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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Question: Explain how to determine the time of vibration of a given tuning-fork, and state what apparatus you would require for the purpose.
Answer: For this determination I should require an accurate watch beating seconds, and a sensitive ear. I mount the fork on a suitable stand, and then, as the second hand of my watch passes the figure 60 on the dial, I draw the bow neatly across one of its prongs. I wait. I listen intently. The throbbing air particles are receiving the pulsations; the beating prongs are giving up their original force; and slowly yet surely the sound dies away. Still I can hear it, but faintly and with close attention; and now only by pressing the bones of my head against its prongs. Finally the last trace disappears. I look at the time and leave the room, having determined the time of vibration of the common “pitch” fork. This process deteriorates the fork considerably, hence a different operation must be performed on a fork which is only lent.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 176-7, Question 4. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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As the nineteenth century drew to a close, scientists could reflect with satisfaction that they had pinned down most of the mysteries of the physical world: electricity, magnetism, gases, optics, acoustics, kinetics and statistical mechanics ... all had fallen into order before the. They had discovered the X ray, the cathode ray, the electron, and radioactivity, invented the ohm, the watt, the Kelvin, the joule, the amp, and the little erg.
A Short History of Nearly Everything. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 172.
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At the Lawrence Radiation Laboratory, we have long had a tradition of close cooperation between physicists and technicians.
From Nobel Lecture (11 Dec 1968). Collected in Yong Zhou (ed.), Nobel Lecture: Physics, 1963-1970 (2013), 250.
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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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Galaxies themselves cannot close the Universe.
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General Relativity is at least very close to the truth.
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However, if we consider that all the characteristics which have been cited are only differences in degree of structure, may we not suppose that this special condition of organization of man has been gradually acquired at the close of a long period of time, with the aid of circumstances which have proved favorable? What a subject for reflection for those who have the courage to enter into it!
In Recherches sur l'Organization des corps vivans (1802), as translated in Alpheus Spring Packard, Lamarck, the Founder of Evolution: His Life and Work (1901), 363. Packard's italics.
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I am sorry that the distinguished leader of the Republican Party in the House states that he is not versed in botany and publicly admits that he does not know anything of these terms or what it is all about; but, Mr. Chairman, it is indeed a sad day for the people of this country when we must close the doors of the laboratories doing research work for the people of the United States.
Speaking (28 Dec 1932) as a member of the 72nd Congress, early in the Great Depression, in opposition to an attempt to eliminate a small amount from the agricultural appropriation bill. As quoted in 'Mayor-Elect La Guardia on Research', Science (1933), New Series, 78, No. 2031, 511.
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I am willing to believe that my unobtainable sixty seconds within a sponge or a flatworm might not reveal any mental acuity that I would care to ca ll consciousness. But I am also confident ... that vultures and sloths, as close evolutionary relatives with the same basic set of organs, lie on our side of any meaningful (and necessarily fuzzy) border–and that we are therefore not mistaken when we look them in the eye and see a glimmer of emotional and conceptual affinity.
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I respect Kirkpatrick both for his sponges and for his numinous nummulosphere. It is easy to dismiss a crazy theory with laughter that debars any attempt to understand a man’s motivation–and the nummulosphere is a crazy theory. I find that few men of imagination are not worth my attention. Their ideas may be wrong, even foolish, but their methods often repay a close study ... The different drummer often beats a fruitful tempo.
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If that's how it all started, then we might as well face the fact that what's left out there is a great deal of shrapnel and a whole bunch of cinders (one of which is, fortunately, still hot enough and close enough to be good for tanning). Trying to find some sense and order in this mess may be as futile as trying to … reconstruct the economy of Iowa from a bowl of popcorn. [On searching for evidence of the Big Bang.]
From essay 'First Person Secular: Blocking the Gates to Heaven', Mother Jones Magazine (Jun 1986), 48. Collected in The Worst Years of our Lives: Irreverent Notes from a Decade of Greed (1995), 267.
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If the resident zoologist of Galaxy X had visited the earth 5 million years ago while making his inventory of inhabited planets in the universe, he would surely have corrected his earlier report that apes showed more promise than Old World monkeys and noted that monkeys had overcome an original disadvantage to gain domination among primates. (He will confirm this statement after his visit next year–but also add a footnote that one species from the ape bush has enjoyed an unusual and unexpected flowering, thus demanding closer monitoring.)
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In old age, you realise that while you're divided from your youth by decades, you can close your eyes and summon it at will. As a writer it puts one at a distinct advantage.
Interview with Sarah Crown, in The Guardian (25 Jul 2009).
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In the social production of their life, men enter into definite relations that are indispensable and independent of their will; these relations of production correspond to a definite stage of development of their material forces of production. The sum total of these relations of production constitutes the economic structure of society - the real foundation, on which rises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life determines the social, political and intellectual life process in general. It is not the consciousness of men that determines their being, but, on the contrary, their social being that determines their consciousness. At a certain stage of their development, the material productive forces in society come in conflict with the existing relations of production, or - what is but a legal expression for the same thing - with the property relations within which they have been at work before. From forms of development of the productive forces these relations turn into fetters. Then begins an epoch of social revolution. With the change of the economic foundation the entire immense superstructure is more or less rapidly transformed. In considering such transformations a distinction should always be made between the material transformation of the economic conditions of production, which can be determined with the precision of natural science, and the legal, political, religious, aesthetic or philosophic - in short, ideological forms in which men become conscious of this conflict and fight it out. Just as our opinion of an individual is not based on what he thinks of himself, so we can not judge of such a period of transformation by its own consciousness; on the contrary, this consciousness must be explained rather from the contradictions of material life, from the existing conflict between the social productive forces and the relations of production. No social order ever disappears before all the productive forces for which there is room in it have been developed; and new, higher relations of production never appear before the material conditions of their existence have matured in the womb of the old society itself. Therefore, mankind always sets itself only such tasks as it can solve; since, looking at the matter more closely, we will always find that the task itself arises only when the material conditions necessary for its solution already exist or are at least in the process of formation. In broad outlines we can designate the Asiatic, the ancient, the feudal, and the modern bourgeois modes of production as so many progressive epochs in the economic formation of society. The bourgeois relations of production are the last antagonistic form of the social process of production - antagonistic not in the sense of individual antagonism, but of one arising from the social conditions of life of the individuals; at the same time the productive forces developing in the womb of bourgeois society create the material conditions for the solution of that antagonism. This social formation constitutes, therefore, the closing chapter of the prehistoric stage of human society.
Karl Marx
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It is better to trust in the Rock of Ages, than to know the age of the rocks; it is better for one to know that he is close to the Heavenly Father, than to know how far the stars in the heavens are apart.
In chapter, 'The Origin of Man', In His Image (1922), 93.
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It is curious to reflect on how history repeats itself the world over. Why, I remember the same thing was done when I was a boy on the Mississippi River. There was a proposition in a township there to discontinue public schools because they were too expensive. An old farmer spoke up and said if they stopped the schools they would not save anything, because every time a school was closed a jail had to be built.
It's like feeding a dog on his own tail. He'll never get fat. I believe it is better to support schools than jails.
Address at a meeting of the Berkeley Lyceum, New York (23 Nov 1900). Mark Twain's Speeches (2006), 69-70.
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It's much more effective to allow solutions to problems to emerge from the people close to the problem rather than to impose them from higher up.
Interviewed in 'Simple, Yet Complex', CIO (15 Apr 1998), 64.
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It’s important natural history isn’t seen as something that is “out there”, which you have to travel to. It’s right there in your garden. Public awareness of the natural history of the world as a whole has never been as great. But it’s important to know about species close to home.
As reported by Adam Lusher in 'Sir David Attenborough', Daily Mail (28 Feb 2014).
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Many of life’s failures are people who did not realize how close they were to success when they gave up.
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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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No video, no photographs, no verbal descriptions, no lectures can provide the enchantment that a few minutes out-of-doors can: watch a spider construct a web; observe a caterpillar systematically ravaging the edge of a leaf; close your eyes, cup your hands behind your ears, and listen to aspen leaves rustle or a stream muse about its pools and eddies. Nothing can replace plucking a cluster of pine needles and rolling them in your fingers to feel how they’re put together, or discovering that “sedges have edges and grasses are round,” The firsthand, right-and-left-brain experience of being in the out-of-doors involves all the senses including some we’ve forgotten about, like smelling water a mile away. No teacher, no student, can help but sense and absorb the larger ecological rhythms at work here, and the intertwining of intricate, varied and complex strands that characterize a rich, healthy natural world.
Into the Field: A Guide to Locally Focused Teaching
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Now when naturalists observe a close agreement in numerous small details of habits, tastes, and dispositions between two or more domestic races, or between nearly-allied natural forms, they use this fact as an argument that they are descended from a common progenitor who was thus endowed; and consequently that all should be classed under the same species. The same argument may be applied with much force to the races of man.
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Relatively few benefits have flowed to the people who live closest to the more than 3,000 protected areas that have been established in tropical countries during the past 50 years. For this reason, the preservation of biodiversity is often thought of as something that poor people are asked to do to fulfill the wishes of rich people living in comfort thousands of miles away.
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Religion closes off the central questions of existence by attempting to dissuade us from further enquiry by asserting that we cannot ever hope to comprehend. We are, religion asserts, simply too puny.
Essay collected in John Cornwell (ed.), 'The Limitless Power of Science', Nature's Imagination: The Frontiers of Scientific Vision (1995), 125.
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Scientific studies on marine reserves around the world show that if you close a place to fishing, the number of species increases 20 percent, the average size of a fish increases by a third, and the total weight of fish per hectare increases almost five times—in less than a decade.
From interview with Terry Waghorn, 'Can We Eat Our Fish and Protect Them Too?', Forbes (21 Feb 2012)
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Study nature, love nature, stay close to nature. It will never fail you.
As quoted in Carla Lind, Wright Style (1992), 23.
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The development of science has produced an industrial revolution which has brought different peoples in such close contact with one another through colonization and commerce that no matter how some nations may still look down upon others, no country can harbor the illusion that its career is decided wholly within itself.
In Democracy and Education: An Introduction to the Philosophy of Education (1916), 337.
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The health of society thus depends quite as much on the independence of the individuals composing it as on their close political cohesion.
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The mind comprehends a thing the more correctly the closer the thing approaches toward pure quantity as its origin.
Letter to Mästlin (19 Apr 1597). In Gerald James Holton, Thematic Origins of Scientific Thought: Kepler to Einstein (1985), 74.
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The rocks are not so close akin to us as the soil; they are one more remove from us; but they lie back of all, and are the final source of all. ... Time, geologic time, looks out at us from the rocks as from no other objects in the landscape.
From Under the Apple-Trees (1916), Chap. 2, 'The Friendly Rocks', 40.
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There is a place with four suns in the sky—red, white, blue, and yellow; two of them are so close together that they touch, and star-stuff flows between them. I know of a world with a million moons. I know of a sun the size of the Earth—and made of diamond. There are atomic nuclei a few miles across which rotate thirty times a second. There are tiny grains between the stars, with the size and atomic composition of bacteria. There are stars leaving the Milky Way, and immense gas clouds falling into it. There are turbulent plasmas writhing with X- and gamma-rays and mighty stellar explosions. There are, perhaps, places which are outside our universe. The universe is vast and awesome, and for the first time we are becoming a part of it.
Opening paragraph, in 'Introduction' Planetary Exploration (1970), 15.
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They look a little like the monster in ‘Alien.’ They’re horrifying to look at up close. That’s sort of what makes them fun. [About his microscopic study of ants.]
As quoted by Lindsay Whitehurst in 'University of Utah Scientist Discovers Terrifying Ant Species', The Salt Lake Tribune (31 Jul 2013)
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To study men, we must look close by; to study man, we must learn to look afar; if we are to discover essential characteristics, we must first observe differences.
Essai sur l'origine des langues (1781), 384
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Very few people, including authors willing to commit to paper, ever really read primary sources–certainly not in necessary depth and contemplation, and often not at all ... When writers close themselves off to the documents of scholarship, and then rely only on seeing or asking, they become conduits and sieves rather than thinkers. When, on the other hand, you study the great works of predecessors engaged in the same struggle, you enter a dialogue with human history and the rich variety of our own intellectual traditions. You insert yourself, and your own organizing powers, into this history–and you become an active agent, not merely a ‘reporter.’
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Wallace’s error on human intellect arose from the in adequacy of his rigid selectionism, not from a failure to apply it. And his argument repays our study today, since its flaw persists as the weak link in many of the most ‘modern’ evolutionary speculations of our current literature. For Wallace’s rigid selectionism is much closer than Darwin’s pluralism to the attitude embodied in our favored theory today, which, ironically in this context, goes by the name of ‘Neo-Darwinism.’
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We may regard [Scheele] not only as having given the first indication of the rich harvest to be reaped by the investigation of the compounds of organic chemistry, but as having been the first to discover and make use of characteristic reactions by which closely allied substances can be detected and separated, so that he must be considered one of the chief founders of analytical chemistry.
In Treatise on Chemistry (1877, 1890), Vol. 1, 23.
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When the Heavens were a little blue Arch, stuck with Stars, methought the Universe was too straight and close: I was almost stifled for want of Air: but now it is enlarged in height and breadth, and a thousand Vortex’s taken in. I begin to breathe with more freedom, and I think the Universe to be incomparably more magnificent than it was before.
In A Plurality of Worlds (1688), 126, as translated by Mr. Glanvill.
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Whereas in The Two Towers you have different races, nations, cultures coming together and examining their conscience and unifying against a very real and terrifying enemy. What the United States has been doing for the past year is bombing innocent civilians without having come anywhere close to catching Osama bin Laden or any presumed enemy.
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You should look at the entire Bible as a whole rather then narrowly, if you can, under close scrutiny and with juxtaposition of passages
James Dye
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[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.
Writing as a Professor Emeritus at Harvard University, a former student of Peirce, in 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 6.
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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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- 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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