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Who said: “Science without religion is lame; religion without science is blind.”
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Home > Category Index for Science Quotations > Category Index T > Category: Think

Think Quotes (341 quotes)

... I think the guys who are really controlling their emotions... are going to win; the guy who is controlling his emotions is going to win!
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...the scientific cast of mind examines the world critically, as if many alternative worlds might exist, as if other things might be here which are not. Then we are forced to ask why what we see is present and not something else. Why are the Sun and moon and the planets spheres? Why not pyramids, or cubes, or dodecahedra? Why not irregular, jumbly shapes? Why so symmetrical, worlds? If you spend any time spinning hypotheses, checking to see whether they make sense, whether they conform to what else we know. Thinking of tests you can pose to substantiate or deflate hypotheses, you will find yourself doing science.
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...time and space are modes by which we think and not conditions in which we live.
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Alles Gescheite ist schon gedacht worden; man muss nur versuchen, es noch einmal zu denken.
Everything that is worth thinking has already been thought; one must only try to think it again.
As translated in William Francis Henry King (ed.), Classical and Foreign Quotations: A Polyglot Manual of Historical (1904), 234.
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Ego cogito, ergo sum.
I think, therefore I am.
From the original Latin in Principia Philosophiæ (1644), Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition VII, 7. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 195.
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Lepidoptera are for children to play with, pretty to look at, so some think. Give me the Coleoptera, and the kings of the Coleoptera are the beetles! Lepidoptera and Neuroptera for little folks; Coleoptera for men, sir!
In 'The Poet at the Breakfast Table: III', The Atlantic Monthly (Mar 1872), 29, 344.
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Pour inventor il faut penser à côté.
To invent you must think aside
In Calyampudi Radhakrishna Rao, Statistics and Truth (1997), 31.
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Wer kann was Dummes, wer was Kluges denken, Das nicht die Vorwelt schon gedacht?
What is there, wise or foolish, one can think, That former ages have not thought before?
Words of Mephistopheles written in Faust, Pt. 2, Act 2. As quoted and translated by the editor in in William Francis Henry King (ed.), Classical and Foreign Quotations: A Polyglot Manual of Historical (1904), 234.
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[When recording electrical impulses from a frog nerve-muscle preparation seemed to show a tiresomely oscillating electrical artefact—but only when the muscle was hanging unsupported.] The explanation suddenly dawned on me ... a muscle hanging under its own weight ought, if you come to think of it, to be sending sensory impulses up the nerves coming from the muscle spindles ... That particular day’s work, I think, had all the elements that one could wish for. The new apparatus seemed to be misbehaving very badly indeed, and I suddenly found it was behaving so well that it was opening up an entire new range of data ... it didn’t involve any particular hard work, or any particular intelligence on my part. It was just one of those things which sometimes happens in a laboratory if you stick apparatus together and see what results you get.
From 'Memorable experiences in research', Diabetes (1954), 3, 17-18. As cited in Alan McComa, Galvani's Spark: The Story of the Nerve Impulse (2011), 102-103.
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A good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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A great many people think they are thinking when they are merely rearranging their prejudices
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A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
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A man has a very insecure tenure of a property which another can carry away with his eyes. A few months reduced me to the cruel necessity either of destroying my machine, or of giving it to the public. To destroy it, I could not think of; to give up that for which I had laboured so long, was cruel. I had no patent, nor the means of purchasing one. In preference to destroying, I gave it to the public.
[On his inability to keep for himself a profitable income from his invention of the Spinning Mule.]
As quoted in James Mason, The Great Triumphs of Great Men (1875), 579.
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A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction.
Quoted, without citation, in Howard Whitley Eves, Return to Mathematical Circles (1988), 81.
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A man loses his fortune; he gains earnestness. His eyesight goes; it leads him to a spirituality... We think we are pushing our own way bravely, but there is a great Hand in ours all the time.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 20
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A man should look for what is, and not for what he thinks should be.
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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 small cabin stands in the Glacier Peak Wilderness, about a hundred yards off a trail that crosses the Cascade Range. In midsummer, the cabin looked strange in the forest. It was only twelve feet square, but it rose fully two stories and then had a high and steeply peaked roof. From the ridge of the roof, moreover, a ten-foot pole stuck straight up. Tied to the top of the pole was a shovel. To hikers shedding their backpacks at the door of the cabin on a cold summer evening—as the five of us did—it was somewhat unnerving to look up and think of people walking around in snow perhaps thirty-five feet above, hunting for that shovel, then digging their way down to the threshold.
In Encounters with the Archdruid (1971), 3.
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A. R. Todd
Thinks he’s God.
N. F. Mott
Says he’s not.
Anonymous
Quoted by William Lord in The Times (22 Jan 1997), remarking on the competitiveness between the Physics and Chemistry Departments at the University of Cambridge.
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After that, I thought about what a proposition generally needs in order to be true and certain because, since I had just found one that I knew was such, I thought I should also know what this certainty consists in. Having noticed that there is nothing at all in the proposition “I think, therefore I am” [cogito ergo sum] which convinces me that I speak the truth, apart from the fact that I see very clearly that one has to exist in order to think, I judged that I could adopt as a general rule that those things we conceive very clearly and distinctly are all true. The only outstanding difficulty is in recognizing which ones we conceive distinctly.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 4, 25.
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Amazing that the human race has taken enough time out from thinking about food or sex to create the arts and sciences.
City Aphorisms, Eighth Selection (1991).
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And above all things, never think that you’re not good enough yourself. A man should never think that. My belief is that in life people will take you at your own reckoning.
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And yet I think that the Full House model does teach us to treasure variety for its own sake–for tough reasons of evolutionary theory and nature’s ontology, and not from a lamentable failure of thought that accepts all beliefs on the absurd rationale that disagreement must imply disrespect. Excellence is a range of differences, not a spot. Each location on the range can be occupied by an excellent or an inadequate representative– and we must struggle for excellence at each of these varied locations. In a society driven, of ten unconsciously, to impose a uniform mediocrity upon a former richness of excellence–where McDonald’s drives out the local diner, and the mega-Stop & Shop eliminates the corner Mom and Pop–an understanding and defense of full ranges as natural reality might help to stem the tide and preserve the rich raw material of any evolving system: variation itself.
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Antiessentialist thinking forces us to view the world differently. We must accept shadings and continua as fundamental. We lose criteria for judgment by comparison to some ideal: short people, retarded people, people of other beliefs, colors, and religions are people of full status.
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Anton Chekhov wrote that ‘one must not put a loaded rifle on stage if no one is thinking of firing it.’ Good drama requires spare and purposive action, sensible linking of potential causes with realized effects. Life is much messier; nothing happens most of the time. Millions of Americans (many hotheaded) own rifles (many loaded), but the great majority, thank God, do not go off most of the time. We spend most of real life waiting for Godot, not charging once more unto the breach.
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Archimedes said Eureka,
Cos in English he weren't too aversed in,
when he discovered that the volume of a body in the bath,
is equal to the stuff it is immersed in,
That is the law of displacement,
Thats why ships don't sink,
Its a shame he weren't around in 1912,
The Titanic would have made him think.
From lyrics of song Sod’s Law.
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Are the humanistic and scientific approaches different? Scientists can calculate the torsion of a skyscraper at the wing-beat of a bird, or 155 motions of the Moon and 500 smaller ones in addition. They move in academic garb and sing logarithms. They say, “The sky is ours”, like priests in charge of heaven. We poor humanists cannot even think clearly, or write a sentence without a blunder, commoners of “common sense”. We never take a step without stumbling; they move solemnly, ever unerringly, never a step back, and carry bell, book, and candle.
Quoting himself in Stargazers and Gravediggers: Memoirs to Worlds in Collision (2012), 212.
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As a scientist, I am not sure anymore that life can be reduced to a class struggle, to dialectical materialism, or any set of formulas. Life is spontaneous and it is unpredictable, it is magical. I think that we have struggled so hard with the tangible that we have forgotten the intangible.
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As regards religion, on the other hand, one is generally agreed that it deals with goals and evaluations and, in general, with the emotional foundation of human thinking and acting, as far as these are not predetermined by the inalterable hereditary disposition of the human species. Religion is concerned with man’s attitude toward nature at large, with the establishing of ideals for the individual and communal life, and with mutual human relationship. These ideals religion attempts to attain by exerting an educational influence on tradition and through the development and promulgation of certain easily accessible thoughts and narratives (epics and myths) which are apt to influence evaluation and action along the lines of the accepted ideals.
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Astronomy was thus the cradle of the natural sciences and the starting point of geometrical theories. The stars themselves gave rise to the concept of a ‘point’; triangles, quadrangles and other geometrical figures appeared in the constellations; the circle was realized by the disc of the sun and the moon. Thus in an essentially intuitive fashion the elements of geometrical thinking came into existence.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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At first it seems obvious, but the more you think about it the stranger the deductions from this axiom seem to become; in the end you cease to understand what is meant by it.
As quoted, without citation, in Stories about Sets (1968), 84.
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Be of good cheer. Do not think of today’s failures, but of the success that may come tomorrow. You have set yourself a difficult task, but you will succeed if you persevere; and you will find a joy in overcoming obstacles.
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Bees are not as busy as we think they are. They jest can’t buzz any slower.
As quoted in Henry Wysham Lanier, The Golden Book Magazine (1931), Vol. 13, 85.
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Building goes on briskly at the therapeutic Tower of Babel; what one recommends another condemns; what one gives in large doses another scarce dares to prescribe in small doses; and what one vaunts as a novelty another thinks not worth rescuing from merited oblivion. All is confusion, contradiction, inconceivable chaos. Every country, every place, almost every doctor, have their own pet remedies, without which they imagine their patients can not be cured; and all this changes every year, aye every mouth.
Weekly Medical Gazette, of Vienna
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Charlie Holloway (human): “What we hoped to achieve was to meet our makers. To get answers. Why they even made us in the first place.”
David (AI robot): “Why do you think your people made me?”
Charlie Holloway (human): “We made you because we could.”
David (AI robot): “Can you imagine how disappointing it would be for you to hear the same thing from your creator?”
Charlie Holloway (human): “I guess it’s good you can’t be disappointed.”
Prometheus (2012)
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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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Children must be taught how to think, not what to think.
In 'Education for Choice', Coming of Age in Samoa (1928, 1961), 246.
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Common Sense and Education: The more you think you have of one, the less you think you need of the other.
In The Well-Spoken Thesaurus (2011), 109.
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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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Debate is an art form. It is about the winning of arguments. It is not about the discovery of truth. There are certain rules and procedures to debate that really have nothing to do with establishing fact–which creationists have mastered. Some of those rules are: never say anything positive about your own position because it can be attacked, but chip away at what appear to be the weaknesses in your opponent’s position. They are good at that. I don’t think I could beat the creationists at debate. I can tie them. But in courtrooms they are terrible, because in courtrooms you cannot give speeches. In a courtroom you have to answer direct questions about the positive status of your belief. We destroyed them in Arkansas. On the second day of the two-week trial we had our victory party!
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Descartes said, “I think; therefore I am.” The philosophic evolutionist reverses and negatives the epigram. He says, “I am not; therefore I cannot think.”
In Orthodoxy (1918, 2008), 25.
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Do not enter upon research unless you can not help it. Ask yourself the “why” of every statement that is made and think out your own answer. If through your thoughtful work you get a worthwhile idea, it will get you. The force of the conviction will compel you to forsake all and seek the relief of your mind in research work.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted in J.B. Collip 'Frederick Grant Banting, Discoverer of Insulin', The Scientific Monthly (May 1941), 52, No. 5, 473.
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Doctors think a lot of patients are cured who have simply quit in disgust.
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Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility.
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Don’t think of organ donations as giving up part of yourself to keep a total stranger alive. It’s really a total stranger giving up almost all of themselves to keep part of you alive.
Anonymous
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Doubly galling was the fact that at the same time my roommate was taking a history course … filled with excitement over a class discussion. … I was busy with Ampere’s law. We never had any fascinating class discussions about this law. No one, teacher or student, ever asked me what I thought about it.
In Understanding the Universe: An Inquiry Approach to Astronomy and the Nature of Scientific Research (2013), ix.
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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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Dr. Wallace, in his Darwinism, declares that he can find no ground for the existence of pure scientists, especially mathematicians, on the hypothesis of natural selection. If we put aside the fact that great power in theoretical science is correlated with other developments of increasing brain-activity, we may, I think, still account for the existence of pure scientists as Dr. Wallace would himself account for that of worker-bees. Their function may not fit them individually to survive in the struggle for existence, but they are a source of strength and efficiency to the society which produces them.
In Grammar of Science (1911), Part, 1, 221.
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Einstein’s results again turned the tables and now very few philosophers or scientists still think that scientific knowledge is, or can be, proven knowledge.
In 'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London 1965 (1970), Vol. 4, 92.
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Encryption...is a powerful defensive weapon for free people. It offers a technical guarantee of privacy, regardless of who is running the government... It’s hard to think of a more powerful, less dangerous tool for liberty.
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Engineers think that equations approximate the real world.
Physicists think that the real world approximates equations.
Mathematicians are unable to make the connection.
Anonymous
In Jon Fripp, Michael Fripp and Deborah Fripp, Speaking of Science (2000), 41.
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Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.
In Introduction to Mathematics (1911), 119.
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Even if only one in a hundred of the ten billion suitable planets has actually got life well under way, there would be more than 100 million such planets. No, it is presumptuous to think that we are alone.
In The View From a Distant Star: Man's Future in the Universe (1964), 64.
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Every good thought you think is contributing its share to the ultimate result of your life.
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Everyone thinks of changing the world, but no one thinks of changing himself.
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Faraday thinks from day to day, against a background of older thinking, and anticipating new facts of tomorrow. In other words, he thinks in three dimensions of time; past, present, and future.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 1.
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Feeling weightless… it’s so many things together. A feeling of pride, of healthy solitude, of dignified freedom from everything that’s dirty, sticky. You feel exquisitely comfortable . . . and you feel you have so much energy, such an urge to do things, such an ability to do things. And you work well, yes, you think well, without sweat, without difficulty as if the biblical curse in the sweat of thy face and in sorrow no longer exists, As if you’ve been born again.
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Few people think more than two or three times a year. I have made an international reputation for myself by thinking once or twice a week.
As given in 'Quotable Quotes', Reader’s Digest (May 1933). It does not appear in a work written by Shaw. It may have been contributed to the magazine as a personal recollection, though that is not specified in that source.
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Finally, from what we now know about the cosmos, to think that all this was created for just one species among the tens of millions of species who live on one planet circling one of a couple of hundred billion stars that are located in one galaxy among hundreds of billions of galaxies, all of which are in one universe among perhaps an infinite number of universes all nestled within a grand cosmic multiverse, is provincially insular and anthropocentrically blinkered. Which is more likely? That the universe was designed just for us, or that we see the universe as having been designed just for us?
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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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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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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Geometrical axioms are neither synthetic a priori conclusions nor experimental facts. They are conventions: our choice, amongst all possible conventions, is guided by experimental facts; but it remains free, and is only limited by the necessity of avoiding all contradiction. ... In other words, axioms of geometry are only definitions in disguise.
That being so what ought one to think of this question: Is the Euclidean Geometry true?
The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 110.
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Good sense is, of all things among men, the most equally distributed ; for every one thinks himself so abundantly provided with it, that those even who are the most difficult to satisfy in everything else, do not usually desire a larger measure of this quality than they already possess.
In Discours de la Méthode (1637), Part 1. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 3. Also seen translated as “Of all things, good sense is the most fairly distributed: everyone thinks he is so well supplied with it that even those who are the hardest to satisfy in every other respect never desire more of it than they already have,” or “Good sense is of all things in the world the most equally distributed, for everybody thinks he is so well supplied with it that even those most difficult to please in all other matters never desire more of it than they already possess.” From the original French, “Le bon sens est la chose du monde la mieux partagée; car chacun pense en être si bien pourvu, que ceux même qui sont les plus difficiles à contenter en toute autre chose n'ont point coutume d'en désirer plus qu'ils en ont.”
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Governments and parliaments must find that astronomy is one of the sciences which cost most dear: the least instrument costs hundreds of thousands of dollars, the least observatory costs millions; each eclipse carries with it supplementary appropriations. And all that for stars which are so far away, which are complete strangers to our electoral contests, and in all probability will never take any part in them. It must be that our politicians have retained a remnant of idealism, a vague instinct for what is grand; truly, I think they have been calumniated; they should be encouraged and shown that this instinct does not deceive them, that they are not dupes of that idealism.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 84.
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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 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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Here’s to the crazy ones. The misfits. The rebels. The troublemakers. The round heads in the square holes. The ones who see things differently. They’re not fond of rules. You can quote them. Disagree with them. Glorify or vilify them. But the only thing you can’t do is ignore them. Because they change things. They push the human race forward. And while some may see them as the crazy ones, we see genius. Because the people who are crazy enough to think they can change the world, are the ones who do.
In Apple Computer newspaper advertisement (1997) as quoted and cited in Tad Lathrop and Jim Pettigrew, This Business of Music Marketing and Promotion (1999), 55.
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How can a modern anthropologist embark upon a generalization with any hope of arriving at a satisfactory conclusion? By thinking of the organizational ideas that are present in any society as a mathematical pattern.
In Rethinking Anthropology (1961), 2.
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How strange is the lot of us mortals! Each of us is here for a brief sojourn; for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people–first of all for those upon whose smiles and well-being our own happiness is wholly dependent, and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving.
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Human societies increased the abundance and distribution of useful species. This can also be used to preserve the forest, I think. We can use this as an opportunity to reduce the impacts of deforestation. Now we have huge plantations of soybeans that are destroying the Amazon—while in the forest we have lots of plants that can be used while maintaining the forest as it is.
As quoted in Robinson Meyer, 'The Amazon Rainforest Was Profoundly Changed by Ancient Humans', The Atlantic (2 Mar 2017).
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I almost think it is the ultimate destiny of science to exterminate the human race.
Written for fictional character, the Rev. Dr. Opimian, in Gryll Grange (1861), collected in Sir Henry Cole (ed.) The Works of Thomas Love Peacock(1875), Vol. 2, 382. [Hans Øersted discovered electromagnetism in 1820. Presumably the next reference to magnetism refers to a compass needle for navigation. —Webmaster]
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I am a firm believer in the theory that you can do or be anything that you wish in this world, within reason, if you are prepared to make the sacrifices, think and work hard enough and long enough.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted and cited in Editorial Section, 'Sir Frederick Banting', Canadian Public Health Journal (May 1941), 32, No. 5, 266-267.
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I am not unmindful of the journalist’s quip that yesterday’s paper wraps today’s garbage. I am also not unmindful of the outrages visited upon our forests to publish redundant and incoherent collections of essays; for, like Dr. Seuss’ Lorax, I like to think that I speak for the trees. Beyond vanity, my only excuses for a collection of these essays lie in the observation that many people like (and as many people despise) them, and that they seem to cohere about a common theme–Darwin’s evolutionary perspective as an antidote to our cosmic arrogance.
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I came by the horror naturally. Surgery is the one branch of medicine that is the most violent. After all, it’s violent to take up a knife and cut open a person’s body and rummage around with your hands. I think I was attracted to the horrific.
As quoted in Randy Hutter Epstein, 'Richard Selzer, Who Fictionalized Medicine’s Absurdity and Gore, Dies at 87', New York Times (15 Jun 2016). Explaining why his first fiction writing was horror stories.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I can’t recall a single problem in my life, of any sort, that I ever started on that I didn't solve, or prove that I couldn’t solve it. I never let up, until I had done everything that I could think of, no matter how absurd it might seem as a means to the end I was after.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 186.
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I do not mind if you think slowly. But I do object when you publish more quickly than you think.
As quoted, without citation, in William H. Cropper, Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking (2001), 257.
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I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified. The comparative smallness of what we know today as gravitational effects is not a conclusive reason for ignoring the principle of general relativity in theoretical investigations of a fundamental character. In other words, I do not believe that it is justifiable to ask: What would physics look like without gravitation?
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I do not think it is possible really to understand the successes of science without understanding how hard it is—how easy it is to be led astray, how difficult it is to know at any time what is the next thing to be done.
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I do not think that this peace based on force is, can be, or should be, an ultimate end.
From debate (20 Feb 1958) between Linus Pauling and Edward Teller on WQED-TV, San Francisco. Transcript published as Fallout and Disarmament: The Pauling-Teller Debate (1958). Reprinted in 'Fallout and Disarmament: A Debate between Linus Pauling and Edward Teller', Daedalus (Spring 1958), 87, No. 2, 154.
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I do not think that, practically or morally, we can defend a policy of saving every distinctive local population of organisms. I can cite a good rationale for the preservation of species, for each species is a unique and separate natural object that, once lost, can never be reconstituted. But subspecies are distinctive local populations of species with broader geographic range. Subspecies are dynamic, interbreedable, and constantly changing: what then are we saving by declaring them all inviolate?
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I don’t think there is one unique real universe. ... Even the laws of physics themselves may be somewhat observer dependent.
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I have always tried to fit knowledge that I acquired into my understanding of the world. … When something comes along that I don’t understand, that I can’t fit in, that bothers me, I think about it, mull over it, and perhaps ultimately do some work with it. That’s perhaps the reason that I’ve been able to make discoveries in molecular biology.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 739.
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I have before mentioned mathematics, wherein algebra gives new helps and views to the understanding. If I propose these it is not to make every man a thorough mathematician or deep algebraist; but yet I think the study of them is of infinite use even to grown men; first by experimentally convincing them, that to make anyone reason well, it is not enough to have parts wherewith he is satisfied, and that serve him well enough in his ordinary course. A man in those studies will see, that however good he may think his understanding, yet in many things, and those very visible, it may fail him. This would take off that presumption that most men have of themselves in this part; and they would not be so apt to think their minds wanted no helps to enlarge them, that there could be nothing added to the acuteness and penetration of their understanding.
In The Conduct of the Understanding, Sect. 7.
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I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …
In The Conduct of the Understanding, Sect. 7.
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I have never seen a food writer mention this, but all shrimp imported into the United States must first be washed in chlorine bleach to kill bugs. What this does for the taste, I do not know, but I think we should be told.
In The End of the Line: How Overfishing Is Changing the World and What We Eat (2008), 301.
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I heard … xenon was a good anesthesia. … I thought, “How can xenon, which doesn’t form any chemical compounds, serve as a general anesthetic? … I lay awake at night for a few minutes before going to sleep, and during the next couple of weeks each night I would think, “…how do anesthetic agents work?" Then I forgot to do it after a while, but I’d trained my unconscious mind to keep this question alive and to call [it] to my consciousness whenever a new idea turned up…. So seven years went by. [One day I] put my feet up on the desk and started reading my mail, and here was a letter from George Jeffrey … an x-ray crystallographer, on his determination of the structure of a hydrate crystal. Immediately I sat up, took my feet off the desk, and said, “I understand anesthesia!” … I spent a year [and] determined the structure of chloroform hydrate, and then I wrote my paper published in June of 1961.
Interview with George B. Kauffman and Laurie M. Kauffman, in 'Linus Pauling: Reflections', American Scientist (Nov-Dec 1994), 82, No. 6, 522-523.
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I never pick up an item without thinking of how I might improve it. I never perfected an invention that I did not think about in terms of the service it might give others. I want to save and advance human life, not destroy it. I am proud of the fact that I never invented weapons to kill. The dove is my emblem.
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I read them. Not to grade them. No, I read them to see how I am doing. Where am I failing? What don’t they understand? Why do they give wrong answers? Why do they have some point of view that I don’t think is right? Where am I failing? Where do I need to build up.
In The Essential Deming.
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I remember growing up thinking that astronauts and their job was the coolest thing you could possibly do... But I absolutely couldn’t identify with the people who were astronauts. I thought they were movie stars.
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I see trees of green, red roses too,
I see them bloom for me and you,
And I think to myself, what a wonderful world.
Verse of song made popular by Louis Armstrong, written by George Weiss and Bob Thiele
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I should be the last to discard the law of organic heredity ... but the single word “heredity” cannot dispense science from the duty of making every possible inquiry into the mechanism of organic growth and of organic formation. To think that heredity will build organic beings without mechanical means is a piece of unscientific mysticism.
In 'On the Principles of Animal Morphology', Proceedings of the Royal Society of Edinburgh (1888), 15, 294-295. Original as Letter to Mr John Murray, communicated to the Society by Professor Sir William Turner. Page given as in collected volume published 1889.
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I shuddered when I saw a crimson flame through the porthole instead of the usual starry sky at the night horizon of the planet. Vast pillars of light were bursting into the sky, melting into it, and flooding over with all the colors of the rainbow. An area of red luminescence merged smoothly into the black of the cosmos. The intense and dynamic changes in the colors and forms of the pillars and garlands made me think of visual music. Finally, we saw that we had entered directly into the aurora borealis.
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I sometimes ask myself how it came about that I was the one to develop the theory of relativity. The reason, I think, is that a normal adult never stops to think about the problem of space and time. These are things which he has thought of as a child. But my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had already grown up.
In Ronald W. Clark, Einstein: The Life and Times (1971), 10.
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I stand almost with the others. They believe the world was made for man, I believe it likely that it was made for man; they think there is proof, astronomical mainly, that it was made for man, I think there is evidence only, not proof, that it was made for him. It is too early, yet, to arrange the verdict, the returns are not all in. When they are all in, I think that they will show that the world was made for man; but we must not hurry, we must patiently wait till they are all in.
Attributed.
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I think a future flight should include a poet, a priest and a philosopher… we might get a much better idea of what we saw.
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I think and think for months and years. Ninety-nine times, the conclusion is false. The hundredth time I am right.
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I think it would be desirable that this form of word [mathematics] should be reserved for the applications of the science, and that we should use mathematic in the singular to denote the science itself, in the same way as we speak of logic, rhetoric, or (own sister to algebra) music.
In Presidential Address to the British Association, Exeter British Association Report (1869); Collected Mathematical Papers, Vol. 2, 669.
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I think it [the World Series] should be called the World Sequence.
As given in essay, Ronald Coifman and Robert S. Strichartz, 'The School of Antoni Zygmund', collected in Peter Duren (ed.), A Century of Mathematics in America (1989), 348. The essay states Zygmund was “walking past a lounge in the University of Chicago that was filled with a loud crowd watching TV, he asked one of his students what was going on. The student told him that the crowd was watching the World Series and explained to him some of the features of this baseball phenomenon. Zygmund thought about it all for a few minutes and commented” with the subject quote above. The authors acknowledge students of Zygmund provided personal recollections to them for the essay in general. Webmaster speculates the quote is from a student recollection, and not necessarily verbatim.
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I think it’s a mistake to ever look for hope outside of one’s self.
After the Fall. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 250
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I think it’s going to be great if people can buy a ticket to fly up and see black sky and the stars. I’d like to do it myself - but probably after it has flown a serious number of times first!
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I think it’s in my basement… let me go upstairs and check. —M.C. Escher [joke attribution]
Anonymous
Widely seen feral on the web. Webmaster has not yet found a primary source for this a quote, and regards it as an anonymous joke, with a false attribution to Escher as part of the joke (because Escher’s work is known for distorted reality). Compare the authentic quote, “Are you really sure that a floor can’t also be a ceiling?” on the M.C. Escher Quotes page of this site.
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I think of the ocean as the blue heart of the planet. Well, how much of your heart do you want to protect?
From narration to the short, hand-drawn animated film for World Ocean’s Day 2013, Ideas For Change.
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I think physicists are the Peter Pans of the human race. They never grow up, and they keep their curiosity.
In Jeremy Bernstein, 'Rabi: The Modern Age', Experiencing Science (1978), 102. Part of Rabi’s response to Bernstein’s interview question, about at which age, in his opinion, physicists tend to run down. Previously published in 'Physicist', The New Yorker (1970).
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I think science has enjoyed an extraordinary success because it has such a limited and narrow realm in which to focus its efforts. Namely, the physical universe.
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I think that a particle must have a separate reality independent of the measurements. That is an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it.
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I think that Alfred Nobel would have been pleased that his prize emphasizes the continuity of science, as well as its novelties.
From Speech (10 Dec 1963) at the Nobel Banquet in Stockholm, Sweden. Collected inGöran Liljestrand (ed.), Les Prix Nobel en 1963, (1964).
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I think that harping on [earthquake] prediction is something between a will-o'-the-wisp and a red herring. Attention is thereby diverted away from positive measures to eliminate earthquake risk.
From interview in the Earthquake Information Bulletin (Jul-Aug 1971), 3, No. 4, as abridged in article on USGS website.
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I think that I cannot preserve my health and spirits, unless I spend four hours a day at least—and it is commonly more than that—sauntering through the woods and over the hills and fields, absolutely free from all worldly engagements.
In 'Walking', The Atlantic (Jun 1862), 9, No. 56, 657-674. Collected in Walking (1841, 1914), 9.
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I think that only daring speculation can lead us further and not accumulation of facts.
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I think that our cooperative conservation approaches get people to sit down and grapple with problem solving.
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I think that space flight is a condition of Nature that comes into effect when an intelligent species reaches the saturation point of its planetary habitat combined with a certain level of technological ability... I think it is a built-in gene-directed drive for the spreading of the species and its continuation.
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I think the real miracle is not to walk either on water or in thin air, but to walk on earth.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 8
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I think there is something more important than believing: Action! The world is full of dreamers, there aren’t enough who will move ahead and begin to take concrete steps to actualize their vision.
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I think we all have a little voice inside us that will guide us. It may be God, I don’t know. But I think that if we shut out all the noise and clutter from our lives and listen to that voice, it will tell us the right thing to do.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 142
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I used to think the human brain was the most fascinating part of the body. But then I realised, Well …look what’s telling me that?
In The Reader’s Digest (1998), 152, 166. (The ellipsis itself is part of the quote, indicating a pause.)
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I would think I knew nothing in physics if I could say only how things could be but, without demonstrating that they can’t be otherwise.
From the original French, “Pour la Physique, ie croyrois n’y rien sçauoir, si ie ne sçauois que dire comment les choses peuuent estre, sans demonstrer qu’elles ne peuuent estre autrement,” in letter (11 Mar 1640) to Père Marin Mersenne, collected in Lettres de Mr Descartes (1659), Vol. 2, 213. As translated by John Cottingham, et al., (trans.), in The Philosophical Writings of Descartes: Volume 3, The Correspondence (1991), 145.
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I write to discover what I think. After all, the bars aren’t open that early.
On his habit of writing in the early morning hours. As quoted in Wall Street Journal (31 Dec 1985).
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If faith cannot be reconciled with rational thinking, it has to be eliminated as an anachronistic remnant of earlier stages of culture and replaced by science dealing with facts and theories which are intelligible and can be validated.
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If I dared to say just what I think, I should add that it is chiefly in the service where the medication is the most active and heroic that the mortality is the greatest. Gentlemen, medicine is charlatanism.
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If I were not a physicist, I would probably be a musician. I often think in music. I live my dreams in music. I see my life in terms of music... I get most joy in life out of music.
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If I were not an atheist, I would believe in a God who would choose to save people on the basis of the totality of their lives and not the pattern of their words. I think he would prefer an honest and righteous atheist to a TV preacher whose every word is
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If the entire Mandelbrot set were placed on an ordinary sheet of paper, the tiny sections of boundary we examine would not fill the width of a hydrogen atom. Physicists think about such tiny objects; only mathematicians have microscopes fine enough to actually observe them.
In 'Can We See the Mandelbrot Set?', The College Mathematics Journal (Mar 1995), 26, No. 2, 90.
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If we work, it is less to obtain those positive results the common people think are our only interest, than to feel that aesthetic emotion and communicate it to those able to experience it.
From the original French, “Si nous travaillons, c’est moins pour obtenir ces résultats auxquels le vulgaire nous croit uniquement attachés, que pour ressentir cette émotion esthétique et la communiquer à ceux qui sont capables de l’éprouver,” quoted in Henri Poincaré,'Notice sur Halphen', Journal de l’École Polytechnique (1890), 60, 143, cited in Oeuvres de G.H. Halphen (1916), Vol. 1, xxiv. As translated in Armand Borel, 'On the Place of Mathematics in Culture', in Armand Borel: Œvres: Collected Papers (1983), Vol. 4, 421.
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If you ask a person, “What were you thinking?” you may get an answer that is richer and more revealing of the human condition than any stream of thoughts a novelist could invent. I try to see through people’s faces into their minds and listen through their words into their lives, and what I find there is beyond imagining.
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If you ask mathematicians what they do, you always get the same answer. They think. They think about difficult and unusual problems. (They never think about ordinary problems—they just write down the answers.)
As translated from Russian in 'A byl li brak?', Literaturnaya Gazeta (5 Dec 1979), 49, 12, as quoted and cited in The American Mathematical Monthly (Nov 1980), 87, No. 97, 696.
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If you see an antimatter version of yourself running towards you, think twice before embracing.
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If you walked into Netscape headquarters with a plain old modem from CompUSA they’d think it was a garage-door opener.
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In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements. Clearly, then, systematic knowledge of nature must start with an attempt to settle questions about principles.
Aristotle
In Physics Book 1, Chap 1, as translated in J.L. Ackrill, A New Aristotle Reader (1988), 81.
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In biology, nothing is clear, everything is too complicated, everything is a mess, and just when you think you understand something, you peel off a layer and find deeper complications beneath. Nature is anything but simple.
The Hot Zone
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In geologists’ own lives, the least effect of time is that they think in two languages, function on two different scales. … “A million years is a short time—the shortest worth messing with for most problems.”
In Basin and Range (1981), 134.
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In her book My Life With the Chimpanzees, Goodall told the story of “Mike,” a chimp who maintained his dominance by kicking a series of kerosene cans ahead of him as he moved down a road, creating confusion and noise that made his rivals flee and cower. She told me she would be thinking of Mike as she watched [Donald Trump in] the upcoming debates.
In magazine article by 'When Donald Meets Hillary', The Atlantic (Oct 2016). The reporter stated “Jane Goodall … told me shortly before Trump won the GOP nomination.”
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In light of new knowledge ... an eventual world state is not just desirable in the name of brotherhood, it is necessary for survival ... Today we must abandon competition and secure cooperation. This must be the central fact in all our considerations of international affairs; otherwise we face certain disaster. Past thinking and methods did not prevent world wars. Future thinking must prevent wars.
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In my position you can’t go out and just say, “I think,” because it’s a very serious thing. So if you get up and say climate is changing because of CO2 emissions, you better bloody well be right.
As quoted in interview with Joe Shute, 'David Attenborough at 90: ‘I think about my mortality every day’', The Telegraph (29 Oct 2016). Note: Elsewhere, Attenborough says that the evidence of climate change is now, in fact, “ironclad.”
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In recent weeks we learned that scientists have created human embryos in test tubes solely to experiment on them. This is deeply troubling, and a warning sign that should prompt all of us to think through these issues very carefully.
'Address to the Nation on Stem Cell Research', (9 Aug 2001) in Public Papers Of The Presidents Of The United States, George W. Bush, 2001 (2004), Book 2, 955.
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In the secondary schools mathematics should be a part of general culture and not contributory to technical training of any kind; it should cultivate space intuition, logical thinking, the power to rephrase in clear language thoughts recognized as correct, and ethical and esthetic effects; so treated, mathematics is a quite indispensable factor of general education in so far as the latter shows its traces in the comprehension of the development of civilization and the ability to participate in the further tasks of civilization.
The purposes of instruction in mathematics in secondary schools formulated by the German Society for the Advancement of Instruction. From Unterrichtsblätter fur Mathematik und Naturwissenschaft (1904), 128. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 72-73.
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In the year 1692, James Bernoulli, discussing the logarithmic spiral [or equiangular spiral, ρ = αθ] … shows that it reproduces itself in its evolute, its involute, and its caustics of both reflection and refraction, and then adds: “But since this marvellous spiral, by such a singular and wonderful peculiarity, pleases me so much that I can scarce be satisfied with thinking about it, I have thought that it might not be inelegantly used for a symbolic representation of various matters. For since it always produces a spiral similar to itself, indeed precisely the same spiral, however it may be involved or evolved, or reflected or refracted, it may be taken as an emblem of a progeny always in all things like the parent, simillima filia matri. Or, if it is not forbidden to compare a theorem of eternal truth to the mysteries of our faith, it may be taken as an emblem of the eternal generation of the Son, who as an image of the Father, emanating from him, as light from light, remains ὁμοούσιος with him, howsoever overshadowed. Or, if you prefer, since our spira mirabilis remains, amid all changes, most persistently itself, and exactly the same as ever, it may be used as a symbol, either of fortitude and constancy in adversity, or, of the human body, which after all its changes, even after death, will be restored to its exact and perfect self, so that, indeed, if the fashion of Archimedes were allowed in these days, I should gladly have my tombstone bear this spiral, with the motto, ‘Though changed, I arise again exactly the same, Eadem numero mutata resurgo.’”
In 'The Uses of Mathesis', Bibliotheca Sacra, Vol. 32, 516-516. [The Latin phrase “simillima filia matri” roughly translates as “the daughter resembles the mother”. “Spira mirabilis” is Latin for “marvellous spiral”. The Greek word (?µ???s???) translates as “consubstantial”, meaning of the same substance or essence (used especially of the three persons of the Trinity in Christian theology). —Webmaster]
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Incompetency is a greater obstacle to perfection than one would think.
In The Maxims and Reflections of Goethe (1906), 201.
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Is any knowledge worthless? Try to think of an example.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 169.
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It frequently happens that two persons, reasoning right on a mechanical subject, think alike and invent the same thing without any communication with each other.
As quoted by Coleman Sellers, Jr., in his Lecture (20 Nov 1885) delivered at the Franklin Institute. Printed in Coleman Sellers, Jr., 'Oliver Evans and his Inventions', Journal of the Franklin Institute (Jul 1886), 122, No. 1, 15.
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It is an irony of fate that I myself have been the recipient of excessive admiration and reverence from my fellow-beings, through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the few ideas to which I have with my feeble powers attained through ceaseless struggle. I am quite aware that for any organisation to reach its goals, one man must do the thinking and directing and generally bear the responsibility. But the led must not be coerced, they must be able to choose their leader.
In 'What I Believe', Forum and Century (1930), 84, 193-194.
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It is by no means hopeless to expect to make a machine for really very difficult mathematical problems. But you would have to proceed step-by-step. I think electricity would be the best thing to rely on.
In Charles Sanders Peirce, Max Harold Fisch, Christian J. W. Kloesel Writings of Charles S. Peirce: 1884-1886 (1993), 422.
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It is exciting to think that it costs nothing to create a new particle,…
In Lectures on Gravitation: 1962-62, quoted by John Preskill and Kip S. Thorne, 'Foreword to Feynman Lectures on Gravitation' (15 May 1995). The authors of the Foreword explain: “Because the total energy of the universe could really be zero, … matter creation is possible because the rest energy of the matter is actually canceled by its gravitational potential energy.”
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It is hard to tell what causes the pervasive timidity. One thinks of video-induced stupor, intake of tranquilizers, fear of not living to enjoy the many new possessions and toys, the example of our betters in cities and on campuses who high-mindedly surrender to threats of violence and make cowardice fashionable.
In 'Thoughts on the Present', First Things, Last Things (1971), 111.
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It is not enough that a few brilliant men can create computers to “think” for us; for the greatest thinking machine is inside each of us.
In Best of Sydney J. Harris (1976), 82.
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It is not necessary to probe into the nature of things, as was done by those whom the Greeks call physici; nor need we be in alarm lest the Christian should be ignorant of the force and number of the elements—the motion, and order, and eclipses of the heavenly bodies; the form of the heavens; the species and the natures of animals, plants, stones, fountains, rivers, mountains; about chronology and distances; the signs of coming storms; and a thousand other things which those philosophers either have found out, or think they have found out. … It is enough for the Christian to believe that the only cause of all created things, whether heavenly or earthly … is the goodness of the Creator, the one true God.
In Marcus Dods (ed.), J.F. Shaw (trans.), The Enchiridion of Augustine, Chap. 9, collected in The Works of Aurelius Augustine, Bishop of Hippo: A new translation (1873), Vol. 9, 180-181. The physici are natural philosophers.
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It is not possible to find in all geometry more difficult and more intricate questions or more simple and lucid explanations [than those given by Archimedes]. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearance, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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It seems to me that the older subjects, classics and mathematics, are strongly to be recommended on the ground of the accuracy with which we can compare the relative performance of the students. In fact the definiteness of these subjects is obvious, and is commonly admitted. There is however another advantage, which I think belongs in general to these subjects, that the examinations can be brought to bear on what is really most valuable in these subjects.
In Conflict of Studies and other Essays (1873), 6-7.
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It seems to me that there is a good deal of ballyhoo about scientific method. I venture to think that the people who talk most about it are the people who do least about it. Scientific method is what working scientists do, not what other people or even they themselves may say about it. No working scientist, when he plans an experiment in the laboratory, asks himself whether he is being properly scientific, nor is he interested in whatever method he may be using as method.
…...
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It still fascinates me to think that here in this room you have radio signals from stations all over the world going through, and we can stick up an antenna and receive them.
Recalling how his lifelong “natural interest in how things work” began as a youth, which included such activities as building a Tesla coil and assembling crystal radios. In interview, Rushworth M. Kidder, 'Grounded in Space Science', Christian Science Monitor (22 Dec 1989).
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It would not be difficult to come to an agreement as to what we understand by science. Science is the century-old endeavor to bring together by means of systematic thought the perceptible phenomena of this world into as thoroughgoing an association as possible. To put it boldly, it is the attempt at the posterior reconstruction of existence by the process of conceptualization. But when asking myself what religion is I cannot think of the answer so easily. And even after finding an answer which may satisfy me at this particular moment, I still remain convinced that I can never under any circumstances bring together, even to a slight extent, the thoughts of all those who have given this question serious consideration.
…...
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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It’s humbling to think that all animals, including human beings, are parasites of the plant world.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 39.
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It’s the lies that undo us. It’s the lies we think we need to survive. When was the last time you told the truth?
Character in TV series, Homeland.
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I’m just a speck, standing on this big planet. … The Earth is orbiting the Sun, and the Sun is a huge star. And our star may be a big deal to us, but, my friends, our star is just another speck. … It’s not really in downtown Milky Way, it’s way out on the side. … I'm a speck, living on a speck, orbiting a speck in the middle of specklessness. But … I have this brain … to think about all of this. To think about the vast emptiness of space. I can reason that I'm a speck on a speck in the middle of specklessness. And that’s cool. That’s worthy of respect.
Bill Nye
From narration to PBS TV program, 'Astrobiology', The Eyes of Nye (2005), Ep. 1, Introduction before titles. Also seen quoted as: “We are just a speck, on a speck, orbiting a speck, in the corner of a speck, in the middle of nowhere.”
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I’m not an animal lover if that means you think things are nice if you can pat them, but I am intoxicated by animals.
Interview by Simon Gage in 'David Attenborough: I’m not an animal lover', Metro (29 Jan 2013, London).
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I’m not an atheist and I don’t think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many different languages. The child knows someone must have written those books. It doe s not know how. The child dimly suspects a mysterious order in the arrangement of the books but doesn’t know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God.
…...
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Let us tenderly and kindly cherish, therefore, the means of knowledge. Let us dare to read, think, speak, and write.
Dissertation on the Canon and Feudal Law (as it was later known), originally published untitled and with no author credited in the Boston Gazette (Aug 1765). Collected in John Adams and Charles Francis Adams (ed.), The Works of John Adams (1851), Vol. 3, 462.
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Man is the Reasoning Animal. Such is the claim. I think it is open to dispute. Indeed, my experiments have proven to me that he is the Unreasoning Animal. Note his history, as sketched above. It seems plain to me that whatever he is he is not a reasoning animal. His record is the fantastic record of a maniac. I consider that the strongest count against his intelligence is the fact that with that record back of him he blandly sets himself up as the head animal of the lot: whereas by his own standards he is the bottom one.
In truth, man is incurably foolish. Simple things which the other animals easily learn, he is incapable of learning. Among my experiments was this. In an hour I taught a cat and a dog to be friends. I put them in a cage. In another hour I taught them to be friends with a rabbit. In the course of two days I was able to add a fox, a goose, a squirrel and some doves. Finally a monkey. They lived together in peace; even affectionately.
Next, in another cage I confined an Irish Catholic from Tipperary, and as soon as he seemed tame I added a Scotch Presbyterian from Aberdeen. Next a Turk from Constantinople; a Greek Christian from Crete; an Armenian; a Methodist from the wilds of Arkansas; a Buddhist from China; a Brahman from Benares. Finally, a Salvation Army Colonel from Wapping. Then I stayed away two whole days. When I came back to note results, the cage of Higher Animals was all right, but in the other there was but a chaos of gory odds and ends of turbans and fezzes and plaids and bones and flesh—not a specimen left alive. These Reasoning Animals had disagreed on a theological detail and carried the matter to a Higher Court.
In Letters from the Earth: Uncensored Writings (),
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Many a person thinks he is hard-boiled when he is only half-baked.
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Many people are shrinking from the future and from participation in the movement toward a new, expanded reality. And, like homesick travelers abroad, they are focusing their anxieties on home. The reasons are not far to seek. We are at a turning point in human history... We could turn our attention to the problems that going to the moon certainly will not solve ... But I think this would be fatal to our future... A society that no longer moves forward does not merely stagnate; it begins to die.
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Many people would sooner die than think. In fact they do.
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Many persons have inquired concerning a recent message of mine that “a new type of thinking is essential if mankind is to survive and move to higher levels.”
From interview with Michael Amrine, 'The Real Problem is in the Hearts of Men', New York Times Magazine, (23 Jun 1946), 7. See more of the message from which Einstein quoted himself, see the longer quote that begins, “Our world faces a crisis as yet unperceived…,” on the Albert Einstein Quotes page of this website.
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Many times every day I think of taking off in that missile. I’ve tried a thousand times to visualize that moment, to anticipate how I’ll feel if I’m first, which I very much want to be. But whether I go first or go later. I approach it now with some awe, and I’m sure I’ll approach it with even more awe on my day. In spite of the fact that I will he very busy getting set and keeping tabs on all the instruments, there’s no question that I’ll need—and will have—all my confidence.
As he wrote in an article for Life (14 Sep 1959), 38.
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Men are more sentimental than women. It blurs their thinking.
In 'From the Notebooks of Lazarus Long', Time Enough for Love: The Lives of Lazarus Long (1973), 256.
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Men, accustomed to think of men as possessing sex attributes and other things besides, are accustomed to think of women as having sex, and nothing else.
In “Common Sense” Applied to Woman Suffrage (1894), 180.
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Men, it has been well said, think in herds; it will be seen that they go mad in herds, while they only recover their senses slowly, one by one.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 3.
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Minds think with ideas, not information No amount of data, bandwidth, or processing power can substitute for inspired thought.
In Silicon Snake Oil: Second Thoughts on the Information Highway (1996), 194.
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Modern man is weighed down more by the burden of responsibility than by the burden of sin. We think him more a savior who shoulders our responsibilities than him who shoulders our sins. If instead of making decisions we have but to obey and do our duty, we feel it as a sort of salvation.
In The Passionate State of Mind (1955), 53.
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Most American citizens think that life without the telephone is scarcely worth living. The American public telephone system is therefore enormous. Moreover the system belongs to an organization, the Bell companies, which can both control it and make the equipment needed. There is no surer way of getting efficient functional design than having equipment designed by an organization which is going to have to use it. Humans who would have to live with their own mistakes tend to think twice and to make fewer mistakes.
In 'Musical Acoustics Today', New Scientist (1 Nov 1962), 16 No. 311, 256.
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Most inventors who have an idea never stop to think whether their invention will be saleable when they get it made. Unless a man has plenty of money to throw away, he will find that making inventions is about the costliest amusement he can find.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 186.
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Most of us have had moments in childhood when we touched the divine presence. We did not think it extraordinary because it wasn’t; it was just a beautiful moment filled with love. In those simple moments our hearts were alive, and we saw the poignant beauty of life vividly with wonder and appreciation.
David McArthur and Bruce McArthur
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Most people would rather die than think: many do.
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Most people would rather die than think; many do.
This is an commonly seen paraphrase. For the verbatim words, see it as a part of a longer quote that begins, “We all have a tendency to think…” on the Bertrand Russell Quotes page of this website. In The ABC of Relativity (1925), 166.
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Most scientists think wars and national boundaries are a menace to the true creative spirit by which science must live, they hate war and they are terrified of atomic war—because they know its possibilities.
As quoted in Michael Amrine, 'I’m A Frightened Man', Collier’s (1946), 117, 51.
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My mother, my dad and I left Cuba when I was two [January, 1959]. Castro had taken control by then, and life for many ordinary people had become very difficult. My dad had worked [as a personal bodyguard for the wife of Cuban president Batista], so he was a marked man. We moved to Miami, which is about as close to Cuba as you can get without being there. It’s a Cuba-centric society. I think a lot of Cubans moved to the US thinking everything would be perfect. Personally, I have to say that those early years were not particularly happy. A lot of people didn’t want us around, and I can remember seeing signs that said: “No children. No pets. No Cubans.” Things were not made easier by the fact that Dad had begun working for the US government. At the time he couldn’t really tell us what he was doing, because it was some sort of top-secret operation. He just said he wanted to fight against what was happening back at home. [Estefan’s father was one of the many Cuban exiles taking part in the ill-fated, anti-Castro Bay of Pigs invasion to overthrow dictator Fidel Castro.] One night, Dad disappered. I think he was so worried about telling my mother he was going that he just left her a note. There were rumours something was happening back home, but we didn’t really know where Dad had gone. It was a scary time for many Cubans. A lot of men were involved—lots of families were left without sons and fathers. By the time we found out what my dad had been doing, the attempted coup had taken place, on April 17, 1961. Intitially he’d been training in Central America, but after the coup attempt he was captured and spent the next wo years as a political prisoner in Cuba. That was probably the worst time for my mother and me. Not knowing what was going to happen to Dad. I was only a kid, but I had worked out where my dad was. My mother was trying to keep it a secret, so she used to tell me Dad was on a farm. Of course, I thought that she didn’t know what had really happened to him, so I used to keep up the pretence that Dad really was working on a farm. We used to do this whole pretending thing every day, trying to protect each other. Those two years had a terrible effect on my mother. She was very nervous, just going from church to church. Always carrying her rosary beads, praying her little heart out. She had her religion, and I had my music. Music was in our family. My mother was a singer, and on my father’s side there was a violinist and a pianist. My grandmother was a poet.
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My profession often gets bad press for a variety of sins, both actual and imagined: arrogance, venality, insensitivity to moral issues about the use of knowledge, pandering to sources of funding with insufficient worry about attendant degradation of values. As an advocate for science, I plead ‘mildly guilty now and then’ to all these charges. Scientists are human beings subject to all the foibles and temptations of ordinary life. Some of us are moral rocks; others are reeds. I like to think (though I have no proof) that we are better, on average, than members of many other callings on a variety of issues central to the practice of good science: willingness to alter received opinion in the face of uncomfortable data, dedication to discovering and publicizing our best and most honest account of nature’s factuality, judgment of colleagues on the might of their ideas rather than the power of their positions.
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My success will not depend on what A or B thinks of me. My success will be what I make of my work.
Quoted in India Today (Apr 2008), 33, No 16, as cited on webpage of Dhirubhai Ambani Institute of Information and Communication Technology.
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My visceral perception of brotherhood harmonizes with our best modern biological knowledge ... Many people think (or fear) that equality of human races represents a hope of liberal sentimentality probably squashed by the hard realities of history. They are wrong. This essay can be summarized in a single phrase, a motto if you will: Human equality is a contingent fact of history. Equality is not true by definition; it is neither an ethical principle (though equal treatment may be) nor a statement about norms of social action. It just worked out that way. A hundred different and plausible scenarios for human history would have yielded other results (and moral dilemmas of enormous magnitude). They didn’t happen.
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Nazis started the Science of Eugenics. It’s the theory that to them, justified the holocaust. The problem is the Science has been broadly accepted around the world, including the United States. We even went as far as to hire the Scientists that were working on it and brought them over here rather then charging them with war crimes. [Project Paperclip] I think it is a very dangerous Science that contains ideologies that are a grave danger to the entire world.
James Dye
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Newton could not admit that there was any difference between him and other men, except in the possession of such habits as … perseverance and vigilance. When he was asked how he made his discoveries, he answered, “by always thinking about them;” and at another time he declared that if he had done anything, it was due to nothing but industry and patient thought: “I keep the subject of my inquiry constantly before me, and wait till the first dawning opens gradually, by little and little, into a full and clear light.”
In History of the Inductive Sciences, Bk. 7, chap, 1, sect. 5.
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No one in his senses, or imbued with the slightest knowledge of physics, will ever think that the earth, heavy and unwieldy from its own weight and mass, staggers up and down around its own center and that of the sun; for at the slightest jar of the earth, we would see cities and fortresses, towns and mountains thrown down.
Universae Naturae Theatrum (1597). In Dorothy Stimson, The Gradual Acceptance of the Copernican Theory of the Universe (1917), 45.
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No one thinks of concealing the truth from a cardiac patient: there is nothing shameful about a heart attack. Cancer patients are lied to, not just because the disease is (or is thought to be) a death sentence, but because it is felt to be obscene—in the original meaning of that word: ill-omened, abominable, repugnant to the senses.
In Illness as a Metaphor (1978), 8,
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No! What we need are not prohibitory marriage laws, but a reformed society, an educated public opinion which will teach individual duty in these matters. And it is to the women of the future that I look for the needed reformation. Educate and train women so that they are rendered independent of marriage as a means of gaining a home and a living, and you will bring about natural selection in marriage, which will operate most beneficially upon humanity. When all women are placed in a position that they are independent of marriage, I am inclined to think that large numbers will elect to remain unmarried—in some cases, for life, in others, until they encounter the man of their ideal. I want to see women the selective agents in marriage; as things are, they have practically little choice. The only basis for marriage should be a disinterested love. I believe that the unfit will be gradually eliminated from the race, and human progress secured, by giving to the pure instincts of women the selective power in marriage. You can never have that so long as women are driven to marry for a livelihood.
In 'Heredity and Pre-Natal Influences. An Interview With Dr. Alfred Russel Wallace', Humanitarian (1894), 4, 87.
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Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to this idea in its elf, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?
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Nor do I know any study which can compete with mathematics in general in furnishing matter for severe and continued thought. Metaphysical problems may be even more difficult; but then they are far less definite, and, as they rarely lead to any precise conclusion, we miss the power of checking our own operations, and of discovering whether we are thinking and reasoning or merely fancying and dreaming.
In Conflict of Studies (1873), 13.
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Not every collision,
not every punctilious trajectory
by which billiard-ball complexes
arrive at their calculable meeting places
lead to reaction. ...
Men (and women) are not
as different from molecules
as they think.
Hoffmann, as a chemist-turned-poet is making the analogy of random intermolecular interactions to those of humans. From poem, 'Men and Molecules', The Metamict State (1984), 43. Cited as an epigraph in William L. Masterton and Cecile N. Hurley Chemistry: Principles and Reactions, Updated Edition (2005), 282.
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Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Now when we think that each of these stars is probably the centre of a solar system grander than our own, we cannot seriously take ourselves to be the only minds in it all.
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Often in evolutionary processes a species must adapt to new conditions in order to survive. Today the atomic bomb has altered profoundly the nature of the world as we know it, and the human race consequently finds itself in a new habitat to which it must adapt its thinking.
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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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Only the individual can think, and thereby create new values for society–nay, even set up new moral standards to which the life of the community conforms. Without creative, independently thinking and judging personalities the upward development of society is as unthinkable as the development of the individual personality without the nourishing soil of the community.
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Our ability to think is the one survival tool we have. Science is applied thought. Without science, we’re living in caves and eating cockroaches.
(2010)
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Our failure to discern a universal good does not record any lack of insight or ingenuity, but merely demonstrates that nature contains no moral messages framed in human terms. Morality is a subject for philosophers, theologians, students of the humanities, indeed for all thinking people. The answers will not be read passively from nature; they do not, and cannot, arise from the data of science. The factual state of the world does not teach us how we, with our powers for good and evil, should alter or preserve it in the most ethical manner.
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Our sun is one of 100 billion stars in our galaxy. Our galaxy is one of billions of galaxies populating the universe. It would be the height of presumption to think that we are the only living things in that enormous immensity.
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People are not going to care about animal conservation unless they think that animals are worthwhile.
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People usually consider walking on water or in thin air a miracle. But I think the real miracle is not to walk either on water or in thin air, but to walk on earth. Every day we are engaged in a miracle which we don’t even recognize: a blue sky, white clouds, green leaves, the black, curious eyes of a child - our own two eyes. All is a miracle.
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People who wouldn’t think of talking with their mouths full often speak with their heads empty.
In Wolfgang Mieder, Wolfgang Mieder, Stewart A. Kingsbury (eds.), A Dictionary of American Proverbs (1992), 472.
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Phony psychics like Uri Geller have had particular success in bamboozling scientists with ordinary stage magic, because only scientists are arrogant enough to think that they always observe with rigorous and objective scrutiny, and therefore could never be so fooled–while ordinary mortals know perfectly well that good performers can always find a way to trick people.
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Physicists are, as a general rule, highbrows. They think and talk in long, Latin words, and when they write anything down they usually include at least one partial differential and three Greek letters.
In 'A Newsman Looks at Physicists', Physics Today (May 1948), 1, No. 1, 15.
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Physicists can only think the same damn thing over and over.
In 'Loose Ends', QED: The Strange Theory of Light and Matter (1985), Chap. 4, 149.
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Physicists like to think that all you have to do is say, these are the conditions, now what happens next?
In Messenger Lecture (1964), at Cornell University, 'The Distinction of Past and Future', collected in The Character of Physical Law (1967, 2017), 114.
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Physicists still tend to regard biologists as men condemned by their lack of mathematics to follow an imprecise science. Some biologists think that, life is too complex to be amenable to mathematical study.
From A.S. Curtis, 'The Value of Mathematics in Biology',New Scientist (25 Jan 1962), 223.
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Probably I am very naive, but I also think I prefer to remain so, at least for the time being and perhaps for the rest of my life.
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Rational thinking which is free from assumptions ends therefore in mysticism.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 41
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Read no newspapers, try to find a few friends who think as you do, read the wonderful writers of earlier times, Kant, Goethe, Lessing, and the classics of other lands, and enjoy the natural beauties of Munich’s surroundings. Make believe all the time that you are living, so to speak, on Mars among alien creatures and blot out any deeper interest in the actions of those creatures. Make friends with a few animals. Then you will become a cheerful man once more and nothing will be able to trouble you.
Letter (5 Apr 1933). As quoted in Jamie Sayen, Einstein in America: The Scientist’s Conscience in the Age of Hitler and Hiroshima (1985), 12. This is part of Einstein’s reply to a letter from a troubled, unemployed musician, presumably living in Munich.
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Reading, after a certain age, diverts the mind too much from its creative pursuits. Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
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Realistic thinking accrues only after mistake making, which is the cosmic wisdom's most cogent way of teaching each of us how to carry on.
In Buckminster Fuller and Answar Dil, Humans in Universe (1983), 218.
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Religion is, in reality, living. Our religion is not what we profess, or what we say, or what we proclaim; our religion is what we do, what we desire, what we seek, what we dream about, what we fantasize, what we think—all these things.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 21
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Science and technology multiply around us. To an increasing extent they dictate the languages in which we speak and think. Either we use those languages, or we remain mute.
In the Introduction to the French edition (1984) of Crash (1974),
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Science is the only truth and it is the great lie. It knows nothing, and people think it knows everything. It is misrepresented. People think that science is electricity, automobilism, and dirigible balloons. It is something very different. It is life devouring itself. It is the sensibility transformed into intelligence. It is the need to know stifling the need to live. It is the genius of knowledge vivisecting the vital genius.
repr. In Selected Writings, ed. and trans. by Glen S. Burne (1966). 'Art and Science,' Promenades Philosophiques (1905-1909).
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Science is what scientists do, not what nonscientists think they do or ought to be doing.
Wetenschap is wat wetenschappers doen.
Flanagan's motto as magazine editor for selecting content to put in Scientific American. Because he heard, and liked the sound of this slogan in Dutch, he put that version on a banner in his office. As quoted in obituary by Marc Santora, 'Dennis Flanagan, 85, Editor of Scientific American, for 37 Years', New york Times (17 Jan 2005), B6.
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Scientific research can reduce superstition by encouraging people to think and survey things in terms of cause and effect. Certain it is that a conviction, akin to religious feeling, of the rationality or intelligibility of the world lies behind all scientific work of a higher order.
From 'Scientific Truth' in Essays in Science (1934, 2004), 11.
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Shortly after electrons were discovered it was thought that atoms were like little solar systems, made up of a … nucleus and electrons, which went around in “orbits,” much like the planets … around the sun. If you think that’s the way atoms are, then you’re back in 1910.
In QED: The Strange Theory of Light and Matter (1985, 2006), 84.
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Some of Feynman’s ideas about cosmology have a modern ring. A good example is his attitude toward the origin of matter. The idea of continuous matter creation in the steady state cosmology does not seriously offend him (and he notes … that the big bang cosmology has a problem just as bad, to explain where all the matter came from in the beginning). … He emphasizes that the total energy of the universe could really be zero, and that matter creation is possible because the rest energy of the matter is actually canceled by its gravitational potential energy. “It is exciting to think that it costs nothing to create a new particle, …”
In John Preskill and Kip S. Thorne, 'Foreword to Feynman Lectures on Gravitation' (15 May 1995). Feynman delivered his lectures in 1962–63.
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Some of the scientists, I believe, haven’t they been changing their opinion a little bit on global warming? There’s a lot of differing opinions and before we react I think it’s best to have the full accounting, full understanding of what’s taking place.
Presidential Debate (2000). In Historic Documents of 2000 (2001), 823.
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Sometimes I think we’re alone in the universe, and sometimes I think we’re not. In either case, the idea is quite staggering.
…...
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Sooner or later in every talk, [David] Brower describes the creation of the world. He invites his listeners to consider the six days of Genesis as a figure of speech for what has in fact been 4 billion years. On this scale, one day equals something like six hundred and sixty-six million years, and thus, all day Monday and until Tuesday noon, creation was busy getting the world going. Life began Tuesday noon, and the beautiful organic wholeness of it developed over the next four days. At 4 p.m. Saturday, the big reptiles came on. At three minutes before midnight on the last day, man appeared. At one-fourth of a second before midnight Christ arrived. At one-fortieth of a second before midnight, the Industrial Revolution began. We are surrounded with people who think that what we have been doing for that one-fortieth of a second can go on indefinitely. They are considered normal, but they are stark. raving mad.
In Encounters with the Archdruid (1971), 79-80.
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Standing now in diffused light, with the wind at my back, I experience suddenly a feeling of completeness–not a feeling of having achieved something or of being stronger than everyone who was ever here before, not a feeling of having arrived at the ultimate point, not a feeling of supremacy. Just a breath of happiness deep inside my mind and my breast. The summit seemed suddenly to me to be a refuge, and I had not expected to find any refuge up here. Looking at the steep, sharp ridges below us, I have the impression that to have come later would have been too late. Everything we now say to one another, we only say out of embarrassment. I don’t think anymore. As I pull the tape recorder, trancelike, from my rucksack, and switch it on wanting to record a few appropriate phrases, tears again well into my eyes. “Now we are on the summit of Everest,” I begin, “it is so cold that we cannot take photographs…” I cannot go on, I am immediately shaken with sobs. I can neither talk nor think, feeling only how this momentous experience changes everything. To reach only a few meters below the summit would have required the same amount of effort, the same anxiety and burden of sorrow, but a feeling like this, an eruption of feeling, is only possible on the summit itself.
In Everest: Expedition to the Ultimate (1979), 180.
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Strategy is a style of thinking, a conscious and deliberate process, an intensive implementation system, the science of insuring future success.
…...
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Stupidity is no excuse for not thinking.
Unkempt Thoughts (1962), 77.
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Success is a lousy teacher. It seduces smart people into thinking they can’t lose.
…...
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Suppose that you are in love with a lady on Neptune and that she returns the sentiment. It will be some consolation for the melancholy separation if you can say to yourself at some possibly pre-arranged moment, “She is thinking of me now.” Unfortunately a difficulty has arisen because we have had to abolish Now. There is no absolute Now, but only the various relative Nows, differing according to their reckoning of different observers and covering the whole neutral wedge which at the distance of Neptune is about eight hours thick. She will have to think of you continuously for eight hours on end in order to circumvent the ambiguity “Now.”
In The Nature of the Physical World (1929), 49.
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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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Teaching thermal physics
Is as easy as a song:
You think you make it simpler
When you make it slightly wrong!
In The Physics Teacher (Sep 1970). As quoted and cited in Clifford Swartz, Cliff's Nodes: Editorials from The Physics Teacher (2006), 192.
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The ability to imagine relations is one of the most indispensable conditions of all precise thinking. No subject can be named, in the investigation of which it is not imperatively needed; but it can be nowhere else so thoroughly acquired as in the study of mathematics.
In Darwinism and other Essays (1893), 296.
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The aim of science is to apprehend this purely intelligible world as a thing in itself, an object which is what it is independently of all thinking, and thus antithetical to the sensible world.... The world of thought is the universal, the timeless and spaceless, the absolutely necessary, whereas the world of sense is the contingent, the changing and moving appearance which somehow indicates or symbolizes it.
'Outlines of a Philosophy of Art,' Essays in the Philosophy of Art, Indiana University Press (1964).
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The axioms of geometry are—according to my way of thinking—not arbitrary, but sensible. statements, which are, in general, induced by space perception and are determined as to their precise content by expediency.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 142.
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The belief is growing on me that the disease is communicated by the bite of the mosquito. … She always injects a small quantity of fluid with her bite—what if the parasites get into the system in this manner.
Letter (27 May 1896) to Patrick Manson. In The Great Malaria Problem and Its Solution: From the Memoirs of Ronald Ross (1988), 72. Ross asked for Manson’s opinion; the ellipsis above, in full is: “What do you think?” As quoted in William Derek Foster, A History of Parasitology (1965), 173. (It was for this insight that Ross was awarded a Nobel Prize.)
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The chances for favorable serendipity are increased if one studies an animal that is not one of the common laboratory species. Atypical animals, or preparations, force one to use non-standard approaches and non-standard techniques, and even to think nonstandard ideas. My own preference is to seek out species which show some extreme of adaptation. Such organisms often force one to abandon standard methods and standard points of view. Almost inevitably they lead one to ask new questions, and most importantly in trying to comprehend their special and often unusual adaptations one often serendipitously stumbles upon new insights.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 234.
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The computational formalism of mathematics is a thought process that is externalised to such a degree that for a time it becomes alien and is turned into a technological process. A mathematical concept is formed when this thought process, temporarily removed from its human vessel, is transplanted back into a human mold. To think ... means to calculate with critical awareness.
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.
In The Search For Truth (1934), 117.
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The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors, so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.
…...
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The essayist is … sustained by the childish belief that everything he thinks about, everything that happens to him, is of general interest.
First line of Foreword in Essays of E.B. White (1977, 2014), vii.
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The fundamental essence of science, which I think we've lost in our education system, is poking something with a stick and seeing what happens. Embrace that process of inquiry.
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The future of Thought, and therefore of History, lies in the hands of the physicists, and … the future historian must seek his education in the world of mathematical physics. A new generation must be brought up to think by new methods, and if our historical departments in the Universities cannot enter this next phase, the physical departments will have to assume this task alone.
In The Degradation of the Democratic Dogma (1920), 283.
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The general public has long been divided into two parts those who think science can do anything, and those who are afraid it will.
From interview with Graham Chedd, 'The Lady Gets Her Way', New Scientist (5 Jul 1973), 59, No. 853, 15-16.
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The history of the universe is in every one of us. Every particle in our bodies has a multibillion-year past, every cell and every bodily organ has a multimillion-year past, and many of our ways of thinking have multithousand-year pasts.
As co-author with Nancy Ellen Abrams, in The View from the Center of the Universe: Discovering Our Extraordinary Place in the Cosmos (2006), 151.
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The human mind needs nature in order to think most deeply. Pretending to be other creatures, children practise metaphor and empathy alike.
In 'Fifty Years On, the Silence of Rachel Carson’s Spring Consumes Us', The Guardian (25 Sep 2012),
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The human race knows enough about thinking to prevent it.
In The Decline and Fall of Science (1976).
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The Internet’s been so great, and it’s so nice to have fans do nice, elaborate websites, but I think the downside is some of the things... for real fans to go on and see that 90 percent of the information isn’t true or to see pictures that aren’t really me, or for them to be able to sell these things, that’s one of the downsides, I think.
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The large collection of problems which our modern Cambridge books supply will be found to be almost an exclusive peculiarity of these books; such collections scarcely exist in foreign treatises on mathematics, nor even in English treatises of an earlier date. This fact shows, I think, that a knowledge of mathematics may be gained without the perpetual working of examples. … Do not trouble yourselves with the examples, make it your main business, I might almost say your exclusive business, to understand the text of your author.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 74.
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The most remarkable thing was his [Clifford’s] great strength as compared with his weight, as shown in some exercises. At one time he could pull up on the bar with either hand, which is well known to be one of the greatest feats of strength. His nerve at dangerous heights was extraordinary. I am appalled now to think that he climbed up and sat on the cross bars of the weathercock on a church tower, and when by way of doing something worse I went up and hung by my toes to the bars he did the same.
Anonymous
Quoted from a letter by one of Clifford’s friends to F. Pollock, in Clifford’s Lectures and Essays (1901), Vol. 1, Introduction, 8.
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The observing mind is not a physical system, it cannot interact with any physical system. And it might be better to reserve the term ‘subject ‘ for the observing mind ... For the subject, if anything, is the thing that senses and thinks. Sensations and thoughts do not belong to the ‘world of energy.’
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The original question, “Can machines think?,” I believe too meaningless to deserve discussion. Nevertheless I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.
(1950) As quoted in The World of Mathematics (1956), 2083.
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The price of progress is trouble, and I don’t think the price is too high.
As quoted in book review, T.A. Boyd, 'Charles F. Kettering: Prophet of Progress', Science (30 Jan 1959), 256.
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The priest persuades a humble people to endure their hard lot, a politician urges them to rebel against it, and a scientist thinks of a method that does away with the hard lot altogether.
Max Percy
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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 question of whether Machines Can Think ... is about as relevant as the question of whether Submarines Can Swim.
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The real danger is not that computers will begin to think like men, but that men will begin to think like computers.
As quoted, without citation, in Howard W. Eves, Return to Mathematical Circles, (1988), 63.
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The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane.
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The secular world is more spiritual than it thinks, just as the ecclesiastical world is more materialist than it cares to acknowledge.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 27
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The soul seems to be a very tenuous substance … [and] seems to be made of a most subtle texture, extremely mobile or active corpuscles, not unlike those of flame or heat; indeed, whether they are spherical, as the authors of atoms propound, or pyramidical as Plato thought, or some other form, they seem from their own motion and penetration through bodies to create the heat which is in the animal.
As quoted in Margaret J. Osler and Paul Lawrence Farber (eds.), Religion, Science, and Worldview: Essays in Honor of Richard S. Westfall (2002), 169.
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The strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects. This is the discipline that deals with the universe’s divine revolutions, the stars’ motions, sizes, distances, risings and settings . . . for what is more beautiful than heaven?
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The tools we use have a profound (and devious!) influence on our thinking habits, and, therefore, on our thinking abilities.
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The truth of the matter is that, though mathematics truth may be beauty, it can be only glimpsed after much hard thinking. Mathematics is difficult for many human minds to grasp because of its hierarchical structure: one thing builds on another and depends on it.
As co-author with D.T.E. Marjoram, Mathematics in a Changing World (1973).
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The use of traveling is to regulate the imagination by reality, and instead of thinking how things may be, to see them as they are.
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The whole question of imagination in science is often misunderstood by people in other disciplines. They try to test our imagination in the following way. They say, “Here is a picture of some people in a situation. What do you imagine will happen next?” When we say, “I can’t imagine,” they may think we have a weak imagination. They overlook the fact that whatever we are allowed to imagine in science must be consistent with everything else we know; that the electric fields and the waves we talk about are not just some happy thoughts which we are free to make as we wish, but ideas which must be consistent with all the laws of physics we know. We can’t allow ourselves to seriously imagine things which are obviously in contradiction to the laws of nature. And so our kind of imagination is quite a difficult game. One has to have the imagination to think of something that has never been seen before, never been heard of before. At the same time the thoughts are restricted in a strait jacket, so to speak, limited by the conditions that come from our knowledge of the way nature really is. The problem of creating something which is new, but which is consistent with everything which has been seen before, is one of extreme difficulty
In The Feynman Lectures in Physics (1964), Vol. 2, Lecture 20, p.20-10 to p.20-11.
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There are many fine things which you mean to do some day, under what you think will be more favorable circumstances. But the only time that is yours is the present.
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There are still psychologists who, in a basic misunderstanding, think that gestalt theory tends to underestimate the role of past experience. Gestalt theory tries to differentiate between and-summative aggregates, on the one hand, and gestalten, structures, on the other, both in sub-wholes and in the total field, and to develop appropriate scientific tools for investigating the latter. It opposes the dogmatic application to all cases of what is adequate only for piecemeal aggregates. The question is whether an approach in piecemeal terms, through blind connections, is or is not adequate to interpret actual thought processes and the role of the past experience as well. Past experience has to be considered thoroughly, but it is ambiguous in itself; so long as it is taken in piecemeal, blind terms it is not the magic key to solve all problems.
In Productive Thinking (1959), 65.
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There are things out there that are very simple and you never think would work. … Wikipedia is one of those that it would never occur to me that something like that would work. … But it does work. … People who have taken fairly simple ideas, … at a certain scale and after they gain a certain amount of momentum, they can really take off and work. And that’s really an amazing thing.
Guest Lecture, UC Berkeley, 'Search Engines, Technology, and Business' (3 Oct 2005). At 1:13 in the YouTube video.
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There are those who will say “unless we announce disasters, no one will listen”, but I’m not one of them. It’s not the sort of thing I would ever say. It’s quite the opposite of what I think and it pains me to see this quote being used repeatedly in this way. I would never say we should hype up the risk of climate disasters in order to get noticed.
In Steve Connor, 'Fabricated quote used to discredit climate scientist', The Independent (10 Feb 2010).
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There are two kinds of biologists, those who are looking to see if there is one thing that can be understood and those who keep saying it is very complicated and that nothing can be understood. ... You must study the simplest system you think has the properties you are interested in.
As quoted, without source, by John R. Platt in 'Science, Strong Inference', Science (16 Oct 1964), 146, No. 3642, 349.
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There is an insistent tendency among serious social scientists to think of any institution which features rhymed and singing commercials, intense and lachrymose voices urging highly improbable enjoyment, caricatures of the human esophagus in normal and impaired operation, and which hints implausibly at opportunities for antiseptic seduction as inherently trivial. This is a great mistake. The industrial system is profoundly dependent on commercial television and could not exist in its present form without it.
In The New Industrial State (1967), 208.
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Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all The second time you go through it, you think you understand it, except for one or two points. The third time you go through it, you know you don't understand it, but by that time you are so used to the subject, it doesn't bother you anymore.
Quoted, without citation, in Stanley W. Angrist and Loren G. Hepler, Order and Chaos: Laws of Energy and Entropy (1967), 215. The authors identify it as “perhaps apocryphal.” The quote is used as epigraph, dated as 1950 in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 50. The quote is introduced as “When asked why he did not write on that field he replied somewhat as follows,” by Keith J. Laidler in Physical Chemistry with Biological Applications (1978), 145.
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These thoughts did not come in any verbal formulation. I rarely think in words at all. A thought comes, and I may try to express it in words afterward.
As quoted as a comment to an unnamed friend, “when discussing the genesis of his ideas,” in Howard W. Eves Mathematical Circles Adieu, (1977), 59. Eves also states that “Dr. Gerald Holton, professor of physics at Harvard University, believed Einstein’s habit, from infancy on, of thinking in concepts rather than words played a key role in Einstein’s scientific work.”
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Think impossible and dreams get discarded, projects get abandoned, and hope for wellness is torpedoed. But let someone yell the words it’s possible, and resources we hadn’t been aware of come rushing in to assist us in our quest.
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Think, In mounting higher,
The angels would press on us, and aspire
To drop some golden orb of perfect song
Into our deep, dear silence.
From poem, 'Sonnets From the Portuguese' (1826), XXII. In Elizabeth Barrett Browning and Harriet Waters Preston (ed.), The Complete Poetical Works of Mrs. Browning (1900), 219.
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Thinking about the universe has now been handed over to specialists. The rest of us merely read about it.
City Aphorisms, Seventh Selection (1990).
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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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Thinking is the hardest work there is. Which is the probable reason why so few engage in it.
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Thinking is the most unhealthy thing in the world, and people die of it just as they die of any other disease.
In 'Decay of Lying', The Writings of Oscar Wilde: Epigrams, Phrases and Philosophies For the Use of the Young (1907), 6.
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Thinking must never submit itself, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, if not to facts themselves, because, for it, to submit would be to cease to be.
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This isn’t just about today, this about generations to come. And you’ve got a chance to be the greatest conservation President since Theodore Roosevelt, and I think he’s done it.
From transcript, 'Exit Interview: Bruce Babbit', PBS Newshour (5 Jan 2001). On pbs.org website.
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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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Those who have few affairs to attend to are great speakers: the less men think, the more they talk.
As quoted, without citation, in Day's Collacon: an Encyclopaedia of Prose Quotations (1884), 923.
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Through purely logical thinking we can attain no knowledge whatsoever of the empirical world.
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 215.
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Till Algebra, that great Instrument and Instance of Humane Sagacity, was discovered, Men, with amazement, looked on several of the Demonstrations of ancient Mathematicians, and could scarce forbear to think the finding some of those Proofs, more than humane.
In 'Of Reason', Essay Concerning Humane Understanding (1690), Book 4, Ch. 17, Sec. 11, 345. Note: humane (obsolete) = human.
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To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know. And yet those with the courage to tread this path to real discovery are not only offered practically no guidance on how to do so, they are actively discouraged and have to set about it in secret, pretending meanwhile to be diligently engaged in the frantic diversions and to conform with the deadening personal opinions which are continually being thrust upon them.
In 'Appendix 1', The Laws of Form (1969), 110.
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To me, it [the 1962 space flight of Friendship 7] is not something that happened a long time ago. It seems like a couple of days ago, really. It’s a rare day I don’t think about it, relive it in my mind. I can remember every switch I flipped, every move I made, every word I spoke and every word spoken to me. Clear as a bell.
As reported by Howard Wilkinson in 'John Glenn Had the Stuff U.S. Heroes are Made of', The Cincinnati Enquirer (20 Feb 2002).
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To pray is to think about the meaning of life.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 178
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To think I have spent my life on absolute muck.
Exclaimed after Littlewood explained Eddington’s writings about relativity to Russell, who at that time knew no such physics. In John E. Littlewood and Béla Bollobás (ed.), A Mathematician’s Miscellany, (1953, 1986), 129.
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To think the thinkable—that is the mathematician’s aim.
In 'The Universe and Beyond', Hibbert Journal, 3 (1904-1905), 312.
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Truth and understanding are not such wares as to be monopolized and traded in by tickets and statutes and standards. We must not think to make a staple commodity of all the knowledge in the land, to mark and license it like our broadcloth and our woolpacks.
In Areopagitica: A speech of Mr John Milton for the Liberty of Unlicenced printing to the Parliament of England (23 Nov 1644), 23.
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Truth can only be found by the human intellect, exercised in perfect freedom, and trained to submit itself to the facts of nature. This is the essence of the Scientific Method, which is the exact opposite of the Theological Method. Science teaches men to think with absolute independence of all arbitrary authority, but to submit all their thoughts to the test of actual experiences of Nature. Christianity teaches them to think only according to its own foregone dogmatic conclusions, and to stick to these dogmatic conclusion in defiance of all possible experience.
Leading article in Francis Ellingwood Abbot (ed.), The Index (1 Jan 1880), Volume 11, No. 523, 1.
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Use your feeling brain, not your thinking brain.
As quoted in 'In Memoriam—Jack J. Leedy (1921–2004)', Journal of Poetry Therapy (2004), 17, No. 4, 231.
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Vagueness is very much more important in the theory of knowledge than you would judge it to be from the writings of most people. Everything is vague to a degree you do not realize till you have tried to make it precise, and everything precise is so remote from everything that we normally think, that you cannot for a moment suppose that is what we really mean when we say what we think.
In The Philosophy of Logical Atomism (1918, 1919), 2.
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Very little comes easily to our poor, benighted species (the first creature, after all, to experiment with the novel evolutionary inventions of self-conscious philosophy and art). Even the most ‘obvious,’ ‘accurate,’ and ‘natural’ style of thinking or drawing must be regulated by history and won by struggle. Solutions must therefore arise within a social context and record the complex interactions of mind and environment that define the possibility of human improvement.
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We all have a tendency to think that the world must conform to our prejudices. The opposite view involves some effort of thought, and most people would die sooner than think–in fact they do so.
In The ABC of Relativity (1925), 166. A paraphrase from this quote is often seen as, “Most people would rather die than think; many do.”
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We all know, from what we experience with and within ourselves, that our conscious acts spring from our desires and our fears. Intuition tells us that that is true also of our fellows and of the higher animals. We all try to escape pain and death, while we seek what is pleasant. We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race. Hunger, love, pain, fear are some of those inner forces which rule the individual’s instinct for self preservation. At the same time, as social beings, we are moved in the relations with our fellow beings by such feelings as sympathy, pride, hate, need for power, pity, and so on. All these primary impulses, not easily described in words, are the springs of man’s actions. All such action would cease if those powerful elemental forces were to cease stirring within us. Though our conduct seems so very different from that of the higher animals, the primary instincts are much alike in them and in us. The most evident difference springs from the important part which is played in man by a relatively strong power of imagination and by the capacity to think, aided as it is by language and other symbolical devices. Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions. In that way imagination and intelligence enter into our existence in the part of servants of the primary instincts. But their intervention makes our acts to serve ever less merely the immediate claims of our instincts.
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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We cannot but think there is something like a fallacy in Mr. Buckle’s theory that the advance of mankind is necessarily in the direction of science, and not in that of morals.
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We cannot doubt of our existence while we doubt, and that this is the first knowledge we acquire when we philosophize in order. … The knowledge, I think, therefore I am, is the first and most certain that occurs to one who philosophizes orderly.
From the original Latin: “Non posse à nobis dubitari, quin existamus dum dubitamus; atque quod ordine philosophando cognoscimus. … Ac proinde hæc cognitio, ego cognito, ergo sum, est omnium | prima & certissima, quæ cuilibet ordine philosophanti occurant,” in Principia Philosophiæ (1644), Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition VII, 6-7. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 195.
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We can’t solve problems by using the same kind of thinking we used when we created them.
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We fooled ourselves into thinking this thing wouldn’t crash. When I was in astronaut training I asked, “what is the likelihood of another accident?” The answer I got was: one in 10,000, with an asterisk. The asterisk meant, “we don’t know.”
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We have taken to the Moon the wealth of this nation,
the vision of its political leaders,
the intelligence of its scientists,
the dedication of its engineers,
the careful craftsmanship of its workers,
and the enthusiastic support of its people.
We have brought back rocks, and I think it is a fair trade . . .
Man has always gone where he has been able to go. It’s that simple.
He will continue pushing back his frontier,
no matter how far it may carry him from his homeland.
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We haven’t got the money, so we’ve got to think!
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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 never be too absorbed by the thought we are pursuing.
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We must really agree with Bamberger, who thinks that the greater part of patients who die, of endocarditis even, have succumbed not to the disease, but to the remedy.
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We need a number of solutions - we need more efficiency and conservation. Efficiency is a big one. I think car companies need to do a lot better in producing more efficient cars. They have the technology, we just need to demand them as consumers.
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We need to think of “blue carbon” and other services provided by healthy marine ecosystems. Mangroves, seagrasses and coastal marshes are great sinks for atmospheric carbon.
From interview with Terry Waghorn, 'Can We Eat Our Fish and Protect Them Too?', Forbes (21 Feb 2012)
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We often think that when we have completed our study of one we know all about two, because “two” is “one and one.” We forget that we still have to make a study of “and.”
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We often think, naïvely, that missing data are the primary impediments to intellectual progress–just find the right facts and all problems will dissipate. But barriers are often deeper and more abstract in thought. We must have access to the right metaphor, not only to the requisite information. Revolutionary thinkers are not, primarily, gatherers of fact s, but weavers of new intellectual structures.
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We seem to think that God speaks by seconding the ideas we’ve already adopted, but God nearly always catches us by surprise...God tends to confound, astonish, and flabbergast.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 154
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We think our civilization near its meridian, but we are yet only at the cock-crowing and the morning star.
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We [Irving Kaplansky and Paul Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free , but when the chips are down we close the office door and compute with matrices like fury.
In Paul Halmos: Celebrating 50 Years of Mathematics (1991), 88.
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We’re inquiring into the deepest nature of our constitutions: How we inherit from each other. How we can change. How our minds think. How our will is related to our thoughts. How our thoughts are related to our molecules.
Newsweek 4 Jul 76
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What is more difficult, to think of an encampment on the moon or of Harlem rebuilt? Both are now within the reach of our resources. Both now depend upon human decision and human will.
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What magnetism is, no-one knows. We can only think of it as a peculiar condition created in space by the motion of electricity. (1925)
As quoted by Stephen T. Keith and Pierre Quédec, in 'Magnetism and Magnetic Materials', an article collected in Out of the Crystal Maze: Chapters from The History of Solid State Physics (1992), 360.
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When I think of vision, I have in mind the ability to see above and beyond the majority.
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When I was a child, I spoke as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
Bible
(circa 325 A.D.)
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When meditating over a disease, I never think of finding a remedy for it, but, instead, a means of preventing it.
From address (15 May 1884), to École Centrale des Arts et Manufactures, Paris. In Maurice Benjamin Strauss, Familiar Medical Quotations (1968), 451.
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When the Heavens were a little blue Arch, stuck with Stars, methought the Universe was too straight and close: I was almost stifled for want of Air: but now it is enlarged in height and breadth, and a thousand Vortex’s taken in. I begin to breathe with more freedom, and I think the Universe to be incomparably more magnificent than it was before.
In A Plurality of Worlds (1688), 126, as translated by Mr. Glanvill.
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When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails us. One need only think of the weather, in which case prediction even for a few days ahead is impossible. Nevertheless no one doubts that we are confronted with a causal connection whose causal components are in the main known to us.
Out of My Later Years (1995), 28.
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When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea.
Only utterance at press conference, directed at the media, after he won his appeal at Croydon Magistrates Court against a prison sentence for his conviction of assault on a hostile fan. Quoted in Simon Midgley, 'When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea', The Independent (31 Mar 1995). According to Maurice Watkins (legal director of Manchester United) the statement was prepared by Cantona before facing the press, though the reporters may have taken it to be spontaneous. In Simon Stone, 'Maurice Watkins reveals role in Eric Cantona’s “seagulls” speech', The Independent (27 Nov 2012).
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When we are young, we think that science has to do with facts, with finding answers and solutions, and that it proceeds like an arrow from the primitive to the sophisticated, from mystery to light. But as we get older, we find that, while science does have to do with facts and laws, it has equally to do with wisdom.
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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When we build, let us think that we build forever. Let it not be for present delight nor for present use alone. Let it be such work as our descendants will thank us for; and let us think, as we lay stone on stone, that a time is to come when those stones will be held sacred because our hands have touched them, and that men will say, as they look upon the labor and wrought substance of them, “See! This our father did for us.”
From Lectures on 'Architecture and Painting' (Nov 1853), delivered at Edinburgh, collected in The Seven Lamps of Architecture (May 1849, 1887), 172.
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When you think about flying, it’s nuts really. Here you are at about 40,000 feet, screaming along at 700 miles an hour and you’re sitting there drinking Diet Pepsi and eating peanuts. It just doesn’t make any sense.
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Whenever I get gloomy with the state of the world, I think about the arrivals gate at Heathrow Airport. General opinion’s starting to make out that we live in a world of hatred and greed, but I don’t see that. It seems to me that love is everywhere. Often it’s not particularly dignified or newsworthy, but it’s always there - fathers and sons, mothers and daughters, husbands and wives, boyfriends, girlfriends, old friends. When the planes hit the Twin Towers, as far as I know none of the phone calls from the people on board were messages of hate or revenge - they were all messages of love. If you look for it, I’ve got a sneaky feeling you’ll find that love actually is all around.
Movie
Love Actually (Prime Minister)
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Whether you think you can, or whether you think you can’t, you’re right.
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Who ever thought up the word “Mammogram?” Every time I hear it, I think I’m supposed to put my breast in an envelope and send it to someone.
Jan King
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Why should [persons of artistic sensibility] stop to think when they are not very good at thinking?
In Art (1913), 5.
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With fame I become more and more stupid, which, of course, is a very common phenomenon. There is far too great a disproportion between what one is and what others think one is, or at least what they say they think one is. But one has to take it all with good humor.
From Letter (Christmas 1919) to his friend Heinrich Zangger, in Einstein archives. Quoted by Helen Dukas and Banesh Hoffman, Albert Einstein: The Human Side (1979, 2013), 8.
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With science fiction I think we are preparing ourselves for contact with them, whoever they may be.
Interview in article by Dean Lamanna, 'It's No Act—He's into UFOs' in UFO Magazine (U.S. Edition, 1994), 9:4.
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Working is thinking, hence it is not always easy to give an exact accounting of one’s time. Usually I work about four to six hours a day. I am not a very diligent man.
In Cosmic Religion: With Other Opinions and Aphorisms (1931), 105.
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Working on the final formulation of technological patents was a veritable blessing for me. It enforced many-sided thinking and also provided important stimuli to physical thought. Academia places a young person under a kind of compulsion to produce impressive quantities of scientific publications–a temptation to superficiality.
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Would you have a man reason well, you must use him to it betimes; exercise his mind in observing the connection between ideas, and following them in train. Nothing does this better than mathematics, which therefore, I think should be taught to all who have the time and opportunity, not so much to make them mathematicians, as to make them reasonable creatures; for though we all call ourselves so, because we are born to it if we please, yet we may truly say that nature gives us but the seeds of it, and we are carried no farther than industry and application have carried us.
In Conduct of the Understanding, Sect. 6.
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You have to think big to be big.
…...
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Your life is your spiritual path. It’s what’s right in front of you. You can’t live anyone else’s life. The task is to live yours and stop trying to copy one you think looks better.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 245
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You’ll be tempted to grouse about the instability of taxonomy; but stability occurs only where people stop thinking and stop working.
In 'Preface', Observing Marine Invertebrates: Drawings from the Laboratory (1987), xvi.
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[A crowd] thinks in images, and the image itself calls up a series of other images, having no logical connection with the first … A crowd scarcely distinguishes between the subjective and the objective. It accepts as real the images invoked in its mind, though they most often have only a very distant relation with the observed facts. * * * Crowds being only capable of thinking in images are only to be impressed by images. It is only images that terrify or attract them and become motives of action.
From Psychologie des Foules (1895), 29 & 56. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap 2, 22 & last sentence, 55. Original French text: “[La foule] pense par images, et l’image évoquée en évoque elle-même une série d’autres n’ayant aucun lien logique avec la première. … La foule ne sépare guère le subjectif de l’objectif. Elle admet comme réelles les images évoquées dans son esprit, et qui le plus souvent n’ont qu’une parenté lointaine avec le fait observé. * * * Les foules, ne pouvant penser que par images,ne se laissent impressionner que par des images. Seules les images les terrifient ou les séduisent, et deviennent des mobiles d’action.”
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[J.J.] Sylvester’s methods! He had none. “Three lectures will be delivered on a New Universal Algebra,” he would say; then, “The course must be extended to twelve.” It did last all the rest of that year. The following year the course was to be Substitutions-Théorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. “I must give one lecture a week on those,” he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not unfrequent in his lectures: “I haven’t proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc.” At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then another and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 265-266.
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