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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Back Quotes (104 quotes)

[On President Bush's plan to get to Mars in 10 years] Stupid. Robots would do a better job and be much cheaper because you don't have to bring them back.
Interview with Deborah Solomon, 'The Science of Second-Guessing', in New York Times Magazine (12 Dec 2004), 37.
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After physiology has taken Humpty Dumpty apart, it is difficult perhaps even unfashionable to put him back together again.
In 'The role of natural history in contemporary biology', BioScience (1986), 36, 327.
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An extra yawn one morning in the springtime, an extra snooze one night in the autumn is all that we ask in return for dazzling gifts. We borrow an hour one night in April; we pay it back with golden interest five months later.
As quoted in David Prerau, Seize the Daylight: The Curious And Contentious Story of Daylight (2006).
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An incidental remark from a German colleague illustrates the difference between Prussian ways and our own. He had apparently been studying the progress of our various crews on the river, and had been struck with the fact that though the masters in charge of the boats seemed to say and do very little, yet the boats went continually faster and faster, and when I mentioned Dr. Young’s book to him, he made the unexpected but suggestive reply: “Mathematics in Prussia! Ah, sir, they teach mathematics in Prussia as you teach your boys rowing in England: they are trained by men who have been trained by men who have themselves been trained for generations back.”
In John Perry (ed.), Discussion on the Teaching of Mathematics (1901), 43. The discussion took place on 14 Sep 1901 at the British Association at Glasgow, during a joint meeting of the mathematics and physics sections with the education section. The proceedings began with an address by John Perry. Langley related this anecdote during the Discussion which followed.
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Are the humanistic and scientific approaches different? Scientists can calculate the torsion of a skyscraper at the wing-beat of a bird, or 155 motions of the Moon and 500 smaller ones in addition. They move in academic garb and sing logarithms. They say, “The sky is ours”, like priests in charge of heaven. We poor humanists cannot even think clearly, or write a sentence without a blunder, commoners of “common sense”. We never take a step without stumbling; they move solemnly, ever unerringly, never a step back, and carry bell, book, and candle.
Quoting himself in Stargazers and Gravediggers: Memoirs to Worlds in Collision (2012), 212.
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As much as we’ve enjoyed it up here, we’re also starting to look forward to seeing all the people back on Earth that we miss and love so much.
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Bradley is one of the few basketball players who have ever been appreciatively cheered by a disinterested away-from-home crowd while warming up. This curious event occurred last March, just before Princeton eliminated the Virginia Military Institute, the year’s Southern Conference champion, from the NCAA championships. The game was played in Philadelphia and was the last of a tripleheader. The people there were worn out, because most of them were emotionally committed to either Villanova or Temple-two local teams that had just been involved in enervating battles with Providence and Connecticut, respectively, scrambling for a chance at the rest of the country. A group of Princeton players shooting basketballs miscellaneously in preparation for still another game hardly promised to be a high point of the evening, but Bradley, whose routine in the warmup time is a gradual crescendo of activity, is more interesting to watch before a game than most players are in play. In Philadelphia that night, what he did was, for him, anything but unusual. As he does before all games, he began by shooting set shots close to the basket, gradually moving back until he was shooting long sets from 20 feet out, and nearly all of them dropped into the net with an almost mechanical rhythm of accuracy. Then he began a series of expandingly difficult jump shots, and one jumper after another went cleanly through the basket with so few exceptions that the crowd began to murmur. Then he started to perform whirling reverse moves before another cadence of almost steadily accurate jump shots, and the murmur increased. Then he began to sweep hook shots into the air. He moved in a semicircle around the court. First with his right hand, then with his left, he tried seven of these long, graceful shots-the most difficult ones in the orthodoxy of basketball-and ambidextrously made them all. The game had not even begun, but the presumably unimpressible Philadelphians were applauding like an audience at an opera.
A Sense of Where You Are: Bill Bradley at Princeton
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Despite the high long-term probability of extinction, every organism alive today, including every person reading this paper, is a link in an unbroken chain of parent-offspring relationships that extends back unbroken to the beginning of life on earth. Every living organism is a part of an enormously long success story—each of its direct ancestors has been sufficiently well adapted to its physical and biological environments to allow it to mature and reproduce successfully. Viewed thus, adaptation is not a trivial facet of natural history, but a biological attribute so central as to be inseparable from life itself.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 330.
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Drive out Nature with a fork, she comes running back.
Emerson's translation of a much earlier saying, as given in 'Compensation', collected in The Complete Works of Ralph Waldo Emerson (1903), 105. A note on p.399 shows the same sentiment in the original Latin by Horace in his Epistles, i, x, 24: “Naturam expelles furca, tamen usque recurret,/Et mala perrumpet furtim fastidia victrix.” The first part of the couplet translates as above; the second part adds “And will burst through your foolish contempt, triumphant.” More examples, predating Emerson, are given in George Latimer Apperson and Martin H. Manser, The Concise Dictionary of English Etymology (1993, 2006), 158.
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Every cent we earn from Crocodile Hunter goes straight back into conservation. Every single cent.
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Every creature alive on the earth today represents an unbroken line of life that stretches back to the first primitive organism to appear on this planet; and that is about three billion years.
In talk, 'Origin of Death' (1970).
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Every mathematical book that is worth reading must be read “backwards and forwards”, if I may use the expression. I would modify Lagrange’s advice a little and say, “Go on, but often return to strengthen your faith.” When you come on a hard or dreary passage, pass it over; and come back to it after you have seen its importance or found the need for it further on.
In Algebra, Part 2 (1889), Preface, viii.
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Flaming enthusiasm, backed by horse sense and persistence, is the quality that most frequently makes for success.
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For all these years you were merely
A smear of light through our telescopes
On the clearest, coldest night; a hint
Of a glint, just a few pixels wide
On even your most perfectly-framed portraits.
But now, now we see you!
Swimming out of the dark - a great
Stone shark, your star-tanned skin pitted
And pocked, scarred after eons of drifting
Silently through the endless ocean of space.
Here on Earth our faces lit up as we saw
You clearly for the first time; eyes wide
With wonder we traced the strangely familiar
Grooves raked across your sides,
Wondering if Rosetta had doubled back to Mars
And raced past Phobos by mistake –
Then you were gone, falling back into the black,
Not to be seen by human eyes again for a thousand
Blue Moons or more. But we know you now,
We know you; you’ll never be just a speck of light again.
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For the saving the long progression of the thoughts to remote and first principles in every case, the mind should provide itself several stages; that is to say, intermediate principles, which it might have recourse to in the examining those positions that come in its way. These, though they are not self-evident principles, yet, if they have been made out from them by a wary and unquestionable deduction, may be depended on as certain and infallible truths, and serve as unquestionable truths to prove other points depending upon them, by a nearer and shorter view than remote and general maxims. … And thus mathematicians do, who do not in every new problem run it back to the first axioms through all the whole train of intermediate propositions. Certain theorems that they have settled to themselves upon sure demonstration, serve to resolve to them multitudes of propositions which depend on them, and are as firmly made out from thence as if the mind went afresh over every link of the whole chain that tie them to first self-evident principles.
In The Conduct of the Understanding, Sect. 21.
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From the level of pragmatic, everyday knowledge to modern natural science, the knowledge of nature derives from man’s primary coming to grips with nature; at the same time it reacts back upon the system of social labour and stimulates its development.
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Hold fast to dreams,
Let them stay with you forever.
Don’t let them die.
You might fly up in the sky
On a silver unicorn’s back,
Dreaming of the ocean,
Listening to the dolphins sing.
Dreams, hold on to them forever.
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Human interest in exploring the heavens goes back centuries. This is what human nature is all about.
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I am not insensible to natural beauty, but my emotional joys center on the improbable yet sometimes wondrous works of that tiny and accidental evolutionary twig called Homo sapiens. And I find, among these works, nothing more noble than the history of our struggle to understand nature—a majestic entity of such vast spatial and temporal scope that she cannot care much for a little mammalian afterthought with a curious evolutionary invention, even if that invention has, for the first time in so me four billion years of life on earth, produced recursion as a creature reflects back upon its own production and evolution. Thus, I love nature primarily for the puzzles and intellectual delights that she offers to the first organ capable of such curious contemplation.
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I believe citizens are beginning to realize that their birthright, a healthy ecosystem, has been stolen, and they want it back.
In The End of the Line: How Overfishing is Changing the World and what We Eat (2004), 317.
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I cannot judge my work while I am doing it. I have to do as painters do, stand back and view it from a distance, but not too great a distance. How great? Guess.
Quoted without citation in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966), 291. Webmaster has tried without success to locate a primary source. Can you help?
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I don't mind going back to daylight saving time. With inflation, the hour will be the only thing I've saved all year.
In Gene Perret and Terry Martin, Hilarious Roasts, Toasts & One-Liners (2004), 360.
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I feel that to be a director of a laboratory should not be, by definition, a permanent mission. People should have the courage to step down and go back to science. I believe you will never have a good director of a scientific laboratory unless that director knows he is prepared to become a scientist again. … I gave my contribution; I spent five years of my life to work hard for other people’s interest. … It’s time to go back to science again. I have some wonderful ideas, I feel I’m re-born.
From 'Asking Nature', collected in Lewis Wolpert and Alison Richards (eds.), Passionate Minds: The Inner World of Scientists (1997), 202.
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I have always played with the fancy that some contagion from outer space had been the seed of man. Our passionate preoccupation with the sky, the stars, and a God somewhere in outer space is a homing impulse. We are drawn back to where we came from.
Commenting on the first moon landing. In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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I have no doubt that it is possible to give a new direction to technological development, a direction that shall lead it back to the real needs of man, and that also means: to the actual size of man. Man is small, and, therefore, small is beautiful. To go
Small is Beautiful (1973).
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I hear one day the word “mountain,” and I ask someone “what is a mountain? I have never seen one.”
I join others in discussions of mountains.
One day I see in a book a picture of a mountain.
And I decide I must climb one.
I travel to a place where there is a mountain.
At the base of the mountain I see there are lots of paths to climb.
I start on a path that leads to the top of the mountain.
I see that the higher I climb, the more the paths join together.
After much climbing the many paths join into one.
I climb till I am almost exhausted but I force myself and continue to climb.
Finally I reach the top and far above me there are stars.
I look far down and the village twinkles far below.
It would be easy to go back down there but it is so beautiful up here.
I am just below the stars.
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I raised the visor on my helmet cover and looked out to try to identify constellations. As I looked out into space, I was overwhelmed by the darkness. I felt the flesh crawl on my back and the hair rise on my neck.
In How Do You Go To The Bathroom In Space?: All the Answers to All the Questions You Have About Living in Space (1999), 118.
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I would rather have a big burden and a strong back, than a weak back and a caddy to carry life’s luggage.
Aphorism in The Philistine (Dec 1904), 20, No. 1, 26.
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If somebody’d said before the flight, “Are you going to get carried away looking at the earth from the moon?” I would have say, “No, no way.” But yet when I first looked back at the earth, standing on the moon, I cried.
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If we turn our backs on things as yet untried within our own small realm of reference, we’re guilty of a sin against ourselves: An unwillingness to experiment.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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If you throw a stone in a pond... the waves which strike against the shores are thrown back towards the spot where the stone struck; and on meeting other waves they never intercept each other’s course... In a small pond one and the same stroke gives birth to many motions of advance and recoil.
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If you want to grow old as a pilot, you’ve got to know when to push it, and when to back off.
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If you were going to risk all that, not just risk the hardship and the pain but risk your life. Put everything on line for a dream, for something that’s worth nothing, that can’t be proved to anybody. You just have the transient moment on a summit and when you come back down to the valley it goes. It is actually a completely illogical thing to do. It is not justifiable by any rational terms. That’s probably why you do it.
The Beckoning Silence
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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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In every work of genius we recognize our own rejected thoughts; they come back to us with a certain alienated majesty.
In 'Self-Reliance', The Prose Works of Ralph Waldo Emerson (1870), Vol. 1, 241.
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Indeed, we need not look back half a century to times which many now living remember well, and see the wonderful advances in the sciences and arts which have been made within that period. Some of these have rendered the elements themselves subservient to the purposes of man, have harnessed them to the yoke of his labors and effected the great blessings of moderating his own, of accomplishing what was beyond his feeble force, and extending the comforts of life to a much enlarged circle, to those who had before known its necessaries only.
From paper 'Report of the Commissioners Appointed to Fix the Site of the University of Virginia' (Dec 1818), reprinted in Annual Report of the Board of Visitors of the University of Virginia for the Fiscal Year Ending May 31, 1879 (1879), 10. Collected in Commonwealth of Virginia, Annual Reports of Officers, Boards, and Institutions of the Commonwealth of Virginia, for the Year Ending September 30, 1879 (1879).
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It had long since come to my attention that people of accomplishment rarely sat back and let things happen to them. They went out and happened to things.
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It is a common rule with primitive people not to waken a sleeper, because his soul is away and might not have time to get back.
In The Golden Bough: A Study in Magic and Religion: Part II: Taboo and the Perils of the Soul (1890, 1911), 39.
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It is an old dream: To travel on the back of a benevolent sea beast down to some secret underwater garden.
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It is clear that all the valuable things, material, spiritual, and moral, which we receive from society can be traced back through countless generations to certain creative individuals. The use of fire, the cultivation of edible plants, the steam engine–each was discovered by one man.
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It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
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It is not always possible to know what one has learned, or when the dawning will arrive. You will continue to shift, sift, to shake out and to double back. The synthesis that finally occurs can be in the most unexpected place and the most unexpected time. My charge ... is to be alert to the dawnings.
…...
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It needs scarcely be pointed out that in placing Mathematics at the head of Positive Philosophy, we are only extending the application of the principle which has governed our whole Classification. We are simply carrying back our principle to its first manifestation. Geometrical and Mechanical phenomena are the most general, the most simple, the most abstract of all,— the most irreducible to others, the most independent of them; serving, in fact, as a basis to all others. It follows that the study of them is an indispensable preliminary to that of all others. Therefore must Mathematics hold the first place in the hierarchy of the sciences, and be the point of departure of all Education whether general or special.
In Auguste Comte and Harriet Martineau (trans.), The Positive Philosophy (1858), Introduction, Chap. 2, 50.
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It’s amazing how quickly nature consumes human places after we turn our backs on them. Life is a hungry thing.
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I’ve never looked through a keyhole without finding someone was looking back.
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Knowledge and wonder are the dyad of our worthy lives as intellectual beings. Voyager did wonders for our knowledge, but performed just as mightily in the service of wonder–and the two elements are complementary, not independent or opposed. The thought fills me with awe–a mechanical contraption that could fit in the back of a pickup truck, traveling through space for twelve years, dodging around four giant bodies and their associated moons, and finally sending exquisite photos across more than four light-hours of space from the farthest planet in our solar system.
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Let him [the author] be permitted also in all humility to add … that in consequence of the large arrears of algebraical and arithmetical speculations waiting in his mind their turn to be called into outward existence, he is driven to the alternative of leaving the fruits of his meditations to perish (as has been the fate of too many foregone theories, the still-born progeny of his brain, now forever resolved back again into the primordial matter of thought), or venturing to produce from time to time such imperfect sketches as the present, calculated to evoke the mental co-operation of his readers, in whom the algebraical instinct has been to some extent developed, rather than to satisfy the strict demands of rigorously systematic exposition.
In Philosophic Magazine (1863), 460.
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Looking back over the geological record it would seem that Nature made nearly every possible mistake before she reached her greatest achievement Man—or perhaps some would say her worst mistake of all. ... At last she tried a being of no great size, almost defenseless, defective in at least one of the more important sense organs; one gift she bestowed to save him from threatened extinction—a certain stirring, a restlessness, in the organ called the brain.
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Mars was surprising in its way but not flabbergasting; it was a disappointment not to find evidences of life, and there was some sadness in the pictures sent back to earth from the Mars Lander, that lonely long-legged apparatus poking about with its jointed arm, picking up sample after sample of the barren Mars soil, looking for any flicker of life and finding none; the only sign of life on Mars was the Lander itself, an extension of the human mind all the way from earth to Mars, totally alone.
In Late Night Thoughts on Listening to Mahler’s Ninth Symphony (1984), 22.
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May the road rise to meet you. May the wind always be at your back. May the sun shine warm upon your face, the rains fall soft upon your fields and, until we meet again, may God hold you in the palm of his hand.
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Most people assume that meditation is all about stopping thoughts, getting rid of emotions, somehow controlling the mind. But actually it’s … about stepping back, seeing the thought clearly, witnessing it coming and going.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 184
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My mother, my dad and I left Cuba when I was two [January, 1959]. Castro had taken control by then, and life for many ordinary people had become very difficult. My dad had worked [as a personal bodyguard for the wife of Cuban president Batista], so he was a marked man. We moved to Miami, which is about as close to Cuba as you can get without being there. It’s a Cuba-centric society. I think a lot of Cubans moved to the US thinking everything would be perfect. Personally, I have to say that those early years were not particularly happy. A lot of people didn’t want us around, and I can remember seeing signs that said: “No children. No pets. No Cubans.” Things were not made easier by the fact that Dad had begun working for the US government. At the time he couldn’t really tell us what he was doing, because it was some sort of top-secret operation. He just said he wanted to fight against what was happening back at home. [Estefan’s father was one of the many Cuban exiles taking part in the ill-fated, anti-Castro Bay of Pigs invasion to overthrow dictator Fidel Castro.] One night, Dad disappered. I think he was so worried about telling my mother he was going that he just left her a note. There were rumours something was happening back home, but we didn’t really know where Dad had gone. It was a scary time for many Cubans. A lot of men were involved—lots of families were left without sons and fathers. By the time we found out what my dad had been doing, the attempted coup had taken place, on April 17, 1961. Intitially he’d been training in Central America, but after the coup attempt he was captured and spent the next wo years as a political prisoner in Cuba. That was probably the worst time for my mother and me. Not knowing what was going to happen to Dad. I was only a kid, but I had worked out where my dad was. My mother was trying to keep it a secret, so she used to tell me Dad was on a farm. Of course, I thought that she didn’t know what had really happened to him, so I used to keep up the pretence that Dad really was working on a farm. We used to do this whole pretending thing every day, trying to protect each other. Those two years had a terrible effect on my mother. She was very nervous, just going from church to church. Always carrying her rosary beads, praying her little heart out. She had her religion, and I had my music. Music was in our family. My mother was a singer, and on my father’s side there was a violinist and a pianist. My grandmother was a poet.
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Naturam expelles furca, tamen usque recurret,
Et mala perrumpet furtim fastidia victrix.
[Drive Nature out with a pitchfork, yet she hurries back,
And will burst through your foolish contempt, triumphant.]

Horace
From Epistles, i, x, 24. First line as translated by Ralph Waldo Emerson. Second line Google translation by Webmaster. English variants, from 1539 and later, are given in George Latimer Apperson and Martin H. Manser, The Concise Dictionary of English Etymology (1993, 2006), 158.
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Nature, the parent of all things, designed the human backbone to be like a keel or foundation. It is because we have a backbone that we can walk upright and stand erect. But this was not the only purpose for which Nature provided it; here, as elsewhere, she displayed great skill in turning the construction of a single member to a variety of different uses.
It Provides a Path for the Spinal Marrow, Yet is Flexible.
Firstly, she bored a hole through the posterior region of the bodies of all the vertebrae, thus fashioning a suitable pathway for the spinal marrow which would descend through them.
Secondly, she did not make the backbone out of one single bone with no joints. Such a unified construction would have afforded greater stability and a safer seat for the spinal marrow since, not having joints, the column could not have suffered dislocations, displacements, or distortions. If the Creator of the world had paid such attention to resistance to injury and had subordinated the value and importance of all other aims in the fabric of parts of the body to this one, he would certainly have made a single backbone with no joints, as when someone constructing an animal of wood or stone forms the backbone of one single and continuous component. Even if man were destined only to bend and straighten his back, it would not have been appropriate to construct the whole from one single bone. And in fact, since it was necessary that man, by virtue of his backbone, be able to perform a great variety of movements, it was better that it be constructed from many bones, even though as a result of this it was rendered more liable to injury.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, 57-58, as translated by William Frank Richardson, in 'Nature’s Skill in Creating a Backbone to Hold Us Erect', On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), 138.
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Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Of course we have no means of staying back for any length of Time, any more than a savage or an animal has of staying six feet above the ground. But a civilized man is better off than the savage in this respect. He can go up against gravitation in a balloon, and why should he not hope that ultimately he may be able to stop or accelerate his drift along the Time-Dimension, or even turn about and travel the other way?
In The Time Machine (1898), 13.
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On the way back [from the moon] we had an EVA [extra-vehicular activity, or spacewalk] I had a chance to look around while I was outside and Earth was off to the right, 180,000 miles away, a little thin sliver of blue and white like a new moon surrounded by this blackness of space. Back over my left shoulder was almost a full moon. I didn’t feel like I was a participant. It was like sitting in the last row of the balcony, looking down at all of that play going on down there. I had that insignificant feeling of the immensity of this, God’s creation.
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One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.
In How to Solve It: A New Aspect of Mathematical Method (2004), 15.
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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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She has the sort of body you go to see in marble. She has golden hair. Quickly, deftly, she reaches with both hands behind her back and unclasps her top. Setting it on her lap, she swivels ninety degrees to face the towboat square. Shoulders back, cheeks high, she holds her pose without retreat. In her ample presentation there is defiance of gravity. There is no angle of repose. She is a siren and these are her songs.
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Sometime in my early teens, I started feeling an inner urgency, ups and downs of excitement and frustration, caused by such unlikely occupations as reading Granville’s course of calculus ... I found this book in the attic of a friend’s apartment. Among other standard stuff, it contained the notorious epsilon-delta definition of continuous functions. After struggling with this definition for some time (it was the hot Crimean summer, and I was sitting in the shadow of a dusty apple tree), I got so angry that I dug a shallow grave for the book between the roots, buried it there, and left in disdain. Rain started in an hour. I ran back to the tree and exhumed the poor thing. Thus, I discovered that I loved it, regardless.
'Mathematics as Profession and vocation', in V. Arnold et al. (eds.), Mathematics: Frontiers and Perspectives (2000), 153. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 79.
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Space is so close: It took only eight minutes to get there and twenty to get back.
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Standing now in diffused light, with the wind at my back, I experience suddenly a feeling of completeness–not a feeling of having achieved something or of being stronger than everyone who was ever here before, not a feeling of having arrived at the ultimate point, not a feeling of supremacy. Just a breath of happiness deep inside my mind and my breast. The summit seemed suddenly to me to be a refuge, and I had not expected to find any refuge up here. Looking at the steep, sharp ridges below us, I have the impression that to have come later would have been too late. Everything we now say to one another, we only say out of embarrassment. I don’t think anymore. As I pull the tape recorder, trancelike, from my rucksack, and switch it on wanting to record a few appropriate phrases, tears again well into my eyes. “Now we are on the summit of Everest,” I begin, “it is so cold that we cannot take photographs…” I cannot go on, I am immediately shaken with sobs. I can neither talk nor think, feeling only how this momentous experience changes everything. To reach only a few meters below the summit would have required the same amount of effort, the same anxiety and burden of sorrow, but a feeling like this, an eruption of feeling, is only possible on the summit itself.
In Everest: Expedition to the Ultimate (1979), 180.
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Strong, deeply rooted desire is the starting point of all achievement. Just as the electron is the last unit of matter discernible to the scientist. DESIRE is the seed of all achievement; the starting place, back of which there is nothing, or at least there is nothing of which we have any knowledge.
…...
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Technology... is a queer thing. It brings you great gifts with one hand, and it stabs you in the back with the other.
New York Times (15 Mar 1971).
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The advanced course in physics began with Rutherford’s lectures. I was the only woman student who attended them and the regulations required that women should sit by themselves in the front row. There had been a time when a chaperone was necessary but mercifully that day was past. At every lecture Rutherford would gaze at me pointedly, as I sat by myself under his very nose, and would begin in his stentorian voice: “Ladies and Gentlemen”. All the boys regularly greeted this witticism with thunderous applause, stamping with their feet in the traditional manner, and at every lecture I wished I could sink into the earth. To this day I instinctively take my place as far back as possible in a lecture room.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 118.
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The computational formalism of mathematics is a thought process that is externalised to such a degree that for a time it becomes alien and is turned into a technological process. A mathematical concept is formed when this thought process, temporarily removed from its human vessel, is transplanted back into a human mold. To think ... means to calculate with critical awareness.
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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The contributions of physiological knowledge to an understanding of distribution are necessarily inferential. Distribution is a historical phenomenon, and the data ordinarily obtained by students of physiology are essentially instantaneous. However, every organism has a line of ancestors which extends back to the beginning of life on earth and which, during this immensity of time, has invariably been able to avoid, to adapt to, or to compensate for environmental changes.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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The dog writhing in the gutter, its back broken by a passing car, knows what it is to be alive. So too with the aged elk of the far north woods, slowly dying in the bitter cold of winter. The asphalt upon which the dog lies knows no pain. The snow upon which the elk has collapsed knows not the cold. But living beings do. … Are you conscious? Then you can feel more pain. … Perhaps we even suffer more than the dumb animals.
In The Symbiotic Universe: Life and Mind in the Cosmos (1988), 194-195. As quoted and cited in Robert E. Zinser, The Fascinated God: What Science Says to Faith and Faith to Scientists (2003), 521.
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The first question which you will ask and which I must try to answer is this, “What is the use of climbing Mount Everest ?” and my answer must at once be, “It is no use.” There is not the slightest prospect of any gain whatsoever. Oh, we may learn a little about the behavior of the human body at high altitudes, and possibly medical men may turn our observation to some account for the purposes of aviation. But otherwise nothing will come of it. We shall not bring back a single bit of gold or silver, not a gem, nor any coal or iron. We shall not find a single foot of earth that can be planted with crops to raise food. It’s no use. So, if you cannot understand that there is something in man which responds to the challenge of this mountain and goes out to meet it, that the struggle is the struggle of life itself upward and forever upward, then you won’t see why we go. What we get from this adventure is just sheer joy. And joy is, after all, the end of life. We do not live to eat and make money. We eat and make money to be able to enjoy life. That is what life means and what life is for.
…...
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The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.
In Proofs and Refutations: The Logic of Mathematical Discovery (1976), 2
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The hope that new experiments will lead us back to objective events in time and space is about as well founded as the hope of discovering the end of the world in the unexplored regions of the Antarctic.
…...
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The human brain is a machine which alone accounts for all our actions, our most private thoughts, our beliefs. ... To choose a spouse, a job, a religious creed—or even choose to rob a bank—is the peak of a causal chain that runs back to the origin of life and down to the nature of atoms and molecules.
The Mind Machine (1998), 145. In Vinoth Ramachandra, Subverting Global Myths: Theology and the Public Issues Shaping our World (2008), 179.
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The most important distinction between the two qualities [talent and genius] is this: one, in conception, follows mechanical processes; the other, vital. Talent feebly conceives objects with the senses and understanding; genius, fusing all its powers together in the alembic of an impassioned imagination, clutches every thing in the concrete, conceives objects as living realities, gives body to spiritual abstractions, and spirit to bodily appearances, and like
“A gate of steel
Fronting the sun, receives and renders back
His figure and his heat!”
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 203. The quotation at the end is from Wiliam Shakespeare, Tr. & Cress. iii, 3.
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The path isn’t a straight line; it’s a spiral. You continually come back to things you thought you understood and see deeper truths.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 246
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The solution, as all thoughtful people recognize, must lie in properly melding the themes of inborn predisposition and shaping through life’s experiences. This fruitful joining cannot take the false form of percentages adding to 100–as in ‘intelligence is 80 percent nature and 20 percent nurture,’ or ‘homosexuality is 50 percent inborn and 50 percent learned,’ and a hundred other harmful statements in this foolish format. When two ends of such a spectrum are commingled, the result is not a separable amalgam (like shuffling two decks of cards with different backs), but an entirely new and higher entity that cannot be decomposed (just as adults cannot be separated into maternal and paternal contributions to their totality).
…...
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The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d. Some of his sayings are handed down from generation to generation:
“In order to solve this differential equation you look at it till a solution occurs to you.”
“This principle is so perfectly general that no particular application of it is possible.”
“Geometry is the science of correct reasoning on incorrect figures.”
“My method to overcome a difficulty is to go round it.”
“What is the difference between method and device? A method is a device which you used twice.”
In How to Solve It: A New Aspect of Mathematical Method (2004), 208.
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The vast spread
Of darkness
That speaks of mystery
The darkness that reveals
The beauty that lies beneath
In the form of glittering
Stars, a countless beauty
That seemed to conceal
A million stories
That can make the mankind
Take a new look at life
And the majestic moon
That silently looks at mankind
Wondering how its serenity
Was disturbed by the little steps
Of a man from the beautiful earth
Yet softly smiling back
And let the world sleep
In its magical glow
A glow that soothes
The world’s senses
And forget the pain of reality
…...
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The Vermin only teaze and pinch
Their foes superior by an Inch.
So, Naturalists observe, a Flea
Hath smaller Fleas that on him prey,
And these have smaller Fleas to bite 'em.
And so proceed ad infinitum.
On Poetry: A Rhapsody (1735), lines 339-44.
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There is no failure for the man who realizes his power, who never knows when he is beaten; there is no failure for the determined endeavor; the unconquerable will. There is no failure for the man who gets up every time he falls, who rebounds like a rubber ball, who persist when everyone else gives up, who pushes on when everyone else turns back.
…...
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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They were in orbit around the planet now, and its giant curving bulk loomed so huge that he could see nothing else, nothing but the bands and swirls of clouds that raced fiercely across Jupiter’s face. The clouds shifted and flowed before his eyes, spun into eddies the size of Asia, moved and throbbed and pulsed like living creatures. Lightning flashed down there, sudden explosions of light that flickered back and forth across the clouds, like signalling lamps.
Ben Bova
Jupiter
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This is Friendship 7. Can see clear back; a big cloud pattern way back across towards the Cape. Beautiful sight.
From the transcript of in-flight communications, 5 min 35 sec after launch, about his view through the porthole.
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Thurst [thrust] out nature with a croche [crook], yet woll she styll runne back agayne.
From Proverbs or Adagies out of Erasmus (1539), 44, given with other English variants, in George Latimer Apperson and Martin H. Manser, The Concise Dictionary of English Etymology (1993, 2006), 158. The dictionary also gives the original sentiment expressed by Horace: “Naturam expelles furca, tamen usque recurret” in Epistles, i, 10, 24.
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To choose art means to turn one's back on the world, or at least on certain of its distractions.
In Christian Science Monitor (10 Apr 1985). Cited in Michael C. Thomsett and Linda Rose Thomsett, A Speaker's Treasury of Quotations: Maxims, Witticisms and Quips for Speeches and Presentations (2009), 13.
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Two managers decided they would go moose hunting. They shot a moose, and as they were about to drag the animal by the hind legs, a biologist and an engineer came along.
The Biologist said, “You know, the hair follicles on a moose have a grain to them that causes the hair to lie toward the back.”
The Engineer said, “So dragging the moose that way increases your coefficient of friction by a tremendous amount. Pull from the other end, and you will find the work required to be quite minimal.”
The managers thanked the two and started dragging the moose by the antlers.
After about an hour, one manager said, “I can’t believe how easy it is to move this moose this way. I sure am glad we ran across those two.”
“Yeah,” said the other.“But we’re getting further and further away from our truck.”
Anonymous
In Jon Fripp, Michael Fripp and Deborah Fripp, Speaking of Science (2000), 193.
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Unless the materials involved can be traced back to the material of common sense concern there is nothing whatever for scientific concern to be concerned with.
In 'Common Sense and Science: Their Respective Frames of Reference', The Journal of Philosophy (8 Apr 1948), 45, No. 8, 206.
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We had the sky up there, all speckled with stars, and we used to lay on our backs and look up at them, and discuss whether they was made or just happened.
In The Adventures of Huckleberry Finn (Tom Sawyer's Comrade) (1885), Vol. 1, 214.
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We have taken to the Moon the wealth of this nation,
the vision of its political leaders,
the intelligence of its scientists,
the dedication of its engineers,
the careful craftsmanship of its workers,
and the enthusiastic support of its people.
We have brought back rocks, and I think it is a fair trade . . .
Man has always gone where he has been able to go. It’s that simple.
He will continue pushing back his frontier,
no matter how far it may carry him from his homeland.
…...
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We have to come back to something like ordinary language after all when we want to talk “about” mathematics!
As co-author with Bertha Swirles Jeffreys, in Methods of Mathematical Physics (1946, 1999), 2.
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We know less about the ocean's bottom than about the moon's back side.
Quoted in obituary, Physics Today (Feb 1992) 120.
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We must somehow keep the dreams of space exploration alive, for in the long run they will prove to be of far more importance to the human race than the attainment of material benefits. Like Darwin, we have set sail upon an ocean: the cosmic sea of the Universe. There can be no turning back. To do so could well prove to be a guarantee of extinction. When a nation, or a race or a planet turns its back on the future, to concentrate on the present, it cannot see what lies ahead. It can neither plan nor prepare for the future, and thus discards the vital opportunity for determining its evolutionary heritage and perhaps its survival.
…...
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We should be most careful about retreating from the specific challenge of our age. We should be reluctant to turn our back upon the frontier of this epoch… We cannot be indifferent to space, because the grand slow march of our intelligence has brought us, in our generation, to a point from which we can explore and understand and utilize it. To turn back now would be to deny our history, our capabilities.
At a 1979 U.S. Senate hearing. As quoted in House Congressional Record (21 Jun 1991), 13874. Also quoted in James E. Oberg, Mission to Mars: Plans and Concepts for the First Manned Landing (2017), 174.
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We want them to use the education to be leaders in their community with an understanding of ecology and conservation for the wild outdoors far beyond their legislators back home. We expect these people to he a grain of sand on the beach of future leadership.
…...
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We would be 1,500 years ahead if it hadn't been for the church dragging science back by its coat tails and burning our best minds at the stake.
In Dave Lane, Isn't Religion Weird? Quotations for Atheists (2008), 18.
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When going ahead in space, it is also important to go back in time.
Gordon Lill and Arthur Maxwell, quoting a proverb of the American Miscellaneous Society (AMSOC, which Lill co-founded), 'The Earth's Mantle', Science (22 May 1959), 129, No. 3360, 1410.
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When I came back from Munich, it was September, and I was Professor of Mathematics at the Eindhoven University of Technology. Later I learned that I had been the Department’s third choice, after two numerical analysts had turned the invitation down; the decision to invite me had not been an easy one, on the one hand because I had not really studied mathematics, and on the other hand because of my sandals, my beard and my ‘arrogance’ (whatever that may be).
…...
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When I was … a teenager … like, 14, … the space program was getting started, and I wanted to be an astronaut. I wrote to NASA and I said, “What do I have to do to be prepared to be an astronaut?” And they wrote back and said, “Thank you very much but we’re not taking girls.” … That thankfully changed with Sally Ride and a lot of the other great women astronauts.
At Town Hall Meeting, Dover, New Hampshire (16 Jul 2015). As quoted in Clare Foran, 'Hillary Clinton: I Wanted to Be an Astronaut', National Journal (16 Jul 2015).
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When we look back beyond one hundred years over the long trails of history, we see immediately why the age we live in differs from all other ages in human annals. … It remained stationary in India and in China for thousands of years. But now it is moving very fast. … A priest from Thebes would probably have felt more at home at the council of Trent, two thousand years after Thebes had vanished, than Sir Isaac Newton at a modern undergraduate physical society, or George Stephenson in the Institute of Electrical Engineers. The changes have have been so sudden and so gigantic, that no period in history can be compared with the last century. The past no longer enables us even dimly to measure the future.
From 'Fifty Years Hence', Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57, No. 3, 393.
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When you have made a thorough and reasonably long effort, to understand a thing, and still feel puzzled by it, stop, you will only hurt yourself by going on. Put it aside till the next morning; and if then you can’t make it out, and have no one to explain it to you, put it aside entirely, and go back to that part of the subject which you do understand.
From letter to Edith Rix with hints for studying (about Mar 1885), in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 240.
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You can always tell the pioneers because they are face down in the mud with arrows in their backs.
Anonymous
Seen in various paraphrases, such as $ldquo;in the dirt”.
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You do what you can for as long as you can, and when you finally can’t, you do the next best thing. You back up but you don’t give up.
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You see but your shadow when you turn your back to the sun.
In Kahlil Gibran: The Collected Works (207), 188.
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[Public cynicism towards professional expertise is] entirely wrong, and it’s the road back to the cave. The way we got out of the caves and into modern civilisation is through the process of understanding and thinking. Those things were not done by gut instinct. Being an expert does not mean that you are someone with a vested interest in something; it means you spend your life studying something. You’re not necessarily right–but you’re more likely to be right than someone who’s not spent their life studying it.
Brian Cox
As quoted in interview with Decca Aitkenhead, 'Prof Brian Cox: Being anti-expert – that’s the way back to the cave', The Guardian (2 Jul 2016)
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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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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