been able to test fully. At its simplest, then, an induction is a habit or an adaptation—the habit of expecting tomorrow’s weather to be like today’s, the adaptation to the unwritten conventions of community life.
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Induction, then, is that operation of the mind by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.
In A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation (1843), Vol. 1, 352.
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Is there a God? Who knows? Is there an angry unicorn on the dark side of the moon?
In 'Philosophy, Religion, and So Forth', A Voice Crying in the Wilderness (1989), 2.
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Isn’t it marvelous how those scientists know the names of all those stars?
Anonymous
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It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.
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It has always seemed to me extreme presumptuousness on the part of those who want to make human ability the measure of what nature can and knows how to do, since, when one comes down to it, there is not one effect in nature, no matter how small, that even the most speculative minds can fully understand.
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It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability. That a scientific investigation pursued on account of its probability will generally lead to truth, rather than falsehood, is at the best only probable.
In A Treatise on Probability (1921), 322.
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It has been said that astronomy is a humbling and character building experience. There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we’ve ever known.
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It is a good thing for a physician to have prematurely grey hair and itching piles. The first makes him appear to know more than he does, and the second gives him an expression of concern which the patient interprets as being on his behalf.
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It is above all the duty of the methodical text-book to adapt itself to the pupil’s power of comprehension, only challenging his higher efforts with the increasing development of his imagination, his logical power and the ability of abstraction. This indeed constitutes a test of the art of teaching, it is here where pedagogic tact becomes manifest. In reference to the axioms, caution is necessary. It should be pointed out comparatively early, in how far the mathematical body differs from the material body. Furthermore, since mathematical bodies are really portions of space, this space is to be conceived as mathematical space and to be clearly distinguished from real or physical space. Gradually the student will become conscious that the portion of the real space which lies beyond the visible stellar universe is not cognizable through the senses, that we know nothing of its properties and consequently have no basis for judgments concerning it. Mathematical space, on the other hand, may be subjected to conditions, for instance, we may condition its properties at infinity, and these conditions constitute the axioms, say the Euclidean axioms. But every student will require years before the conviction of the truth of this last statement will force itself upon him.
In Methodisches Lehrbuch der Elementar-Mathemalik (1904), Teil I, Vorwort, 4-5.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is always, our eyes alone, our way of looking at things. Nature alone knows what she means now, and what she had meant in the past.
In The Maxims and Reflections of Goethe (1906), 203.
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It is another aphorism that no one knows everything about anything. That need not dull the pleasure and fascination of the fact that a great deal is known about some things.
In Splendid Isolation (1980), 38.
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It is bad enough to know the past; it would be intolerable to know the future.
As quoted in Richard Hughes, Foreign Devil: Thirty Years of Reporting From the Far East (1972) 209.
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It is difficult to know how to treat the errors of the age. If a man oppose them, he stands alone; if he surrender to them, they bring him neither joy nor credit.
In The Maxims and Reflections of Goethe (1906), 185.
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It is disconcerting that present-day young who did not know Stalin and Hitler are displaying the old naïveté. After all that has happened they still do not know that you cannot build utopia without terror, and that before long terror is all that’s left.
In Before the Sabbath (1979), 120.
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It is easy to make out three areas where scientists will be concentrating their efforts in the coming decades. One is in physics, where leading theorists are striving, with the help of experimentalists, to devise a single mathematical theory that embraces all the basic phenomena of matter and energy. The other two are in biology. Biologists—and the rest of us too—would like to know how the brain works and how a single cell, the fertilized egg cell, develops into an entire organism
Article 'The View From Mars', in Annals of the New York Academy of Sciences: Research Facilities of the Future (1994), 735, 37.
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It is hard to believe that a man is telling the truth when you know that you would lie if you were in his place.
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It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.
In J.R. Newman (ed.), 'Commentary on The Foundations of Mathematics', The World of Mathematics (1956), Vol. 3, 1614.
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It is high time that laymen abandoned the misleading belief that scientific enquiry is a cold dispassionate enterprise, bleached of imaginative qualities, and that a scientist is a man who turns the handle of discovery; for at every level of endeavour scientific research is a passionate undertaking and the Promotion of Natural Knowledge depends above all on a sortee into what can be imagined but is not yet known.
The Times Literary Supplement (London), 1963 October 25 (p. 850)
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It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 37-38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112.
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It is more important to pave the way for the child to want to know than to put him on a diet of facts he is not ready to assimilate.
In The Sense of Wonder (1956, 1965), 45.
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It is not always possible to know what one has learned, or when the dawning will arrive. You will continue to shift, sift, to shake out and to double back. The synthesis that finally occurs can be in the most unexpected place and the most unexpected time. My charge ... is to be alert to the dawnings.
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It is not merely as an investigator and discoverer, but as a high-principled and unassuming man, that Scheele merits our warmest admiration. His aim and object was the discovery of truth. The letters of the man reveal to us in the most pleasant way his high scientific ideal, his genuinely philosophic temper, and his simple mode of thought. “It is the truth alone that we desire to know, and what joy there is in discovering it!” With these words he himself characterizes his own efforts.
From History of Chemistry (1899). As quoted in Victor Robinson, Pathfinders in Medicine (1912), 121.
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It is not sufficient to see and to know the beauty of a work. We must feel and be affected by it.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is nothing short of scandalous that we probably only know one out of every ten species on earth, let alone where they are or, various aspects of their biology, and … unless we really know what there is, and where it is, we’re gonna make some mistakes without even knowing we’ve made them.
From Reith Lecture, 'Biodiversity', on BBC Radio 4 (19 Apr 2000). Transcript and audio on BBC website.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It is the unknown that excites the ardor of scholars, who, in the known alone, would shrivel up with boredom.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 217.
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It is true that M. Fourier believed that the main aim of mathematics was public utility and the explanation of natural phenomena; but a philosopher of his ability ought to have known that the sole aim of science is the honour of the human intellect, and that on this ground a problem in numbers is as important as a problem on the system of the world.
In Letter to Legendre, as quoted in an Address by Emile Picard to the Congress of Science and Art, St. Louis (22 Sep 1904), translated in 'Development of Mathematical Analysis', The Mathematical Gazette (Jul 1905), 3, No. 52, 200. A different translation begins, “It is true that Fourier had the opinion…” on the Karl Jacobi Quotes web page on this site.
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It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.
Proclus
In scholium to Book X of Euclid t. V, 417 as quoted and cited in Ettore Carruccio and Isabel Quigly (trans.), Mathematics And Logic in History And in Contemporary Thought (1964), 27.
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It may be argued that to know one kind of beetle is to know them all. But a species is not like a molecule in a cloud of molecules—it is a unique population.
'The Biological Diversity Crisis: A Challenge to Science', Issues in Science and Technology (Fall 1985), 2:1, 22. Reprinted in Nature Revealed: Selected Writings, 1949-2006 (2006), 622.
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It must be gently but firmly pointed out that analogy is the very corner-stone of scientific method. A root-and-branch condemnation would invalidate any attempt to explain the unknown in terms of the known, and thus prune away every hypothesis.
In 'On Analogy', The Cambridge Magazine (2 Mar 1918), 476. As quoted in Robert Scott Root-Bernstein and Michèle Root-Bernstein, Sparks of Genius: The Thirteen Thinking Tools of the World’s Most Creative (2001), 144.
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It seems that the rivers know the theory. It only remains to convince the engineers of the validity of this analysis.
Epigraph, without citation, in Péter Érdi, Complexity Explained (2007), 339. In French, “Il semble que les rivières connaissent déjà la théorie Il ne reste qu'à convaincre les ingénieurs de la validité de cette analyse.”
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It took me so long to understand what I was writing about, that I knew how to write about it so most readers would understand it.
As quoted in Alex Bellos, 'Martin Gardner Obituary', The Guardian (27 May 2010)
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It was not until 1901 that humanity knew that nuclear energy existed. It is understandable now—but useless—to wish that we still lived in the ignorance of 1900.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 176.
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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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It’s a case of many oceans around the world being degraded by negligence. The ocean is the lifeblood of our world. If we were to lose our fish that we appreciate so much by overfishing; or if we were to lose some of our favorite beaches to overbuilding and pollution, then how would we feel? It’s become a case of not knowing what you’ve got until it’s gone. But by no means is it too late.
From transcript of interview, 'Olympic swimmer: Oceans need our help', NBC News Today web site (14 Nov 2008).
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It’s important natural history isn’t seen as something that is “out there”, which you have to travel to. It’s right there in your garden. Public awareness of the natural history of the world as a whole has never been as great. But it’s important to know about species close to home.
As reported by Adam Lusher in 'Sir David Attenborough', Daily Mail (28 Feb 2014).
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It’s no trick to get the right answer when you have all the data. The real creative trick is to get the right answer when you have only half of the data in hand and half of it is wrong and you don't know which half is wrong. When you get the right answer under these circumstances, you are doing something creative.
In autobiography, Following the Trail of Light: A Scientific Odyssey (1992), 134.
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It’s very good jam, said the Queen.
“Well, I don’t want any to-day, at any rate.”
“You couldn’t have it if you did want it,” the Queen said.
“The rule is jam tomorrow and jam yesterday but never jam to-day.”
“It must come sometimes to “jam to-day,” Alice objected.
“No it can’t,” said the Queen.
“It’s jam every other day; to-day isn’t any other day, you know.”
“I don’t understand you,” said Alice. “It’s dreadfully confusing.”
From Through the Looking Glass. In Alice’s Adventures in Wonderland And, Through the Looking Glass (1898), 149.
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It’s what you learn after you know it all that counts.
…...
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I’m not an atheist and I don’t think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many different languages. The child knows someone must have written those books. It doe s not know how. The child dimly suspects a mysterious order in the arrangement of the books but doesn’t know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God.
…...
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I’m very good at integral and differential calculus,
I know the scientific names of beings animalculous:
In short, in matters vegetable, animal, and mineral,
I am the very model of a modern Major-General.
In The Pirates of Penzance (1879), Act 1.
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Just as knowing how a magic trick is done spoils its wonder, so let us be grateful that wherever science and reason turn they finally plunge into darkness.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren’t There More Happy People?: Smart Quotes for Dumb Times (2009), 274.
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Kepler’s suggestion of gravitation with the inverse distance, and Bouillaud’s proposed substitution of the inverse square of the distance, are things which Newton knew better than his modern readers. I have discovered two anagrams on his name, which are quite conclusive: the notion of gravitation was not new; but Newton went on.
In Budget of Paradoxes (1872), 82.
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Kids like their fossils. I’ve taken my godson fossil-hunting and there’s nothing more magical than finding a shiny shell and knowing you’re the first person to have seen it for 150 million years.
As reported by Adam Lusher in 'Sir David Attenborough', Daily Mail (28 Feb 2014).
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Know thyself! This is the source of all wisdom, said the great thinkers of the past, and the sentence was written in golden letters on the temple of the gods. To know himself, Linnæus declared to be the essential indisputable distinction of man above all other creatures. I know, indeed, in study nothing more worthy of free and thoughtful man than the study of himself. For if we look for the purpose of our existence, we cannot possibly find it outside ourselves. We are here for our own sake.
As translated and quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 9, The History of Creation (1886), Vol. 1, 244.
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Knowing Pains
I studied parts
of a flower
to understand
its flowering.
I learned much
about my limits.
I had forgotten
Earth and climate.
Poem, in Starting Points: Poems (1971), 38. As quoted in Arthur Lerner, 'Poetry Therapy', The American Journal of Nursing (Aug 1973), 73, No. 8, 1338.
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Knowing, henceforth, the physiognomy of the disease when allowed to run its own course, you can, without risk of error, estimate the value of the different medications which have been employed. You will discover which remedies have done no harm, and which have notably curtailed the duration of the disease; and thus for the future you will have a standard by which to measure the value of the medicine which you see employed to counteract the malady in question. What you have done in respect of one disease, you will be able to do in respect of many; and by proceeding in this way you will be able, on sure data, to pass judgment on the treatment pursued by your masters.
In Armand Trousseau, as translated by P. Victor and John Rose Cormack, Lectures on Clinical Medicine: Delivered at the Hôtel-Dieu, Paris (1873), Vol. 1, 40-41.
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Knowledge begets knowledge. The more I see, the more impressed I am not with what we know but with how tremendous the areas are as yet unexplored.
…...
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Knowledge conceald and not broached for a publicke use, is like to a pearelesse gemme interred in the center of the earth, whereof no man knows but he that hid it.
In 'To the Reader', The Optick Glass of Humors (1607), 10.
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Learning begets humility because the more a man knows, the more he discovers his ignorance.
Anonymous
In Hialmer Day Gould, New Practical Spelling (1905), 27
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Leave the beaten track occasionally and dive into the woods. Every time you do so you will be certain to find something that you have never seen before. Of course, it will be a little thing, but do not ignore it. Follow it up, explore all around it: one discovery will lead to another, and before you know it, you will have something worth thinking about to occupy your mind. All really big discoveries are the results of thought.
Address (22 May 1914) to the graduating class of the Friends’ School, Washington, D.C. Printed in 'Discovery and Invention', The National Geographic Magazine (1914), 25, 650.
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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Man is a god to his fellow-man, if he know his duty.
From the original Latin, “Homo homini deus est, si suum officium sciat,” in Fragment XVI. As translated in Thomas Benfield Harbottle, Dictionary of Quotations (Classical) (1897), 44.
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Man, so far as natural science by itself is able to teach us, is no longer the final cause of the universe, the heaven-descended heir of all the ages. His very existence is an accident, his story a brief and discreditable episode in the life of one of the meanest of the planets. Of the combination of causes which first converted a piece or pieces of unorganised jelly into the living progenitors of humanity, science indeed, as yet, knows nothing.
In 'The Religion of Humanity', Essays and Addresses by the Right Hon. Arthur J. Balfour (1893), 307.
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Marx never did a day’s work in his life, and knew as much about the proletariat as I do about chorus girls.
In Before the Sabbath (1979), 60.
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Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon commonplaces as French was once used in diplomatic communications. …. To be sure, mathematics can be extended to any branch of knowledge, including economics, provided the concepts are so clearly defined as to permit accurate symbolic representation. That is only another way of saying that in some branches of discourse it is desirable to know what you are talking about.
In J.R. Newman (ed.), Commentary on Cournot, Jevons and the Mathematics of Money', The World of Mathematics (1956), Vol. 2, 1200.
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Mathematicians … believed that prediction was just a function of keeping track of things. If you knew enough, you could predict anything. … Chaos theory throws it right out the window because … in fact there are great categories of phenomena that are inherently unpredictable.
In novel, Jurassic Park (1990, 1991), 158.
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Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.
…...
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Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy.
In Opus Majus, Part 4, Distinctia Prima, cap. 1.
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Mathematics is the science of definiteness, the necessary vocabulary of those who know.
In A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays (1908), 7.
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Mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true.
In 'Recent Work on the Principles of Mathematics', International Monthly (1901), 4, 84. This sentence is part of a longer quote that begins, “Pure mathematics consists entirely…”, on the Bertrand Russell Quotes page of this website.
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Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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Mathematics, the science of the ideal, becomes the means of investigating, understanding and making known the world of the real. The complex is expressed in terms of the simple. From one point of view mathematics may be defined as the science of successive substitutions of simpler concepts for more complex.
In A Scrap-book of Elementary Mathematics (1908), 215.
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Men in most cases continue to be sexually competent until they are sixty years old, and if that limit be overpassed then until seventy years; and men have been actually known to procreate children at seventy years of age.
Aristotle
In The Works of Aristotle: Historia Animalium (350 BC), (The History of Animals), Book VII, Part 6, 585b5 translated in William David Ross and John Alexander Smith (eds.), D’Arcy Wentworth Thompson (trans.), (1910), Vol. 4, 4
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Men thought dialectically long before they knew what dialectics was, just as they spoke prose long before the term prose existed
In Friedrick Engels and Austin Lewis (trans., ed.), Landmarks of Scientific Socialism: "Anti-Dühring", (1907), 175.
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Mortal as I am, I know that I am born for a day. But when I follow at my pleasure the serried multitude of the stars in their circular course, my feet no longer touch the earth.
Ptolemy
…...
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Most impediments to scientific understanding are conceptual locks, not factual lacks. Most difficult to dislodge are those biases that escape our scrutiny because they seem so obviously, even ineluctably, just. We know ourselves best and tend to view other creatures as mirrors of our own constitution and social arrangements. (Aristotle, and nearly two millennia of successors, designated the large bee that leads the swarm as a king.)
…...
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Most scientists think wars and national boundaries are a menace to the true creative spirit by which science must live, they hate war and they are terrified of atomic war—because they know its possibilities.
As quoted in Michael Amrine, 'I’m A Frightened Man', Collier’s (1946), 117, 51.
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Mssr. Fermat—what have you done?
Your simple conjecture has everyone
Churning out proofs,
Which are nothing but goofs!
Could it be that your statement’s an erudite spoof?
A marginal hoax
That you’ve played on us folks?
But then you’re really not known for your practical jokes.
Or is it then true
That you knew what to do
When n was an integer greater than two?
Oh then why can’t we find
That same proof…are we blind?
You must be reproved, for I’m losing my mind.
In 'Fermat's Last Theorem', Mathematics Magazine (Apr 1986), 59, No. 2, 76.
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My mother, my dad and I left Cuba when I was two [January, 1959]. Castro had taken control by then, and life for many ordinary people had become very difficult. My dad had worked [as a personal bodyguard for the wife of Cuban president Batista], so he was a marked man. We moved to Miami, which is about as close to Cuba as you can get without being there. It’s a Cuba-centric society. I think a lot of Cubans moved to the US thinking everything would be perfect. Personally, I have to say that those early years were not particularly happy. A lot of people didn’t want us around, and I can remember seeing signs that said: “No children. No pets. No Cubans.” Things were not made easier by the fact that Dad had begun working for the US government. At the time he couldn’t really tell us what he was doing, because it was some sort of top-secret operation. He just said he wanted to fight against what was happening back at home. [Estefan’s father was one of the many Cuban exiles taking part in the ill-fated, anti-Castro Bay of Pigs invasion to overthrow dictator Fidel Castro.] One night, Dad disappered. I think he was so worried about telling my mother he was going that he just left her a note. There were rumours something was happening back home, but we didn’t really know where Dad had gone. It was a scary time for many Cubans. A lot of men were involved—lots of families were left without sons and fathers. By the time we found out what my dad had been doing, the attempted coup had taken place, on April 17, 1961. Intitially he’d been training in Central America, but after the coup attempt he was captured and spent the next wo years as a political prisoner in Cuba. That was probably the worst time for my mother and me. Not knowing what was going to happen to Dad. I was only a kid, but I had worked out where my dad was. My mother was trying to keep it a secret, so she used to tell me Dad was on a farm. Of course, I thought that she didn’t know what had really happened to him, so I used to keep up the pretence that Dad really was working on a farm. We used to do this whole pretending thing every day, trying to protect each other. Those two years had a terrible effect on my mother. She was very nervous, just going from church to church. Always carrying her rosary beads, praying her little heart out. She had her religion, and I had my music. Music was in our family. My mother was a singer, and on my father’s side there was a violinist and a pianist. My grandmother was a poet.
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Nature has no compassion.… [It] accepts no excuses and the only punishment it knows is death.
In Between the Devil and the Dragon: The Best Essays and Aphorisms of Eric Hoffer (1982), 7.
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Nature knows no difference between weeds and flowers.
City Aphorisms, Second Selection (1985).
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Nature! … She performs a play; we know not whether she sees it herself, and yet she acts for us, the lookers-on.
Jeremy Naydler (ed.), Goethe On Science: An Anthology of Goethe's Scientific Writings (1996), 60
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Nature! … She tosses her creatures out of nothingness, and tells them not whence they came, nor whither they go. It is their business to run, she knows the road.
As quoted by T.H. Huxley, in Norman Lockyer (ed.), 'Nature: Aphorisms by Goethe', Nature (1870), 1, 9.
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Nature! … We live in her midst and know her not. She is incessantly speaking to us, but betrays not her secret. We constantly act upon her, and yet have no power over her.
As quoted by T.H. Huxley, in Norman Lockyer (ed.), 'Nature: Aphorisms by Goethe', Nature (1870), 1, 9.
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Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does.
In 'Reminiscences of an Octogenarian Mathematician', The American Mathematical Monthly (Nov 1971), 78, No. 9, 960-961.
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Never regard study as a duty, but as the enviable opportunity to learn to know the liberating influence of beauty in the realm of the spirit for your own personal joy and to the profit of the community to which your later work belongs.
…...
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No known roof is as beautiful as the skies above.
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No one believes the results of the computational modeler except the modeler, for only he understands the premises. No one doubts the experimenter’s results except the experimenter, for only he knows his mistakes.
Anonymous
See a similar idea expressed by W.I.B. Beveredge, beginning “No one believes an hypothesis…” on the W.I.B. Beveredge Quotes web page on this site.
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None of us knows anything, not even whether we know or do not know, nor do we know whether not knowing and knowing exist, nor in general whether there is anything or not.
…...
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Nor do I know any study which can compete with mathematics in general in furnishing matter for severe and continued thought. Metaphysical problems may be even more difficult; but then they are far less definite, and, as they rarely lead to any precise conclusion, we miss the power of checking our own operations, and of discovering whether we are thinking and reasoning or merely fancying and dreaming.
In Conflict of Studies (1873), 13.
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Nothing is so firmly believed as what we least know; nor any people so confident as those who entertain us with fabulous stories, such as your alchemists, judicial astrologers, fortune-tellers, and physicians.
In Charles Cotton (trans.), Essays of Michael Seigneur de Montaigne: In Three Books (1693), Vol. 1, 339.
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Now, it may be stretching an analogy to compare epidemics of cholera—caused by a known agent—with that epidemic of violent crime which is destroying our cities. It is unlikely that our social problems can be traced to a single, clearly defined cause in the sense that a bacterial disease is ‘caused’ by a microbe. But, I daresay, social science is about as advanced in the late twentieth century as bacteriological science was in the mid nineteenth century. Our forerunners knew something about cholera; they sensed that its spread was associated with misdirected sewage, filth, and the influx of alien poor into crowded, urban tenements. And we know something about street crime; nowhere has it been reported that a member of the New York Stock Exchange has robbed ... at the point of a gun. Indeed, I am naively confident that an enlightened social scientist of the next century will be able to point out that we had available to us at least some of the clues to the cause of urban crime.
'Cholera at the Harvey,' Woods Hole Cantata: Essays on Science and Society (1985).
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Nurses that attend lying-in women ought to have provided, and in order, every thing that may be necessary for the woman, accoucheur, midwife, and child; such as linnen and cloaths, well aired and warm, for the woman and the bed, which she must know how to prepare when there is occasion; together with nutmeg, sugar, spirit of hartshorn, vinegar, Hungary water, white or brown caudle ready made, and a glyster-pipe fitted.
In A Treatise on the Theory and Practice of Midwifery (1766), 444
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Of course I know that “knickers” begins with a “k”. I’ve been to Oxford—it’s one of the first things they teach you.
As quoted in William Reville, 'The Science of Writing a Good Joke', The Irish Times (5 Jun 2000).
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Of what significance is one’s one existence, one is basically unaware. What does a fish know about the water in which he swims all his life? The bitter and the sweet come from outside. The hard from within, from one’s own efforts. For the most part I do what my own nature drives me to do. It is embarrassing to earn such respect and love for it.
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Often in evolutionary processes a species must adapt to new conditions in order to survive. Today the atomic bomb has altered profoundly the nature of the world as we know it, and the human race consequently finds itself in a new habitat to which it must adapt its thinking.
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Once I found out the secret of the universe. I have forgotten what it was, but I know that the Creator does not take Creation seriously, for I remember that He sat in Space with all His work in front of Him and laughed.
In The Hashish Man, collected in E.F. Bleiler (ed.), Gods, Men and Ghosts: The Best Supernatural Fiction of Lord Dunsany (1972), 158.
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Once when lecturing to a class he [Lord Kelvin] used the word “mathematician,” and then interrupting himself asked his class: “Do you know what a mathematician is?” Stepping to the blackboard he wrote upon it:— [an integral expression equal to the square root of pi]
Then putting his finger on what he had written, he turned to his class and said: “A mathematician is one to whom that is as obvious as that twice two makes four is to you. Liouville was a mathematician.”
In Life of Lord Kelvin (1910), 1139.
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Once you go from 10 people to 100, you already don’t know who everyone is. So at that stage you might as well keep growing, to get the advantages of scale.
As quoted, without citation, in Can Akdeniz, Fast MBA (2014), 281.
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One day the zoo-keeper noticed that the orangutan was reading two books—the Bible and Darwin’s Origin of Species. In surprise, he asked the ape,“Why are you reading both those books?”
“Well,” said the orangutan, “I just wanted to know if I was my brother’s keeper, or my keeper’s brother.”
Anonymous
In Jon Fripp, Michael Fripp and Deborah Fripp, Speaking of Science (2000), 27.
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One man that has a mind and knows it can always beat ten men who havn’t and don’t.
Character Proteus, in The Apple Cart (1929), Act 1. Collected in The Collected Works of Bernard Shaw (1930), Vol. 17, 212. Note: Apostrophes in the last words were not used in the text.
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One must learn by doing the thing; though you think you know it, you have no certainty until you try.
Sophocles
In play, 'Trachiniae', collected in George Young (trans.), The Dramas of Sophocles: Rendered in English Verse: Dramatic and Lyric (1916), 191.
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One never knows how hard a problem is until it has been solved. You don’t necessarily know that you will succeed if you work harder or longer.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 739.
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One never knows what remains undiscovered simply because the right equipment is not there at the right time.
As quoted in T.W. Hänsch, 'From (Incr)edible Lasers to New Spectroscopy', collected in William M. Yen and Marc D. Levenson (eds.), Lasers, Spectroscopy and New Ideas: A Tribute to Arthur L. Schawlow (2013), 6.
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One of his followers said to him, “O Perfect One, why do you do this thing? For though we find joy in it, we know not the celestial reason nor the correspondency of it.” And Sabbah answered: “I will tell you first what I do; I will tell you the reasons afterward.”
In 'The Perfect One'. The Century Magazine (Dec 1918), 95, No. 2, 320. Collected in Ironical Tales (1927), 17.
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One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics.
As quoted in L.A. Steen and D.J. Albers (eds.), Teaching Teachers, Teaching Students (1981), 89.
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One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.
Malay Archipelago
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One of the most impressive discoveries was the origin of the energy of the stars, that makes them continue to burn. One of the men who discovered this was out with his girl friend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine.
She said “Look at how pretty the stars shine!”
He said, “Yes, and right now I am the only man in the world who knows why they shine.”
She merely laughed at him. She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well, it is sad to be alone, but that is the way it is in this world.
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One thing only I know, and that is that I know nothing.
Socrates
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One way to open your eyes to unnoticed beauty is to ask yourself, “What if I had never seen this before? What if I knew I would never see it again?”
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One word characterises the most strenuous of the efforts for the advancement of science that I have made perseveringly during fifty-five years; that word is failure. I know no more of electric and magnetic force, or of the relation between ether, electricity and ponderable matter, or of chemical affinity, than I knew and tried to teach to my students of natural philosophy fifty years ago in my first session as Professor.
Address (16 Jun 1896), at Celebration for his Jubilee as Professor, at Glasgow University. Printed in The Electrician (19 Jun 1896), 37, 247.
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One would have to have completely forgotten the history of science so as not to remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 79.
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Only human beings were given the power of speech, because only to them was it necessary. It was not necessary that either angels or the lower animals should be able to speak; rather, this power would have been wasted on them, and nature, of course, hates to do anything superfluous. … As for the lower animals, since they are guided only by their natural instinct, it was not necessary for them to be given the power of speech. For all animals that belong to the same species are identical in respect of action and feeling; and thus they can know the actions and feelings of others by knowing their own. Between creatures of different species, on the other hand, not only was speech unnecessary, but it would have been injurious, since there could have been no friendly exchange between them.
In Dante Alighieri and Steven Botterill (trans.), De Vulgari Eloquentia (1305), Book 1, Chap 2. from the Latin original.
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Organisms ... are directed and limited by their past. They must remain imperfect in their form and function, and to that extent unpredictable since they are not optimal machines. We cannot know their future with certainty, if only because a myriad of quirky functional shifts lie within the capacity of any feature, however well adapted to a present role.
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Orthodoxy can be as stubborn in science as in religion. I do not know how to shake it except by vigorous imagination that inspires unconventional work and contains within itself an elevated potential for inspired error. As the great Italian economist Vilfredo Pareto wrote: ‘Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.’ Not to mention a man named Thomas Henry Huxley who, when not in the throes of grief or the wars of parson hunting, argued that ‘irrationally held truths may be more harmful than reasoned errors.’
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Our credulity is greatest concerning the things we know least about. And since we know least about ourselves, we are ready to believe all that is said about us. Hence the mysterious power of both flattery and calumny.... It is thus with most of us: we are what other people say we are. We know ourselves chiefly by hearsay.
In The Passionate State of Mind (1955), 80.
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Our situation on this earth seems strange. Every one of us appears here involuntarily and uninvited for a short stay, without knowing the whys and the wherefore. In our daily lives we only feel that man is here for the sake of others, for those whom we love and for many other beings whose fate is connected with our own. I am often worried at the thought that my life is based to such a large extent on the work of my fellow human beings and I am aware of my great indebtedness to them.
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Out of all possible universes, the only one which can exist, in the sense that it can be known, is simply the one which satisfies the narrow conditions necessary for the development of intelligent life.
From In the Centre of Immensities: Creation (1979), as cited in Bill Swainson, The Encarta Book of Quotations (2000), 579.
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Pathology would remain a lovely science, even if there were no therapeutics, just as seismology is a lovely science, though no one knows how to stop earthquakes.
In A Mencken Chrestomathy (1949, 1956), 625-626.
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People know they are lacking something, they are constantly wanting some kind of spiritual guidance.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 13
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People who know little talk much; people who know much talk little.
In Wolfgang Mieder, Wolfgang Mieder, Stewart A. Kingsbury (eds.), A Dictionary of American Proverbs (1992), 22.
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Phony psychics like Uri Geller have had particular success in bamboozling scientists with ordinary stage magic, because only scientists are arrogant enough to think that they always observe with rigorous and objective scrutiny, and therefore could never be so fooled–while ordinary mortals know perfectly well that good performers can always find a way to trick people.
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Physics tries to discover the pattern of events which controls the phenomena we observe. But we can never know what this pattern means or how it originates; and even if some superior intelligence were to tell us, we should find the explanation unintelligible.
In Physics And Philosophy: the Revolution In Modern Science (1942), 16.
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Physics, as we know it, will be over in six months.
Max Born
As quoted in Stephen Hawking, Black Holes and Baby Universes and Other Essays (1993), 50. The context given with the quote was that in the late 1920s Max Born told made this remark to a group of scientists visiting Gottingen. This was shortly after the discovery by Paul Dirac, of the Dirac equation, which governs the behavior of the electron. (It seemed a comprehensive theory was imminent to unify the theories of physics.)
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Plainly, then, these are the causes, and this is how many they are. They are four, and the student of nature should know them all, and it will be his method, when stating on account of what, to get back to them all: the matter, the form, the thing which effects the change, and what the thing is for.
Aristotle
From Physics, Book II, Part 7, 198a21-26. As quoted in Stephen Everson, 'Aristotle on the Foundations of the State', Political Studies (1988), 36, 89-101. Reprinted in Lloyd P. Gerson (ed.), Aristotle: Politics, Rhetoric and Aesthetics (1999), 74.
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Pumbaa: “Timon, ever wonder what those sparkly dots are up there?”
Timon: “Pumbaa, I don’t wonder; I know.”
Pumbaa: “Oh. What are they?”
Timon: “They’re fireflies that got stuck up in that bluish-black thing”.
Pumbaa: “Oh, gee. I always thought they were balls of gas burning billions of miles away.”
Timon: “Pumbaa, with you, everything’s gas.”
Lion King
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Quietly, like a night bird, floating, soaring, wingless.
We glide from shore to shore, curving and falling
but not quite touching;
Earth: a distant memory seen in an instant of repose,
crescent shaped, ethereal, beautiful,
I wonder which part is home, but I know it doesn’t matter . . .
the bond is there in my mind and memory;
Earth: a small, bubbly balloon hanging delicately
in the nothingness of space.
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Read, and found correct.
Written, with Einstein’s signature, below this statement written by an admirer: “A Short Definition of Relativity: There is no hitching post in the Universe—as far as we know.”
As described in Ronald William Clark, Einstein: The Life and Times (1995), 248-249.
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Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason ;knows no compromise, no practical limitations, no barrier to the creative activity.
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Reason has so many forms that we do not know which to choose—Experiment has no fewer.
Quoted in René Dugas, A History of Mechanics (1988), 320. The author writes that in the frontispiece of one of his papers, Coulomb quotes this saying of Montaigne (Essais, Book 3, Chap. 8).
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Reason is the slow and tortuous method by which those who do not know the truth discover it.
Anonymous
Webmaster presently believes this is an orphan quote, best attributed to Anonymous. It seem to be unsupported when attributed to Blaise Pascal, for example, as quoted, without citation, in Morris Kline, 'Ancients versus Moderns, A New Battle of the Books', The Mathematics Teacher (Oct 1958), 51, No. 6, 423. Also later published, without citation, in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972), 296. Webmaster has not yet found a primary source for this as a quote by Pascal - not in English, not in French, and not in any earlier books. This is suspicious. (Can you help?) Furthermore, this sentence is also often seen in more recent books and online quotes pages as a first sentence, followed by a second sentence, “The heart has its reasons, which reason does not know.” The second sentence is a known Pascal quote verified in original French texts. However, Webmaster has not yet found, in any original French text, any instance of these two sentences together. Thus, putting them together more definitely appears to be a misquote. Can you help? [It is included on the Blaise Pascal page to link it with this cautionary note. —Webmaster]
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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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Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns, there are things we know we know.
We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know. ... And each year, we discover a few more of those unknown unknowns.
Answering a question concerning Iraq, on the facts about weapons of mass destruction, at a Press Conference, NATO Headquarters, Brussels, Belgium (6 June 2002). From transcript on U.S. Department of Defense website.
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Research is what I’m doing when I don’t know what I’m doing.
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Results! Why, man, I have gotten a lot of results. I know several thousand things that won’t work.
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Say what you know, do what you must, come what may.
The motto on her winning entry in the 1888 Prix Bordin competition of the French Academy. While being judged, the 15 submissions were anonymous, except for a motto inscribed on them. The author’s name was sealed in an envelope bearing the same motto, opened only after the winning paper was selected. The prize was presented to her on Christmas Eve of 1888. Her exceptional paper was, 'Sur le problème de la rotation d’un corps solide autour d’un point fixe' ('On the Problem of the Rotation of a Solid Body about a Fixed Point'), subsequently published in Acta Mathematica (22 Jan 1889), 12, H.2, 177-232. Motto as translated in Pelagei︠a︡ I︠A︡kovlevna Kochina, Sophia Vasilyevna Kovalevskaya, Her Life and Work (1957), 60.
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Science and technology, like all original creations of the human spirit, are unpredictable. If we had a reliable way to label our toys good and bad, it would be easy to regulate technology wisely. But we can rarely see far enough ahead to know which road leads to damnation. Whoever concerns himself with big technology, either to push it forward or to stop it, is gambling in human lives.
In Disturbing the Universe (1979), 7.
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Science derives its conclusions by the laws of logic from our sense perceptions, Thus it does not deal with the real world, of which we know nothing, but with the world as it appears to our senses. … All our sense perceptions are limited by and attached to the conceptions of time and space. … Modern physics has come to the same conclusion in the relativity theory, that absolute space and absolute time have no existence, but, time and space exist only as far as things or events fill them, that is, are forms of sense perception.
In 'Religion and Modern Science', The Christian Register (16 Nov 1922), 101, 1089. The article is introduced as “the substance of an address to the Laymen’s League in All Soul’s Church (5 Nov 1922).
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Science fiction is the most important literature in the history of the world, because it’s the history of ideas, the history of our civilization birthing itself; Science fiction is central to everything we’ve ever done, and people who make fun of science fiction writers don’t know what they’’re talking about
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Science fiction writers, I am sorry to say, really do not know anything. We can’t talk about science, because our knowledge of it is limited and unofficial, and usually our fiction is dreadful.
'How to Build a Universe That Doesn't Fall Apart Two Days Later,' introduction, I Hope I Shall Arrive Soon (1986).
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Science has found that nothing can disappear without a trace. Nature does not know extinction. All it knows is transformation.
In This Week Magazine (24 Jan 1960), 2. As quoted in Martin A. Recio, From the Threshold of Heaven (2008), 102.
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Science is a method for testing claims about the natural world, not an immutable compendium of absolute truths. The fundamentalists, by ‘knowing’ the answers before they start, and then forcing nature into the straitjacket of their discredited preconceptions, lie outside the domain of science–or of any honest intellectual inquiry.
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Science is the only truth and it is the great lie. It knows nothing, and people think it knows everything. It is misrepresented. People think that science is electricity, automobilism, and dirigible balloons. It is something very different. It is life devouring itself. It is the sensibility transformed into intelligence. It is the need to know stifling the need to live. It is the genius of knowledge vivisecting the vital genius.
repr. In Selected Writings, ed. and trans. by Glen S. Burne (1966). 'Art and Science,' Promenades Philosophiques (1905-1909).
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Science is what you know, philosophy what you don’t know.
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Science will continue to surprise us with what it discovers and creates; then it will astound us by devising new methods to surprise us. At the core of science’s self-modification is technology. New tools enable new structures of knowledge and new ways of discovery. The achievement of science is to know new things; the evolution of science is to know them in new ways. What evolves is less the body of what we know and more the nature of our knowing.
'Speculations on the Future of Science'. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 172.
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Scientists repeatedly return to established theories to test them in new ways, and tend towards testiness with those priests, religious or secular, who know the answers already—whatever the questions are.
In Terry Pratchett, Ian Stewart and Jack Cohen, The Science of Discworld (2014), 90.
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She knew only that if she did or said thus-and-so, men would unerringly respond with the complimentary thus-and-so. It was like a mathematical formula and no more difficult, for mathematics was the one subject that had come easy to Scarlett in her schooldays.
In Gone With the Wind (1936), 60.
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Since an organism is inseparable from its environment, any person who attempts to understand an organism’s distribution must keep constantly in mind that the item being studied is neither a stuffed skin, a pickled specimen, nor a dot on a map. It is not even the live organism held in the hand, caged in a laboratory, or seen in the field. It is a complex interaction between a self-sustaining physicochemical system and the environment. An obvious corollary is that to know the organism it is necessary to know its environment.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 83.
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Since we proposed punctuated equilibria to explain trends, it is infuriating to be quoted again and again by creationists–whether through design or stupidity, I do not know–as admitting that the fossil record includes no transitional forms. Transitional forms are generally lacking at the species level, but they are abundant between larger groups.
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So much is human genius limited, by the limits of human nature, that we just know what our five senses teach.
In The Works of Thomas Sydenham, (1850), Vol. 2, 182.
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So why fret and care that the actual version of the destined deed was done by an upper class English gentleman who had circumnavigated the globe as a vigorous youth, lost his dearest daughter and his waning faith at the same time, wrote the greatest treatise ever composed on the taxonomy of barnacles, and eventually grew a white beard, lived as a country squire just south of London, and never again traveled far enough even to cross the English Channel? We care for the same reason that we love okapis, delight in the fossil evidence of trilobites, and mourn the passage of the dodo. We care because the broad events that had to happen, happened to happen in a certain particular way. And something unspeakably holy –I don’t know how else to say this–underlies our discovery and confirmation of the actual details that made our world and also, in realms of contingency, assured the minutiae of its construction in the manner we know, and not in any one of a trillion other ways, nearly all of which would not have included the evolution of a scribe to record the beauty, the cruelty, the fascination, and the mystery.
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Somewhere, there is something incredible waiting to be known.
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Speaking of libraries: A big open-stack academic or public library is no small pleasure to work in. You’re, say, trying to do a piece on something in Nevada, and you go down to C Floor, deep in the earth, and out to what a miner would call a remote working face. You find 10995.497S just where the card catalog and the online computer thought it would be, but that is only the initial nick. The book you knew about has led you to others you did not know about. To the ceiling the shelves are loaded with books about Nevada. You pull them down, one at a time, and sit on the floor and look them over until you are sitting on a pile five feet high, at which point you are late home for dinner and you get up and walk away. It’s an incomparable boon to research, all that; but it is also a reason why there are almost no large open-stack libraries left in the world.
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Statistician: One who knows which numbers to use in any eventuality.
Anonymous
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Steel doesn't know how old it is.
Anonymous
In Timothy Aeppel, 'Old machines show why Trump tax breaks may not spark new company spending' article on reuters.com (19 May 2017), quoting it as a favorite saying Dan Moore, CEO of the Dan T. Moore Co., explaining how to get value out of rebuilding and updating good used industrial machines.
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Students who have attended my [medical] lectures may remember that I try not only to teach them what we know, but also to realise how little this is: in every direction we seem to travel but a very short way before we are brought to a stop; our eyes are opened to see that our path is beset with doubts, and that even our best-made knowledge comes but too soon to an end.
In Notes on the Composition of Scientific Papers (1904), 3.
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Study the hindrances, acquaint yourself with the causes which have led up to the disease. Don’t guess at them, but know them through and through if you can; and if you do not know them, know that you do not, and still inquire. “Cannot” is a word for the idle, the indifferent, the self-satisfied, but it is not admissible in science. “I do not know” is manly if it does not stop there, but to say “I cannot” is a judgment both entirely illogical, and in itself bad as favouring rest in ignorance.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), lix.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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Tact in audacity consists in knowing how far we may go too far.
In A Call to Order (1926), 7.
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Tait once urged the advantage of Quaternions on Cayley (who never used them), saying: “You know Quaternions are just like a pocket-map.” “That may be,” replied Cayley, “but you’ve got to take it out of your pocket, and unfold it, before it’s of any use.” And he dismissed the subject with a smile.
In Life of Lord Kelvin (1910), 1137.
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That night I lie out under the stars again. The Pleiades are there winking at me. I am no longer on my way from one place to another. I have changed lives. My life now is as black and white as night and day; a life of fierce struggle under the sun, and peaceful reflection under the night sky. I feel as though I am floating on a raft far, far away from any world I ever knew.
Ted Simon
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That’s the nature of research—you don’t know what in hell you’re doing.
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The actuality of us being cognizant and accepting of the fact we are but a speck of sand in a universe sized desert, whose existence is irrelevant to any facet of universal function is a hard pill to swallow. Knowing the world will go on for another billion years after death and you will have no recollection of anything, just as you have no recollection of the billion years before your birth is a mind-boggling intuition.
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The Arctic has a call that is compelling. The distant mountains [of the Brooks Range in Alaska] make one want to go on and on over the next ridge and over the one beyond. The call is that of a wilderness known only to a few…. This last American wilderness must remain sacrosanct.
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The art of writing history is the art of emphasizing the significant facts at the expense of the insignificant. And it is the same in every field of knowledge. Knowledge is power only if a man knows what facts not to bother about.
In The Orange Tree: A Volume of Essays (1926), 60.
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The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
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