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Today in Science History - Quickie Quiz
Who said: “Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.”
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Home > Category Index for Science Quotations > Category Index I > Category: Imagine

Imagine Quotes (164 quotes)

From thus meditating on the great similarity of the structure of the warm-blooded animals, and at the same time of the great changes they undergo both before and after their nativity; and by considering in how minute a portion of time many of the changes of animals above described have been produced; would it be too bold to imagine that, in the great length of time since the earth began to exist, perhaps millions of ages before the commencement of the history of mankind would it be too bold to imagine that all warm-blooded animals have arisen from one living filament, which THE GREAT FIRST CAUSE endued with animality, with the power of acquiring new parts, attended with new propensities, directed by irritations, sensations, volitions and associations, and thus possessing the faculty of continuing to improve by its own inherent activity, and of delivering down these improvements by generation to its posterity, world without end!
Zoonomia, Or, The Laws of Organic Life, in three parts (1803), Vol. 1, 397.
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...in an infinite universe, anything that could be imagined might somewhere exist.”
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Die Politik ist keine Wissenschaft, wie viele der Herren Professoren sich einbilden, sondern eine Kunst, sie ist ebensowenig.
Politics is not a science, as many of the professors imagine, but an art, it is just like that.
Original German in Otto von Bismarck, Horst Kohl, Bismarckreden: 1847-1895 (1899), 255. As quoted in translation in William Roscoe Thayer 'Cavour and Bismarck', The Atlantic (Mar 1909), 103, 343.
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Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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Primo enim paranda est Historia Naturalis et Experimentalis, suffidens et bona; quod fundamentum rei est: neque enim fingendum, aut excogitandum, sed inveniendum, quid natura faciat aut ferat.
For first of all we must prepare a Natural and Experimental History, sufficient and good; and this is the foundation of all; for we are not to imagine or suppose, but to discover, what nature does or may be made to do.
In Novum Organum, Book 2, Aphorism 10. As translated in Francis Bacon and James Spedding with ‎Robert Leslie Ellis (eds.), 'The New Organon', The Works of Francis Bacon: Translations of the Philosophical Works (1858), Vol. 4, 127. Also seen in epigraphs as a shorter quote, “Non fingendum, aut excogitandum, sed inveniendum, quid natura faciat aut ferat,” which can also be translated as “We have not to imagine or to think out, but to find out what Nature does or produces.”
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Quelquefois, par exemple, je me figure que je suis suspendu en l’air, et que j’y demeure sans mouvement, pendant que la Terre tourne sous moi en vingt-quatre heures. Je vois passer sous mes yeux tous ces visages différents, les uns blancs, les autres noirs, les autres basanés, les autres olivâtres. D’abord ce sont des chapeaux et puis des turbans, et puis des têtes chevelues, et puis des têtes rasées; tantôt des villes à clochers, tantôt des villes à longues aiguilles qui ont des croissants, tantôt des villes à tours de porcelaine, tantôt de grands pays qui n’ont que des cabanes; ici de vastes mers, là des déserts épouvantables; enfin, toute cette variété infinie qui est sur la surface de la Terre.
Sometimes, for instance, I imagine that I am suspended in the air, and remain there motionless, while the earth turns under me in four-and-twenty hours. I see pass beneath me all these different countenances, some white, others black, others tawny, others olive-colored. At first they wear hats, and then turbans, then heads with long hair, then heads shaven; sometimes towns with steeples, sometimes towns with long spires, which have crescents, sometimes towns with porcelain towers, sometimes extensive countries that have only huts; here wide seas; there frightful deserts; in short, all this infinite variety on the surface of the earth.
In 'Premier Soir', Entretiens Sur La Pluralité Des Mondes (1686, 1863), 43. French and translation in Craufurd Tait Ramage, Beautiful Thoughts from French and Italian Authors (1866), 117-118.
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Where faith commences, science ends. Both these arts of the human mind must be strictly kept apart from each other. Faith has its origin in the poetic imagination; knowledge, on the other hand, originates in the reasoning intelligence of man. Science has to pluck the blessed fruits from the tree of knowledge, unconcerned whether these conquests trench upon the poetical imaginings of faith or not.
In Ernst Haeckel and E. Ray Lankester (trans.), The History of Creation (1880), Vol. 1, 9.
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CLAUDIO: Death is a fearful thing.
ISABELLA: And shamed life a hateful.
CLAUDIO: Ay, but to die, and go we know not where;
To lie in cold obstruction, and to rot;
This sensible warm motion to become
A kneaded clod; and the delighted spirit
To bathe in fiery floods, or to reside
In thrilling region of thick-ribbed ice;
To be imprisioned in the viewless winds,
And blown with restless violence round about
The pendant world; or to be worst than worst
Of those lawless and incertain thought
Imagine howling—'tis too horrible!
The weariest and most loathed worldly life
That age, ache, penury, and imprisionment
Can lay on nature is a paradise
To what we fear of death.
Measure for Measure (1604), III, i.
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A formative influence on my undergraduate self was the response of a respected elder statesmen of the Oxford Zoology Department when an American visitor had just publicly disproved his favourite theory. The old man strode to the front of the lecture hall, shook the American warmly by the hand and declared in ringing, emotional tones: ‘My dear fellow, I wish to thank you. I have been wrong these fifteen years.’ And we clapped our hands red. Can you imagine a Government Minister being cheered in the House of Commons for a similar admission? “Resign, Resign” is a much more likely response!
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A good method of discovery is to imagine certain members of a system removed and then see how what is left would behave: for example, where would we be if iron were absent from the world: this is an old example.
Aphorism 258 in Notebook J (1789-1793), as translated by R. J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 181.
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A person is smart. People are dumb ... Fifteen hundred years ago everybody knew the Earth was the center of the universe. Five hundred years ago, everybody knew the Earth was flat, and fifteen minutes ago, you knew that humans were alone on this planet. Imagine what you'll know tomorrow.
Anonymous
Character Agent K in movie Men in Black(1997), screen story and screenplay by Ed Solomon. Quoted in George Aichele, Culture, Entertainment and the Bible (2000), 26. In a footnote, from the post-movie novel by Steve Perry, Men in Black (1997), 66, is added, 'Yeah. A hundred years from now, whoever is here will probably pee themselves laughing at what we believe.'
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A pessimist is a person who is always right but doesn’t get any enjoyment out of it, while an optimist, is one who imagines that the future is uncertain. It is a duty to be an optimist, because if you imagine that the future is uncertain, then you must do something about it.
In The Pursuit of Simplicity (1980, 1981), 149, footnote 19.
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Adam Smith says that nobody ever imagined a god of weight—and he might have added, of the multiplication table either. It may be that the relations of Nature are all as inevitable as that twice two are four.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 178.
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Admit for a moment, as a hypothesis, that the Creator had before his mind a projection of the whole life-history of the globe, commencing with any point which the geologist may imagine to have been a fit commencing point, and ending with some unimaginable acme in the indefinitely distant future. He determines to call this idea into actual existence, not at the supposed commencing point, but at some stage or other of its course. It is clear, then, that at the selected stage it appears, exactly as it would have appeared at that moment of its history, if all the preceding eras of its history had been real.
Omphalos: An Attempt to Untie the Geological Knot (1857), 351.
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All successful people are big dreamers. They imagine what their future could be, ideal in every respect, and then they work every day toward their distant vision, that goal or purpose.
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Although Lewis Carroll thought of The Hunting of the Snark as a nonsense ballad for children, it is hard to imagine—in fact one shudders to imagine—a child of today reading and enjoying it.
In 'Introduction', The Annotated Snark (1962), 11.
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At the present rate of progress, it is almost impossible to imagine any technical feat that cannot be achieved, if it can be achieved at all, within the next five hundred years.
Profiles of the Future (1973), xvi.
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Building goes on briskly at the therapeutic Tower of Babel; what one recommends another condemns; what one gives in large doses another scarce dares to prescribe in small doses; and what one vaunts as a novelty another thinks not worth rescuing from merited oblivion. All is confusion, contradiction, inconceivable chaos. Every country, every place, almost every doctor, have their own pet remedies, without which they imagine their patients can not be cured; and all this changes every year, aye every mouth.
Weekly Medical Gazette, of Vienna
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But from the time I was in college I learned that there is nothing one could imagine which is so strange and incredible that it was not said by some philosopher; and since that time, I have recognized through my travels that all those whose views are different from our own are not necessarily, for that reason, barbarians or savages, but that many of them use their reason either as much as or even more than we do. I also considered how the same person, with the same mind, who was brought up from infancy either among the French or the Germans, becomes different from what they would have been if they had always lived among the Chinese or among the cannibals, and how, even in our clothes fashions, the very thing that we liked ten years ago, and that we may like again within the next ten years, appears extravagant and ridiculous to us today. Thus our convictions result from custom and example very much more than from any knowledge that is certain... truths will be discovered by an individual rather than a whole people.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 14-5.
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But if the heavens are moved by a daily movement, it is necessary to assume in the principal bodies of the universe and in the heavens two ways of movement which are contrary to each other: one from east to west and the other from west to east, as has often been said. And with this, it is proper to assume an excessively great speed, for anyone who reckons and considers well the height of distance of the heavens and the magnitude of these and of their circuit, if such a circuit were made in a day, could not imagine or conceive how marvelously and excessively swift would be the movement of the heavens, and how unbelievable and unthinkable.
In Isaac Asimov and Jason A. Shulman (eds.), Isaac Asimov’s Book of Science and Nature Quotations (1988), 329. Webmaster so far has been unable to locate the primary source (can you help?)
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But neither thirty years, nor thirty centuries, affect the clearness, or the charm, of Geometrical truths. Such a theorem as “the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the sides” is as dazzlingly beautiful now as it was in the day when Pythagoras first discovered it, and celebrated its advent, it is said, by sacrificing a hecatomb of oxen—a method of doing honour to Science that has always seemed to me slightly exaggerated and uncalled-for. One can imagine oneself, even in these degenerate days, marking the epoch of some brilliant scientific discovery by inviting a convivial friend or two, to join one in a beefsteak and a bottle of wine. But a hecatomb of oxen! It would produce a quite inconvenient supply of beef.
Written without pseudonym as Charles L. Dodgson, in Introduction to A New Theory of Parallels (1888, 1890), xvi. Note: a hecatomb is a great public sacrifice, originally of a hundred oxen.
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By research in pure science I mean research made without any idea of application to industrial matters but solely with the view of extending our knowledge of the Laws of Nature. I will give just one example of the ‘utility’ of this kind of research, one that has been brought into great prominence by the War—I mean the use of X-rays in surgery. Now, not to speak of what is beyond money value, the saving of pain, or, it may be, the life of the wounded, and of bitter grief to those who loved them, the benefit which the state has derived from the restoration of so many to life and limb, able to render services which would otherwise have been lost, is almost incalculable. Now, how was this method discovered? It was not the result of a research in applied science starting to find an improved method of locating bullet wounds. This might have led to improved probes, but we cannot imagine it leading to the discovery of X-rays. No, this method is due to an investigation in pure science, made with the object of discovering what is the nature of Electricity. The experiments which led to this discovery seemed to be as remote from ‘humanistic interest’ —to use a much misappropriated word—as anything that could well be imagined. The apparatus consisted of glass vessels from which the last drops of air had been sucked, and which emitted a weird greenish light when stimulated by formidable looking instruments called induction coils. Near by, perhaps, were great coils of wire and iron built up into electro-magnets. I know well the impression it made on the average spectator, for I have been occupied in experiments of this kind nearly all my life, notwithstanding the advice, given in perfect good faith, by non-scientific visitors to the laboratory, to put that aside and spend my time on something useful.
In Speech made on behalf of a delegation from the Conjoint Board of Scientific Studies in 1916 to Lord Crewe, then Lord President of the Council. In George Paget Thomson, J. J. Thomson and the Cavendish Laboratory in His Day (1965), 167-8.
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Charlie Holloway (human): “What we hoped to achieve was to meet our makers. To get answers. Why they even made us in the first place.”
David (AI robot): “Why do you think your people made me?”
Charlie Holloway (human): “We made you because we could.”
David (AI robot): “Can you imagine how disappointing it would be for you to hear the same thing from your creator?”
Charlie Holloway (human): “I guess it’s good you can’t be disappointed.”
Prometheus (2012)
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Consciousness is never experienced in the plural, only in the singular. Not only has none of us ever experienced more than one consciousness, but there is also no trace of circumstantial evidence of this ever happening anywhere in the world. If I say that there cannot be more than one consciousness in the same mind, this seems a blunt tautology–we are quite unable to imagine the contrary.
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Do not imagine that mathematics is harsh and crabbed, and repulsive to common sense. It is merely the etherealisation of common sense.
'The Six Gateways of Knowledge', Presidential Address to the Birmingham and Midland Institute, Birmingham (3 Oct 1883). In Popular Lectures and Addresses (1891), Vol. 1, 280.
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Einstein’s 1905 paper came out and suddenly changed people’s thinking about space-time. We’re again [2007] in the middle of something like that. When the dust settles, time—whatever it may be—could turn out to be even stranger and more illusory than even Einstein could imagine.
Quoted by Tim Folger in 'Newsflash: Time May Not Exist', Discover Magazine (Jun 2007).
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Endowed with two qualities, which seemed incompatible with each other, a volcanic imagination and a pertinacity of intellect which the most tedious numerical calculations could not daunt, Kepler conjectured that the movements of the celestial bodies must be connected together by simple laws, or, to use his own expression, by harmonic laws. These laws he undertook to discover. A thousand fruitless attempts, errors of calculation inseparable from a colossal undertaking, did not prevent him a single instant from advancing resolutely toward the goal of which he imagined he had obtained a glimpse. Twenty-two years were employed by him in this investigation, and still he was not weary of it! What, in reality, are twenty-two years of labor to him who is about to become the legislator of worlds; who shall inscribe his name in ineffaceable characters upon the frontispiece of an immortal code; who shall be able to exclaim in dithyrambic language, and without incurring the reproach of anyone, “The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his words.”
In 'Eulogy on Laplace', in Smithsonian Report for the year 1874 (1875), 131-132.
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Everybody firmly believes in it [Nomal Law of Errors] because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.
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Everything that you could possibly imagine, you will find that nature has been there before you.
Attributed to John Berrill in Joseph Silk, The Infinite Cosmos, (2006), 201. Webmaster is tentatively matching this name to Norman John Berrill who is an author of several books, and he is referred to as John Berrill in obituary by Charles R. Scriver in Biographical Memoirs of Fellows of the Royal Society (Nov 1999), 45, 21-34. Please contact webmaster if you have either confirmation or correction.
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Experiments in geology are far more difficult than in physics and chemistry because of the greater size of the objects, commonly outside our laboratories, up to the earth itself, and also because of the fact that the geologic time scale exceeds the human time scale by a million and more times. This difference in time allows only direct observations of the actual geologic processes, the mind having to imagine what could possibly have happened in the past.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 455-6.
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From our home on the Earth, we look out into the distances and strive to imagine the sort of world into which we were born. Today, we have reached far into space. Our immediate neighborhood we know rather intimately. But with increasing distance our knowledge fades … The search will continue. The urge is older than history. It is not satisfied and will not be suppressed.
In 'From Our Home On The Earth', The Land (1946), 5, 145. As cited on the webpage of the Edwin Powell Hubble Papers.
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Further, the same Arguments which explode the Notion of Luck, may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be, as it were, in Competition with each other, for the production of some sorts of Events, and many calculate what Probability there is, that those Events should be rather be owing to the one than to the other.
Doctrine of Chances (1718), Preface, v.
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Furthermore, it’s equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today's organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it’s inconceivable, how any kind of description of the latter, complex organism could have existed in the earlier one. It’s not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produce, something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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Genetics has always turned out to be much more complicated than it seemed reasonable to imagine. Biology is not like physics. The more we know, the less it seems that there is one final explanation waiting to be discovered.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 275.
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Geologists have usually had recourse for the explanation of these changes to the supposition of sundry violent and extraordinary catastrophes, cataclysms, or general revolutions having occurred in the physical state of the earth's surface.
As the idea imparted by the term Cataclysm, Catastrophe, or Revolution, is extremely vague, and may comprehend any thing you choose to imagine, it answers for the time very well as an explanation; that is, it stops further inquiry. But it also has had the disadvantage of effectually stopping the advance of science, by involving it in obscurity and confusion.
Considerations on Volcanoes (1825), iv.
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He [Louis Pasteur] imagined further experiments, to bring more light, for contradictions excited him to new investigations.
As quoted in René J. Dubos, Louis Pasteur, Free Lance of Science (1960, 1986), 76.
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He [Robert Hooke] is but of midling stature, something crooked, pale faced, and his face but little belowe, but his head is lardge; his eie full and popping, and not quick; a grey eie. He haz a delicate head of haire, browne, and of an excellent moist curle. He is and ever was very temperate, and moderate in dyet, etc. As he is of prodigious inventive head, so is a person of great vertue and goodnes. Now when I have sayd his Inventive faculty is so great, you cannot imagine his Memory to be excellent, for they are like two Bucketts, as one goes up, the other goes downe. He is certainly the greatest Mechanick this day in the World.
Brief Lives (1680), edited by Oliver Lawson Dick (1949), 165.
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How strange it would be if the final theory were to be discovered in our lifetimes! The discovery of the final laws of nature will mark a discontinuity in human intellectual history, the sharpest that has occurred since the beginning of modern science in the seventeenth century. Can we now imagine what that would be like?
In Dreams of a Final Theory (1992), 235.
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Hubble's observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense. Under such conditions all the laws of science, and therefore all ability to predict the future, would break down. If there were events earlier than this time, then they could not affect what happens at the present time. Their existence can be ignored because it would have no observational consequences. One may say that time had a beginning at the big bang, in the sense that earlier times simply would not be defined. It should be emphasized that this beginning in time is very different from those that had been considered previously. In an unchanging universe a beginning in time is something that has to be imposed by some being outside the universe; there is no physical necessity for a beginning. One can imagine that God created the universe at literally any time in the past. On the other hand, if the universe is expanding, there may be physical reasons why there had to be a beginning. One could still imagine that God created the universe at the instant of the big bang, or even afterwards in just such a way as to make it look as though there had been a big bang, but it would be meaningless to suppose that it was created before the big bang. An expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job!
A Brief History of Time: From the Big Bang to Black Holes (1988), 8-9.
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Human civilization is but a few thousand years long. Imagine having the audacity to think that we can devise a program to store lethal radioactive materials for a period of time that is longer than all of human culture to date.
In Jeremy Rifkin and Ted Howard, Entropy: Into the Greenhouse World (1980), 110.
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Humans are not by nature the fact-driven, rational beings we like to think we are. We get the facts wrong more often than we think we do. And we do so in predictable ways: we engage in wishful thinking. We embrace information that supports our beliefs and reject evidence that challenges them. Our minds tend to take shortcuts, which require some effort to avoid … [and] more often than most of us would imagine, the human mind operates in ways that defy logic.
As co-author with Kathleen Hall Jamieson, in unSpun: Finding Facts in a World of Disinformation (2007), 69.
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I always rejoice to hear of your being still employed in experimental researches into nature, and of the success you meet with. The rapid progress true science now makes, occasions my regretting sometimes that I was born so soon: it is impossible to imagine the height to which may be carried, in a thousand years, the power of man over matter; we may perhaps learn to deprive large masses of their gravity, and give them absolute levity for the sake of easy transport. Agriculture may diminish its labour and double its produce; all diseases may by sure means be prevented or cured (not excepting even that of old age), and our lives lengthened at pleasure even beyond the antediluvian standard. Oh! that moral science were in as fair a way of improvement; that men would cease to be wolves to one another; and that human beings would at length learn what they now improperly call humanity!
Letter to Dr Priestley, 8 Feb 1780. In Memoirs of Benjamin Franklin (1845), Vol. 2, 152.
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I am absolutely convinced that no wealth in the world can help humanity forward, even in the hands of the most devoted worker. The example of great and pure individuals is the only thing that can lead us to noble thoughts and deeds. Money only appeals to selfishness and irresistibly invites abuse. Can anyone imagine Moses, Jesus or Ghandi armed with the moneybags of Carnegie?
…...
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I cannot imagine a God who rewards and punishes the objects of his creation, whose purposes are modeled after our own–a God, in short, who is but a reflection of human frailty. Neither can I believe that the individual survives the death of his body, although feeble souls harbor such thoughts through fear or ridiculous egotism. It is enough for me to contemplate the mystery of conscious life perpetuating itself through all eternity, to reflect upon the marvelous structure of the universe which we can dimly perceive, and to try humbly to comprehend even an infinitesimal part of the intelligence manifested in nature.
From 'What I Believe: Living Philosophies XIII', Forum and Century (Oct 1930), 84, No. 4, 194. Article in full, reprinted in Edward H. Cotton (ed.), Has Science Discovered God? A Symposium of Modern Scientific Opinion (1931), 97.
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I found out that the main ability to have was a visual, and also an almost tactile, way to imagine the physical situations, rather than a merely logical picture of the problems. … Very soon I discovered that if one gets a feeling for no more than a dozen … radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships.
In Adventures of a Mathematician (1976), 147.
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I grew up in Brooklyn, New York … a city neighborhood that included houses, lampposts, walls, and bushes. But with an early bedtime in the winter, I could look out my window and see the stars, and the stars were not like anything else in my neighborhood. [At age 5] I didn’t know what they were.
[At age 9] my mother … said to me, “You have a library card now, and you know how to read. Take the streetcar to the library and get a book on stars.” … I stepped up to the big librarian and asked for a book on stars. … I sat down and found out the answer, which was something really stunning.
I found out that the stars are glowing balls of gas. I also found out that the Sun is a star but really close and that the stars are all suns except really far away I didn’t know any physics or mathematics at that time, but I could imagine how far you’d have to move the Sun away from us till it was only as bright as a star. It was in that library, reading that book, that the scale of the universe opened up to me. There was something beautiful about it.
At that young age, I already knew that I’d be very happy if I could devote my life to finding out more about the stars and the planets that go around them. And it’s been my great good fortune to do just that.
Quoted in interview with Jack Rightmyer, in 'Stars in His Eyes', Highlights For Children (1 Jan 1997). Ages as given in Tom Head (ed.), Conversations with Carl Sagan (2006), x.
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I had at one time a very bad fever of which I almost died. In my fever I had a long consistent delirium. I dreamt that I was in Hell, and that Hell is a place full of all those happenings that are improbable but not impossible. The effects of this are curious. Some of the damned, when they first arrive below, imagine that they will beguile the tedium of eternity by games of cards. But they find this impossible, because, whenever a pack is shuffled, it comes out in perfect order, beginning with the Ace of Spades and ending with the King of Hearts. There is a special department of Hell for students of probability. In this department there are many typewriters and many monkeys. Every time that a monkey walks on a typewriter, it types by chance one of Shakespeare's sonnets. There is another place of torment for physicists. In this there are kettles and fires, but when the kettles are put on the fires, the water in them freezes. There are also stuffy rooms. But experience has taught the physicists never to open a window because, when they do, all the air rushes out and leaves the room a vacuum.
'The Metaphysician's Nightmare', Nightmares of Eminent Persons and Other Stories (1954), 38-9.
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I have no doubt that in reality the future will be vastly more surprising than anything I can imagine. Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.
In Possible Worlds and Other Papers (1927), 298.
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I imagine that when we reach the boundaries of things set for us, or even before we reach them, we can see into the infinite, just as on the surface of the earth we gaze out into immeasurable space.
Aphorism 52 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 51.
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I learned this, at least, by my experiment: that if one advances confidently in the direction of his dreams, and endeavors to live the life which he has imagined, he will meet with a success unexpected in common hours.
In Walden: or, Life in the Woods (1854, 1893), 496.
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I would picture myself as a virus, or as a cancer cell, for example, and try to sense what it would be like to be either. I would also imagine myself as the immune system, and I would try to reconstruct what I would do as an immune system engaged in combating a virus or cancer cell. When I had played through a series of such scenarios on a particular problem and had acquired new insights, I would design laboratory experiments accordingly… Based upon the results of the experiment, I would then know what question to ask next… When I observed phenomena in the laboratory that I did not understand, I would also ask questions as if interrogating myself: “Why would I do that if I were a virus or a cancer cell, or the immune system?” Before long, this internal dialogue became second nature to me; I found that my mind worked this way all the time.
In Anatomy of Reality: Merging of Intuition and Reason (1983), 7, footnote b, as quoted and cited in Roger Frantz, Two Minds: Intuition and Analysis in the History of Economic Thought (2006), 7.
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I would “like” to be positivistic, [and do] research; but I can’t impress myself sufficiently by the “importance” of any possible research which I can imagine, to embark upon it.… The terrible secret is that I don’t believe in natural science. And yet I do, I do.
From notebook K12 manuscript, 2-3. As quoted and cited in Allan Beveridge, Portrait of the Psychiatrist as a Young Man: The Early Writing and Work of R.D. Laing, 1927-1960 (2011), 45.
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Ideologues of all persuasions think they know how the economy will respond to the Administration’s strange mixture of Lafferism and monetarism. Indeed, their self-confidence is so vast, and their ability to rationalize so crafty, that one cannot imagine a scenario for the next few years, that they would regard as falsifying their dogma. The failure of any prediction can always be blamed on quirky political decisions or unforeseen historical events.
In 'Mathematical Games: The Laffer Curve', Scientific American (Dec 1981), 245, No. 6, 30. Collected in The Night Is Large: Collected Essays, 1938-1995 (1997), 135.
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If the earth’s population continues to double every 50 years (as it is now doing) then by 2550 A.D. it will have increased 3,000-fold. … by 2800 A.D., it would reach 630,000 billion! Our planet would have standing room only, for there would be only two-and-a-half square feet per person on the entire land surface, including Greenland and Antarctica. In fact, if the human species could be imagined as continuing to multiply further at the same rate, by 4200 A.D. the total mass of human tissue would be equal to the mass of the earth.
In The Intelligent Man's Guide to Science: The Biological Sciences (1960), 117. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 237.
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If we imagine an observer to approach our planet from outer space, and, pushing aside the belts of red-brown clouds which obscure our atmosphere, to gaze for a whole day on the surface of the earth as it rotates beneath him, the feature, beyond all others most likely to arrest his attention would be the wedge-like outlines of the continents as they narrow away to the South.
The Face of the Earth (1904), Vol. 1, 1.
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If you ask a person, “What were you thinking?” you may get an answer that is richer and more revealing of the human condition than any stream of thoughts a novelist could invent. I try to see through people’s faces into their minds and listen through their words into their lives, and what I find there is beyond imagining.
…...
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Imagination is the beginning of creation. You imagine what you desire, you will what you imagine and at last you create what you will.
From Back to Methuselah: A Metabiological Pentateuch (1921), 9.
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Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.
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Imagine a room awash in gasoline, and there are two implacable enemies in that room. One of them has nine thousand matches. The other has seven thousand matches. Each of them is concerned about who's ahead, who's stronger. Well that's the kind of situation we are actually in. The amount of weapons that are available to the United States and the Soviet Union are so bloated, so grossly in excess of what's needed to dissuade the other, that if it weren't so tragic, it would be laughable. What is necessary is to reduce the matches and to clean up the gasoline.
From Sagan's analogy about the nuclear arms race and the need for disarmament, during a panel discussion in ABC News Viewpoint following the TV movie The Day After (20 Nov 1983). Transcribed by Webmaster from a video recording. It is seen misquoted in summary form as “The nuclear arms race is like two sworn enemies standing waist deep in gasoline, one with three matches, the other with five.”
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Imagine a school-boy who has outgrown his clothes. Imagine the repairs made on the vestments where the enlarged frame had burst the narrow limits of the enclosure. Imagine the additions made where the projecting limbs had fairly and far emerged beyond the confines of the garment. Imagine the boy still growing, and the clothes, mended allover, now more than ever in want of mending—such is chemistry, and such is nomenclature.
Chemical Recreations (1834), 206, footnote.
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Imagine Aristotle revivified and visiting Manhattan. Nothing in our social, political, economic, artistic, sexual or religious life would mystify him, but he would be staggered by our technology. Its products—skyscrapers, cars, airplanes, television, pocket calculators—would have been impossible without calculus.
In book review, 'Adventures Of a Mathematician: The Man Who Invented the H-Bomb', New York Times (9 May 1976), 201.
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Imagine life as a game in which you are juggling five balls in the air. You name them - work, family, health, friends, and spirit - and you’re keeping all of these in the air. You will soon understand that work is a rubber ball. If you drop it, it will bounce back. But the other four balls - family, health, friends, and spirit are made of glass. If you drop one of these, they will be irrevocably scuffed, marked, nicked, damaged, or even shattered. They will never be the same. You must understand that and strive for balance in your life.
…...
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Imagine spending four billion years stocking the oceans with seafood, filling the ground with fossil fuels, and drilling the bees in honey production—only to produce a race of bed wetters!
In 'Stop Beaching, Think Positive', Mother Jones Magazine (Oct 1988), 14, No. 8, 8. [Note: drilling = training, like math drill.]
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Imagine that … the world is something like a great chess game being played by the gods, and we are observers of the game. … If we watch long enough, we may eventually catch on to a few of the rules…. However, we might not be able to understand why a particular move is made in the game, merely because it is too complicated and our minds are limited…. We must limit ourselves to the more basic question of the rules of the game.
If we know the rules, we consider that we “understand” the world.
In 'Basic Physics', The Feynman Lectures on Physics (1964, 2013), Vol. 1, 2-1.
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Imagine the chaos that would arise if time machines were as common as automobiles, with tens of millions of them commercially available. Havoc would soon break loose, tearing at the fabric of our universe. Millions of people would go back in time to meddle with their own past and the past of others, rewriting history in the process. … It would thus be impossible to take a simple census to see how many people there were at any given time.
In Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and The Tenth Dimension (1994, 1995), 234.
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Imagine the people who believe such things and who are not ashamed to ignore, totally, all the patient findings of thinking minds through all the centuries since the Bible was written. And it is these ignorant people, the most uneducated, the most unimaginative, the most unthinking among us, who would make themselves the guides and leaders of us all; who would force their feeble and childish beliefs on us; who would invade our schools and libraries and homes. I personally resent it bitterly.
In The Roving Mind (1983), 26.
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Imagine the world so greatly magnified that particles of light look like twenty-four-pound cannon balls.
As given, without source, in James Geary, Geary's Guide to the World's Great Aphorists (2008), 341.
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In every true searcher of Nature there is a kind of religious reverence, for he finds it impossible to imagine that he is the first to have thought out the exceedingly delicate threads that connect his perceptions.
1920, in Conversations with Einstein by Alexander Moszkowski (1970).
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In science, probably ninety-nine percent of the knowable has to be discovered. We know only a few streaks about astronomy. We are only beginning to imagine the force and composition of the atom. Physics has not yet found any indivisible matter, or psychology a sensible soul.
'This World Depression of Ours is Chock-full of Good News', Hearst's International Combined with Cosmopolitan, (Oct 1932), 26. Reprinted in Ella Winter and Herbert Shapiro The World of Lincoln Steffens (1962), 216.
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Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
…...
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Is it absurd to imagine that our social behavior, from amoeba to man, is also planned and dictated, from stored Information, by the cells? And that the time has come for men to be entrusted with the task, through heroic efforts, of bringing life to other worlds?
From Nobel Prize Lecture (Dec 1974), 'The Coming Age of the Cell'. Collected in Jan Lindsten (ed.) Nobel Lectures, Physiology or Medicine 1971-1980 (1992).
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It did not cause anxiety that Maxwell’s equations did not apply to gravitation, since nobody expected to find any link between electricity and gravitation at that particular level. But now physics was faced with an entirely new situation. The same entity, light, was at once a wave and a particle. How could one possibly imagine its proper size and shape? To produce interference it must be spread out, but to bounce off electrons it must be minutely localized. This was a fundamental dilemma, and the stalemate in the wave-photon battle meant that it must remain an enigma to trouble the soul of every true physicist. It was intolerable that light should be two such contradictory things. It was against all the ideals and traditions of science to harbor such an unresolved dualism gnawing at its vital parts. Yet the evidence on either side could not be denied, and much water was to flow beneath the bridges before a way out of the quandary was to be found. The way out came as a result of a brilliant counterattack initiated by the wave theory, but to tell of this now would spoil the whole story. It is well that the reader should appreciate through personal experience the agony of the physicists of the period. They could but make the best of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays, and Fridays they must look on light as a wave; on Tuesdays, Thursdays, and Saturdays, as a particle. On Sundays they simply prayed.
The Strange Story of the Quantum (1947), 42.
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It has been said that computing machines can only carry out the processes that they are instructed to do. This is certainly true in the sense that if they do something other than what they were instructed then they have just made some mistake. It is also true that the intention in constructing these machines in the first instance is to treat them as slaves, giving them only jobs which have been thought out in detail, jobs such that the user of the machine fully understands what in principle is going on all the time. Up till the present machines have only been used in this way. But is it necessary that they should always be used in such a manner? Let us suppose we have set up a machine with certain initial instruction tables, so constructed that these tables might on occasion, if good reason arose, modify those tables. One can imagine that after the machine had been operating for some time, the instructions would have altered out of all recognition, but nevertheless still be such that one would have to admit that the machine was still doing very worthwhile calculations. Possibly it might still be getting results of the type desired when the machine was first set up, but in a much more efficient manner. In such a case one would have to admit that the progress of the machine had not been foreseen when its original instructions were put in. It would be like a pupil who had learnt much from his master, but had added much more by his own work. When this happens I feel that one is obliged to regard the machine as showing intelligence.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 122-3.
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It has just occurred to me to ask if you are familiar with Lissajous’ experiments. I know nothing about them except what I found in Flammarion’s great “Astronomie Populaire.” One extraordinary chapter on numbers gives diagrams of the vibrations of harmonics—showing their singular relation to the geometrical designs of crystal-formation;—and the chapter is aptly closed by the Pythagorian quotation: Ἀεὶ ὁ θεὸς ὁ μέγας γεωμετρεῖ—“God geometrizes everywhere.” … I should imagine that the geometry of a fine opera would—were the vibrations outlined in similar fashion—offer a network of designs which for intricate beauty would double discount the arabesque of the Alhambra.
In letter to H.E. Krehbiel (1887), collected in Elizabeth Bisland The Writings of Lafcadio Hearn (1922), Vol. 14, 8.
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It is an error to imagine that evolution signifies a constant tendency to increased perfection. That process undoubtedly involves a constant remodeling of the organism in adaptation to new conditions; but it depends on the nature of those conditions whether the direction of the modifications effected shall be upward or downward.
'The Struggle for Existence in Human Society' (1888). In Collected Essays (1894), Vol. 9, 199.
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It is certainly true in the United States that there is an uneasiness about certain aspects of science, particularly evolution, because it conflicts, in some people’s minds, with their sense of how we all came to be. But you know, if you are a believer in God, it’s hard to imagine that God would somehow put this incontrovertible evidence in front of us about our relationship to other living organisms and expect us to disbelieve it. I mean, that doesn't make sense at all.
From video of interview with Huffington post reporter at the 2014 Davos Annual Meeting, World Economic Forum (25 Jan 2014). On web page 'Dr. Francis Collins: “There Is An Uneasiness” About Evolution'
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It is difficult to imagine a greater imposition [than adding] genes to future generations that changes the nature of future people.
in The Second Creation: Dolly and the Age of Biological Control
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It is hard to imagine while strenuously walking in the heart of an equatorial rain forest, gasping for every breath in a stifling humid sauna, how people could have ever adapted to life under these conditions. It is not just the oppressive climate - the tall forest itself is dark, little light reaching the floor from the canopy, and you do not see any animals. It is a complete contrast to the herbivore-rich dry savannahs of tropical Africa. Yet there are many animals here, evident by the loud, continual noise of large cryptic insects and the constant threat of stepping on a deadly king cobra. This was my first impression of the rain forest in Borneo.
The Humans Who Went Extinct
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It is high time that laymen abandoned the misleading belief that scientific enquiry is a cold dispassionate enterprise, bleached of imaginative qualities, and that a scientist is a man who turns the handle of discovery; for at every level of endeavour scientific research is a passionate undertaking and the Promotion of Natural Knowledge depends above all on a sortee into what can be imagined but is not yet known.
The Times Literary Supplement (London), 1963 October 25 (p. 850)
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It is impossible to imagine the universe run by a wise, just and omnipotent God, but it is quite easy to imagine it run by a board of gods. If such a board actually exists it operates precisely like the board of a corporation that is losing money.
Minority Report: H. L. Mencken's Notebooks (1956), Sample 79, 63.
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It is not easy to imagine how little interested a scientist usually is in the work of any other, with the possible exception of the teacher who backs him or the student who honors him.
Pensées d'un Biologiste (1939). Translated in The Substance of Man (1962), 195.
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It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
Letter to Farkas Wolfgang Bolyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It may seem rash indeed to draw conclusions valid for the whole universe from what we can see from the small corner to which we are confined. Who knows that the whole visible universe is not like a drop of water at the surface of the earth? Inhabitants of that drop of water, as small relative to it as we are relative to the Milky Way, could not possibly imagine that beside the drop of water there might be a piece of iron or a living tissue, in which the properties of matter are entirely different.
Space and Time (1926), 227.
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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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It's hard to imagine anything more difficult to study than human sexuality, on every level from the technical to the political. One has only to picture monitoring orgasm in the lab to begin to grasp the challenge of developing testing techniques that are thorough and precise, yet respectful.
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Language is a guide to 'social reality.' Though language is not ordinarily thought of as essential interest to the students of social science, it powerfully conditions all our thinking about social problems and processes. Human beings do not live in the objective world alone, nor alone in the world of social activity as ordinarily understood, but are very much at the mercy of the particular language which has become the medium of expression for their society. It is quite an illusion to imagine that one adjusts to reality essentially without the use of language and that language is merely an incidental means of solving specific problems of communication or reflection. The fact of the matter is that the 'real world' is to a large extent unconsciously built up on the language habits of the group. No two languages are ever sufficiently similar to be considered as representing the same social reality. The worlds in which different societies live are distinct worlds, not merely the same world with different labels attached.
'The Status of Linguistics as a Science', Language (1929), 5, 207-14. In David Mandelbaum (ed.), Selected Writings of Edward Sapir in Language, Culture, and Personality (1949), 162.
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Learning how to access a continuity of common sense can be one of your most efficient accomplishments in this decade. Can you imagine common sense surpassing science and technology in the quest to unravel the human stress mess? In time, society will have a new measure for confirming truth. It’s inside the people-not at the mercy of current scientific methodology. Let scientists facilitate discovery, but not invent your inner truth.
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Leibnitz believed he saw the image of creation in his binary arithmetic in which he employed only two characters, unity and zero. Since God may be represented by unity, and nothing by zero, he imagined that the Supreme Being might have drawn all things from nothing, just as in the binary arithmetic all numbers are expressed by unity with zero. This idea was so pleasing to Leibnitz, that he communicated it to the Jesuit Grimaldi, President of the Mathematical Board of China, with the hope that this emblem of the creation might convert to Christianity the reigning emperor who was particularly attached to the sciences.
In 'Essai Philosophique sur les Probabiliés', Oeuvres (1896), t. 7, 119.
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Let me describe briefly how a black hole might be created. Imagine a star with a mass 10 times that of the sun. During most of its lifetime of about a billion years the star will generate heat at its center by converting hydrogen into helium. The energy released will create sufficient pressure to support the star against its own gravity, giving rise to an object with a radius about five times the radius of the sun. The escape velocity from the surface of such a star would be about 1,000 kilometers per second. That is to say, an object fired vertically upward from the surface of the star with a velocity of less than 1,000 kilometers per second would be dragged back by the gravitational field of the star and would return to the surface, whereas an object with a velocity greater than that would escape to infinity.
When the star had exhausted its nuclear fuel, there would be nothing to maintain the outward pressure, and the star would begin to collapse because of its own gravity. As the star shrank, the gravitational field at the surface would become stronger and the escape velocity would increase. By the time the radius had got down to 10 kilometers the escape velocity would have increased to 100,000 kilometers per second, the velocity of light. After that time any light emitted from the star would not be able to escape to infinity but would be dragged back by the gravitational field. According to the special theory of relativity nothing can travel faster than light, so that if light cannot escape, nothing else can either. The result would be a black hole: a region of space-time from which it is not possible to escape to infinity.
'The Quantum Mechanics of Black Holes', Scientific American, 1977, 236, 34-40.
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Let us only imagine that birds had studied their own development and that it was they in turn who investigated the structure of the adult mammal and of man. Wouldn’t their physiological textbooks teach the following? “Those four and two-legged animals bear many resemblances to embryos, for their cranial bones are separated, and they have no beak, just as we do in the first live or six days of incubation; their extremities are all very much alike, as ours are for about the same period; there is not a single true feather on their body, rather only thin feather-shafts, so that we, as fledglings in the nest, are more advanced than they shall ever be … And these mammals that cannot find their own food for such a long time after their birth, that can never rise freely from the earth, want to consider themselves more highly organized than we?”
Über Entwicklungsgeschichte der Thiere: Beobachtung und Reflexion (1828), 203. Trans. Stephen Jay Gould, Ontogeny and Phylogeny (1977), 54.
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Little could Plato have imagined, when, indulging his instinctive love of the true and beautiful for their own sakes, he entered upon these refined speculations and revelled in a world of his own creation, that he was writing the grammar of the language in which it would be demonstrated in after ages that the pages of the universe are written.
From Lecture (4 Dec 1854) delivered to the Gresham Committee and the members of the Common Council of the City of London, 'A Probationary Lecture on Geometry', collected in Collected Mathematical Papers of James Joseph Sylvester (1908), Vol. 2, 7.
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Mapping the human genome has been compared with putting a man on the moon, but I believe it is more than that. This is the outstanding achievement not only of our lifetime, but in terms of human history. A few months ago I compared the project to the invention of the wheel. On reflection, it is more than that. I can well imagine technology making the wheel obsolete. But this code is the essence of mankind, and as long as humans exists, this code is going to be important and will be used.
Quoted in the press release 'The first draft of the Book of Humankind has been read', 26 Jun 2000. On the Sanger Institute web site at www.sanger.ac.uk/HGP/draft2000/mainrelease.shtml
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Men will gather knowledge no matter what the consequences. Science will go on whether we are pessimistic or optimistic, as I am. More interesting discoveries than we can imagine will be made, and I am awaiting them, full of curiosity and enthusiasm.
'Dr Linus Pauling, Atomic Architect', Science Illustrated (1948), 3, 40.
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Most people regard scientists as explorers … Imagine a handful of people shipwrecked on a strange island and setting out to explore it. One of them cuts a solitary path through the jungle, going on and on until he is exhausted or lost or both. He eventually returns to his companions, and they listen to him with goggling eyes as he describes what he saw; what he fell into, and what bit him. After a rest he demands more supplies and sets off again to explore the unknown. Many of his companions will be doing the same, each choosing his own direction and pursuing his pioneering path.
In The Development of Design (1981), 1.
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My profession often gets bad press for a variety of sins, both actual and imagined: arrogance, venality, insensitivity to moral issues about the use of knowledge, pandering to sources of funding with insufficient worry about attendant degradation of values. As an advocate for science, I plead ‘mildly guilty now and then’ to all these charges. Scientists are human beings subject to all the foibles and temptations of ordinary life. Some of us are moral rocks; others are reeds. I like to think (though I have no proof) that we are better, on average, than members of many other callings on a variety of issues central to the practice of good science: willingness to alter received opinion in the face of uncomfortable data, dedication to discovering and publicizing our best and most honest account of nature’s factuality, judgment of colleagues on the might of their ideas rather than the power of their positions.
…...
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Not only is the universe stranger than we imagine, it is stranger than we can imagine.
Anonymous
This often seen attributed—incorrectly&mash;to Sir Arthur S. Eddington, for example, in Norman K. Glendenning, Our Place in the Universe (2007), 1. It is similar to a quote by J.B.S. Haldane, "The Universe is not only queerer than we suppose, but queerer than we can suppose." In Possible Worlds and Other Papers (1927), 286.
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On the afternoon of October 19, 1899, I climbed a tall cherry tree and, armed with a saw which I still have, and a hatchet, started to trim the dead limbs from the cherry tree. It was one of the quiet, colorful afternoons of sheer beauty which we have in October in New England, and as I looked towards the fields at the east, I imagined how wonderful it would be to make some device which had even the possibility of ascending to Mars. I was a different boy when I descended the tree from when I ascended for existence at last seemed very purposive.
In The Papers of Robert H. Goddard: 1898-1924 (1970), 9.
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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 of the great achievements of the 1950s and 1960s was a [TV] series called Your Life in Their Hands, which dealt with medical science. It presented the scientific evidence for the connection between tobacco and cancer, against the entrenched opposition, all of which you can quite easily imagine. … The “television doctor” … presented the evidence of the connection between the two over and over again on television. A lot of people tried to stop it, but he carried on. It ruined his career, I suspect, in the medical sense, but he stuck to his guns. It’s one of early television’s badges of honour.
From interview with Brian Cox and Robert Ince, in 'A Life Measured in Heartbeats', New Statesman (21 Dec 2012), 141, No. 5138, 32.
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One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.
Malay Archipelago
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One-story intellects, two-story intellects, three-story intellects with skylights. All fact-collectors, who have no aim beyond their facts, are one-story men. Two-story men compare, reason, generalize, using the labors of the fact-collectors as well as their own. Three-story men idealize, imagine, predict; their best illumination comes from above, through the skylight. There are minds with large ground-floors, that can store an infinite amount of knowledge; some librarians, for instance, who know enough of books to help other people, without being able to make much other use of their knowledge, have intellects of this class. Your great working lawyer has two spacious stories; his mind is clear, because his mental floors are large, and he has room to arrange his thoughts so that lie can get at them,—facts below, principles above, and all in ordered series; poets are often narrow below, incapable of clear statement, and with small power of consecutive reasoning, but full of light, if sometimes rather bare of furniture, in the attics.
The Poet at the Breakfast Table (1883), 50.
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Our imagination is stretched to the utmost, not as in fiction, to imagine things which are not really there, but just to comprehend those things which are there.
In The Character of Physical Law (1965, reprint 2001), 127-128.
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Our most trustworthy safeguard in making general statements on this question is imagination. If we can imagine the breaking of a law of physics then… it is in some degree an empirical law. With a purely rational law we could not conceive an alternative… This ultimate criterion serves as an anchor to keep us from drifting unduly in a perilous sea of thought.
From concluding paragraph of 'Transition to General Relativity', The Special Theory of Relativity (1940, 2014), Chap 8, 91.
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Our posturing, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.
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Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range of his sensuous impressions. He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. He may call this ideal limit the objective truth.
Albert Einstein and Leopold Infeld, The Evolution of Physics (1938), 33.
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Professor [Max] Planck, of Berlin, the famous originator of the Quantum Theory, once remarked to me that in early life he had thought of studying economics, but had found it too difficult! Professor Planck could easily master the whole corpus of mathematical economics in a few days. He did not mean that! But the amalgam of logic and intuition and the wide knowledge of facts, most of which are not precise, which is required for economic interpretation in its highest form is, quite truly, overwhelmingly difficult for those whose gift mainly consists in the power to imagine and pursue to their furthest points the implications and prior conditions of comparatively simple facts which are known with a high degree of precision.
'Alfred Marshall: 1842-1924' (1924). In Geoffrey Keynes (ed.), Essays in Biography (1933), 191-2
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Science becomes dangerous only when it imagines that it has reached its goal.
In Preface to the play, The Doctor’s Dilemma (1911), xc.
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So numerous are the objects which meet our view in the heavens, that we cannot imagine a point of space where some light would not strike the eye;—innumerable stars, thousands of double and multiple systems, clusters in one blaze with their tens of thousands of stars, and the nebulae amazing us by the strangeness of their forms and the incomprehensibility of their nature, till at last, from the limit of our senses, even these thin and airy phantoms vanish in the distance.
On the Connexion of the Physical Sciences (1858), 420.
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Spherical space is not very easy to imagine. We have to think of the properties of the surface of a sphere—the two-dimensional case—and try to conceive something similar applied to three-dimensional space. Stationing ourselves at a point let us draw a series of spheres of successively greater radii. The surface of a sphere of radius r should be proportional to r2; but in spherical space the areas of the more distant spheres begin to fall below the proper proportion. There is not so much room out there as we expected to find. Ultimately we reach a sphere of biggest possible area, and beyond it the areas begin to decrease. The last sphere of all shrinks to a point—our antipodes. Is there nothing beyond this? Is there a kind of boundary there? There is nothing beyond and yet there is no boundary. On the earth’s surface there is nothing beyond our own antipodes but there is no boundary there
In Space, Time and Gravitation: An Outline of the General Relativity Theory (1920, 1921), 158-159.
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Take care of your health. ... Imagine Hercules as oarsman in a rotten boat; what can he do there but by the very force of his stroke expedite the ruin of his craft. Take care of the timbers of your boat. ... The formation of right habits is essential to your permanent security. They diminish your chance of falling when assaulted, and they augment your chance of recovery when overthrown.
Concluding remark from 'An Address to Students of University College, London' (1869), in Fragments of Science for Unscientific People (1871), 105.
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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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The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite.
Letter to H. Oldenburg, 9 Oct 1676. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 75.
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The ability to imagine relations is one of the most indispensable conditions of all precise thinking. No subject can be named, in the investigation of which it is not imperatively needed; but it can be nowhere else so thoroughly acquired as in the study of mathematics.
In Darwinism and other Essays (1893), 296.
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
Science and Hypothesis, translated by William John Greenstreet, (1905, 1952), xxiv.
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The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
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The custom of eating the lover after consummation of the nuptials, of making a meal of the exhausted pigmy, who is henceforth good for nothing, is not so difficult to understand, since insects can hardly be accused of sentimentality; but to devour him during the act surpasses anything the most morbid mind could imagine. I have seen the thing with my own eyes, and I have not yet recovered from my surprise.
In Jean-Henri Fabre and B. Miall (trans.), Social Life in the Insect World (1912), 84.
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The distributed architecture and its technique of packet switching were built around the problem of getting messages delivered despite blockages, holes and malfunctions. Imagine the poor censor faced with such a system. There is no central exchange to seize and hold; messages actively “seek out” alternative routes so that even if one path is blocked another may open up. Here is the civil libertarian’s dream.
As quoted in Richard Rogers, 'The Internet Treats Censorship as a Malfunction and Routes Around It? : A New Media Approach to the Study of State Internet Censorship', collected in Jussi Parikka and Tony D. Sampson (eds.), The Spam Book: On Viruses, Porn, and Other Anomalies from the Dark Side of Digital Culture (2009), 243.
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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 experience was more fulfilling than I could have ever imagined. I have a newfound sense of wonder seeing the Earth and stars from such an incredible perspective. Certainly, through my training I was prepared for the technical aspects, but I had no idea that I would be flooded with such amazement and joy after seeing my first sunrise and sunset from space.
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The genius of Leonardo da Vinci imagined a flying machine, but it took the methodical application of science by those two American bicycle mechanics to create it.
In Time/CBS News, 'The Wright Brothers, People of the Century (1999), 42.
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The magnitude of the railway works undertaken in this country will be still more clearly exhibited, if you consider the extent of the Earth-Works. Taking them at an average of 70,000 cubic yards to a mile, they will measure 550,000,000 cubic yards. What does this represent? We are accustomed to regard St. Paul’s as a test for height and space; but by the side of the pyramid of earth these works would rear, St. Paul’s would be but as a pigmy by a giant. Imagine a mountain half a mile in diameter at its base, and soaring into the clouds one mile and a half in height;—that would be the size of the mountain of earth which these earth-works would form.
From 'Railway System and its Results' (Jan 1856) read to the Institution of Civil Engineers, reprinted in Samuel Smiles, Life of George Stephenson (1857), 512.
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The mathematic, then, is an art. As such it has its styles and style periods. It is not, as the layman and the philosopher (who is in this matter a layman too) imagine, substantially unalterable, but subject like every art to unnoticed changes form epoch to epoch. The development of the great arts ought never to be treated without an (assuredly not unprofitable) side-glance at contemporary mathematics.
In Oswald Spengler and Charles Francis Atkinson (trans.), The Decline of the West (1926), 62.
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The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God. If he can find, in experience, sets of entities which obey the same logical scheme as his mathematical entities, then he has applied his mathematics to the external world; he has created a branch of science.
Aspects of Science: Second Series (1926), 92.
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The most important discoveries will provide answers to questions that we do not yet know how to ask and will concern objects that we can not yet imagine.
In Hubble Space Telescope flaw: hearing before the Committee on Science, Space, and Technology, U.S. House of Representatives, One Hundred First Congress, second session, July 13, 1990 (1990), 105.
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The need to make music, and to listen to it, is universally expressed by human beings. I cannot imagine, even in our most primitive times, the emergence of talented painters to make cave paintings without there having been, near at hand, equally creative people making song. It is, like speech, a dominant aspect of human biology.
In 'The Music of This Sphere', The Lives of a Cell: Notes of a Biology Watcher (1974), 25.
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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The origin of an adaptive structure and the purposes it comes to fulfill are only chance combinations. Purposefulness is a very human conception for usefulness. It is usefulness looked at backwards. Hard as it is to imagine, inconceivably hard it may appear to many, that there is no direct relation between the origin of useful variations and the ends they come to serve, yet the modern zoologist takes his stand as a man of science on this ground. He may admit in secret to his father confessor, the metaphysician, that his poor intellect staggers under such a supposition, but he bravely carries forward his work of investigation along the only lines that he has found fruitful.
'For Darwin', The Popular Science Monthly (1909), 74, 380.
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The primary rocks, ... I regard as the deposits of a period in which the earth's crust had sufficiently cooled down to permit the existence of a sea, with the necessary denuding agencies,—waves and currents,—and, in consequence, of deposition also; but in which the internal heat acted so near the surface, that whatever was deposited came, matter of course, to be metamorphosed into semi-plutonic forms, that retained only the stratification. I dare not speak of the scenery of the period. We may imagine, however, a dark atmosphere of steam and vapour, which for age after age conceals the face of the sun, and through which the light of moon or star never penetrates; oceans of thermal water heated in a thousand centres to the boiling point; low, half-molten islands, dim through the log, and scarce more fixed than the waves themselves, that heave and tremble under the impulsions of the igneous agencies; roaring geysers, that ever and anon throw up their intermittent jets of boiling fluid, vapour, and thick steam, from these tremulous lands; and, in the dim outskirts of the scene, the red gleam of fire, shot forth from yawning cracks and deep chasms, and that bears aloft fragments of molten rock and clouds of ashes. But should we continue to linger amid a scene so featureless and wild, or venture adown some yawning opening into the abyss beneath, where all is fiery and yet dark,—a solitary hell, without suffering or sin,—we would do well to commit ourselves to the guidance of a living poet of the true faculty,—Thomas Aird and see with his eyes.
Lecture Sixth, collected in Popular Geology: A Series of Lectures Read Before the Philosophical Institution of Edinburgh, with Descriptive Sketches from a Geologist's Portfolio (1859), 297-298.
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The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc’d to a Mathematical Reasoning, and when they cannot, it’s a sign our Knowledge of them is very small and confus’d; and where a mathematical reasoning can be had, it’s as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.
Of the Laws of Chance, or, a Method of the Hazards of Game (1692), Preface.
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The scientific world-picture vouchsafes a very complete understanding of all that happens–it makes it just a little too understandable. It allows you to imagine the total display as that of a mechanical clockwork which, for all that science knows, could go on just the same as it does, without there being consciousness, will, endeavor, pain and delight and responsibility connected with it–though they actually are. And the reason for this disconcerting situation is just this: that for the purpose of constructing the picture of the external world, we have used the greatly simplifying device of cutting our own personality out, removing it; hence it is gone, it has evaporated, it is ostensibly not needed.
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The universe is not only queerer than we imagine, but it is queerer than we can imagine.
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The whole question of imagination in science is often misunderstood by people in other disciplines. ... They overlook the fact that whatever we are allowed to imagine in science must be consistent with everything else we know.
In The Feynman Lectures in Physics (1964), Vol. 2, Lecture 20, p.20-10. As quoted by James Gleick in Genius: The Life and Science of Richard Feynman (1992), 324.
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The whole question of imagination in science is often misunderstood by people in other disciplines. They try to test our imagination in the following way. They say, “Here is a picture of some people in a situation. What do you imagine will happen next?” When we say, “I can’t imagine,” they may think we have a weak imagination. They overlook the fact that whatever we are allowed to imagine in science must be consistent with everything else we know; that the electric fields and the waves we talk about are not just some happy thoughts which we are free to make as we wish, but ideas which must be consistent with all the laws of physics we know. We can’t allow ourselves to seriously imagine things which are obviously in contradiction to the laws of nature. And so our kind of imagination is quite a difficult game. One has to have the imagination to think of something that has never been seen before, never been heard of before. At the same time the thoughts are restricted in a strait jacket, so to speak, limited by the conditions that come from our knowledge of the way nature really is. The problem of creating something which is new, but which is consistent with everything which has been seen before, is one of extreme difficulty
In The Feynman Lectures in Physics (1964), Vol. 2, Lecture 20, p.20-10 to p.20-11.
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The world's forests need to be seen for what they are—giant global utilities, providing essential public services to humanity on a vast scale. They store carbon, which is lost to the atmosphere when they burn, increasing global warming. The life they support cleans the atmosphere of pollutants and feeds it with moisture. They act as a natural thermostat, helping to regulate our climate and sustain the lives of 1.4 billion of the poorest people on this Earth. And they do these things to a degree that is all but impossible to imagine.
Speech (25 Oct 2007) at the World Wildlife Fund gala dinner, Hampton Court Palace, announcing the Prince's Rainforests Project. On the Prince of Wales website.
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There is another approach to the extraterrestrial hypothesis of UFO origins. This assessment depends on a large number of factors about which we know little, and a few about which we know literally nothing. I want to make some crude numerical estimate of the probability that we are frequently visited by extraterrestrial beings.
Now, there is a range of hypotheses that can be examined in such a way. Let me give a simple example: Consider the Santa Claus hypothesis, which maintains that, in a period of eight hours or so on December 24-25 of each year, an outsized elf visits one hundred million homes in the United States. This is an interesting and widely discussed hypothesis. Some strong emotions ride on it, and it is argued that at least it does no harm.
We can do some calculations. Suppose that the elf in question spends one second per house. This isn't quite the usual picture—“Ho, Ho, Ho,” and so on—but imagine that he is terribly efficient and very speedy; that would explain why nobody ever sees him very much-only one second per house, after all. With a hundred million houses he has to spend three years just filling stockings. I have assumed he spends no time at all in going from house to house. Even with relativistic reindeer, the time spent in a hundred million houses is three years and not eight hours. This is an example of hypothesis-testing independent of reindeer propulsion mechanisms or debates on the origins of elves. We examine the hypothesis itself, making very straightforward assumptions, and derive a result inconsistent with the hypothesis by many orders of magnitude. We would then suggest that the hypothesis is untenable.
We can make a similar examination, but with greater uncertainty, of the extraterrestrial hypothesis that holds that a wide range of UFOs viewed on the planet Earth are space vehicles from planets of other stars.
The Cosmic Connection: An Extraterrestrial Perspective (1973), 200.
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There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
'The Study of the Natural Sciences: An Introductory Lecture to the Course of Experimental Chemistry in the University of Munich, for the Winter Session of 1852-53,' as translated and republished in The Medical Times and Gazette (22 Jan 1853), N.S. Vol. 6, 82.
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There’s no question in my mind that the capability of [the space shuttle] to put 65,000 pounds in low earth orbit—to put payloads up there cheaper than we’ve been able to do it before, not having to throw away the booster—will absolutely revolutionize the way we do business here on earth in ways that we just can’t imagine. It will help develop science and technology. With the space shuttle—when we get it operational—we’ll be able to do in 5 or 10 years what it would take us 20 to 30 years to do otherwise in science and technology development.
Interview for U.S. News & World Report (13 Apr 1981), 56.
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This is the question
Marry
Children—(if it Please God)—Constant companion (& friend in old age) who will feel interested in one—object to be beloved and played with—better than a dog anyhow. Home, & someone to take care of house—Charms of music and female chit-chat.—These things good for one’s health.—but terrible loss of time.—
My God, it is Intolerable to think of spending ones whole life, like a neuter bee, working, working—& nothing after all.—No, no, won’t do. Imagine living all one’s day solitary in smoky dirty London House.—Only picture to yourself a nice soft wife on a sofa with good fire, & books & music perhaps-—Compare this vision with the dingy reality of Grt. Marlbro’ Street.
Not Marry
Freedom to go where one liked—choice of Society and little of it. —Conversation of clever men at clubs—Not forced to visit relatives, & to bend in every trifle. —to have the expense and anxiety of children—perhaps quarreling—Loss of time. —cannot read in the Evenings—fatness & idleness—Anxiety & responsibility—less money for books &c—if many children forced to gain one’s bread. —(but then it is very bad for ones health to work too much)
Perhaps my wife won’t like London; then the sentence is banishment & degradation into indolent, idle fool.
Marry—Marry—Marry Q.E.D.
It being proved necessary to Marry When? Soon or late?
Notes on Marriage, July 1838. In F. Burkhardt and S. Smith (eds.), The Correspondence of Charles Darwin 1837-1843 (1986), Vol. 2, 444.
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This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
In The Philosophy of the Inductive Sciences Part 1, Bk. 2, chap. 4, sect. 8 (1868).
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This whole theory of electrostatics constitutes a group of abstract ideas and general propositions, formulated in the clear and precise language of geometry and algebra, and connected with one another by the rules of strict logic. This whole fully satisfies the reason of a French physicist and his taste for clarity, simplicity and order. The same does not hold for the Englishman. These abstract notions of material points, force, line of force, and equipotential surface do not satisfy his need to imagine concrete, material, visible, and tangible things. 'So long as we cling to this mode of representation,' says an English physicist, 'we cannot form a mental representation of the phenomena which are really happening.' It is to satisfy the need that he goes and creates a model.
The French or German physicist conceives, in the space separating two conductors, abstract lines of force having no thickness or real existence; the English physicist materializes these lines and thickens them to the dimensions of a tube which he will fill with vulcanised rubber. In place of a family of lines of ideal forces, conceivable only by reason, he will have a bundle of elastic strings, visible and tangible, firmly glued at both ends to the surfaces of the two conductors, and, when stretched, trying both to contact and to expand. When the two conductors approach each other, he sees the elastic strings drawing closer together; then he sees each of them bunch up and grow large. Such is the famous model of electrostatic action imagined by Faraday and admired as a work of genius by Maxwell and the whole English school.
The employment of similar mechanical models, recalling by certain more or less rough analogies the particular features of the theory being expounded, is a regular feature of the English treatises on physics. Here is a book* [by Oliver Lodge] intended to expound the modern theories of electricity and to expound a new theory. In it are nothing but strings which move around pulleys, which roll around drums, which go through pearl beads, which carry weights; and tubes which pump water while others swell and contract; toothed wheels which are geared to one another and engage hooks. We thought we were entering the tranquil and neatly ordered abode of reason, but we find ourselves in a factory.
*Footnote: O. Lodge, Les Théories Modernes (Modern Views on Electricity) (1889), 16.
The Aim and Structure of Physical Theory (1906), 2nd edition (1914), trans. Philip P. Wiener (1954), 70-1.
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Throughout his last half-dozen books, for example, Arthur Koestler has been conducting a campaign against his own misunderstanding of Darwinism. He hopes to find some ordering force, constraining evolution to certain directions and overriding the influence of natural selection ... Darwinism is not the theory of capricious change that Koestler imagines. Random variation may be the raw material of change, but natural selection builds good design by rejecting most variants while accepting and accumulating the few that improve adaptation to local environments.
In The Panda’s Thumb: More Reflections in Natural History (1990, 2010), 38.
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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
From 'Les Mathématiques et la Logique', Science et Méthode (1908, 1920), Livre 2, Chap. 3, Sec. 2, 157. English as in Henri Poincaré and George Bruce Halsted (trans.), 'Mathematics and Logic', Science and Method collected in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method (1913), 451. From the French, “Ainsi, c’est bien entendu, pour démontrer un théorème, il n’est pas nécessaire ni même utile de savoir ce qu’il veut dire. On pourrait remplacer le géomètre par le piano à raisonner imaginé par Stanley Jevons; ou, si l’on aime mieux, on pourrait imaginer une machine où l’on introduirait les axiomes par un bout pendant qu’on recueillerait les théorèmes à l’autre bout, comme cette machine légendaire de Chicago où les porcs entrent vivants et d’où ils sortent transformés en jambons et en saucisses. Pas plus que ces machines, le mathématicien n’a besoin de comprendre ce qu’il fait”.
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To take one of the simplest cases of the dissipation of energy, the conduction of heat through a solid—consider a bar of metal warmer at one end than the other and left to itself. To avoid all needless complication, of taking loss or gain of heat into account, imagine the bar to be varnished with a substance impermeable to heat. For the sake of definiteness, imagine the bar to be first given with one half of it at one uniform temperature, and the other half of it at another uniform temperature. Instantly a diffusing of heat commences, and the distribution of temperature becomes continuously less and less unequal, tending to perfect uniformity, but never in any finite time attaining perfectly to this ultimate condition. This process of diffusion could be perfectly prevented by an army of Maxwell’s ‘intelligent demons’* stationed at the surface, or interface as we may call it with Prof. James Thomson, separating the hot from the cold part of the bar.
* The definition of a ‘demon’, according to the use of this word by Maxwell, is an intelligent being endowed with free will, and fine enough tactile and perceptive organisation to give him the faculty of observing and influencing individual molecules of matter.
In 'The Kinetic Theory of the Dissipation of Energy', Nature (1874), 9, 442.
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To treat your facts with imagination is one thing, to imagine your facts is quite another.
Journal, October 24,1907.
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To wage war with Marchand or anyone else again will benefit nobody and bring little profit to science. You consume yourself in this way, you ruin your liver and eventually your nerves with Morrison pills. Imagine the year 1900 when we have disintegrated into carbonic acid, ammonia and water and our bone substance is perhaps once more a constituent of the bones of the dog who defiles our graves. Who will then worry his head as to whether we have lived in peace or anger, who then will know about your scientific disputes and of your sacrifice of health and peace of mind for science? Nobody. But your good ideas and the discoveries you have made, cleansed of all that is extraneous to the subject, will still be known and appreciated for many years to come. But why am I trying to advise the lion to eat sugar.
Letter from Wohler to Liebig (9 Mar 1843). In A. W. Hofmann (ed.), Aus Justus Liebigs und Friedrich Wohlers Briefwechsel (1888), Vol. 1, 224. Trans. Ralph Oesper, The Human Side of Scientists (1975), 205.
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Traveling is a brutality. It forces you to trust strangers and to lose sight of all that familiar comfort of home and friends. You are constantly off balance. Nothing is yours except the essential things - air, sleep, dreams, the sea, the sky - all things tending towards the eternal or what we imagine of it.
…...
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Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languages of the world than to master all mathematics at present known. The languages could, I imagine, be learnt in a lifetime; mathematics certainly could not. Nor is the subject static.
In 'The Extent of Mathematics', Prelude to Mathematics (1955), 11.
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We fondly imagine that evolution drives toward higher intelligence. But eagles would think evolution favored flight, elephants would naturally prefer the importance of great strength. Sharks would feel that swimming was the ultimate desirable trait, and eminent Victorians would be quite convinced that evolution preferred Victorians.
Eater (2000). In Gary Westfahl, Science Fiction Quotations: From the Inner Mind to the Outer Limits (2006), 116.
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We have an extraordinary opportunity that has arisen only twice before in the history of Western civilization—the opportunity to see everything afresh through a new cosmological lens. We are the first humans privileged to see a face of the universe no earlier culture ever imagined.
As co-author with Nancy Ellen Abrams, in The View from the Center of the Universe: Discovering Our Extraordinary Place in the Cosmos (2006), 297.
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We have no organ at all for knowledge, for ‘truth’: we ‘know’ (or believe or imagine) precisely as much as may be useful in the interest of the human herd, the species: and even what is here called ‘usefulness’ is in the end only a belief, something imagined and perhaps precisely that most fatal piece of stupidity by which we shall one day perish.
Sämtliche Werke: Kritische Studienausgabe, vol. 3, p. 593, eds. Giorgio Colli and Mazzino Montinari, Berlin, de Gruyter (1980). The Gay Science, second edition, 'Fifth Book: We Fearless Ones,' section 354 (1887).
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We may fondly imagine that we are impartial seekers after truth, but with a few exceptions, to which I know that I do not belong, we are influenced—and sometimes strongly—by our personal bias; and we give our best thoughts to those ideas which we have to defend.
(Said in Boston, 1929.) As quoted by E. Snorrason, 'Krogh, Schack August Steenberg', in Charles Coulton Gillispie (ed.), Dictionary of Scientific Biography (1973), Vol 7, 503.
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We may, perhaps, imagine that the creation was finished long ago. But that would be quite wrong. It continues still more magnificently, and at the highest levels of the world.
In The Divine Milieu (1927, 1968), 62.
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We often frame our understanding of what the [Hubble] space telescope will do in terms of what we expect to find, and actually it would be terribly anticlimactic if in fact we find what we expect to find. … The most important discoveries will provide answers to questions that we do not yet know how to ask and will concern objects we have not yet imagined.
As quoted in Timothy Ferris, 'The Space Telescope: A Sign of Intelligent Life', New York Times (29 Apr 1990), A1.
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We should have positive expectations of what is in the universe, not fears and dreads. We are made with the realization that we’re not Earthbound, and that our acceptance of the universe offers us room to explore and extend outward. It’s like being in a dark room and imagining all sorts of terrors. But when we turn on the light – technology - suddenly it’s just a room where we can stretch out and explore. If the resources here on Earth are limited, they are not limited in the universe. We are not constrained by the limitations of our planet. As children have to leave the security of family and home life to insure growth into mature adults, so also must humankind leave the security and familiarity of Earth to reach maturity and obtain the highest attainment possible for the human race.
…...
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We were flying over America and suddenly I saw snow, the first snow we ever saw from orbit. I have never visited America, but I imagined that the arrival of autumn and winter is the same there as in other places, and the process of getting ready for them is the same. And then it struck me that we are all children of our Earth.
As quoted in Kevin W. Kelley (ed.), The Home Planet (1988). Source cited as “submitted by Lev Demin”.
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What is now proved was once only imagin’d.
In 'Proverbs', The Poems: With Specimens of the Prose Writings of William Blake (1885), 280.
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When we try to imagine a chaos we fail. ... In its very fiber the mind is an order and refuses to build a chaos.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 170.
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Why are you so sure parallel lines exist?
Believe nothing, merely because you have been told it, or because it is traditional, or because you have imagined it.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 47.
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Why do the laws that govern [the universe] seem constant in time? One can imagine a Universe in which laws are not truly law-full. Talk of miracle does just this, invoking God to make things work. Physics aims to find the laws instead, and hopes that they will be uniquely constrained, as when Einstein wondered whether God had any choice when He made the Universe.
Gregory Benford, in John Brockman, What We Believe But Cannot Prove. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 182-183.
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With respect to those who may ask why Nature does not produce new beings? We may enquire of them in turn, upon what foundation they suppose this fact? What it is that authorizes them to believe this sterility in Nature? Know they if, in the various combinations which she is every instant forming, Nature be not occupied in producing new beings, without the cognizance of these observers? Who has informed them that this Nature is not actually assembling, in her immense elaboratory, the elements suitable to bring to light, generations entirely new, that will have nothing in common with those of the species at present existing? What absurdity then, or what want of just inference would there be, to imagine that the man, the horse, the fish, the bird will be no more? Are these animals so indispensably requisite to Nature, that without them she cannot continue her eternal course? Does not all change around us? Do we not ourselves change? ... Nature contains no one constant form.
The System of Nature (1770), trans. Samuel Wilkinson (1820), Vol. 1, 94-95.
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You can hardly imagine how I am struggling to exert my poetical ideas just now for the discovery of analogies & remote figures respecting the earth, Sun & all sorts of things—for I think it is the true way (corrected by judgement) to work out a discovery.
Letter to C. Schrenbein, 13th Nov, 1845. In Frank A. J. L. James (ed.), The Correspondence of Michael Faraday (1996), Vol. 3, 428.
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[Experimental Physicist] Phys. I cannot imagine myself perceiving non-Euclidean space!
Math. Look at the reflection of the room in a polished doorknob, and imagine yourself one of the actors in what you see going on there.
In Space, Time and Gravitation: An Outline of the General Relativity Theory (1920, 1921), 11.
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~~[Attributed, authorship undocumented]~~ Mathematical demonstrations are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even in subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedaemonians seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those, who had not, men of imperfect judgments, and unfit to rule and govern.
From an article which appeared as 'The Usefulness of Mathematics', Pennsylvania Gazette (30 Oct 1735), No. 360. Collected, despite being without clear evidence of Franklin’s authorship, in The Works of Benjamin Franklin (1809), Vol. 4, 377. Evidence of actual authorship by Ben Franklin for the newspaper article has not been ascertained, and scholars doubt it. See Franklin documents at the website founders.archives.gov. The quote is included here to attach this caution.
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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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Euclid
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
Pierre Fermat
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- 30 -
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- 20 -
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