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Who said: “Dangerous... to take shelter under a tree, during a thunder-gust. It has been fatal to many, both men and beasts.”
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Explain Quotes (107 quotes)
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Et j’espère que nos neveux me sauront gré, non seulement des choses que j'ai ici expliquées, mais aussi de celles que j'ai omises volontairement, afin de leur laisser le plaisir de les inventer.
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also as to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
Concluding remark in Géométrie (1637), as translated by David Eugene Smith and Marcia L. Latham, in The Geometry of René Descartes (1925, 1954), 240.
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A living organism must be studied from two distinct aspects. One of these is the causal-analytic aspect which is so fruitfully applicable to ontogeny. The other is the historical descriptive aspect which is unravelling lines of phylogeny with ever-increasing precision. Each of these aspects may make suggestions concerning the possible significance of events seen under the other, but does not explain or translate them into simpler terms.
'Embryology and Evolution', in G. R. de Beer (ed.), Evolution: Essays on Aspects of Evolutionary Biology presented to Professor E. S. Goodrich on his Seventieth Birthday (1938), 76-7.
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A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.
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A theory that you can’t explain to a bartender is probably no damn good.
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Abstract as it is, science is but an outgrowth of life. That is what the teacher must continually keep in mind. … Let him explain … science is not a dead system—the excretion of a monstrous pedantism—but really one of the most vigorous and exuberant phases of human life.
In 'The Teaching of the History of Science', The Scientific Monthly (Sep 1918), 195-196.
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After seeking in vain for the construction of a perpetual motion machine, the relations were investigated which must subsist between the forces of nature if such a machine is to be impossible; and this inverted question led to the discovery of the law of the conservation of energy, which, again, explained the impossibility of perpetual motion in the sense originally intended.
Opening of Lecture (1900), 'Mathematische Probleme' (Mathematical Problems), to the International Congress of Mathematicians, Paris. From the original German reprinted in David Hilbert: Gesammelte Abhandlungen (Collected Treatises, 1970), Vol. 3. For full citation, see the quote that begins, “This conviction of the solvability…”, on the David Hilbert Quotes page on this website.
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Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.
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An old French geometer used to say that a mathematical theory was never to be considered complete till you had made it so clear that you could explain it to the first man you met in the street.
In Nature (1873), 8, 458.
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As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
President’s address (1883) to the British Association for the Advancement of Science, in The Collected Mathematical Papers (1895), Vol. 8, xxii.
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Dalton transformed the atomic concept from a philosophical speculation into a scientific theory—framed to explain quantitative observations, suggesting new tests and experiments, and capable of being given quantitative form through the establishment of relative masses of atomic particles.
Development of Concepts of Physics. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 175.
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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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English science … isolates the reptile or mollusk it assumes to explain; whilst reptile or mollusk only exists in system, in relation.
In essay, 'Literature', English Traits (1856), collected in Works of Ralph Waldo Emerson: Essays First and Second Series (1883), 341.
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Everybody now wants to discover universal laws which will explain the structure and behavior of the nucleus of the atom. But actually our knowledge of the elementary particles that make up the nucleus is tiny. The situation calls for more modesty. We should first try to discover more about these elementary particles and about their laws. Then it will be the time for the major synthesis of what we really know, and the formulation of the universal law.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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Fools and savages explain ; wise men investigate.
One of Gull’s favorite sayings, as given by the Editor in Preface to Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xvi.
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For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.
Letter (4 Aug 1597) to Kepler, expressing thanks and interest in the book Kepler sent him. As quoted in translation in Jackson J. Spielvogel, Western Civilization: Alternate Volume: Since 1300 (2010), Vol. 2, 494.
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Geology is part of that remarkable dynamic process of the human mind which is generally called science and to which man is driven by an inquisitive urge. By noticing relationships in the results of his observations, he attempts to order and to explain the infinite variety of phenomena that at first sight may appear to be chaotic. In the history of civilization this type of progressive scientist has been characterized by Prometheus stealing the heavenly fire, by Adam eating from the tree of knowledge, by the Faustian ache for wisdom.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 454.
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I can no more explain why I like “natural history” than why I like California canned peaches; nor why I do not care for that enormous brand of natural history which deals with invertebrates any more than why I do not care for brandied peaches. All I can say is that almost as soon as I began to read at all I began to like to read about the natural history of beasts and birds and the more formidable or interesting reptiles and fishes.
In 'My Life as a Naturalist', American Museum Journal (May 1918), 18, 321. As cited in Maurice Garland Fulton (ed.) Roosevelt's Writings: Selections from the Writings of Theodore Roosevelt (1920), 247.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I can’t explain it, but spiritually it makes sense— though I don’t understand how it does make sense.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 120
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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 profess to be able thus to account for all the [planetary] motions at the same time; but I shall show that each by itself is well explained by its proper hypothesis.
Ptolemy
(c. 100 AD). From introduction to 'Hypotheses', translated into French by Abbé N. Halma, Hypothèses et époques des planètes de Cl. Ptolémée et Hypotyposes de Proclus Diadochus (1820), 41-42. As quoted, in English, in John Louis Emil Dreyer History of the Planetary Systems from Thales to Kepler (1906), 201. In French, “Je ne prétends pas pouvoir ainsi rendre raison de tous ces mouvemens à la fois; mais je veux montrer que chacun à part s'explique très-bien par son hypothèse propre.”
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I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, “Oh, I see. That’s how it must be.” This is a sign that they explain it to themselves from within their own system.
Lichtenberg: A Doctrine of Scattered Occasions: Reconstructed From: Reconstructed From His Aphorisms and Reflections (1959), 291.
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I must … explain how I was led to concern myself with the pathogenic protozoa. … I was sent to Algeria and put in charge of a department of the hospital at Bone. A large number of my patients had malarial fevers and I was naturally led to study these fevers of which I had only seen rare and benign forms in France.
From Nobel Lecture (11 Dec 1907), 'Protozoa as Causes of Diseases', collected in Nobel Lectures, Physiology or Medicine 1901-1921 (1967, 1999), 264.
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Ideas, like ghosts (according to the common notion of a ghost), must be spoken to a little before they will explain themselves.
From Dealings With the Firm of Dombey and Son (1846), Vol. 1, 184.
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If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
…...
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If I were working in astrophysics I would find it quite hard to explain to people what I was doing. Natural history is a pretty easy thing to explain. It does have its complexities, but nowhere do you speak about things that are outside people’s experience. You might speak about a species that is outside their experience, but nothing as remote as astrophysics.
From interview with Michael Bond, 'It’s a Wonderful Life', New Scientist (14 Dec 2002), 176, No. 2373, 48.
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In a nutshell, the universe is 4% visible, 23% undetectable and 73% unimaginable. Welcome to the cosmos, full of mass you can measure but not manhandle, driven by a force you can infer but not explain.
In 'Dark Side of Creation', The Guardian (12 Feb 2004).
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In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
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In modern Europe, the Middle Ages were called the Dark Ages. Who dares to call them so now? … Their Dante and Alfred and Wickliffe and Abelard and Bacon; their Magna Charta, decimal numbers, mariner’s compass, gunpowder, glass, paper, and clocks; chemistry, algebra, astronomy; their Gothic architecture, their painting,—are the delight and tuition of ours. Six hundred years ago Roger Bacon explained the precession of the equinoxes, and the necessity of reform in the calendar; looking over how many horizons as far as into Liverpool and New York, he announced that machines can be constructed to drive ships more rapidly than a whole galley of rowers could do, nor would they need anything but a pilot to steer; carriages, to move with incredible speed, without aid of animals; and machines to fly into the air like birds.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 475.
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In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world “simplest.” It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = κ(d²x/dy²) much less simple than “it oozes,” of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plain man, namely the rate of change of a rate of change.
In 'Science and Theology as Art-Forms', Possible Worlds (1927), 227.
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In the endeavor to clearly comprehend and explain the functions of the combination of forces called “brain,” the physiologist is hindered and troubled by the views of the nature of those cerebral forces which the needs of dogmatic theology have imposed on mankind.
In 'General Conclusions, Anatomy of the Vertebrates (1868, 2011), Vol. 3, Chap 40, 823. Excerpt in Noah Porter (ed.), Half Hours with Modern Scientists (1872), 71.
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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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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 admitted, on all hands, that the Scriptures are not intended to resolve physical questions, or to explain matters in no way related to the morality of human actions; and if, in consequence of this principle, a considerable latitude of interpretation were not allowed, we should continue at this moment to believe, that the earth is flat; that the sun moves round the earth; and that the circumference of a circle is no more than three times its diameter.
In The Works of John Playfair: Vol. 1: Illustrations of the Huttonian Theory of the Earth (1822), 137.
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It is better to have recourse to a Quack, if he can cure our disorder, although he cannot explain it than to a Physician, if he can explain our disease but cannot cure it.
Reflection 323, in Lacon: Or Many Things in Few Words, Addressed to Those who Think (1820), 166.
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It is the business of scientists to explain away the magic in the world. The largest coherent body of magic remaining is the behavior of (humans) and animals.
In paper co-authored by William G. Quinn and James L. Gould, 'Nerves and genes', Nature (1 Mar 1979), 278, No. 5699, 23. As partially quoted in Michael F. Roberts and Anne E. Kruchten, Receptor Biology (2016), 238.
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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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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 among the intelligentsia … that we often find the glib compulsion to explain everything and to understand nothing.
The Rape of the Mind World 56
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It’s hard to explain to people what the significance of an invention is, so it’s hard to get funding. The first thing they say is that it can’t be done. Then they say, “You didn't do it right.” Then, when you’ve done it, they finally say, “Well, it was obvious anyway.”
http://www.thetech.org/nmot/detail.cfm?id=95&st=awardDate&qt=1997&kiosk=Off
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Isaac Asimov quote It’s the bees and the flowers.
Macro photo of bee by Forest Wander (cc by-sa 2.0) (source)
I’m tired of that stupid phrase, “the birds and the bees” which is supposed to represent “the facts of life” or the beginnings of the sex instruction of the young. … Well for heaven’s sake, has anyone ever tried to explain sex by talking about the birds and the bees? What have the birds and the bees to do with it? IT’S THE BEES AND THE FLOWERS. Will you get that through your head? IT’S THE BEES AND THE FLOWERS. The bee travels to one flower and picks up pollen from the stamens. The pollen contains the male sex cells of the plant. The bee then travels to another flower (of the same species) and the pollen brushes off onto the pistil, which contains the female sex cells of the plant. … Now in the human being … we don’t rely on bees to do it for us.
From Isaac Asimov’s letter in 'Hue and Cry' letter column in magazine, James L. Quinn (ed.), IF: Worlds of Science Fiction (Dec 1957), 7, No. 6, 119
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Kepler’s principal goal was to explain the relationship between the existence of five planets (and their motions) and the five regular solids. It is customary to sneer at Kepler for this. … It is instructive to compare this with the current attempts to “explain” the zoology of elementary particles in terms of irreducible representations of Lie groups.
In Celestial Mechanics (1969), Vol. 1, 95.
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Mathematic is either Pure or Mixed: To Pure Mathematic belong those sciences which handle Quantity entirely severed from matter and from axioms of natural philosophy. These are two, Geometry and Arithmetic; the one handling quantity continued, the other dissevered. … Mixed Mathematic has for its subject some axioms and parts of natural philosophy, and considers quantity in so far as it assists to explain, demonstrate and actuate these.
In De Augmentis, Bk. 3; Advancement of Learning, Bk. 2.
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Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics.
In 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97.
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Modern discoveries have not been made by large collections of facts, with subsequent discussion, separation, and resulting deduction of a truth thus rendered perceptible. A few facts have suggested an hypothesis, which means a supposition, proper to explain them. The necessary results of this supposition are worked out, and then, and not till then, other facts are examined to see if their ulterior results are found in Nature.
In A Budget of Paradoxes (1872), 55.
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Natural science does not simply describe and explain nature; it is part of the interplay between nature and ourselves; it describes nature as exposed to our method of questioning.
In Physics and Philosophy: The Revolution in Modern Science (1959, 1962), 81.
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Neither physical science nor psychology can ever ‘explain’ human consciousness. To me then, human consciousness lies outside science, and it is here that I seek the relationship between God and man.
In Can scientists believe? (1991), 8.
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No one really understood music unless he was a scientist, her father had declared, and not just a scientist, either, oh, no, only the real ones, the theoreticians, whose language mathematics. She had not understood mathematics until he had explained to her that it was the symbolic language of relationships. “And relationships,” he had told her, “contained the essential meaning of life.”
In The Goddess Abides, (1972), 20.
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No theory of physics that deals only with physics will ever explain physics. I believe that as we go on trying to understand the universe, we are at the same time trying to understand man.
In The Intellectual Digest (June 1973), as quoted and cited in Mark Chandos, 'Philosophical Essay: Story Theory", Kosmoautikon: Exodus From Sapiens (2015).
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No, this trick wont work ... How on earth are you ever going to explain in terms of chemistry and physics so important a biological phenomenon as first love?
…...
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Not explaining science seems to me perverse. When you’re in love, you want to tell the world.
In 'With Science on Our Side', Washington Post (9 Jan 1994).
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Obviously, what our age has in common with the age of the Reformation is the fallout of disintegrating values. What needs explaining is the presence of a receptive audience. More significant than the fact that poets write abstrusely, painters paint abstractly, and composers compose unintelligible music is that people should admire what they cannot understand; indeed, admire that which has no meaning or principle.
In Reflections on the Human Condition (1973), 62.
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Of all obstacles to a thoroughly penetrating account of existence, none looms up more dismayingly than “time.” Explain time? Not without explaining existence. Explain existence? Not without explaining time. To uncover the deep and hidden connection between time and existence, to close on itself our quartet of questions, is a task for the future.
In article, 'Hermann Weyl and the Unity of Knowledge', American Scientist (Jul-Aug 1986), 74, 372. In the online pdf on the website weylmann.com, p. 26.
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One evening at a Joint Summer Research Congerence in the early 1990’s Nicholai Reshetikhin and I [David Yetter] button-holed Flato, and explained at length Shum’s coherence theorem and the role of categories in “quantum knot invariants”. Flato was persistently dismissive of categories as a “mere language”. I retired for the evening, leaving Reshetikhin and Flato to the discussion. At the next morning’s session, Flato tapped me on the shoulder, and, giving a thumbs-up sign, whispered, “Hey! Viva les categories! These new ones, the braided monoidal ones.”
In David N. Yetter, Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants (2001), 8. Yetter writes this personal anecdote is given as a narrative in his own words. Presumable the phrases in quotation marks are based on recollection when written years later.
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One wonders whether the rare ability to be completely attentive to, and to profit by, Nature’s slightest deviation from the conduct expected of her is not the secret of the best research minds and one that explains why some men turn to most remarkably good advantage seemingly trivial accidents. Behind such attention lies an unremitting sensitivity.
In The Furtherance of Medical Research (1941), 98.
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Paleontology is a very visual inquiry. All paleontologists scribble on napkins at coffee breaks, making sketches to explain their thinking
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Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.
From the second Fubini Lecture, delivered at the Villa Gualino, Torino (2 Jun 1998), 'What is Invariant Theory, Really?' Collected in Henry H. Crapo and D. Senato (eds.), Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota (2001), 55.
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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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Rutherford was as straightforward and unpretentious as a physicist as he was elsewhere in life, and that no doubt was one of the secrets of his success. “I was always a believer in simplicity, being a simple man myself,” he said. If a principle of physics could not be explained to a barmaid, he insisted, the problem was with the principle, not the barmaid.
In Great Physicists (2001), 328.
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Science can explain why and how books are written; but it cannot account for the process being accompanied by consciousness.
Letter to E.C. Chapman (29 Jul 1891), Dan H. Laurence (ed.), Collected Letters (1965), Vol. 1, 303.
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Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking; love has found.
The Works of Honoré de Balzac (1896), Vol. 19, 80.
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Science is what we understand well enough to explain to a computer. Art is everything else we do.
…...
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Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zürich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1113.
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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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Spong and I had also several fine discourses upon the globes this afternoon, particularly why the fixed stars do not rise and set at the same hour all the year long, which he could not demonstrate nor I neither.
Entry for 19 Aug 1666. In Samuel Pepys and Henry B. Wheatley (ed.), The Diary of Samuel Pepys (1895, 1900), Vol. 5, 382. He spent the day with Mr Reeves and Mr Spong.
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Stop the mindless wishing that things would be different. Rather than wasting time and emotional and spiritual energy in explaining why we don’t have what we want, we can start to pursue other ways to get it.
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String theorists can explain plausible models of a unified universe, but unfortunately they cannot explain why we inhabit a particular one
In Book Review 'Pulling the Strings,' of Lawrence Krauss's Hiding in the Mirror: The Mysterious Lure of Extra Dimensions, from Plato to String Theory and Beyond in Nature (22 Dec 2005), 438, 1082.
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Suppose physics soon succeeds, as Stephen Hawking and a few other physicists hope and believe, in reducing physics to a single equation or a small set of equations that will “explain” all of nature’s fundamental laws. We can then ask the unanswerable question, "Why this set of equations?”
In Introduction, The Night Is Large: Collected Essays 1938-1995 (1996), xvii.
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The anxious precision of modern mathematics is necessary for accuracy, … it is necessary for research. It makes for clearness of thought and for fertility in trying new combinations of ideas. When the initial statements are vague and slipshod, at every subsequent stage of thought, common sense has to step in to limit applications and to explain meanings. Now in creative thought common sense is a bad master. Its sole criterion for judgment is that the new ideas shall look like the old ones, in other words it can only act by suppressing originality.
In Introduction to Mathematics (1911), 157.
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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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The best and safest way of philosophising seems to be, first to enquire diligently into the properties of things, and to establish those properties by experiences [experiments] and then to proceed slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them; unless so far as they may furnish experiments.
Letter to the French Jesuit, Gaston Pardies. Translation from the original Latin, as in Richard S. Westfall, Never at Rest: a Biography of Isaac Newton (1983), 242.
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The catastrophist constructs theories, the uniformitarian demolishes them. The former adduces evidence of an Origin, the latter explains the evidence away.
Aphorism 110, 'Aphorisms Concerning Ideas', The Philosophy of the Inductive Sciences (1840), Vol. 1, xxxvi.
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The equation eπi = -1 has been called the eutectic point of mathematics, for no matter how you boil down and explain this equation, which relates four of the most remarkable numbers of mathematics, it still has a certain mystery about it that cannot be explained away.
Anonymous
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The history of civilization proves beyond doubt just how sterile the repeated attempts of metaphysics to guess at nature’s laws have been. Instead, there is every reason to believe that when the human intellect ignores reality and concentrates within, it can no longer explain the simplest inner workings of life’s machinery or of the world around us.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 2.
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The history of thought should warn us against concluding that because the scientific theory of the world is the best that has yet been formulated, it is necessarily complete and final. We must remember that at bottom the generalizations of science or, in common parlance, the laws of nature are merely hypotheses devised to explain that ever-shifting phantasmagoria of thought which we dignify with the high-sounding names of the world and the universe. In the last analysis magic, religion, and science are nothing but theories of thought.
In The Golden Bough: A Study in Magic and Religion (1890, 1900), Vol. 3, 460.
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The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals.
In The Study of the History of Mathematics (1936), 28.
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The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires.
In Thoughts of a Christian Optimist: The Words of William Arthur Ward (1968), 16
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The more the subject is examined the more complex must we suppose the constitution of matter in order to explain the remarkable effects observed.
In Radio-activity (1905), 1.
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The more you understand the significance of evolution, the more you are pushed away from the agnostic position and towards atheism. Complex, statistically improbable things are by their nature more difficult to explain than simple, statistically probable things.
From edited version of a speech, at the Edinburgh International Science Festival (15 Apr 1992), as reprinted from the Independent newspaper in Alec Fisher, The Logic of Real Arguments (2004), 84.
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The number of rational hypotheses that can explain any given phenomenon is infinite.
In Zen and the Art of Motorcycle Maintenance: An inquiry into Values (1974), 107.
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The present state of the earth and of the organisms now inhabiting it, is but the last stage of a long and uninterrupted series of changes which it has undergone, and consequently, that to endeavour to explain and account for its present condition without any reference to those changes (as has frequently been done) must lead to very imperfect and erroneous conclusions.
In 'On the Law which has regulated the Introduction of New Species', The Annals and Magazine of Natural History (1855), 16, No. 93, 184.
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The prominent reason why a mathematician can be judged by none but mathematicians, is that he uses a peculiar language. The language of mathesis is special and untranslatable. In its simplest forms it can be translated, as, for instance, we say a right angle to mean a square corner. But you go a little higher in the science of mathematics, and it is impossible to dispense with a peculiar language. It would defy all the power of Mercury himself to explain to a person ignorant of the science what is meant by the single phrase “functional exponent.” How much more impossible, if we may say so, would it be to explain a whole treatise like Hamilton’s Quaternions, in such a wise as to make it possible to judge of its value! But to one who has learned this language, it is the most precise and clear of all modes of expression. It discloses the thought exactly as conceived by the writer, with more or less beauty of form, but never with obscurity. It may be prolix, as it often is among French writers; may delight in mere verbal metamorphoses, as in the Cambridge University of England; or adopt the briefest and clearest forms, as under the pens of the geometers of our Cambridge; but it always reveals to us precisely the writer’s thought.
In North American Review (Jul 1857), 85, 224-225.
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The reason I love the sea I cannot explain - it’s physical. When you dive you begin to feel like an angel. It’s a liberation of your weight.
…...
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The role of biology today, like the role of every other science, is simply to describe, and when it explains it does not mean that it arrives at finality; it only means that some descriptions are so charged with significance that they expose the relationship of cause and effect.
As quoted in Isaac Asimov and Jason A. Shulman (eds.), Isaac Asimov’s Book of Science and Nature Quotations (1988), 37. Webmaster so far has not found the primary source (can you help?)
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The special vital forces that distinguish living things from the nonliving are emergent, holistic properties, not properties of their physiochemical components. Nor can they be explained in mechanistic terms.
Interview in 'Vital Holistic Phenomena and Properties of Living', The World & I (1986), 1, No. 5-6, 265.
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The theory of quantum mechanics also explained all kinds of details, such as why an oxygen atom combines with two hydrogen atoms to make water, and so on. Quantum mechanics thus supplied the theory behind chemistry. So, fundamental theoretical chemistry is really physics.
In 'Introduction', QED: The Strange Theory of Light and Matter (1985), 5.
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The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.
From 'On Recent Discoveries in Mechanical Conversion of Motion', Proceedings of the Royal Institution of Great Britain (1873-75), 7, 179-198, reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 23.
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The ultimate aim of the modern movement in biology is in fact to explain all biology in terms of physics and chemistry.
In 'The Nature of Vitalism', Of Molecules and Men (1966), 10.
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The value of mathematical instruction as a preparation for those more difficult investigations, consists in the applicability not of its doctrines but of its methods. Mathematics will ever remain the past perfect type of the deductive method in general; and the applications of mathematics to the simpler branches of physics furnish the only school in which philosophers can effectually learn the most difficult and important of their art, the employment of the laws of simpler phenomena for explaining and predicting those of the more complex. These grounds are quite sufficient for deeming mathematical training an indispensable basis of real scientific education, and regarding with Plato, one who is … as wanting in one of the most essential qualifications for the successful cultivation of the higher branches of philosophy
In System of Logic, Bk. 3, chap. 24, sect. 9.
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Then I have more than an impression—it amounts to a certainty—that algebra is made repellent by the unwillingness or inability of teachers to explain why we suddenly start using a and b, what exponents mean apart from their handling, and how the paradoxical behavior of + and — came into being. There is no sense of history behind the teaching, so the feeling is given that the whole system dropped down readymade from the skies, to be used only by born jugglers. This is what paralyzes—with few exceptions—the infant, the adolescent, or the adult who is not a juggler himself.
In Teacher in America (1945), 82.
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There being only one universe to be explained, nobody could repeat the act of Newton, the luckiest of mortals
As stated, without quotation marks, without citation, in Alexandre Koyré, 'The Significance of the Newtonian Synthesis', The Journal of General Education (Jul 1950), 4, 265.
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They wanted facts. Facts! They demanded facts from him, as if facts could explain anything.
In Lord Jim (1900), 24.
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To speak of this subject you must... explain the nature of the resistance of the air, in the second the anatomy of the bird and its wings, in the third the method of working the wings in their various movements, in the fourth the power of the wings and the tail when the wings are not being moved and when the wind is favorable to serve as guide in various movements.
…...
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We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
From Isaac Newton, Rules of Reasoning in Philosophy, Rule 1, as translated by Andrew Motte in The Mathematical Principles of Natural Philosophy (1803), Vol. 2, 160.
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We debase the richness of both nature and our own minds if we view the great pageant of our intellectual history as a compendium of new in formation leading from primal superstition to final exactitude. We know that the sun is hub of our little corner of the universe, and that ties of genealogy connect all living things on our planet, because these theories assemble and explain so much otherwise disparate and unrelated information–not because Galileo trained his telescope on the moons of Jupiter or because Darwin took a ride on a Galápagos tortoise.
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When physicists speak of “beauty” in their theories, they really mean that their theory possesses at least two essential features: 1. A unifying symmetry 2. The ability to explain vast amounts of experimental data with the most economical mathematical expressions.
In 'Quantum Heresy', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 127.
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When you have made a thorough and reasonably long effort, to understand a thing, and still feel puzzled by it, stop, you will only hurt yourself by going on. Put it aside till the next morning; and if then you can’t make it out, and have no one to explain it to you, put it aside entirely, and go back to that part of the subject which you do understand.
From letter to Edith Rix with hints for studying (about Mar 1885), in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 240.
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When you try to explain the behavior of water, remember to demonstrate the experiment first and the cause next.
As quoted in George H. de Thierry, Journal of the Boston Society of Civil Engineers (Jan 1928), 15, No. 1, 2.
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While the method of the natural sciences is... analytic, the method of the social sciences is better described as compositive or synthetic. It is the so-called wholes, the groups of elements which are structurally connected, which we learn to single out from the totality of observed phenomena... Insofar as we analyze individual thought in the social sciences the purpose is not to explain that thought, but merely to distinguish the possible types of elements with which we shall have to reckon in the construction of different patterns of social relationships. It is a mistake... to believe that their aim is to explain conscious action ... The problems which they try to answer arise only insofar as the conscious action of many men produce undesigned results... If social phenomena showed no order except insofar as they were consciously designed, there would indeed be no room for theoretical sciences of society and there would be, as is often argued, only problems of psychology. It is only insofar as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised which demands a theoretical explanation... people dominated by the scientistic prejudice are often inclined to deny the existence of any such order... it can be shown briefly and without any technical apparatus how the independent actions of individuals will produce an order which is no part of their intentions... The way in which footpaths are formed in a wild broken country is such an instance. At first everyone will seek for himself what seems to him the best path. But the fact that such a path has been used once is likely to make it easier to traverse and therefore more likely to be used again; and thus gradually more and more clearly defined tracks arise and come to be used to the exclusion of other possible ways. Human movements through the region come to conform to a definite pattern which, although the result of deliberate decision of many people, has yet not be consciously designed by anyone.
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Who does not know Maxwell’s dynamic theory of gases? At first there is the majestic development of the variations of velocities, then enter from one side the equations of condition and from the other the equations of central motions, higher and higher surges the chaos of formulas, suddenly four words burst forth: “Put n = 5.” The evil demon V disappears like the sudden ceasing of the basso parts in music, which hitherto wildly permeated the piece; what before seemed beyond control is now ordered as by magic. There is no time to state why this or that substitution was made, he who cannot feel the reason may as well lay the book aside; Maxwell is no program-musician who explains the notes of his composition. Forthwith the formulas yield obediently result after result, until the temperature-equilibrium of a heavy gas is reached as a surprising final climax and the curtain drops.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 29-30, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 187. From the original German, “Wer kennt nicht seine dynamische Gastheorie? – Zuerst entwickeln sich majestätisch die Variationen der Geschwindigkeiten, dann setzen von der einen Seite die Zustands-Gleichungen, von der anderen die Gleichungen der Centralbewegung ein, immer höher wogt das Chaos der Formeln; plötzlich ertönen die vier Worte: „Put n=5.“Der böse Dämon V verschwindet, wie in der Musik eine wilde, bisher alles unterwühlende Figur der Bässe plötzlich verstummt; wie mit einem Zauberschlage ordnet sich, was früher unbezwingbar schien. Da ist keine Zeit zu sagen, warum diese oder jene Substitution gemacht wird; wer das nicht fühlt, lege das Buch weg; Maxwell ist kein Programmmusiker, der über die Noten deren Erklärung setzen muss. Gefügig speien nun die Formeln Resultat auf Resultat aus, bis überraschend als Schlusseffect noch das Wärme-Gleichgewicht eines schweren Gases gewonnen wird und der Vorhang sinkt.” A condensed alternate translation also appears on the Ludwig Boltzmann Quotes page of this website.
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You don’t need an explanation for everything. Recognize that there are such things as miracles - events for which there are no ready explanations. Later knowledge may explain those events quite easily.
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You explain nothing, O poet, but thanks to you all things become explicable.
In La Ville (1890), Act 1.
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[F. Werner, while a student in Princeton,] came to me and expressed his bewilderment with the fact that we make a rather narrow selection when choosing the data on which we test our theories. “How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?” It has to be admitted that we have no definite evidence that there is no such theory.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 535.
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[Music as a] language may be the best we have for explaining what we are like to others in space, with least ambiguity. I would vote for Bach, all of Bach, streamed out into space, over and over again … to put the best possible face on at the beginning of such an acquaintance. We can tell the harder truths later.
In 'Ceti', The Lives of a Cell: Notes of a Biology Watcher (1974), 53.
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[Quantum mechanics is] a phenomenon which is impossible, absolutely impossible, to explain in any classical way.
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[Someone] remarked to me once: Physicians should not say, I have cured this man, but, This man didn’t die in my care. In physics too one might say, For such and such a phenomenon I have determined causes whose absurdity cannot finally be proved, instead of saying, I have explained it.
As quoted in Joseph Peter Stern, Lichtenberg: A Doctrine of Scattered Occasions: Reconstructed From His Aphorisms and Reflections (1959), 297.
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“Why,” said the Dodo, “the best way to explain it is to do it.”
Alice's Adventures in Wonderland (1865, 1869), 33.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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