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Who said: “Genius is two percent inspiration, ninety-eight percent perspiration.”
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Ac astronomye is an hard thyng,
And yvel for to knowe;
Geometrie and geomesie,
So gynful of speche,
Who so thynketh werche with tho two
Thryveth ful late,
For sorcerie is the sovereyn book
That to tho sciences bilongeth.

Now, astronomy is a difficult discipline, and the devil to learn;
And geometry and geomancy have confusing terminology:
If you wish to work in these two, you will not succeed quickly.
For sorcery is the chief study that these sciences entail.
In William Langland and B. Thomas Wright (ed.) The Vision and Creed of Piers Ploughman (1842), 186. Modern translation by Terrence Tiller in Piers Plowman (1981, 1999), 94.
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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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Hoc age ['do this'] is the great rule, whether you are serious or merry; whether ... learning science or duty from a folio, or floating on the Thames. Intentions must be gathered from acts.
In James Boswell, The Life of Samuel Johnson (1821), 139.
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Mikroskopisch sehen lernen.
Learn to see microscopically.
In 'Festnummer zu Ehren Rudolf Virchow', Deutsche Medicinische Wochenschrift (1891), 42, 1166. As quoted in Erwin H. Ackerknecht, Rudolf Virchow: Doctor Statesman Anthropologist (1953), 21.
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A celebrated author and divine has written to me that “he has gradually learnt to see that it is just as noble a conception of the Deity to believe that He created a few original forms capable of self-development into other and needful forms, as to believe that He required a fresh act of creation to supply the voids caused by the action of His laws.”
In Origin of Species (1860), 417.
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A child of the new generation
Refused to learn multiplication.
He said “Don’t conclude
That I’m stupid or rude;
I am simply without motivation.”
…...
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A free soul ought not to pursue any study slavishly; for while bodily labors performed under constraint do not harm the body, nothing that is learned under compulsion stays with the mind.
Plato
From The Republic 7 536e, as translated by Paul Shorey (1930).
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A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that “E is dense in E” does not mean the same thing as “E is dense in itself”.
Given, without citation, in A Mathematician’s Miscellany (1953), reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 57.
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A man's own addition to what he learns is cement to bind an otherwise loose heap of stones into a structure of unity, strength, and use.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 180.
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A neurotic person can be most simply described as someone who, while he was growing up, learned ways of behaving that are self-defeating in his society.
In Margaret Mead and Rhoda Bubendey Métraux (ed.), Margaret Mead, Some Personal Views (1979), 216.
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A quarter-horse jockey learns to think of a twenty-second race as if it were occurring across twenty minutes—in distinct parts, spaced in his consciousness. Each nuance of the ride comes to him as he builds his race. If you can do the opposite with deep time, living in it and thinking in it until the large numbers settle into place, you can sense how swiftly the initial earth packed itself together, how swiftly continents have assembled and come apart, how far and rapidly continents travel, how quickly mountains rise and how quickly they disintegrate and disappear.
Annals of the Former World
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A statistician is one who has learned how to get valid evidence from statistics and how (usually) to avoid being misled by irrelevant facts. It’s too bad that we apply the same name to this kind of person that we use for those who only tabulate. It’s as if we had the same name for barbers and brain surgeons because they both work on the head.
In How to Tell the Liars from the Statisticians (1983), 1.
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A success learns how to make hay from the grass that grows under other people's feet.
Anonymous
Collected in Perry Tanksley, Of Silver and Gold: A Wealth of Thought for Someone I Treasure (1970), 72.
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A university should be a place of light, of liberty, and of learning.
Speech (11 Mar 1873) in the House of Commons, on University Education (Ireland) Bill, HC Deb 11 March 1873 vol 214 cc1814.
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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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Acceleration of knowledge generation also emphasizes the need for lifelong education. The trained teacher, scientist or engineer can no longer regard what they have learned at the university as supplying their needs for the rest of their lives.
In article Total Quality: Its Origins and its Future (1995), published at the Center for Quality and Productivity Improvement.
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Access to more information isn’t enough—the information needs to be correct, timely, and presented in a manner that enables the reader to learn from it. The current network is full of inaccurate, misleading, and biased information that often crowds out the valid information. People have not learned that “popular” or “available” information is not necessarily valid.
Response to the Pew Research Center survey question, “Is Google making us stupid?” Posted 19 Feb 2010 on page 'Future of the Internet IV' at pewinternet.org website.
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Alexander the king of the Macedonians, began like a wretch to learn geometry, that he might know how little the earth was, whereof he had possessed very little. Thus, I say, like a wretch for this, because he was to understand that he did bear a false surname. For who can be great in so small a thing? Those things that were delivered were subtile, and to be learned by diligent attention: not which that mad man could perceive, who sent his thoughts beyond the ocean sea. Teach me, saith he, easy things. To whom his master said: These things be the same, and alike difficult unto all. Think thou that the nature of things saith this. These things whereof thou complainest, they are the same unto all: more easy things can be given unto none; but whosoever will, shall make those things more easy unto himself. How? With uprightness of mind.
In Thomas Lodge (trans.), 'Epistle 91', The Workes of Lucius Annaeus Seneca: Both Morrall and Naturall (1614), 383. Also in Robert Édouard Moritz, Memorabilia Mathematica (1914), 135.
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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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Although the ocean’s surface seems at first to be completely homogeneous, after half a month we began to differentiate various seas and even different parts of oceans by their characteristic shades. We were astonished to discover that, during an flight, you have to learn anew not only to look, but also to see. At first the finest nuances of color elude you, but gradually your vision sharpens and your color perception becomes richer, and the planet spreads out before you with all its indescribable beauty.
…...
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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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And, in this case, science could learn an important lesson from the literati–who love contingency for the same basic reason that scientists tend to regard the theme with suspicion. Because, in contingency lies the power of each person, to make a difference in an unconstrained world bristling with possibilities, and nudgeable by the smallest of unpredictable inputs into markedly different channels spelling either vast improvement or potential disaster.
…...
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Angling may be said to be so like the mathematics, that it can never be fully learnt.
In Izaak Walton and Charles Cotton, 'Walton to the Reader', The Complete Angler (1653, 1824), Vol. 1, lxv.
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Any man who says he doesn’t like applause and recognition is either a fool or a liar. You learn from mistakes, but success gives you the courage to go on and do even more.
As quoted in Lawrence K. Altman, 'Christiaan Barnard, 78, Surgeon For First Heart Transplant, Dies', New York Times (3 Sep 2001)
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As a second year high school chemistry student, I still have a vivid memory of my excitement when I first saw a chart of the periodic table of elements. The order in the universe seemed miraculous, and I wanted to study and learn as much as possible about the natural sciences.
In Tore Frängsmyr and Jan E. Lindsten (eds.), Nobel Lectures: Physiology Or Medicine: 1981-1990 (1993), 555.
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As an exercise of the reasoning faculty, pure mathematics is an admirable exercise, because it consists of reasoning alone, and does not encumber the student with an exercise of judgment: and it is well to begin with learning one thing at a time, and to defer a combination of mental exercises to a later period.
In Annotations to Bacon’s Essays (1873), Essay 1, 493.
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As the issues are greater than men ever sought to realize before, the recriminations will be fiercer and pride more desperately hurt. It may help to recall that many recognized before the bomb ever feel that the time had already come when we must learn to live in One World.
…...
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As we advance in life we learn the limits of our abilities.
Inaugural Address Delivered to the University of St. Andrews, March 19, 1869 (1869), 3.
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As we discern a fine line between crank and genius, so also (and unfortunately) we must acknowledge an equally graded trajectory from crank to demagogue. When people learn no tools of judgment and merely follow their hopes, the seeds of political manipulation are sown.
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As we push ever more deeply into the universe, probing its secrets, discovering its way, we must also constantly try to learn to cooperate across the frontiers that really divide earth’s surface.
In 'The President’s News Conference at the LBJ Ranch' (29 Aug 1965). Collected in Public Papers of the Presidents of the United States: Lyndon B. Johnson: 1965 (1966), 945.
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Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a²-b² but was floored because the examiner unkindly asked for the factors of p²–q².
In 'Recent Developments in Invariant Theory', The Mathematical Gazette (Dec 1926), 13, No. 185, 217. [Note: A poll-man is a student who takes the ordinary university degree, without honours. -Webmaster]
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Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.
In Introduction to Mathematics (1911), 59.
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Before the printing press, the young learned by listening, watching, doing.
In 'Classroom Without Walls', Explorations (May 1957), No. 7. Collected in Edmund Carpenter and Marshall McLuhan (eds.), Explorations in Communication, an Anthology (1960), 1.
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Better far off to leave half the ruins and nine-tenths of the churches unseen and to see well the rest; to see them not once, but again and often again; to watch them, to learn them, to live with them, to love them, till they have become a part of life and life’s recollections.
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Biological evolution is a system of constant divergence without subsequent joining of branches. Lineages, once distinct, are separate forever. In human history, transmission across lineages is, perhaps, the major source of cultural change. Europeans learned about corn and potatoes from Native Americans and gave them smallpox in return.
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Botany is the school for patience, and it’s amateurs learn resignation from daily disappointments.
In letter to Madame de Tessé (25 Apr 1788). In Thomas Jefferson Correspondence: Printed from the Originals (1916), 7. The errant apostrophe in “it’s” appears in more than one texts checked by Webmaster.
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But come, hear my words, for truly learning causes the mind to grow. For as I said before in declaring the ends of my words … at one time there grew to be the one alone out of many, and at another time it separated so that there were many out of the one; fire and water and earth and boundless height of air, and baneful Strife apart from these, balancing each of them, and Love among them, their equal in length and breadth.
From The Fragments, Bk. 1, line 74. In Arthur Fairbanks (ed., trans.), Quotations from The First Philosophers of Greece (1898), 167-168.
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But when great and ingenious artists behold their so inept performances, not undeservedly do they ridicule the blindness of such men; since sane judgment abhors nothing so much as a picture perpetrated with no technical knowledge, although with plenty of care and diligence. Now the sole reason why painters of this sort are not aware of their own error is that they have not learnt Geometry, without which no one can either be or become an absolute artist; but the blame for this should be laid upon their masters, who are themselves ignorant of this art.
In The Art of Measurement (1525). As quoted in Albrecht Dürer and R.T. Nichol (trans.), 'Preface', Of the Just Shaping of Letters (1965), Book 3, 1-2.
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By three methods we may learn wisdom: first, by reflection, which is noblest; second, by imitation, which is easiest; and third, by experience, which is the most bitter.
Confucius
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 109
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Children are told that an apple fell on Isaac Newton’s head and he was led to state the law of gravity. This, of course, is pure foolishness. What Newton discovered was that any two particles in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is not learned from a falling apple, but by observing quantities of data and developing a mathematical theory that can be verified by additional data. Data gathered by Galileo on falling bodies and by Johannes Kepler on motions of the planets were invaluable aids to Newton. Unfortunately, such false impressions about science are not universally outgrown like the Santa Claus myth, and some people who don’t study much science go to their graves thinking that the human race took until the mid-seventeenth century to notice that objects fall.
In How to Tell the Liars from the Statisticians (1983), 127.
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Cosmology does, I think, affect the way that we perceive humanity’s role in nature. One thing we’ve learnt from astronomy is that the future lying ahead is more prolonged than the past. Even our sun is less than halfway through its life.
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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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Education consists in co-operating with what is already inside a child's mind … The best way to learn geometry is to follow the road which the human race originally followed: Do things, make things, notice things, arrange things, and only then reason about things.
In Mathematician's Delight (1943), 27.
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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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Education is not learning, but the training of the mind that it may learn.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), lxii. (by typo, shown on the age as xlii).
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Education is what remains after one has forgotten everything he learned in school.
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Education is what survives when what has been learned has been forgotten.
In 'New Methods and New Aims in Teaching', New Scientist (21 May 1964), 22, No. 392, 484. One of several articles on the theme, 'Education in 1984'.
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Euler could repeat the Aeneid from the beginning to the end, and he could even tell the first and last lines in every page of the edition which he used. In one of his works there is a learned memoir on a question in mechanics, of which, as he himself informs us, a verse of Aeneid gave him the first idea. [“The anchor drops, the rushing keel is staid.”]
In Letters of Euler (1872), Vol. 1, 24.
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Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bn) / n = x, donc Dieu existe; repondez!

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.
In Budget of Paradoxes (1878), 251. [The declaration in French expresses, “therefore God exists; please answer!” This Euler-Diderot anecdote, as embellished by De Morgan, is generally regarded as entirely fictional. Diderot before he became an encyclopedist was an accomplished mathematician and fully capable of recognizing—and responding to—the absurdity of an algebraic expression in proving the existence of God. See B.H. Brown, 'The Euler-Diderot Anecdote', The American Mathematical Monthly (May 1942), 49, No. 5, 392-303. —Webmaster.]
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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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Everything you’ve learned in school as “obvious” becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There’s not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines.
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Face this world. Learn its ways, watch it, be careful of too hasty guesses at its meaning. In the end you will find clues to it all.
In The Time Machine (1898), 90.
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Failure is success if we learn from it.
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First, it must be a pleasure to study the human body the most miraculous masterpiece of nature and to learn about the smallest vessel and the smallest fiber. But second and most important, the medical profession gives the opportunity to alleviate the troubles of the body, to ease the pain, to console a person who is in distress, and to lighten the hour of death of many a sufferer.
Reasons for his choice of medicine as a career, from essay written during his last year in the Gymnasium (high school). As quoted in Leslie Dunn, Rudolf Virchow: Now You Know His Name (2012), 8-9.
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Five centuries ago the printing press sparked a radical reshaping of the nature of education. By bringing a master’s words to those who could not hear a master’s voice, the technology of printing dissolved the notion that education must be reserved for those with the means to hire personal tutors. Today we are approaching a new technological revolution, one whose impact on education may be as far-reaching as that of the printing press: the emergence of powerful computers that are sufficiently inexpensive to be used by students for learning, play and exploration. It is our hope that these powerful but simple tools for creating and exploring richly interactive environments will dissolve the barriers to the production of knowledge as the printing press dissolved the barriers to its transmission.
As co-author with A.A. diSessa, from 'Preface', Turtle Geometry: The Computer as a Medium for Exploring Mathematics (1986), xiii.
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For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That’s a linear response. If you hit a person twice as hard they’re unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork. - When Things Start to Think, 1999.
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For behavior, men learn it, as they take diseases, one of another.
As quoted in 'Solitude and Society', The Atlantic Monthly (Dec 1857), Vol. 1, 228.
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For example, there are numbers of chemists who occupy themselves exclusively with the study of dyestuffs. They discover facts that are useful to scientific chemistry; but they do not rank as genuine scientific men. The genuine scientific chemist cares just as much to learn about erbium—the extreme rarity of which renders it commercially unimportant—as he does about iron. He is more eager to learn about erbium if the knowledge of it would do more to complete his conception of the Periodic Law, which expresses the mutual relations of the elements.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 20.
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For too much learning makes no man mad!
From poem, 'An Essay on Mind' (1826), line 584. In Elizabeth Barrett Browning and Harriet Waters Preston (ed.), 'Appendix: Juvenilia', The Complete Poetical Works of Mrs. Browning (1900), 505.
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For undemocratic reasons and for motives not of State, they arrive at their conclusions—largely inarticulate. Being void of self-expression they confide their views to none; but sometimes in a smoking room, one learns why things were done.
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For, in mathematics or symbolic logic, reason can crank out the answer from the symboled equations—even a calculating machine can often do so—but it cannot alone set up the equations. Imagination resides in the words which define and connect the symbols—subtract them from the most aridly rigorous mathematical treatise and all meaning vanishes. Was it Eddington who said that we once thought if we understood 1 we understood 2, for 1 and 1 are 2, but we have since found we must learn a good deal more about “and”?
In 'The Biological Basis of Imagination', American Thought: 1947 (1947), 81.
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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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From my father I learned to build things, to take them apart, and to fix mechanical and electrical equipment in general. I spent vast hours in a woodworking shop he maintained in the basement of our house, building gadgets, working both with my father and alone, often late into the night. … This play with building, fixing, and designing was my favorite activity throughout my childhood, and was a wonderful preparation for my later career as an experimentalist working on the frontiers of chemistry and physics.
From 'Richard E. Smalley: Biographical', collected in Tore Frängsmyr (ed.), Les Prix Nobel: The Nobel Prizes 1996 (1997).
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From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.
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General preparatory instruction must continue to be the aim in the instruction at the higher institutions of learning. Exclusive selection and treatment of subject matter with reference to specific avocations is disadvantageous.
In Resolution adopted by the German Association for the Advancement of Scientific and Mathematical Instruction, in Jahresbericht der Deutschen Mathematiker Vereinigung (1896), 41. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 72.
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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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Has Matter more than Motion? Has it Thought,
Judgment, and Genius? Is it deeply learn’d
In Mathematics? Has it fram’d such Laws,
Which, but to guess, a Newton made immortal?—
If so, how each sage Atom laughs at me,
Who think a Clod inferior to a Man!
The Complaint: or, Night-Thoughts on Life, Death, and Immortality (1742, 1750), Night 9, 279.
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He is a learned man that understands one subject, a very learned man that understands two.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws.
In A Week on the Concord and Merrimack Rivers (1862), 381.
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He that desires to learn Truth should teach himself by Facts and Experiments; by which means he will learn more in a Year than by abstract reasoning in an Age.
In Academical Lectures on the Theory of Physic (1751), Vol. 1. As quoted in Thomas Steele Hall, A Source Book in Animal Biology (1951), 485.
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He who neglects learning in his youth loses the past and is dead for the future
Euripides
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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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Helmholtz—the physiologist who learned physics for the sake of his physiology, and mathematics for the sake of his physics, and is now in the first rank of all three.
In 'Aims and Instruments of Scientific Thought', Lectures and Essays, Vol. 1 (1901), 165.
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History shows that the human animal has always learned but progress used to be very slow. This was because learning often depended on the chance coming together of a potentially informative event on the one hand and a perceptive observer on the other. Scientific method accelerated that process.
In article Total Quality: Its Origins and its Future (1995), published at the Center for Quality and Productivity Improvement.
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Humanity is about to learn that a lunatic (touched by the moon) is not a crazy man but one so sane, well-informed, well-coordinated, self-disciplined, cooperative and fearless as to be the first earthian human to have been ferried to a physical landing upon the moon, and thereafter to have been returned safely to reboard his mother space vehicle earth.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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Humility is not a state of mind conducive to the advancement of learning.
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Hypotheses are cradle-songs by which the teacher lulls his scholars to sleep. The thoughtful and honest observer is always learning more and more of his limitations; he sees that the further knowledge spreads, the more numerous are the problems that make their appearance.
In The Maxims and Reflections of Goethe (1906), 195.
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I am always willing to learn, however I do not always like to be taught.
Speech in the House of Commons (4 Nov 1952). As quoted in Colin Coote, Sir Winston Churchill: A Self-Portrait (1954), 35.
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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 ask any one who has adopted the calling of an engineer, how much time he lost when he left school, because he had to devote himself to pursuits which were absolutely novel and strange, and of which he had not obtained the remotest conception from his instructors? He had to familiarize himself with ideas of the course and powers of Nature, to which his attention had never been directed during his school-life, and to learn, for the first time, that a world of facts lies outside and beyond the world of words.
From After-Dinner Speech (Apr 1869) delivered before the Liverpool Philomathic Society, 'Scientific Education', collected in Lay Sermons, Addresses, and Reviews (1870), 63. Previously published in Macmillan’s Magazine.
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I became expert at dissecting crayfish. At one point I had a crayfish claw mounted on an apparatus in such a way that I could operate the individual nerves. I could get the several-jointed claw to reach down and pick up a pencil and wave it around. I am not sure that what I was doing had much scientific value, although I did learn which nerve fiber had to be excited to inhibit the effects of another fiber so that the claw would open. And it did get me interested in robotic instrumentation, something that I have now returned to. I am trying to build better micromanipulators for surgery and the like.
In Jeremy Bernstein, 'A.I.', The New Yorker (14 Dec 1981).
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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 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 do not fancy this acquiescence in second-hand hearsay knowledge; for, though we may be learned by the help of another’s knowledge, we can never be wise but by our own wisdom.
In 'Of Pedantry', collected in The Essays of Michael Seigneur de Montaigne: Translated Into English (1759), Vol. 1, 144.
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I found that I could find the energy…that I could find the determination to keep on going. I learned that your mind can amaze your body, it you just keep telling yourself, I can do it…I can do it…I can do it!
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I grew up in love with science, asking the same questions all children ask as they try to codify the world to find out what makes it work. “Who is the smartest person in the world?” and “Where is the tallest mountain in the world?” turned into questions like, “How big is the universe?” and “What is it that makes us alive?”
In Introduction to Isaac Asimov and Jason A. Shulman (eds.), Isaac Asimov’s Book of Science and Nature Quotations (1988), xix.
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I have learned to use the word “impossible” with the greatest caution.
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I learned this, at least, by my experiment: that if one advances confidently in the direction of his dreams, and endeavors to live the life which he has imagined, he will meet with a success unexpected in common hours.
In Walden: or, Life in the Woods (1854, 1893), 496.
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I learned, and later had to unlearn in order to become a scientist myself, that science is simply measurement and the answers are in print.
This View of Life: the World of an Evolutionist (1964), 27.
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I like to handle babies. You can learn a lot from the way they respond, the way they slide down your hips, the way they trust you. The first thing a child must learn is to trust.
As quoted in Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 144.
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I think I’ve had more failures than successes, but I don’t see the failures as mistakes because I always learned something from those experiences. I see them as having not achieved the initial goal, nothing more than that.
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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I think that the unity we can seek lies really in two things. One is that the knowledge which comes to us at such a terrifyingly, inhumanly rapid rate has some order in it. We are allowed to forget a great deal, as well as to learn. This order is never adequate. The mass of ununderstood things, which cannot be summarized, or wholly ordered, always grows greater; but a great deal does get understood.
The second is simply this: we can have each other to dinner. We ourselves, and with each other by our converse, can create, not an architecture of global scope, but an immense, intricate network of intimacy, illumination, and understanding. Everything cannot be connected with everything in the world we live in. Everything can be connected with anything.
Concluding paragraphs of 'The Growth of Science and the Structure of Culture', Daedalus (Winter 1958), 87, No. 1, 76.
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I was always afraid of dying. Always. It was my fear that made me learn everything I could about my airplane and my emergency equipment, and kept me flying respectful of my machine and always alert in the cockpit.
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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 I set out to prove something, I am no real scientist—I have to learn to follow where the facts lead me—I have to learn to whip my prejudices.
Attributed, as cited in Peter McDonald (ed.), Oxford Dictionary of Medical Quotations (2004), 95. Quoted earlier without citation as “If I want to find truth, I must have an open mind. I have to learn to follow where the facts lead me—I have to learn to whip my prejudices,” in World Order (1948), 14, 76.
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If men of science owe anything to us, we may learn much from them that is essential. For they can show how to test proof, how to secure fulness and soundness in induction, how to restrain and to employ with safety hypothesis and analogy.
Lecture, 'The Study of History' (11 Jun 1895) delivered at Cambridge, published as A Lecture on The Study of History (1895), 54.
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If there is one thing I’ve learned in my years on this planet, it’s that the happiest and most fulfilled people I’ve known are those who devoted themselves to something bigger and more profound than merely their own self interest.
From speech (3 Oct 1977) announcing he was donating his papers to Ohio State University. As quoted on the OSU website.
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If we have learned anything at all in this century, it is that all new technologies will be put to use, sooner or later, for better or worse, as it is in our nature to do
In 'Autonomy', The Lives of a Cell: Notes of a Biology Watcher (1974), 79.
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If you are young, then I say: Learn something about statistics as soon as you can. Don’t dismiss it through ignorance or because it calls for thought. … If you are older and already crowned with the laurels of success, see to it that those under your wing who look to you for advice are encouraged to look into this subject. In this way you will show that your arteries are not yet hardened, and you will be able to reap the benefits without doing overmuch work yourself. Whoever you are, if your work calls for the interpretation of data, you may be able to do without statistics, but you won’t do as well.
In Facts from Figures (1951), 463.
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If you look over my Scientific American columns you will see that they get progressively more sophisticated as I began reading math books and learning more about the subject. There is no better way to learn anything than to write about it!
In Kendrick Frazier, 'A Mind at Play: An Interview with Martin Gardner', Skeptical Inquirer (Mar/Apr 1998), 22, No. 2, 36.
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If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don’t listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.
In Herbert Spencer Lecture at Oxford (10 Jun 1933), 'On the Methods of Theoretical Physics'. Printed inPhilosophy of Science (Apr 1934), 1, No. 2, 163.
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If your actions create a legacy that inspires others to dream more, learn more, do more and become more, then, you are an excellent leader.
In Lorne A. Adrain (ed.), The Most Important Thing I Know<: Life Lessons From Colin Powell, Stephen Covey, Maya Angelou and Over 75 Other Eminent Individuals (1997), 60-61. A similar quote is found attributed to John Quincy Adams, but this is likely not authentic, as documented on the quoteinvestigator.com website.
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Imperceptibly a change had been wrought in me until I no longer felt alone in a strange, silent country. I had learned to hear the echoes of a time when every living thing upon this land and even the varied overshadowing skies had its voice, a voice that was attentively heard and devoutly heeded by the ancient people of America. Henceforth, to me the plants, the trees, the clouds and all things had become vocal with human hopes, fears and supplications.
From Preface, Indian Games and Dances with Native Songs (1915), v.
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In a class I was taking there was one boy who was much older than the rest. He clearly had no motive to work. I told him that, if he could produce for me, accurately to scale, drawings of the pieces of wood required to make a desk like the one he was sitting at, I would try to persuade the Headmaster to let him do woodwork during the mathematics hours—in the course of which, no doubt, he would learn something about measurement and numbers. Next day, he turned up with this task completed to perfection. This I have often found with pupils; it is not so much that they cannot do the work, as that they see no purpose in it.
In Mathematician's Delight (1943), 52.
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In all spheres of science, art, skill, and handicraft it is never doubted that, in order to master them, a considerable amount of trouble must be spent in learning and in being trained. As regards philosophy, on the contrary, there seems still an assumption prevalent that, though every one with eyes and fingers is not on that account in a position to make shoes if he only has leather and a last, yet everybody understands how to philosophize straight away, and pass judgment on philosophy, simply because he possesses the criterion for doing so in his natural reason.
From Phänomenologie des Geistes (1807) as translated by J.B. Baillie in 'Preface', The Phenomenology of Mind (1910), Vol. 1, 67.
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In Heaven there'll be no algebra,
No learning dates or names,
But only playing golden harps
And reading Henry James.
Anonymous
Displayed at James’s home, Lambs House in Rye. Said to have been written by Henry James’s nephew in the guest book there, as stated in J.D. McClatchy, Sweet Theft: A Poet's Commonplace Book (2016), 212. https://books.google.com/books?isbn=1619027607 J.D. McClatchy - 2016
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In her starry shade
Of dim and solitary loveliness,
I learn the language of another world.
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In science, as in life, learning and knowledge are distinct, and the study of things, and not of books, is the source of the latter.
In 'On The Study of Zoology', Lay Sermons, Addresses, and Reviews (1870), 112.
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In science, one can learn the most by studying what seems to be the least.
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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In seed time learn, in harvest teach, in winter enjoy.
In 'Proverbs', The Poems: With Specimens of the Prose Writings of William Blake (1885), 279.
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In the whole history of the world there was never a race with less liking for abstract reasoning than the Anglo-Saxon. … Common-sense and compromise are believed in, logical deductions from philosophical principles are looked upon with suspicion, not only by legislators, but by all our most learned professional men.
In Teaching of Mathematics (1902), 20-21.
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Individual dolphins and whales are to be given the legal rights of human individuals. … Research into communication with cetaceans is no longer simply a scientific pursuit…. We must learn their needs, their ethics, their philosophy, to find out who we are on this planet, in this galaxy.
In The Rights of Cetaceans under Human Laws (1978), 138. This shows Lilly’s enthusiasm, but is definitely an over-reach. Edward O. Wilson bluntly rejects it. See the quote beginning “Lilly's writing differs…” on the Edward Wilson Quotation page on this website.
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Instead of being presented with stereotypes by age, sex, color, class, or religion, children must have the opportunity to learn that within each range, some people are loathsome and some are delightful.
In Twentieth Century Faith: Hope and Survival (1972), 61.
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Intelligence is the capacity to learn. Learning is based on the acquisition of new knowledge about the environment. Memory is its retention.
…...
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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 curious to observe how differently these great men [Plato and Bacon] estimated the value of every kind of knowledge. Take Arithmetic for example. Plato, after speaking slightly of the convenience of being able to reckon and compute in the ordinary transactions of life, passes to what he considers as a far more important advantage. The study of the properties of numbers, he tells us, habituates the mind to the contemplation of pure truth, and raises us above the material universe. He would have his disciples apply themselves to this study, not that they may be able to buy or sell, not that they may qualify themselves to be shop-keepers or travelling merchants, but that they may learn to withdraw their minds from the ever-shifting spectacle of this visible and tangible world, and to fix them on the immutable essences of things.
Bacon, on the other hand, valued this branch of knowledge only on account of its uses with reference to that visible and tangible world which Plato so much despised. He speaks with scorn of the mystical arithmetic of the later Platonists, and laments the propensity of mankind to employ, on mere matters of curiosity, powers the whole exertion of which is required for purposes of solid advantage. He advises arithmeticians to leave these trifles, and employ themselves in framing convenient expressions which may be of use in physical researches.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 394.
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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 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 hard to learn more. What is hard is to unlearn when you discover yourself wrong
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It is of interest to note that while some dolphins are reported to have learned English—up to fifty words used in correct context—no human being has been reported to have learned delphinese.
This wording was quoted, without citation, as from a “news item”, in Vernon Ingraham (ed.), Survival: Readings on Environment (1971), Vol. 2, 69, but without any attribution to Carl Sagan. In The Cosmic Connection: An Extraterrestrial Perspective (1973), 136, Carl Sagan describes meeting in Winter 1963 with a researcher, John Lilly, and a dolphin called Elvar. Sagan wrote, “John believed that Elvar had learned some dozens of words of English. To the best of my knowledge, no human has ever learned a single word of delphinese.” Sagan thought he heard Elvar utter “More!”, and that “it was in context,” because he had been scratching the dolphin’s belly. Webmaster speculates the news item referred to a subsequent interview with Sagan during which this subject came up. Can you help identify the primary news source?
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It is of priceless value to the human race to know that the sun will supply the needs of the earth, as to light and heat, for millions of years; that the stars are not lanterns hung out at night, but are suns like our own; and that numbers of them probably have planets revolving around them, perhaps in many cases with inhabitants adapted to the conditions existing there. In a sentence, the main purpose of the science is to learn the truth about the stellar universe; to increase human knowledge concerning our surroundings, and to widen the limits of intellectual life.
In 'The Nature of the Astronomer’s Work', North American Review (Jun 1908), 187, No. 631, 915.
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It is only when a child has learned to hold still that it can be considered a creature of sense.
Aphorism as given by the fictional character Dezhnev Senior, in Fantastic Voyage II: Destination Brain (1987), 170.
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It is the curse of humanity that it learns to tolerate even the most horrible situations by habituation.
From the original German, “Es ist ein Fluch des Menschengeschlechtes, dass es durch Gewöhnung auch das Schrecklichste ertragen lernt,” in 'Mittheilungen über die in Oberschlesien herrschende Typhus-Epidemie', R. Virchow and B. Reinhardt, Archiv für pathologische Anatomie und Physiologie und für klinische Medicin (1848), 2, No. 2, 156. As translated in Rudolf Virchow and L.J. Rather (ed.), 'Report on the Typhus Epidemic in Upper Silesia', Collected Essays in Public Health and Epidemiology, (1985), 213, as reprinted in Social Medicine (2006), 1, No. 1, 16.
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It is the malady of our age that the young are so busy teaching us that they have no time left to learn.
In Reflections on the Human Condition (1973), 22.
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It may be said of some very old places, as of some very old books, that they are destined to be forever new. The nearer we approach them, the more remote they seem: the more we study them, the more we have yet to learn. Time augments rather than diminishes their everlasting novelty; and to our descendants of a thousand years hence it may safely be predicted that they will be even more fascinating than to ourselves. This is true of many ancient lands, but of no place is it. so true as of Egypt.
Opening remark in Pharaohs, Fellahs and Explorers (1891), 3.
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It’s what you learn after you know it all that counts.
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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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Louis Agassiz quote: Lay aside all conceit Learn to read the book of Nature for yourself. Those who have succeeded best have fol
Lay aside all conceit. Learn to read the book of Nature for yourself. Those who have succeeded best have followed for years some slim thread which once in a while has broadened out and disclosed some treasure worth a life-long search.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 145.
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Learn just enough of the subject [metaphysics] to enable your mind to get rid of it.
As quoted in Geoffrey Madan’s Notebooks: A Selection (1984), 61.
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Learn to reverence night and to put away the vulgar fear of it, for, with the banishment of night from the experience of man, there vanishes as well a religious emotion, a poetic mood, which gives depth to the adventure of humanity. By day, space is one with the earth and with man - it is his sun that is shining, his clouds that are floating past; at night, space is his no more. When the great earth, abandoning day, rolls up the deeps of the heavens and the universe, a new door opens for the human spirit, and there are few so clownish that some awareness of the mystery of being does not touch them as they gaze. For a moment of night we have a glimpse of ourselves and of our world islanded in its stream of stars - pilgrims of mortality, voyaging between horizons across eternal seas of space and time. Fugitive though the instant be, the spirit of man is, during it, ennobled by a genuine moment of emotional dignity, and poetry makes its own both the human spirit and experience.
…...
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Learning acquired in youth arrests the evil of old age; and if you understand that old age has wisdom for its food, you will so conduct yourself in youth that your old age will not lack for nourishment.
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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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Learning how to access a continuity of common sense can be one of your most efficient accomplishments in this decade. Can you imagine common sense surpassing science and technology in the quest to unravel the human stress mess? In time, society will have a new measure for confirming truth. It’s inside the people-not at the mercy of current scientific methodology. Let scientists facilitate discovery, but not invent your inner truth.
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Learning how to operate a soul figures to take time.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 22
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Learning is by nature, curiosity.
Philo
…...
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Learning is wealth to the poor, an honor to the rich, an aid to the young, and a support and comfort to the aged.
As cited in Abram N. Coleman (ed.), Proverbial Wisdom: Proverbs, Maxims and Ethical Sentences (1903), 130. Often-seen attribution to John C. Lavater is probably erroneous. Several quote collections of the same era give the quote without citation. In Tryon Edwards, Dictionary of Thoughts (1908), 294, this quote is given without citation, followed by a blank line separator, and then an unrelated quote by Lavater. This juxtaposition is likely the source of confusion in attribution.
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Learning makes a man fit company for himself.
Anonymous
Saying, collected in Thomas Fuller (ed.), Gnomologia: Adagies and Proverbs; Wise Sentences and Witty Sayings (1732), 135. Attributed to Edward Young in Tryon Edwards (ed.), A Dictionary of Thoughts (1891), 295, and other quote collections of the period. Webmaster has not yet found a specific work by Young that includes the quote. Note that in recent use, the quote is widely attributed to Fuller, but he did not write it, just collected it. Fuller included in this compilation interesting adages he had found from books, but did not identify specific sources. Young was a contemporary.
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Learning obscures as well as illustrates; it heaps up chaff when there is no more wheat.
In 'On the Interpretation of Scripture', Essays and Reviews (1860), 337.
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Learning science, learning about nature, is more than the mere right of taxpayers; it is more than the mere responsibility of voters. It is the privilege of the human being.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 202.
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Learning without thought is labor lost; thought without learning is perilous.
Confucius
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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Life is a series of experiences, each one of which makes us bigger, even though it is hard to realize this. For the world was built to develop character, and we must learn that the setbacks and griefs which we endure help us in our marching onward.
…...
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Live and learn; die and forget it all.
Anonymous
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Living with my Indian friends I found I was a stranger in my native land. As time went on, the outward aspect of nature remained the same, but change was wrought in me. I learned to hear the echoes of a time when every living thing even the sky had a voice. That voice devoutly heard by the ancient people of America I desired to make audible to others.
On the plaque over her cremated remains in the patio of the Art Museum at Sante Fe. Edited by William Henry Homes from the preface she wrote in her last book, a small collection of Indian Games and Dances (1915). As stated in concluding pages of Joan T. Mark, A Stranger in Her Native Land: Alice Fletcher and the American Indians (1988), 354-355.
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Logic does not pretend to teach the surgeon what are the symptoms which indicate a violent death. This he must learn from his own experience and observation, or from that of others, his predecessors in his peculiar science. But logic sits in judgment on the sufficiency of that observation and experience to justify his rules, and on the sufficiency of his rules to justify his conduct. It does not give him proofs, but teaches him what makes them proofs, and how he is to judge of them.
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, 11.
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Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.
Opening paragraph in Chap. 1 of Mathematician's Delight (1943, 2012), 7.
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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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Men who have had a great deal of experience learn not to lose their tempers.
Quoted without citation in Tryon Edwards, A Dictionary of Thoughts: Being a Cyclopedia of Laconic Quotations (1891), 565. Webmaster invites help pinpointing the primary source.
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Mere poets are sottish as mere drunkards are, who live in a continual mist, without seeing or judging anything clearly. A man should be learned in several sciences, and should have a reasonable, philosophical and in some measure a mathematical head, to be a complete and excellent poet.
In Notes and Observations on The Empress of Morocco (1674), 70.
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Metaphysics. The science to which ignorance goes to learn its knowledge, and knowledge to learn its ignorance. On which all men agree that it is the key, but no two upon how it is to be put into the lock.
Lest remark in letter to Dr. Whewell (25 May 1850), collected in Sophia Elizabeth De Morgan (ed.), Memoir of Augustus De Morgan (1882), 210.
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Most pilots learn, when they pin on their wings and go out and get in a fighter, especially, that one thing you don’t do, you don’t believe anything anybody tells you about an airplane.
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Much have I learned from my teachers, more from my colleagues, but most from my students.
Talmud
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My mother made me a scientist without ever intending to. Every other Jewish mother in Brooklyn would ask her child after school, “So? Did you learn anything today?” But not my mother. … “Izzy,” she would say, “did you ask a good question today?” That difference - asking good questions - made me become a scientist.
In letters column of New York Times (19 Jan 1988) from Donald Sheff, who quoted what his friend, Arthur Sackler, received in answer, upon asking Rabi why he became a scientist.
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Nature without learning is a blind thing, and learning without nature is an imperfect thing, and practice without both is an ineffective thing. Just as in farming, first of all the soil must be good, secondly, the husbandman skilful, and thirdly, the seed sound, so, after the same manner, nature is like to the soil, the teacher to the farmer and the verbal counsels precepts like to the seed.
Plutarch
In 'On the Education of Children', Moralia (1927), Vol 3, 9, as translated by Frank Cole Babbitt.
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Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music. and it would fear the piano exactly as most students fear what is supposed to be mathematics.
In Mathematician's Delight (1943), 8.
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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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Not every one of our desires can be immediately gratified. We’ve got to learn to wait patiently for our dreams to come true, especially on the path we’ve chosen. But while we wait, we need to prepare symbolically a place for our hopes and dreams.
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Nothing I then learned [in high school] had any bearing at all on the big and real questions. Who am I? What am I doing here? What is the world? What is my relationship to it?
This View of Life: the World of an Evolutionist (1964), 37.
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Once you have learned to fly your plane, it is far less fatiguing to fly than it is to drive a car. You don’t have to watch every second for cats, dogs, children, lights, road signs, ladies with baby carriages and citizens who drive out in the middle of the block against the lights... Nobody who has not been up in the sky on a glorious morning can possibly imagine the way a pilot feels in free heaven.
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One can learn imitation history—kings and dates, but not the slightest idea of the motives behind it all; imitation literature—stacks of notes on Shakespeare’s phrases, and a complete destruction of the power to enjoy Shakespeare.
In Mathematician's Delight (1943), 8.
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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 of the greatest gifts science has brought to the world is continuing elimination of the supernatural, and it was a lesson that my father passed on to me, that knowledge liberates mankind from superstition. We can live our lives without the constant fear that we have offended this or that deity who must be placated by incantation or sacrifice, or that we are at the mercy of devils or the Fates. With increasing knowledge, the intellectual darkness that surrounds us is illuminated and we learn more of the beauty and wonder of the natural world.
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One will weave the canvas; another will fell a tree by the light of his ax. Yet another will forge nails, and there will be others who observe the stars to learn how to navigate. And yet all will be as one. Building a boat isn’t about weaving canvas, forging nails, or reading the sky. It’s about giving a shared taste for the sea, by the light of which you will see nothing contradictory but rather a community of love.
From the French, “Celui-là tissera des toiles, l’autre dans la forêt par l’éclair de sa hache couchera l’arbre. L’autre, encore, forgera des clous, et il en sera quelque part qui observeront les étoiles afin d’apprendre à gouverner. Et tous cependant ne seront qu’un. Créer le navire ce n’est point tisser les toiles, forger les clous, lire les astres, mais bien donner le goût de la mer qui est un, et à la lumière duquel il n’est plus rien qui soit contradictoire mais communauté dans l’amour.” In Citadelle (1948), Sect. 75, 687. An English edition was published as “Wisdom of the Sands.” The translation in the subject quote is given the website quoteinvestigator.com which discusses how it may have been paraphrased anonymously to yield the commonly seen quote as “If you want to build a ship, don’t recruit the men to gather the wood, divide the work and give orders. Instead, teach them to yearn for vast and endless sea.”
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Only go on working so long as the brain is quite clear. The moment you feel the ideas getting confused leave off and rest, or your penalty will be that you will never learn Mathematics at all!
From letter to Edith Rix with hints for studying (about Mar 1885), in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 241.
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Our aim [with poetry therapy] is to help the individual learn the art of helping himself or herself. We believe strongly with Walt Whitman, who wrote, “I am larger, better than I thought/I did not know I held so much goodness.”
As given in obituary, Myrna Oliver, 'Arthur Lerner; Promoted Use of Poetry in Therapy', Los Angeles Times (8 Apr 1998), quoting from a The Times article (1987).
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Our indirect methods have taught us a mountain of things about horses, but if you wished to learn even more, would you rather be Whirlaway in the stretch, than interview Eddie Arcaro afterwards?
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Philosophers no longer write for the intelligent, only for their fellow professionals. The few thousand academic philosophers in the world do not stint themselves: they maintain more than seventy learned journals. But in the handful that cover more than one subdivision of philosophy, any given philosopher can hardly follow more than one or two articles in each issue. This hermetic condition is attributed to “technical problems” in the subject. Since William James, Russell, and Whitehead, philosophy, like history, has been confiscated by scholarship and locked away from the contamination of general use.
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Philosophy is written in that great book that lies before our gaze—I mean the universe—but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written.
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 203.
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Philosophy [the universe] is written in that great book which ever lies before our eyes ... We cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language ... without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.
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Physiology is the experimental science par excellence of all sciences; that in which there is least to be learnt by mere observation, and that which affords the greatest field for the exercise of those faculties which characterize the experimental philosopher.
In 'Educational Value of Natural History Sciences', Lay Sermons, Addresses, and Reviews (1870), 90.
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Science by itself produces a very badly deformed man who becomes rounded out into a useful creative being only with great difficulty and large expenditure of time. … It is a much smaller matter to both teach and learn pure science than it is to intelligently apply this science to the solution of problems as they arise in daily life.
As quoted in Gary W. Matkin, Technology Transfer and the University (1990), 24.
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Science confers power on anyone who takes the trouble to learn it.
In 'With Science on Our Side', Washington Post (9 Jan 1994).
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Science is for those who learn; poetry for those who know.
In Meditations of a Parish Priest: Thoughts, Pt. 1, No. 71, translated from the third French edition by Isabel Florence Hapgood (1886), 43.
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Science may be learned by rote, but Wisdom not.
(1759). From The Life and Opinions of Tristram Shandy, Gentleman, collected in Collection of Ancient and Modern British Novels and Romances (1832), Vol. 38, 311.
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Science should be taught the way mathematics is taught today. Science education should begin in kindergarten. In the first grade one would learn a little more, in the second grade, a little more, and so on. All students should get this basic science training.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 738.
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scientist is a ... learned child. Others must outgrow it. Scientists can stay that way all their life.
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Seeing much, suffering much, and studying much are the three pillars of learning.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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Since we have no choice but to be swept along by [this] vast technological surge, we might as well learn to surf.
in David Western and Mary C. Pearl, Conservation for the 21st Century (1989).
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So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting what he is learning, of propagating through others the ideas and impressions seething in his own brain, without stunting and atrophying his moral nature and drying up the surest sources of his future intellectual replenishment.
In Address (22 Feb 1877) for Commemoration Day at Johns Hopkins University. Published as a pamphlet, and reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 77.
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Someone who had begun to read geometry with Euclid, when he had learned the first proposition, asked Euclid, “But what shall I get by learning these things?” whereupon Euclid called his slave and said, “Give him three-pence, since he must make gain out of what he learns.”
As quoted in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-Book (1914), 152-153, citing Stobaeus, Edition Wachsmuth (1884), Ecl. II.
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Space exploration is risky. It’s hard. And actually, let me say here that I feel like we need to take on more risk than we have been in space exploration. The public doesn’t like risk, and they hate failure. But failures happen. They shouldn’t happen for stupid reasons. But if they happen when you were trying something risky, you learn. That teaches you something. At least it should. And you try harder next time.
On the failure of the Cosmos-1 solar sail (Jun 2005).
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Students should learn to study at an early stage the great works of the great masters instead of making their minds sterile through the everlasting exercises of college, which are of no use whatever, except to produce a new Arcadia where indolence is veiled under the form of useless activity. … Hard study on the great models has ever brought out the strong; and of such must be our new scientific generation if it is to be worthy of the era to which it is born and of the struggles to which it is destined.
In Giornale di matematiche, Vol. 11, 153.
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Study the science of art. Study the art of science. Develop your senses - especially learn how to see. Realize that everything connects to everything else.
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Such is the substance of my faith; and if I were to sum up my credo in a single word, it would be that proud motto of Fustel de Coulanges, Quaero, I seek to learn.
From Conclusion of Presidential Address (29 Dec 1950) read at the annual dinner of the American Historical Association, Chicago, 'Faith of a Historian', The American Historical Review (Jan 1951), 56, No. 2, 261-275.
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Suppose that we are wise enough to learn and know—and yet not wise enough to control our learning and knowledge, so that we use it to destroy ourselves? Even if that is so, knowledge remains better than ignorance. It is better to know—even if the knowledge endures only for the moment that comes before destruction—than to gain eternal life at the price of a dull and swinish lack of comprehension of a universe that swirls unseen before us in all its wonder. That was the choice of Achilles, and it is mine, too.
Widely seen on the Web, but always without citation, so regard attribution as uncertain. Webmaster has not yet found reliable verification. Contact Webmaster if you know a primary print source.
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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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Telescopes are in some ways like time machines. They reveal galaxies so far away that their light has taken billions of years to reach us. We in astronomy have an advantage in studying the universe, in that we can actually see the past.
We owe our existence to stars, because they make the atoms of which we are formed. So if you are romantic you can say we are literally starstuff. If you’re less romantic you can say we’re the nuclear waste from the fuel that makes stars shine.
We’ve made so many advances in our understanding. A few centuries ago, the pioneer navigators learnt the size and shape of our Earth, and the layout of the continents. We are now just learning the dimensions and ingredients of our entire cosmos, and can at last make some sense of our cosmic habitat.
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That learning is most requisite which unlearns evil
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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The adequate study of culture, our own and those on the opposite side of the globe, can press on to fulfillment only as we learn today from the humanities as well as from the sciences.
In An Anthropologist at Work (1959, 2011), 470.
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The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
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The authority of those who profess to teach is often a positive hindrance to those who desire to learn.
In De Natura Deorum: Academica (c. 45 B.C.), as translated to English (1933), 13.
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The dexterous management of terms and being able to fend and prove with them, I know has and does pass in the world for a great part of learning; but it is learning distinct from knowledge, for knowledge consists only in perceiving the habitudes and relations of ideas one to another, which is done without words; the intervention of sounds helps nothing to it. And hence we see that there is least use of distinction where there is most knowledge: I mean in mathematics, where men have determined ideas with known names to them; and so, there being no room for equivocations, there is no need of distinctions.
In Conduct of the Understanding, Sect. 31.
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The difference between what the most and the least learned people know is inexpressibly trivial in relation to that which is unknown.
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The doctor may also learn more about the illness from the way the patient tells the story than from the story itself.
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The faculty for remembering is not diminished in proportion to what one has learnt, just as little as the number of moulds in which you cast sand lessens its capacity for being cast in new moulds.
Religion: a Dialogue, and Other Essays (1890), 99.
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The first question which you will ask and which I must try to answer is this, “What is the use of climbing Mount Everest ?” and my answer must at once be, “It is no use.” There is not the slightest prospect of any gain whatsoever. Oh, we may learn a little about the behavior of the human body at high altitudes, and possibly medical men may turn our observation to some account for the purposes of aviation. But otherwise nothing will come of it. We shall not bring back a single bit of gold or silver, not a gem, nor any coal or iron. We shall not find a single foot of earth that can be planted with crops to raise food. It’s no use. So, if you cannot understand that there is something in man which responds to the challenge of this mountain and goes out to meet it, that the struggle is the struggle of life itself upward and forever upward, then you won’t see why we go. What we get from this adventure is just sheer joy. And joy is, after all, the end of life. We do not live to eat and make money. We eat and make money to be able to enjoy life. That is what life means and what life is for.
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The first step in knowledge is to learn that we are ignorant.
In Hialmer Day Gould, New Practical Spelling (1905), 15.
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The game of chess has always fascinated mathematicians, and there is reason to suppose that the possession of great powers of playing that game is in many features very much like the possession of great mathematical ability. There are the different pieces to learn, the pawns, the knights, the bishops, the castles, and the queen and king. The board possesses certain possible combinations of squares, as in rows, diagonals, etc. The pieces are subject to certain rules by which their motions are governed, and there are other rules governing the players. … One has only to increase the number of pieces, to enlarge the field of the board, and to produce new rules which are to govern either the pieces or the player, to have a pretty good idea of what mathematics consists.
In Book review, 'What is Mathematics?', Bulletin American Mathematical Society (May 1912), 18, 386-387.
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The great art of learning is to undertake but little at a time
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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The great mathematician, like the great poet or naturalist or great administrator, is born. My contention shall be that where the mathematic endowment is found, there will usually be found associated with it, as essential implications in it, other endowments in generous measure, and that the appeal of the science is to the whole mind, direct no doubt to the central powers of thought, but indirectly through sympathy of all, rousing, enlarging, developing, emancipating all, so that the faculties of will, of intellect and feeling learn to respond, each in its appropriate order and degree, like the parts of an orchestra to the “urge and ardor” of its leader and lord.
In Lectures on Science, Philosophy and Art (1908), 22.
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The habitat of an organism is the place where it lives, or the place where one would go to find it. The ecological niche, on the other hand, is the position or status of an organism within its community and ecosystem resulting from the organism’s structural adaptations, physiological responses and specific behavior (inherited and/or learned). The ecological niche of an organism depends not only on where it lives, but also on what it does. By analogy, it may be said that the habitat is the organism’s ‘address,’ and the niche is its ‘profession,’ biologically speaking.
Fundamentals of Ecology
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The heart may give a lesson to the head,
And Learning wiser grow without his books.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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The improver of natural knowledge absolutely refuses to acknowledge authority as such. For him, scepticism is the highest of duties, blind faith the one unpardonable sin. The man of science has learned to believe in justification, not by faith, but by verification.
In Lecture (7 Jan 1866), a Lay Sermon delivered at St. Martin’s Hall, 'Advisableness of Improving Natural Knowledge', Lay Sermons, Addresses, and Reviews (1872), 18. Previously published in Fortnightly Review.
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The individual feels the futility of human desires and aims and the sublimity and marvelous order which reveal themselves both in nature and in the world of thought. Individual existence impresses him as a sort of prison and he wants to experience the universe as a single significant whole. The beginnings of cosmic religious feeling already appear at an early stage of development, e.g., in many of the Psalms of David and in some of the Prophets. Buddhism, as we have learned especially from the wonderful writings of Schopenhauer, contains a much stronger element of this. The religious geniuses of all ages have been distinguished by this kind of religious feeling, which knows no dogma and no God conceived in man’s image; so that there can be no church whose central teachings are based on it. Hence it is precisely among the heretics of every age that we find men who were filled with this highest kind of religious feeling and were in many cases regarded by their contemporaries as atheists, sometimes also as saints. Looked at in this light, men like Democritus, Francis of Assisi, and Spinoza are closely akin to one another.
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The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me—both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.
In I Want to be a Mathematician: An Automathography (1985), 3.
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The layman is delighted to learn that after all, in spite of science being so impossibly difficult to understand, Scientists Are Human!
In What Mad Pursuit (1988), 83.
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The majority of mathematical truths now possessed by us presuppose the intellectual toil of many centuries. A mathematician, therefore, who wishes today to acquire a thorough understanding of modern research in this department, must think over again in quickened tempo the mathematical labors of several centuries. This constant dependence of new truths on old ones stamps mathematics as a science of uncommon exclusiveness and renders it generally impossible to lay open to uninitiated readers a speedy path to the apprehension of the higher mathematical truths. For this reason, too, the theories and results of mathematics are rarely adapted for popular presentation … This same inaccessibility of mathematics, although it secures for it a lofty and aristocratic place among the sciences, also renders it odious to those who have never learned it, and who dread the great labor involved in acquiring an understanding of the questions of modern mathematics. Neither in the languages nor in the natural sciences are the investigations and results so closely interdependent as to make it impossible to acquaint the uninitiated student with single branches or with particular results of these sciences, without causing him to go through a long course of preliminary study.
In Mathematical Essays and Recreations (1898), 32.
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The man who is too old to learn was probably always too old to learn.
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The many who believe they are the wiser for reading accounts of experiments deceive themselves. It is as impossible to learn science from hearsay as to gain wisdom from proverbs.
Said by the fictional character Lydia in Cashel Byron’s Profession (1886, 1906), 87-88.
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The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not.
In Presidential Address to the 60th Meeting of the British Association for the Advancement of Science, Section A (Sep 1890), published in Report of the Annual Meeting (1891), 60, 725.
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The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work.
In Presidential Address British Association for the Advancement of Science, Section A, (1890), Nature, 42, 467.
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The more intelligence mankind bestows upon technology, the less knowledge a child is required to learn. If this pattern is never changed, the generation of the future may become reduced to nothing more than lifeless drones born for nothing except pushing buttons on a machine that lives the lives of their masters.
Devin Dye
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The most learned are often the most narrow-minded.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.
In J.R. Newman (ed.), 'Commentary on The Tears of Mathematics', The World of Mathematics (1956), 1978.
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The national park idea, the best idea we ever had, was inevitable as soon as Americans learned to confront the wild continent not with fear and cupidity but with delight, wonder, and awe.
In Wallace Stegner and Page Stegner (ed.), 'The Best Idea We Ever Had', Marking the Sparrow’s Fall: The Making of the American West (1998, 1999), 137.
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The opinion of Bacon on this subject [geometry] was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was “no less worthy than that which was principal and intended.” But it is evident that his views underwent a change. When near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the pretensions of the mathematicians, “delidas et faslum mathematicorum.” Assuming the well-being of the human race to be the end of knowledge, he pronounced that mathematical science could claim no higher rank than that of an appendage or an auxiliary to other sciences. Mathematical science, he says, is the handmaid of natural philosophy; she ought to demean herself as such; and he declares that he cannot conceive by what ill chance it has happened that she presumes to claim precedence over her mistress.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 395.
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The peculiar character of mathematical truth is, that it is necessarily and inevitably true; and one of the most important lessons which we learn from our mathematical studies is a knowledge that there are such truths, and a familiarity with their form and character.
This lesson is not only lost, but read backward, if the student is taught that there is no such difference, and that mathematical truths themselves are learned by experience.
In Thoughts on the Study of Mathematics. Principles of English University Education (1838).
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The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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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 Question is what is The Question?
Is it all a Magic Show?
Is Reality an Illusion?
What is the framework of The Machine?
Darwin’s Puzzle: Natural Selection?
Where does Space-Time come from?
Is there any answer except that it comes from consciousness?
What is Out There?
T’is Ourselves?
Or, is IT all just a Magic Show?
Einstein told me:
“If you would learn, teach!”
Speaking at the American Physical Society, Philadelphia (Apr 2003). As quoted and cited in Jack Sarfatti, 'Wheeler's World: It From Bit?', collected in Frank H. Columbus and Volodymyr Krasnoholovets (eds.), Developments in Quantum Physics (2004), 42.
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The results of mathematics are seldom directly applied; it is the definitions that are really useful. Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do. This you cannot see unless you take a course in abstract differential equations. What applies is the cultural background you get from a course in differential equations, not the specific theorems. If you want to learn French, you have to live the life of France, not just memorize thousands of words. If you want to apply mathematics, you have to live the life of differential equations. When you live this life, you can then go back to molecular biology with a new set of eyes that will see things you could not otherwise see.
In 'A Mathematician's Gossip', Indiscrete Thoughts (2008), 213.
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The rise of every man he loved to trace,
Up to the very pod O!
And, in baboons, our parent race
Was found by old Monboddo.
Their A, B, C, he made them speak.
And learn their qui, quæ, quod, O!
Till Hebrew, Latin, Welsh, and Greek
They knew as well’s Monboddo!
Anonymous
From Ballad, 'The Memory of Monboddo', in Blackwood’s Magazine (Sep 1861), 90, No. 551, 363, Verse 2 (of 6). Written to the Air, The Looking Glass. It is footnoted to explain that Lord (James Burnett) Monboddo “has written a book about the origin of language, in which he traces monkeys up to men.” The note is quoted and cited from Boswell’s Life of Johnson, Vol. 4, 73.
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The Romans would never have found time to conquer the world if they had been obliged first to learn Latin.
In Heinrich Heinne and Charles Godfrey Leland (trans.), Pictures of Travel (1871), 183.
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The solution, as all thoughtful people recognize, must lie in properly melding the themes of inborn predisposition and shaping through life’s experiences. This fruitful joining cannot take the false form of percentages adding to 100–as in ‘intelligence is 80 percent nature and 20 percent nurture,’ or ‘homosexuality is 50 percent inborn and 50 percent learned,’ and a hundred other harmful statements in this foolish format. When two ends of such a spectrum are commingled, the result is not a separable amalgam (like shuffling two decks of cards with different backs), but an entirely new and higher entity that cannot be decomposed (just as adults cannot be separated into maternal and paternal contributions to their totality).
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The study of taxonomy in its broadest sense is probably the oldest branch of biology or natural history as well as the basis for all the other branches, since the first step in obtaining any knowledge of things about us is to discriminate between them and to learn to recognize them.
From paper presented to New York Entomological Society (12 Dec 1939), 'Some Aspects of Modern Taxonomy', published in Journal of the New York Entomological Society (Sep 1940), 48, No. 3, 245.
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The sweetest and most inoffensive path of life leads through the avenues of science and learning; and whoever can either remove any obstruction in this way, or open up any new prospect, ought, so far, to be esteemed a benefactor to mankind.
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The terror of the thunderstorm led primitive man to the conception of a Supreme Being whose attribute was the thunderbolt. But when Franklin brought the lightning from the clouds and showed it to he a mere electric spark, when we learned to make the lightning harmless by the lightning-rod, and when finally we harnessed electricity to do our work, naturally our reverence for the thrower of the thunderbolt decayed. So the gods of experience vanished.
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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The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms. From this it has come about that our entire contemporary culture, inasmuch as it is based on the intellectual penetration and the exploitation of nature, has its foundations in mathematics. Already Galileo said: one can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are mathematical figures.
Radio broadcast (8 Sep 1930). As quoted in Michael Fitzgerald and Ioan James, The Mind of the Mathematician (2007), 6-7.
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The true man of science will know nature better by his finer organization; he will smell, taste, see, hear, feel, better than other men. His will be a deeper and finer experience.
In 'Natural history of Massachusetts', The Dial: A Magazine for Literature, Philosophy, and Religion (Jul 1842), 3, No. 1, 40.
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The truth is, when all is said and done, one does not teach a subject, one teaches a student how to learn it.
Begin Here: The Forgotten Conditions of Teaching and Learning (1991), 35. In Richard J. Cox, Managing Records as Evidence and Information (2001), 217.
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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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The way you learn anything is that something fails, and you figure out how not to have it fail again.
From Interview (1 Sep 2009), for the NASA Glenn History Collection, Oral History Collection, Cleveland, Ohio. As quoted an cited in Robert S. Arrighi, Pursuit of Power: NASA’s Propulsion and Systems Laboratory No. 1 and 2 (2012), 82. This quote is widely seen on the web, often incorrectly attributed to Arrighi, who was only the author of the book in which the quote by Kobak was given.
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There is no arithmetician like him who hath learned to number his days, and to apply his heart unto wisdom.
In 'The Epistle Dedicatory, The Works of George Swinnock (1868), Vol. 1, 370.
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There is no such whetstone, to sharpen a good wit and encourage a will to learning, as is praise.
The Schoolmaster (1570)
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There is plenty of room left for exact experiment in art, and the gate has been opened for some time. What had been accomplished in music by the end of the eighteenth century has only begun in the fine arts. Mathematics and physics have given us a clue in the form of rules to be strictly observed or departed from, as the case may be. Here salutary discipline is come to grips first of all with the function of forms, and not with form as the final result … in this way we learn how to look beyond the surface and get to the root of things.
Paul Klee
Quoted in The Bulletin of the Atomic Scientists (Feb 1959), 59, citing Bauhaus-Zeitschrijt (1928).
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There isn’t one, not one, instance where it’s known what pattern of neural connectivity realizes a certain cognitive content, inate or learned, in either the infant’s nervous system or the adult’s. To be sure, our brains must somehow register the contents of our mental states. The trouble is: Nobody knows how—by what neurological means—they do so. Nobody can look at the patterns of connectivity (or of anything else) in a brain and figure out whether it belongs to somebody who knows algebra, or who speaks English, or who believes that Washington was the Father of his country.
In Critical Condition: Polemic Essays on Cognitive science and the Philosophy of the Mind (1988), 269-71. In Vinoth Ramachandra, Subverting Global Myths: Theology and the Public Issues Shaping our World (2008), 180.
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There’s nothing between you and oblivion except a pressure suit, and you just can't afford to get out there and get in a big rush and tangle yourself up where nobody can help you. … The biggest thing I've learned from the people that have gone in the past, you simply have to take your time, and you can’t exhaust yourself.
In AP feed newspaper articles, for example, in the Bridgewater, NJ, The Courier-News (7 Sep 1966), 8. First and last phrases quoted in John Barbour, Footprints on the Moon (1969), 110.
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Thinking is merely the comparing of ideas, discerning relations of likeness and of difference between ideas, and drawing inferences. It is seizing general truths on the basis of clearly apprehended particulars. It is but generalizing and particularizing. Who will deny that a child can deal profitably with sequences of ideas like: How many marbles are 2 marbles and 3 marbles? 2 pencils and 3 pencils? 2 balls and 3 balls? 2 children and 3 children? 2 inches and 3 inches? 2 feet and 3 feet? 2 and 3? Who has not seen the countenance of some little learner light up at the end of such a series of questions with the exclamation, “Why it’s always that way. Isn’t it?” This is the glow of pleasure that the generalizing step always affords him who takes the step himself. This is the genuine life-giving joy which comes from feeling that one can successfully take this step. The reality of such a discovery is as great, and the lasting effect upon the mind of him that makes it is as sure as was that by which the great Newton hit upon the generalization of the law of gravitation. It is through these thrills of discovery that love to learn and intellectual pleasure are begotten and fostered. Good arithmetic teaching abounds in such opportunities.
In Arithmetic in Public Education (1909), 13. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 68.
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Those who are good at archery learnt from the bow and not from Yi the Archer. Those who know how to manage boats learnt from boats and not from Wo (the legendary mighty boatman). Those who can think learnt for themselves and not from the sages.
Kuan-Yin
As quoted in Joseph Needham, Science and Civilisation in China: Volume 2: History of Scientific Thought (1956), 73, citing “in the Kuan Yin Tzu, a Taoist book of Thang (perhaps + 8th century).” Also in Alan L. Mackay, A Dictionary of Scientific Quotations (1991), 144, citing Needham.
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To introduce something altogether new would mean to begin all over, to become ignorant again, and to run the old, old risk of failing to learn.
Isaac Asimov, Patricia S. Warrick, Martin Harry Greenberg, Machines That Think: The Best Science Fiction Stories About Robots and Computers? (1984), 2.
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To learn is to incur surprise—I mean really learning, not just refreshing our memory or adding a new fact. And to invent is to bestow surprise—I mean really inventing, not just innovating what others have done.
In How Invention Begins: Echoes of Old Voices in the Rise of New Machines (2006), 217.
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To learn the language of art, copy for ever is my rule.
Marginal note (c. 1808) written on table of contents page in his copy of The Works of Sir Joshua Reynolds (1798), beside “Much copying discountenanced”. As given in William Blake, Edwin John Ellis (ed.) and William Butler Yeats (ed.), The Works of William Blake (1893), Vol. 2, 319.
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To learn… the ordinary arrangement of the different strata of minerals in the earth, to know from their habitual colocations and proximities, where we find one mineral; whether another, for which we are seeking, may be expected to be in its neighborhood, is useful.
In The Writings of Thomas Jefferson (1854), Vol. 7, 443.
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To teach one who has no curiosity to learn, is to sow a field without ploughing it.
From Annotation to Essay 50, 'Of Studies', in Bacon’s Essays: With Annotations (1856), 446.
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Try to learn something about everything and everything about something.
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Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languages of the world than to master all mathematics at present known. The languages could, I imagine, be learnt in a lifetime; mathematics certainly could not. Nor is the subject static.
In 'The Extent of Mathematics', Prelude to Mathematics (1955), 11.
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Watch the stars, and from them learn. To the Master’s honor all must turn, each in its track, without a sound, forever tracing Newton’s ground.
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We are at the very beginning of time for the human race. It is not unreasonable that we grapple with problems. But there are tens of thousands of years in the future. Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on.
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We can learn a lot from living organisms. An organism is a pretty complicated thing, which can tolerate surgery, which can tolerate injury, which can tolerate all kinds of perturbation provided they are not too great and do not come too suddenly. There’s something we call trauma, however. We don’t really understand what it is—but organisations can suffer from it too.
From interview with Graham Chedd, 'The Lady Gets Her Way', New Scientist (5 Jul 1973), 59, No. 853, 16.
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We do not inhabit a perfected world where natural selection ruthlessly scrutinizes all organic structures and then molds them for optimal utility. Organisms inherit a body form and a style of embryonic development; these impose constraint s upon future change and adaptation. In many cases, evolutionary pathways reflect inherited patterns more than current environmental demands. These inheritances constrain, but they also provide opportunity. A potentially minor genetic change ... entails a host of complex, nonadaptive consequences ... What ‘play’ would evolution have if each structure were built for a restricted purpose and could be used for nothing else? How could humans learn to write if our brain had not evolved for hunting, social cohesion, or whatever, and could not transcend the adaptive boundaries of its original purpose?
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We have learned that matter is weird stuff. It is weird enough, so that it does not limit God’s freedom to make it do what he pleases.
From Gifford Lectures (Apr-Nov 1985), 'In Praise of Diversity', given at Aberdeen, Scotland. In Infinite in All Directions (1988), 8.
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We have little more personal stake in cosmic destiny than do sunflowers or butterflies. The transfiguration of the universe lies some 50 to 100 billion years in the future; snap your fingers twice and you will have consumed a greater fraction of your life than all human history is to such a span. ... We owe our lives to universal processes ... and as invited guests we might do better to learn about them than to complain about them. If the prospect of a dying universe causes us anguish, it does so only because we can forecast it, and we have as yet not the slightest idea why such forecasts are possible for us. ... Why should nature, whether hostile or benign, be in any way intelligible to us? Al the mysteries of science are but palace guards to that mystery.
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We learn from experience that men never learn anything from experience.
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We learn wisdom from failure much more than from success. We often discover what will do, by finding out what will not do; and probably he who never made a mistake never made a discovery.
In Self-help: With Illustrations of Character and Conduct (1859, 1861), 349.
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We must learn to think not only logically, but bio-logically.
In One Life at a Time, Please (1988), 68.
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We must not forget … that “influence” is not a simple, but on the contrary, a very complex, bilateral relation. We are not influenced by everything we read or learn. In one sense, and perhaps the deepest, we ourselves determine the influences we are submitting to; our intellectual ancestors are by no means given to, but are freely chosen by, us.
In From the Closed World to the Infinite Universe (1957) 5-6.
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We shall therefore say that a program has common sense if it automatically deduces for itself a sufficient wide class of immediate consequences of anything it is told and what it already knows. ... Our ultimate objective is to make programs that learn from their experience as effectively as humans do.
'Programs with Common Sense', (probably the first paper on AI), delivered to the Teddington Conference on the Mechanization of Thought Processes (Dec 1958). Printed in National Physical Laboratory, Mechanisation of Thought Processes: Proceedings of a Symposium Held at the National Physical Laboratory on 24th, 25th, 26th and 27th November 1958 (1959), 78. Also Summary in John McCarthy and Vladimir Lifschitz (ed.), Formalizing Common Sense: Papers by John McCarthy (1990), 9-10.
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What has been learned in physics stays learned. People talk about scientific revolutions. The social and political connotations of revolution evoke a picture of a body of doctrine being rejected, to be replaced by another equally vulnerable to refutation. It is not like that at all. The history of physics has seen profound changes indeed in the way that physicists have thought about fundamental questions. But each change was a widening of vision, an accession of insight and understanding. The introduction, one might say the recognition, by man (led by Einstein) of relativity in the first decade of this century and the formulation of quantum mechanics in the third decade are such landmarks. The only intellectual casualty attending the discovery of quantum mechanics was the unmourned demise of the patchwork quantum theory with which certain experimental facts had been stubbornly refusing to agree. As a scientist, or as any thinking person with curiosity about the basic workings of nature, the reaction to quantum mechanics would have to be: “Ah! So that’s the way it really is!” There is no good analogy to the advent of quantum mechanics, but if a political-social analogy is to be made, it is not a revolution but the discovery of the New World.
From Physics Survey Committee, U.S. National Academy of Sciences, National Research Council, 'The Nature of Physics', in report Physics in Perspective (1973), 61-62. As cited in I. Bernard Cohen, Revolution in Science (1985), 554-555.
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What matters in learning is not to be taught, but to wake up. A spark must explode the sleeping explosives.
As quoted in Bostonia: The Boston University Alumni Magazine (1949), 22. No. 9, 12.
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Whatever we are to do when we have learnt, these we learn by doing; as by building, men become builders.
Aristotle
From Ethics, book 2, 1103a32-33. As translated in A New Translation of the Nichomachean Ethics (1819), 32, as “printed for R. Pearson.” Often seen quoted briefly as, “What we have to learn to do, we learn by doing.” There are a number of other translations. “We learn an art or craft by doing the things that we shall have to do when we have learnt it: for instance, men become builders by building houses, harpers by playing on the harp,” is given by Harris Rackham, The Nicomachean Ethics (1962), 73. Also “In the case of the arts, that which we have to be taught to do, that we learn to do by doing it. We become masons, for instance, by building; and harpers by playing upon the harp,” in Robert Williams (trans.), The Nicomachean Ethics of Aristotle (1869), 32. Notice the idea that "have to be taught" is in contrast with things that we do by nature.
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What’s the best part of being a mathematician? I'm not a religious man, but it’s almost like being in touch with God when you’re thinking about mathematics. God is keeping secrets from us, and it’s fun to try to learn some of the secrets.
From interview with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 21.
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When I came back from Munich, it was September, and I was Professor of Mathematics at the Eindhoven University of Technology. Later I learned that I had been the Department’s third choice, after two numerical analysts had turned the invitation down; the decision to invite me had not been an easy one, on the one hand because I had not really studied mathematics, and on the other hand because of my sandals, my beard and my ‘arrogance’ (whatever that may be).
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When I was in college studying science, I found the experience fundamentally unsatisfying. I was continually oppressed by the feeling that my only role was to “shut up and learn.” I felt there was nothing I could say to my instructors that they would find interesting. … As I sat in the science lecture hall, I was utterly silent. That’s not a good state to be in when you are 19 years old.
In Understanding the Universe: An Inquiry Approach to Astronomy and the Nature of Scientific Research (2013), ix.
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When science finally locates the center of the universe, some people will be surprised to learn they're not it.
Anonymous
Source uncertain. Often identified as Anonymous. Sometimes attributed to Bernard Bailey, for example, in a chapter heading quote (without citation) in juvenile fiction by P.G. Kain, The Social Experiments of Dorie Dilts: Dumped by Popular Demand (2007), 126. Sometimes found on the web attributed to Bernard Bailey, but just as often it is Anonymous. If you can identify Bernard Bailey or know an original print source, please contact Webmaster.
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When we learn a new word, it is the key to untold treasures.
In Letter (29 May 1898), at age almost 18, to Mrs. Lawrence Hutton, excerpted in The Story of My Life: With her Letters (1887-1901) (1903, 1921), 242.
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When you wish to instruct, be brief; that men's minds take in quickly what you say, learn its lesson, and retain it faithfully. Every word that is unnecessary only pours over the side of a brimming mind.
In Norbert Guterman, The Anchor Book of Latin Quotations (1990), 193.
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Where there is much to learn, there of necessity will be much arguing, much writing, many opinions; for opinion in good men is but knowledge in the making.
In Areopagitica: A speech of Mr John Milton for the Liberty of Unlicenced printing to the Parliament of England (23 Nov 1644), 31.
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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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While there is still much to learn and discover through space exploration, we also need to pay attention to our unexplored world here on earth. Our next big leap into the unknown can be every bit as exciting and bold as our pioneering work in space. It possesses the same “wow” factor: alien worlds, dazzling technological feats and the mystery of the unknown.
In 'Why Exploring the Ocean is Mankind’s Next Giant Leap', contributed to CNN 'Lightyears Blog' (13 Mar 2012)
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Who could have believed that … the introduction into the human body of a small particle of matter from a cow’s udder might be the means of saving thousands of human lives? We learn from these and innumerable similar instances that the highest truths lie hid in the simplest facts; that, unlike human proclamations, nature’s teachings are not by sound of trumpet, but often in the stillest voice, by indirect hints and obscure suggestions.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 109.
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Who has not be amazed to learn that the function y = ex, like a phoenix rising again from its own ashes, is its own derivative?
In François Le Lionnais (ed.), Great Currents of Mathematical Thought: Mathematics in the Arts and Sciences (1971), Vol. 2, 126.
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Whoever does not try, does not learn.
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Why do we do basic research? To learn about ourselves.
From interview with Anthony Liversidge, in 'Walter Gilbert', Omni (Nov 1992), 15, No. 2.
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Wise [persons] learn by others’ mistakes, fools by their own.
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Wonder [admiratio astonishment, marvel] is a kind of desire for knowledge. The situation arises when one sees an effect and does not know its cause, or when the cause of the particular effect is one that exceeds his power of understanding. Hence, wonder is a cause of pleasure insofar as there is annexed the hope of attaining understanding of that which one wants to know. ... For desire is especially aroused by the awareness of ignorance, and consequently a man takes the greatest pleasure in those things which he discovers for himself or learns from the ground up.
From Summa Theologiae Question 32, 'The Causes of Pleasure,' Article 8, 'Is Pleasure Caused by Wondering.'(1a2ae 32.8). As translated in James Vincent Cunningham, Tragic Effect and Tragic Process in Some Plays of Shakespeare (1945). Also in The Collected Essays of J.V. Cunningham (1976), 72-73.
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Words learned by rote a parrot may rehearse,
But talking is not always to converse;
Not more distinct from harmony divine,
The constant creaking of a country sign.
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Write with the learned, pronounce with the vulgar.
In Poor Richard's Almanack (1914), 62. https://books.google.com/books?id=o6lJAAAAIAAJ Benjamin Franklin - 1914
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You can learn a lot about ice and still not understand water.
Transcribed from video of Four-Day Seminar (1992).
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You live and learn. Or you don’t live long.
In 'From the Notebooks of Lazarus Long', Time Enough for Love: The Lives of Lazarus Long (1973), 269.
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[A man] must learn to understand the motives of human beings, their illusions, and their sufferings human beings, their illusions, and their sufferings in order to acquire a proper relationship to individual fellow-men and to the community. These precious things … primarily constitutes and preserves culture. This is what I have in mind when I recommend the “humanities” as important, not just dry specialized knowledge in the fields of history and philosophy.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37.
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[Alexander the Great] was often extremely brutal to his captives, whom he sold into slavery, tortured to death, or forced to learn Greek.
In The Decline and Fall of Practically Everybody (1950), 42, footnote.
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[For] men to whom nothing seems great but reason ... nature ... is a cosmos, so admirable, that to penetrate to its ways seems to them the only thing that makes life worth living. These are the men whom we see possessed by a passion to learn ... Those are the natural scientific men; and they are the only men that have any real success in scientific research.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 19.
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[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity.
In Ueber das Verhältnis der Naturwissenschaften zur Gesammtheit der Wissenschaft, Vorträge und Reden (1896), Bd. 1, 176. Also seen translated as “In mathematics we see the conscious logical activity of our mind in its purest and most perfect form; here is made manifest to us all the labor and the great care with which it progresses, the precision which is necessary to determine exactly the source of the established general theorems, and the difficulty with which we form and comprehend abstract conceptions; but we also learn here to have confidence in the certainty, breadth, and fruitfulness of such intellectual labor”, in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 20. From the original German, “Hier sehen wir die bewusste logische Thätigkeit unseres Geistes in ihrer reinsten und vollendetsten Form; wir können hier die ganze Mühe derselben kennen lernen, die grosse Vorsicht, mit der sie vorschreiten muss, die Genauigkeit, welche nöthig ist, um den Umfang der gewonnenen allgemeinen Sätze genau zu bestimmen, die Schwierigkeit, abstracte Begriffe zu bilden und zu verstehen; aber ebenso auch Vertrauen fassen lernen in die Sicherheit, Tragweite und Fruchtbarkeit solcher Gedankenarbeit.”
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[In my early youth, walking with my father,] “See that bird?” he says. “It’s a Spencer’s warbler.” (I knew he didn’t know the real name.) “Well, in Italian, it’s a Chutto Lapittida. In Portuguese, it’s a Bom da Peida. In Chinese, it’s a Chung-long-tah, and in Japanese, it’s a Katano Tekeda. You can know the name of that bird in all the languages of the world, but when you’re finished, you’ll know absolutely nothing whatever about the bird. You’ll only know about humans in different places, and what they call the bird. So let’s look at the bird and see what it’s doing—that’s what counts.” (I learned very early the difference between knowing the name of something and knowing something.)
In 'The Making of a Scientist', What Do You Care What Other People Think?": Further Adventures of a Curious Character (2001), 13-14.
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[We] do not learn for want of time,
The sciences that should become our country.
In Henry V (1599), Act 5, Scene 2, line 59-60.
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~~[Attributed, authorship undocumented]~~ Mathematical demonstrations are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even in subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedaemonians seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those, who had not, men of imperfect judgments, and unfit to rule and govern.
From an article which appeared as 'The Usefulness of Mathematics', Pennsylvania Gazette (30 Oct 1735), No. 360. Collected, despite being without clear evidence of Franklin’s authorship, in The Works of Benjamin Franklin (1809), Vol. 4, 377. Evidence of actual authorship by Ben Franklin for the newspaper article has not been ascertained, and scholars doubt it. See Franklin documents at the website founders.archives.gov. The quote is included here to attach this caution.
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~~[No known source from Adams]~~ If your actions inspire others to dream more, learn more, do more and become more, you are a leader.
No primary source seems to exist to attribute this quote to Adams. A documented source found on the quoteinvestigator website is from Dolly Parton, in 1997. See the quote that begins, “If your actions create a legacy…”, on the Dolly Parton Quotes page of this website.
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~~[unverified]~~ I’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.
Attribution is uncertain until a primary source is identified. Can you help?
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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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Sophie Germain
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Carl Gauss
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- 90 -
Antoine Lavoisier
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Charles Babbage
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Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
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Bible
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- 70 -
Samuel Morse
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Robert Fulton
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- 60 -
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Paul Dirac
Avicenna
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- 50 -
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- 40 -
Pierre Fermat
Edward Wilson
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JJ Thomson
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Leonardo DaVinci
Archimedes
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- 30 -
Andreas Vesalius
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Richard Feynman
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Benjamin Franklin
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- 20 -
Carl Sagan
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- 10 -
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