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Who said: “The conservation of natural resources is the fundamental problem. Unless we solve that problem it will avail us little to solve all others.”
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Home > Category Index for Science Quotations > Category Index F > Category: Far

Far Quotes (144 quotes)

Aber das Leben ist kurz und die Wahrheit wirkt ferne und lebt lange: sagen wir die Wahrheit.
Life is short and truth works far and lives long: let us speak the truth.
Concluding remark in Preface, written at Dresden in August 1818, first German edition, Die Welt als Wille und Vorstellung, 4 Bücher nebst einem Anhange der die Kritik der Kentischen Philosophie (1819), xvi. As translated by Richard Burton Haldane and John Kemp in The World as Will and Representation (1883, 1907), Vol. 1, xv.
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[Students or readers about teachers or authors.] They will listen with both ears to what is said by the men just a step or two ahead of them, who stand nearest to them, and within arm’s reach. A guide ceases to be of any use when he strides so far ahead as to be hidden by the curvature of the earth.
From Lecture (5 Apr 1917) at Hackley School, Tarrytown, N.Y., 'Choosing Books', collected in Canadian Stories (1918), 150.
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A googleplex is precisely as far from infinity as is the number 1 ... No matter what number you have in mind, infinity is larger.
In Cosmos (1980, 2011), 181.
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A government, at bottom, is nothing more than a gang of men, and as a practical matter most of them are inferior men ... Government is actually the worst failure of civilized man. There has never been a really good one, and even those that are most tolerable are arbitrary, cruel, grasping and unintelligent. Indeed, it would not be far wrong to describe the best as the common enemy of all decent citizens.
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A man’s value to the community depends primarily on how far his feelings, thoughts, and actions are directed towards promoting the good of his fellows. We call him good or bad according to how he stands in this matter. It looks at first sight as if our estimate of a man depended entirely on his social qualities.
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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 skilful leech is better far than half a hundred men of war.
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Above, far above the prejudices and passions of men soar the laws of nature. Eternal and immutable, they are the expression of the creative power they represent what is, what must be, what otherwise could not be. Man can come to understand the: he is incapable of changing them.
Cours d'economie Politique
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Abstruse mathematical researches … are … often abused for having no obvious physical application. The fact is that the most useful parts of science have been investigated for the sake of truth, and not for their usefulness. A new branch of mathematics, which has sprung up in the last twenty years, was denounced by the Astronomer Royal before the University of Cambridge as doomed to be forgotten, on account of its uselessness. Now it turns out that the reason why we cannot go further in our investigations of molecular action is that we do not know enough of this branch of mathematics.
In 'Conditions of Mental Development', Lectures and Essays (1901), Vol. 1, 115.
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Although with the majority of those who study and practice in these capacities [engineers, builders, surveyors, geographers, navigators, hydrographers, astronomers], secondhand acquirements, trite formulas, and appropriate tables are sufficient for ordinary purposes, yet these trite formulas and familiar rules were originally or gradually deduced from the profound investigations of the most gifted minds, from the dawn of science to the present day. … The further developments of the science, with its possible applications to larger purposes of human utility and grander theoretical generalizations, is an achievement reserved for a few of the choicest spirits, touched from time to time by Heaven to these highest issues. The intellectual world is filled with latent and undiscovered truth as the material world is filled with latent electricity.
In Orations and Speeches, Vol. 3 (1870), 513.
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Archimedes … had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly, as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. … the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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As a word, ecology has been so debased by recent political usage that many people employ it to identify anything good that happens far from cities and without human interference.
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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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Better far off to leave half the ruins and nine-tenths of the churches unseen and to see well the rest; to see them not once, but again and often again; to watch them, to learn them, to live with them, to love them, till they have become a part of life and life’s recollections.
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Book-knowledge is a poor resource … In many cases, ignorance is a good thing: the mind retains its freedom of investigation and does not stray along roads that lead nowhither, suggested by one’s reading. … Ignorance can have its advantages; the new is found far from the beaten track.
In Jean-Henri Fabre and Alexander Teixeira de Mattos (trans.), The Life and Love of the Insect (1918), 243.
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But does Man have any “right” to spread through the universe? Man is what he is, a wild animal with the will to survive, and (so far) the ability, against all competition. Unless one accepts that, anything one says about morals, war, politics, you name it, is nonsense. Correct morals arise from knowing what man is, not what do-gooders and well-meaning old Aunt Nellies would like him to be. The Universe will let us know - later - whether or not Man has any “right” to expand through it.
Starship Troopers
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But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
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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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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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Euclid alone
Has looked on Beauty bare.
He turned away at once;
Far too polite to stare.
Parody after Edna St. Vincent Millay. In The Mathematical Intelligencer (Fall 1994), 16, No. 4, 20.
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Every investigator must before all things look upon himself as one who is summoned to serve on a jury. He has only to consider how far the statement of the case is complete and clearly set forth by the evidence. Then he draws his conclusion and gives his vote, whether it be that his opinion coincides with that of the foreman or not.
In The Maxims and Reflections of Goethe (1906), 190.
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Few will deny that even in the first scientific instruction in mathematics the most rigorous method is to be given preference over all others. Especially will every teacher prefer a consistent proof to one which is based on fallacies or proceeds in a vicious circle, indeed it will be morally impossible for the teacher to present a proof of the latter kind consciously and thus in a sense deceive his pupils. Notwithstanding these objectionable so-called proofs, so far as the foundation and the development of the system is concerned, predominate in our textbooks to the present time. Perhaps it will be answered, that rigorous proof is found too difficult for the pupil’s power of comprehension. Should this be anywhere the case,—which would only indicate some defect in the plan or treatment of the whole,—the only remedy would be to merely state the theorem in a historic way, and forego a proof with the frank confession that no proof has been found which could be comprehended by the pupil; a remedy which is ever doubtful and should only be applied in the case of extreme necessity. But this remedy is to be preferred to a proof which is no proof, and is therefore either wholly unintelligible to the pupil, or deceives him with an appearance of knowledge which opens the door to all superficiality and lack of scientific method.
In 'Stücke aus dem Lehrbuche der Arithmetik', Werke, Bd. 2 (1904), 296.
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For me, it is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring.
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Free men are aware of the imperfection inherent in human affairs, and they are willing to fight and die for that which is not perfect. They know that basic human problems can have no final solutions, that our freedom, justice, equality, etc. are far from absolute, and that the good life is compounded of half measures, compromises, lesser evils, and gropings toward the perfect. The rejection of approximations and the insistence on absolutes are the manifestation of a nihilism that loathes freedom, tolerance, and equity.
In The Temper of Our Time (1967), 103.
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Humans everywhere share the same goals when the context is large enough. And the study of the Cosmos provides the largest possible context … . If a human disagrees with you, let him live. In a hundred billion galaxies, you will not find another … . If we are to survive, our loyalties must be broadened further, to include the whole human community, the entire planet Earth.
Cosmos
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I agree with your remark about loving your enemy as far as actions are concerned. But for me the cognitive basis is the trust in an unrestricted causality. ‘I cannot hate him, because he must do what he does.’ That means for me more Spinoza than the prophets.
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I cannot separate land and sea: to me they interfinger like a pattern in a moss agate, positive and negative shapes irrevocably interlocked. My knowledge of this peninsula depends on that understanding: of underwater canyons that are continuations of the land, of the shell fossils far inland that measure continuations of the sea in eons past.
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I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
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I had the ambition to not only go farther than man had gone before, but to go as far as it was possible to go.
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I hate science. It denies a man’s responsibility for his own deeds, abolishes the brotherhood that springs from God’s fatherhood. It is a hectoring, dictating expertise, which makes the least lovable of the Church Fathers seem liberal by contrast. It is far easier for a Hitler or a Stalin to find a mock-scientific excuse for persecution than it was for Dominic to find a mock-Christian one.
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I hear one day the word “mountain,” and I ask someone “what is a mountain? I have never seen one.”
I join others in discussions of mountains.
One day I see in a book a picture of a mountain.
And I decide I must climb one.
I travel to a place where there is a mountain.
At the base of the mountain I see there are lots of paths to climb.
I start on a path that leads to the top of the mountain.
I see that the higher I climb, the more the paths join together.
After much climbing the many paths join into one.
I climb till I am almost exhausted but I force myself and continue to climb.
Finally I reach the top and far above me there are stars.
I look far down and the village twinkles far below.
It would be easy to go back down there but it is so beautiful up here.
I am just below the stars.
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I stand before you as somebody who is both physicist and a priest, and I want to hold together my scientific and my religious insights and experiences . I want to hold them together, as far as I am able, without dishonesty and without compartmentalism. I don’t want to be a priest on Sunday and a physicist on Monday; I want to be both on both days.
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I think that only daring speculation can lead us further and not accumulation of facts.
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I wanted to be a scientist from my earliest school days. The crystallizing moment came when I first caught on that stars are mighty suns, and how staggeringly far away they must be to appear to us as mere points of light. I’m not sure I even knew the word science then, but I was gripped by the prospect of understanding how things work, of helping to uncover deep mysteries, of exploring new worlds.
In 'With Science on Our Side', Washington Post (9 Jan 1994).
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If a man can have only one kind of sense, let him have common sense. If he has that an uncommon sense too, he is not far from genius.
In Hialmer Day Gould, New Practical Spelling (1905), 13.
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If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured and far away.
In Walden: Or, Life in the Woods (1854, 1906), 358.
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If a photographic plate under the center of a lens focused on the heavens is exposed for hours, it comes to reveal stars so far away that even the most powerful telescopes fail to reveal them to the naked eye. In a similar way, time and concentration allow the intellect to perceive a ray of light in the darkness of the most complex problem.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 34.
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If I have not seen as far as others, it is because giants were standing on my shoulders.
As quoted, previously on webpage with short bio of Hal Abelson at publicknowledge.org (as archived from Nov 2004).
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If we had a reliable way to label our toys good and bad, it would be easy to regulate technology wisely. But we can rarely see far enough ahead to know which road leads to damnation. Whoever concerns himself with big technology, either to push it forward
Disturbing the Universe (1979).
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If we knew all the laws of Nature, we should need only one fact or the description of one actual phenomenon to infer all the particular results at that point. Now we know only a few laws, and our result is vitiated, not, of course, by any confusion or irregularity in Nature, but by our ignorance of essential elements in the calculation. Our notions of law and harmony are commonly confined to those instances which we detect, but the harmony which results from a far greater number of seemingly conflicting, but really concurring, laws which we have not detected, is still more wonderful. The particular laws are as our points of view, as to the traveler, a mountain outline varies with every step, and it has an infinite number of profiles, though absolutely but one form. Even when cleft or bored through, it is not comprehended in its entireness.
…...
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If you go far enough out you can see the Universe itself, all the billion light years summed up time only as a flash, just as lonely, as distant as a star on a June night if you go far enough out. And still, my friend, if you go far enough out you are only at the beginning of yourself.
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In addition, each barrel of oil we save through conservation further decreases our dangerous reliance on unstable Middle East oil.
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In an era in which the domain of intellect and politics were almost exclusively male, Theon [her father] was an unusually liberated person who taught an unusually gifted daughter [Hypatia] and encouraged her to achieve things that, as far as we know, no woman before her did or perhaps even dreamed of doing.
From 'Hypatia', in Louise S. Grinstein (ed.), Women of Mathematics, (1987), 74.
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In every walk with nature one receives far more than he seeks.
John Muir
Letter (Salt Lake, Jul 1877), in William Frederic Bade, Steep Trails (1918, 1994), 92.
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In modern Europe, the Middle Ages were called the Dark Ages. Who dares to call them so now? … Their Dante and Alfred and Wickliffe and Abelard and Bacon; their Magna Charta, decimal numbers, mariner’s compass, gunpowder, glass, paper, and clocks; chemistry, algebra, astronomy; their Gothic architecture, their painting,—are the delight and tuition of ours. Six hundred years ago Roger Bacon explained the precession of the equinoxes, and the necessity of reform in the calendar; looking over how many horizons as far as into Liverpool and New York, he announced that machines can be constructed to drive ships more rapidly than a whole galley of rowers could do, nor would they need anything but a pilot to steer; carriages, to move with incredible speed, without aid of animals; and machines to fly into the air like birds.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 475.
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In order to seek truth, it is necessary once in the course of our life, to doubt, as far as possible, of all things.
From the original Latin: “Veritatem inquirenti, semel in vita de omnibus, quantum fieri potest, esse dubitandum,” Principles of Philosophy (1644). Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition I, 5. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 193. Also seen translated as: “If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.”
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In our concern for the whooping crane we are at once symbolizing and concealing a far deeper anxiety—namely, the prospective total extermination of all species.
In My Works and Days: A Personal Chronicle (1979), 452.
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In the moonlight
While drinking homemade wine
My sorrow hung heavy
And my heart felt like lead.
The moon was golden yellow
The night soft and mellow.
There was a smell of jasmine
All around.
And I felt the weight of the world
Upon my shoulders.
I looked at the twinkling stars in the sky
So far and wide
Here’s to you
I lifted my wine
And my eyes looked upon the brilliance
Of the moon and stars
From afar...
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It has long been a complaint against mathematicians that they are hard to convince: but it is a far greater disqualification both for philosophy, and for the affairs of life, to be too easily convinced; to have too low a standard of proof. The only sound intellects are those which, in the first instance, set their standards of proof high. Practice in concrete affairs soon teaches them to make the necessary abatement: but they retain the consciousness, without which there is no sound practical reasoning, that in accepting inferior evidence because there is no better to be had, they do not by that acceptance raise it to completeness.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is easy to follow in the sacred writings of the Jewish people the development of the religion of fear into the moral religion, which is carried further in the New Testament. The religions of all civilized peoples, especially those of the Orient, are principally moral religions. An important advance in the life of a people is the transformation of the religion of fear into the moral religion.
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It is tautological to say that an organism is adapted to its environment. It is even tautological to say that an organism is physiologically adapted to its environment. However, just as in the case of many morphological characters, it is unwarranted to conclude that all aspects of the physiology of an organism have evolved in reference to a specific milieu. It is equally gratuitous to assume that an organism will inevitably show physiological specializations in its adaptation to a particular set of conditions. All that can be concluded is that the functional capacities of an organism are sufficient to have allowed persistence within its environment. On one hand, the history of an evolutionary line may place serious constraints upon the types of further physiological changes that are readily feasible. Some changes might require excessive restructuring of the genome or might involve maladaptive changes in related functions. On the other hand, a taxon which is successful in occupying a variety of environments may be less impressive in individual physiological capacities than one with a far more limited distribution.
In W.R. Dawson, G.A. Bartholomew, and A.F. Bennett, 'A Reappraisal of the Aquatic Specializations of the Galapagos Marine Iguana (Amblyrhynchus cristatus)', Evolution (1977), 31, 891.
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It is the duty of every man of good will to strive steadfastly in his own little world to make this teaching of pure humanity a living force, so far as he can. If he makes an honest attempt in this direction without being crushed and trampled under foot by his contemporaries, he may consider himself and the community to which he belongs lucky.
…...
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It is the middle of the night when a glittering theatre of light suddenly appears in front of the Dhaka. Where, moments before there was only darkness, suddenly there are hundreds of columns of light. The sound of helicopters and car horns carry across to the ship on the breeze. There is the scent of rain after it has evaporated from warm streets. This is unmistakably Singapore, the small city-state at the most southern point of the Asiatic mainland. Singapore was built as a centre for world trade by the British over 250 years ago, and today, Singapore has the largest container harbour in the world. This is where the axes of world trade cross paths: from the Far East to Europe, from the Far East to Southeast Asia/the East, and from the Far East to Australia. Everything runs like clockwork here. Within five hours the Dhaka has been unloaded.
Made on Earth
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It must happen that in some cases the author is not understood, or is very imperfectly understood; and the question is what is to be done. After giving a reasonable amount of attention to the passage, let the student pass on, reserving the obscurity for future efforts. … The natural tendency of solitary students, I believe, is not to hurry away prematurely from a hard passage, but to hang far too long over it; the just pride that does not like to acknowledge defeat, and the strong will that cannot endure to be thwarted, both urge to a continuance of effort even when success seems hopeless. It is only by experience we gain the conviction that when the mind is thoroughly fatigued it has neither the power to continue with advantage its course in .an assigned direction, nor elasticity to strike out a new path; but that, on the other hand, after being withdrawn for a time from the pursuit, it may return and gain the desired end.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 68.
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It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously. I also cannot imagine some will or goal outside the human sphere has been cited as a statement that precedes the last three sentences here, but this might have originated in a paraphrase, a transcription error, or a misquotation; it does not appear in any editions of the essay which have thus far been checked.
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I… formerly had two pair of spectacles, which I shifted occasionally, as in travelling I sometimes read, and often wanted to regard the prospects. Finding this change troublesome, and not always sufficiently ready, I had the glasses cut, and half of each kind associated in the same circle. … By this means, as I wear my spectacles constantly, I have only to move my eyes up or down, as I want to see distinctly far or near, the proper glasses being always ready.
Letter (23 May 1785) to George Wheatley). Collected in William Temple Franklin (ed.), The Works of Dr. Benjamin Franklin (1809), Vol. 6, 168.
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Knowing the plumbing of the universe, intricate and awe-inspiring though that plumbing might be, is a far cry from discovering its purpose.
The Science of God: The Convergence of Scientific and Biblical Wisdom (1997, 2009), 18.
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Knowledge and wonder are the dyad of our worthy lives as intellectual beings. Voyager did wonders for our knowledge, but performed just as mightily in the service of wonder–and the two elements are complementary, not independent or opposed. The thought fills me with awe–a mechanical contraption that could fit in the back of a pickup truck, traveling through space for twelve years, dodging around four giant bodies and their associated moons, and finally sending exquisite photos across more than four light-hours of space from the farthest planet in our solar system.
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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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Mars is the next frontier, what the Wild West was, what America was 500 years ago. It’s time to strike out anew. Mars is where the action is for the next thousand years. The characteristic of human nature, and perhaps our simian branch of the family, is curiosity and exploration. When we stop doing that, we won’t be humans anymore. I’ve seen far more in my lifetime than I ever dreamed. Many of our problems on Earth can only be solved by space technology. The next step is in space. It’s inevitable.
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Mars tugs at the human imagination like no other planet. With a force mightier than gravity, it attracts the eye to its shimmering red presence in the clear night sky. It is like a glowing ember in a field of ethereal lights, projecting energy and promise. It inspires visions of an approachable world. The mind vaults to thoughts of what might have been (if Mars were a litter closer to the warming Sun) and of what could be (if humans were one day to plant colonies there). Mysterious Mars, alluring Mars, fourth planet from the Sun: so far away and yet, on a cosmic scale, so very near.
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Mathematic is either Pure or Mixed: To Pure Mathematic belong those sciences which handle Quantity entirely severed from matter and from axioms of natural philosophy. These are two, Geometry and Arithmetic; the one handling quantity continued, the other dissevered. … Mixed Mathematic has for its subject some axioms and parts of natural philosophy, and considers quantity in so far as it assists to explain, demonstrate and actuate these.
In De Augmentis, Bk. 3; Advancement of Learning, Bk. 2.
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Mathematical reasoning is deductive in the sense that it is based upon definitions which, as far as the validity of the reasoning is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in mathematics, as long as it is considered merely as mathematics.
In Universal Algebra (1898), Preface, vi.
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Mathematics associates new mental images with ... physical abstractions; these images are almost tangible to the trained mind but are far removed from those that are given directly by life and physical experience. For example, a mathematician represents the motion of planets of the solar system by a flow line of an incompressible fluid in a 54-dimensional phase space, whose volume is given by the Liouville measure
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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Modern chemistry, with its far-reaching generalizations and hypotheses, is a fine example of how far the human mind can go in exploring the unknown beyond the limits of human senses.
In 'Introduction', General Chemistry: An Elementary Survey Emphasizing Industrial Applications of Fundamental Principles (1923), 4.
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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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Nirvana is a state of pure blissful knowledge ... It has nothing to do with the individual. The ego or its separation is an illusion. Indeed in a certain sense two ‘I’s are identical namely when one disregards all special contents–their Karma. The goal of man is to preserve his Karma and to develop it further ... when man dies his Karma lives and creates for itself another carrier.
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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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Once you have learned to fly your plane, it is far less fatiguing to fly than it is to drive a car. You don’t have to watch every second for cats, dogs, children, lights, road signs, ladies with baby carriages and citizens who drive out in the middle of the block against the lights... Nobody who has not been up in the sky on a glorious morning can possibly imagine the way a pilot feels in free heaven.
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One summer night, out on a flat headland, all but surrounded by the waters of the bay, the horizons were remote and distant rims on the edge of space. Millions of stars blazed in darkness, and on the far shore a few lights burned in cottages. Otherwise there was no reminder of human life. My companion and I were alone with the stars: the misty river of the Milky Way flowing across the sky, the patterns of the constellations standing out bright and clear, a blazing planet low on the horizon. It occurred to me that if this were a sight that could be seen only once in a century, this little headland would be thronged with spectators. But it can be see many scores of nights in any year, and so the lights burned in the cottages and the inhabitants probably gave not a thought to the beauty overhead; and because they could see it almost any night, perhaps they never will.
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Our intelligence has brought us far, but it has also brought us to the brink of total destruction. It cuts both ways, its application sometimes terrifies us, but it also reveals a humbling, sobering perspective of our cosmological home.
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People are usually surprised to discover that I hate the phrase “constitutional rights.” I hate the phrase because it is terribly misleading. Most of the people who say it or hear it have the impression that the Constitution “grants” them their rights. Nothing could be further from the truth. Strictly speaking it is the Bill of Rights that enumerates our rights, but none of our founding documents bestow anything on you at all [...] The government can burn the Constitution and shred the Bill of Rights, but those actions wouldn’t have the slightest effect on the rights you’ve always had.
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Perhaps a species that has accumulated ... tons of explosive per capita has already demonstrated its biological unfitness beyond any further question.
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Philosophers say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong.
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Publication has been extended far beyond our present ability to make real use of the record.
From article 'As We May Think', in Atlantic Magazine (Jul 1945). Bush was expressing concern that the vastly increasing body of research information and knowledge needed mechanical systems to store and effectively manage its retrieval.
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Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
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Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.
Malay Archipelago
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Returning to the moon is an important step for our space program. Establishing an extended human presence on the moon could vastly reduce the costs of further space exploration, making possible ever more ambitious missions. Lifting heavy spacecraft and fuel out of the Earth’s gravity is expensive. Spacecraft assembled and provisioned on the moon could escape its far lower gravity using far less energy, and thus, far less cost. Also, the moon is home to abundant resources. Its soil contains raw materials that might be harvested and processed into rocket fuel or breathable air. We can use our time on the moon to develop and test new approaches and technologies and systems that will allow us to function in other, more challenging environments. The moon is a logical step toward further progress and achievement.
Speech, NASA Headquarters (14 Jan 2004). In Office of the Federal Register (U.S.) Staff (eds.), Public Papers of the Presidents of the United States, George W. Bush (2007), 58.
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Rulers and generals muster their troops. Magnates muster the sums of money which give them power. The fascist dictators muster the irrational human reactions which make it possible for them to attain and maintain their power over the masses. The scientists muster knowledge and means of research. But, thus far, no organization fighting for freedom has ever mustered the biological arsenal where the weapons are to be found for the establishment and the maintenance of human freedom. All precision of our social existence notwithstanding, there is as yet no definition of the word freedom which would be in keeping with natural science. No word is more misused and misunderstood. To define freedom is the same as to define sexual health. But nobody will openly admit this. The advocacy of personal and social freedom is connected with anxiety and guilt feelings. As if to be free were a sin or at least not quite as it should be. Sex-economy makes this guilt feeling comprehensible: freedom without sexual self-determination is in itself a contradiction. But to be sexual means—according to the prevailing human structure—to be sinful or guilty. There are very few people who experience sexual love without guilt feeling. “Free love” has acquired a degrading meaning: it lost the meaning given it by the old fighters for freedom. In films and in books, to be genital and to be criminal are presented as the same thing.
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Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.
Letter collected in Tamworth Reading Room: Letters on an Address Delivered by Sir Robert Peel, Bart., M.P. on the Establishment of a Reading Room at Tamworth (1841), 32. Excerpted in John Henry Newman, An Essay in Aid of a Grammar of Assent (1870), 89 & 94 footnote.
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Science is a capital or fund perpetually reinvested; it accumulates, rolls up, is carried forward by every new man. Every man of science has all the science before him to go upon, to set himself up in business with. What an enormous sum Darwin availed himself of and reinvested! Not so in literature; to every poet, to every artist, it is still the first day of creation, so far as the essentials of his task are concerned. Literature is not so much a fund to be reinvested as it is a crop to be ever new-grown.
Indoor Studies, vol. 12, Collected Works, Houghton (1913).
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Science only goes so far, then comes God.
The Notebook. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 31
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Simultaneous discovery is utterly commonplace, and it was only the rarity of scientists, not the inherent improbability of the phenomenon, that made it remarkable in the past. Scientists on the same road may be expected to arrive at the same destination, often not far apart.
From review '[Arthur] Koestler’s Theory of the Creative Act: “The Act of Creation”', in New Statesman (19 Jun 1964). According to Michael Scammell in his biography (Koestler: The Literary and Political Odyssey of a Twentieth-Century Skeptic (2009), 491 and 654), Medawar eviscerated the book as “amateurish” with “overstretched metaphors” and “fatuous epigrams” while Koestler’s psychological insights were “in the style of the nineteenth century.” The review, with follow-ups, were reprinted in Medawar’s The Art of the Soluble: Creativity and Originality in Science (1967), 85-98.
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So why fret and care that the actual version of the destined deed was done by an upper class English gentleman who had circumnavigated the globe as a vigorous youth, lost his dearest daughter and his waning faith at the same time, wrote the greatest treatise ever composed on the taxonomy of barnacles, and eventually grew a white beard, lived as a country squire just south of London, and never again traveled far enough even to cross the English Channel? We care for the same reason that we love okapis, delight in the fossil evidence of trilobites, and mourn the passage of the dodo. We care because the broad events that had to happen, happened to happen in a certain particular way. And something unspeakably holy –I don’t know how else to say this–underlies our discovery and confirmation of the actual details that made our world and also, in realms of contingency, assured the minutiae of its construction in the manner we know, and not in any one of a trillion other ways, nearly all of which would not have included the evolution of a scribe to record the beauty, the cruelty, the fascination, and the mystery.
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Sufficient for us is the testimony of things produced in the salt waters and now found again in the high mountains, sometimes far from the sea.
Manuscript held by the Earl of Leicester, 31 a [R984]. In Edward McCurdy (ed.), Leonardo da Vinci's note-books: arranged and rendered into English with introductions (1908), 109.
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Take risks. Ask big questions. Don't be afraid to make mistakes; if you don't make mistakes, you're not reaching far enough.
In Monterey Bay Aquarium Research Institute, MBARI's First Decade: A Retrospective (1997), 3, withoug citation. If you know the primary source, please contact Webmaster.
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Tears are often the telescope by which men see far into heaven.
Life Thoughts (1858), 178.
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Telescopes are in some ways like time machines. They reveal galaxies so far away that their light has taken billions of years to reach us. We in astronomy have an advantage in studying the universe, in that we can actually see the past.
We owe our existence to stars, because they make the atoms of which we are formed. So if you are romantic you can say we are literally starstuff. If you’re less romantic you can say we’re the nuclear waste from the fuel that makes stars shine.
We’ve made so many advances in our understanding. A few centuries ago, the pioneer navigators learnt the size and shape of our Earth, and the layout of the continents. We are now just learning the dimensions and ingredients of our entire cosmos, and can at last make some sense of our cosmic habitat.
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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That night I lie out under the stars again. The Pleiades are there winking at me. I am no longer on my way from one place to another. I have changed lives. My life now is as black and white as night and day; a life of fierce struggle under the sun, and peaceful reflection under the night sky. I feel as though I am floating on a raft far, far away from any world I ever knew.
Ted Simon
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The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
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The coastal zone may be the single most important portion of our planet. The loss of its biodiversity may have repercussions far be-yond our worst fears.
Biodiversity
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The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.
From 'Interaction of physiology and behavior under natural conditions', collected in R.I. Bowman (ed.), The Galapagos (1966), 39.
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The Earth reminded us of a Christmas tree ornament hanging in the blackness of space. As we got farther and farther away it diminished in size. Finally it shrank to the size of a marble, the most beautiful marble you can imagine. That beautiful, warm, living object looked so fragile, so delicate, that if you touched it with a finger it would crumble and fall apart. Seeing this has to change a man, has to make a man appreciate the creation of God and the love of God.
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The effort of the economist is to see, to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.
In Mathematical Investigations in the Theory of Value and Prices (1892), 119.
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The exciting about science and discovery, as much as how far we have come, is how far we still have to go. If we know what we do now, then the future truly is ours.
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The fact that this chain of life existed [at volcanic vents on the seafloor] in the black cold of the deep sea and was utterly independent of sunlight—previously thought to be the font of all Earth's life—has startling ramifications. If life could flourish there, nurtured by a complex chemical process based on geothermal heat, then life could exist under similar conditions on planets far removed from the nurturing light of our parent star, the Sun.
Quoted in Peter Douglas Ward and Donald Brownlee, Rare Earth: Why Complex Life is Uncommon in the Universe (2000), 1, without citation.
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The follow-on space shuttle program has fallen far short of the Apollo program in its appeal to human aspirations. The launching of the Hubble Space Telescope and the subsequent repair and servicing missions by skilled crews are highlights of the shuttle’s service to science. … Otherwise, the shuttle’s contribution to science has been modest, and its contribution to utilitarian applications of space technology has been insignificant.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004).
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The further the spiritual evolution of mankind advances, the more certain it seems to me that the path to genuine religiosity does not lie through the fear of life, and the fear of death, and blind faith, but through striving after rational knowledge.
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The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.
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The maintenance of biological diversity requires special measures that extend far beyond the establishment of nature reserves. Several reasons for this stand out. Existing reserves have been selected according to a number of criteria, including the desire to protect nature, scenery, and watersheds, and to promote cultural values and recreational opportunities. The actual requirements of individual species, populations, and communities have seldom been known, nor has the available information always been employed in site selection and planning for nature reserves. The use of lands surrounding nature reserves has typically been inimical to conservation, since it has usually involved heavy use of pesticides, industrial development, and the presence of human settlements in which fire, hunting, and firewood gathering feature as elements of the local economy.
The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), xii.
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The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive and even elegant. All this is necessary to resemble Lagrange.
In Wilhelm Meister, Wanderjahre, Zweites Buch, in 'Sprüche in Prosa' Natur, VI, 950.
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The message from the Moon which we have flashed to the far corners of this planet is that no problem need any longer be considered insoluble.
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The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.
In J.R. Newman (ed.), 'Commentary on The Tears of Mathematics', The World of Mathematics (1956), 1978.
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The owner of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process is the relation between what the worker produces and what he is paid, both measured in terms of real value. In so far as the labor contract is free what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists’ requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product.
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The product of mental labor—science—always stands far below its value, because the labor-time necessary to reproduce it has no relation at all to the labor-time required for its original production.
Karl Marx
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The real accomplishment of modern science and technology consists in taking ordinary men, informing them narrowly and deeply and then, through appropriate organization, arranging to have their knowledge combined with that of other specialized but equally ordinary men. This dispenses with the need for genius. The resulting performance, though less inspiring, is far more predictable.
In The New Industrial State (1967), 62.
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The science of calculation … is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession to follow for his subsistence.
In Letter (18 Jun 1799) to William G. Munford. On founders.archives.gov website.
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The scientist is society’s scout who goes far into nature’s new territory and brings back a report of what lies there.
Statement prepared for a dinner-symposium on 'Previews of Industrial Progress in the Next century', held in Chicago (25 May 1935), the evening preceding the reopening of the Century of Progress Exposition. In Alfred P. Sloan, Jr., 'Science and Industry in the Coming Century', The Scientific Monthly (Jul 1934), 39, No. 1, 74.
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The student should read his author with the most sustained attention, in order to discover the meaning of every sentence. If the book is well written, it will endure and repay his close attention: the text ought to be fairly intelligible, even without illustrative examples. Often, far too often, a reader hurries over the text without any sincere and vigorous effort to understand it; and rushes to some example to clear up what ought not to have been obscure, if it had been adequately considered. The habit of scrupulously investigating the text seems to me important on several grounds. The close scrutiny of language is a very valuable exercise both for studious and practical life. In the higher departments of mathematics the habit is indispensable: in the long investigations which occur there it would be impossible to interpose illustrative examples at every stage, the student must therefore encounter and master, sentence by sentence, an extensive and complicated argument.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 67.
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The sweetest and most inoffensive path of life leads through the avenues of science and learning; and whoever can either remove any obstruction in this way, or open up any new prospect, ought, so far, to be esteemed a benefactor to mankind.
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The United States is the most powerful technically advanced country in the world to-day. Its influence on the shaping of international relations is absolutely incalculable. But America is a large country and its people have so far not shown much interest in great international problems, among which the problem of disarmament occupies first place today. This must be changed, if only in the essential interests of the Americans. The last war has shown that there are no longer any barriers between the continents and that the destinies of all countries are closely interwoven. The people of this country must realize that they have a great responsibility in the sphere of international politics. The part of passive spectator is unworthy of this country and is bound in the end to lead to disaster all round.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that... or: There is capitalism in so far as... The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills. [p.222]
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There is not, we believe, a single example of a medicine having been received permanently into the Materia Medica upon the sole ground of its physical, chemical, or physiological properties. Nearly every one has become a popular remedy before being adopted or even tried by physicians; by far the greater number were first employed in countries which were and are now in a state of scientific ignorance....
Therapeutics and Materia Medica (2006), 31
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There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,—Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,—we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.
In 'Imagination in Mathematics', North American Review, 86, 223.
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They say that the best weapon is the one you never have to fire. I respectfully disagree. I prefer the weapon you only have to fire once. That’s how Dad did it, that’s how America does it... and it’s worked out pretty well so far. I present to you the newest in Stark Industries’ Freedom line. Find an excuse to let one of these off the chain, and I personally guarantee, the bad guys won’t even wanna come out of their caves. Ladies and gentlemen, for your consideration... the Jericho.
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This has been far more than three men on a mission to the Moon; more still than the efforts of a government and industry team; more, even, than the efforts of one nation. We feel this stands as a symbol of the insatiable curiosity of all mankind to explore the unknown.
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Though thou art far away, thy rays are on Earth;
Though thou art in their faces, no one knows thy going.
Akhenaten
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To appeal to contemporary man to revert, in this twentieth century, to a pagan-like nature worship in order to restrain technology from further encroachment and devastation of the resources of nature, is a piece of atavistic nonsense.
Faith and Doubt (1971).
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To create a human through genetic engineering that is more complex, more refined, more subtle, farther from animals, than the ones we have today.
The Genes of Hope. In Marc J. Madou, Fundamentals of Microfabrication: the Science of Miniaturization (2nd ed., 2002), 467.
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To Descartes, the great philosopher of the 17th century, is due the undying credit of having removed the bann which until then rested upon geometry. The analytical geometry, as Descartes’ method was called, soon led to an abundance of new theorems and principles, which far transcended everything that ever could have been reached upon the path pursued by the ancients.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1884), 10.
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To suppose that so perfect a system as that of Euclid’s Elements was produced by one man, without any preceding model or materials, would be to suppose that Euclid was more than man. We ascribe to him as much as the weakness of human understanding will permit, if we suppose that the inventions in geometry, which had been made in a tract of preceding ages, were by him not only carried much further, but digested into so admirable a system, that his work obscured all that went before it, and made them be forgot and lost.
In Essay on the Powers of the Human Mind (1812), Vol. 2, 368.
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To the east was our giant neighbor Makalu, unexplored and unclimbed, and even on top of Everest the mountaineering instinct was sufficient strong to cause me to spend some moments conjecturing as to whether a route up that mountain might not exist. Far away across the clouds the great bulk of Kangchenjunga loomed on the horizon. To the west, Cho Oyu, our old adversary from 1952, dominated the scene and we could see the great unexplored ranges of Nepal stretching off into the distance. The most important photograph, I felt, was a shot down the north ridge, showing the North Col and the old route that had been made famous by the struggles of those great climbers of the 1920s and 1930s. I had little hope of the results being particularly successful, as I had a lot of difficulty in holding the camera steady in my clumsy gloves, but I felt that they would at least serve as a record. After some ten minutes of this, I realized that I was becoming rather clumsy-fingered and slow-moving, so I quickly replaced my oxygen set and experience once more the stimulating effect of even a few liters of oxygen. Meanwhile, Tenzing had made a little hole in the snow and in it he placed small articles of food – a bar of chocolate, a packet of biscuits and a handful of lollies. Small offerings, indeed, but at least a token gifts to the gods that all devoted Buddhists believe have their home on this lofty summit. While we were together on the South Col two days before, Hunt had given me a small crucifix that he had asked me to take to the top. I, too, made a hole in the snow and placed the crucifix beside Tenzing’s gifts.
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We are concerned to understand the motivation for the development of pure mathematics, and it will not do simply to point to aesthetic qualities in the subject and leave it at that. It must be remembered that there is far more excitement to be had from creating something than from appreciating it after it has been created. Let there be no mistake about it, the fact that the mathematician is bound down by the rules of logic can no more prevent him from being creative than the properties of paint can prevent the artist. … We must remember that the mathematician not only finds the solutions to his problems, he creates the problems themselves.
In A Signpost to Mathematics (1951), 19. As quoted and cited in William L. Schaaf, 'Memorabilia Mathematica', The Mathematics Teacher (Mar 1957), 50, No. 3, 230. Note that this paper incorrectly attributes “A.H. Head”.
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We do live in a conceptual trough that encourages such yearning for unknown and romanticized greener pastures of other times. The future doesn’t seem promising, if only because we can extrapolate some disquieting present trends in to further deterioration: pollution, nationalism, environmental destruction, and aluminum bats. Therefore, we tend to take refuge in a rose-colored past ... I do not doubt the salutary, even the essential, properties of this curiously adaptive human trait, but we must also record the down side. Legends of past golden ages become impediments when we try to negotiate our current dilemma.
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We do not know what is disease, how remedies act, and still less how diseases are cured. We must abandon the way which has thus far been followed
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We entered into shadow. Contact with Moscow was gone. Japan floated by beneath us and I could clearly see its cities ablaze with lights. We left Japan behind to face the dark emptiness of the Pacific Ocean. No moon. Only stars, bright and far away. I gripped the handle like a man hanging onto a streetcar. Very slowly, agonizingly, half an hour passed, and with that, dawn on Earth. First, a slim greenish-blue line on the farthest horizon turning within a couple of minutes into a rainbow that hugged the Earth and in turn exploded into a golden sun. You’re out of your mind, I told myself, hanging onto a ship in space, and to your life, and getting ready to admire a sunrise.
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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 must somehow keep the dreams of space exploration alive, for in the long run they will prove to be of far more importance to the human race than the attainment of material benefits. Like Darwin, we have set sail upon an ocean: the cosmic sea of the Universe. There can be no turning back. To do so could well prove to be a guarantee of extinction. When a nation, or a race or a planet turns its back on the future, to concentrate on the present, it cannot see what lies ahead. It can neither plan nor prepare for the future, and thus discards the vital opportunity for determining its evolutionary heritage and perhaps its survival.
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We want them to use the education to be leaders in their community with an understanding of ecology and conservation for the wild outdoors far beyond their legislators back home. We expect these people to he a grain of sand on the beach of future leadership.
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What clearer evidence could we have had of the different formation of these rocks, and of the long interval which separated their formation, had we actually seen them emerging from the bosom of the deep? … The mind seemed to grow giddy by looking so far into the abyss of time.
As quoted in Dennis R. Dean, James Hutton and the History of Geology (1992), 122.
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When we seek a textbook case for the proper operation of science, the correction of certain error offers far more promise than the establishment of probable truth. Confirmed hunches, of course, are more upbeat than discredited hypotheses. Since the worst traditions of ‘popular’ writing falsely equate instruction with sweetness and light, our promotional literature abounds with insipid tales in the heroic mode, although tough stories of disappointment and loss give deeper insight into a methodology that the celebrated philosopher Karl Popper once labeled as ‘conjecture and refutation.’
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When you are risen on the eastern horizon
You have filled every land with your beauty…
Though you are far away, your rays are on Earth.
Akhenaten
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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.
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Love Actually (Prime Minister)
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Whereas at the outset geometry is reported to have concerned herself with the measurement of muddy land, she now handles celestial as well as terrestrial problems: she has extended her domain to the furthest bounds of space.
In The Story of Euclid. (1902) 14-15.
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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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Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.
…...
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You can’t put a limit on anything. The more you dream, the farther you get.
…...
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[When I was a child] I grew up in Brooklyn, New York, and I was a street kid. … [T]here was one aspect of that environment that, for some reason, struck me as different, and that was the stars. … I could tell they were lights in the sky, but that wasn’t an explanation. I mean, what were they? Little electric bulbs on long black wires, so you couldn’t see what they were held up by? What were they? … My mother said to me, "Look, we’ve just got you a library card … get out a book and find the answer.” … It was in there. It was stunning. The answer was that the Sun was a star, except very far away. … The dazzling idea of a universe vast beyond imagining swept over me. … I sensed awe.
In 'Wonder and Skepticism', Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.
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…so slow is moral progress. True, we have the bicycle, the motor-car, the dirigible airship and other marvellous means of breaking our bones; but our morality is not one rung the higher for it all. One would even say that, the farther we proceed in our conquest of matter, the more our morality recedes. The most advanced of our inventions consists in bringing men down with grapeshot and explosives with the swiftness of the reaper mowing the corn.
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“One must go further, one must go further.” This impulse to go further is an ancient thing in the world.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 5
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
Antoine Lavoisier
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Charles Babbage
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Euclid
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Winston Churchill
- 80 -
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Bible
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- 70 -
Samuel Morse
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- 60 -
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- 50 -
Stephen Hawking
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- 40 -
Pierre Fermat
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- 30 -
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- 20 -
Carl Sagan
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- 10 -
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