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Reach Quotes (281 quotes)

The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest.
Address (1918) for Max Planck's 60th birthday, at Physical Society, Berlin, 'Principles of Research' in Essays in Science (1934), 4.
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... I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
Quoted in Sir Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), 541. Science and Method (1908) 51-52, 392.
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...while science gives us implements to use, science alone does not determine for what ends they will be employed. Radio is an amazing invention. Yet now that it is here, one suspects that Hitler never could have consolidated his totalitarian control over Germany without its use. One never can tell what hands will reach out to lay hold on scientific gifts, or to what employment they will be put. Ever the old barbarian emerges, destructively using the new civilization.
In 'The Real Point of Conflict between Science and Religion', collected in Living Under Tension: Sermons On Christianity Today (1941), 142.
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Copernicus, who rightly did condemn
This eldest systeme, form’d a wiser scheme;
In which he leaves the Sun at Rest, and rolls
The Orb Terrestial on its proper Poles;
Which makes the Night and Day by this Career,
And by its slow and crooked Course the Year.
The famous Dane, who oft the Modern guides,
To Earth and Sun their Provinces divides:
The Earth's Rotation makes the Night and Day,
The Sun revolving through th'Eccliptic Way
Effects the various seasons of the Year,
Which in their Turn for happy Ends appear.
This Scheme or that, which pleases best, embrace,
Still we the Fountain of their Motion trace.
Kepler asserts these Wonders may be done
By the Magnetic Vertue of the Sun,
Which he, to gain his End, thinks fit to place
Full in the Center of that mighty Space,
Which does the Spheres, where Planets roll, include,
And leaves him with Attractive Force endu'd.
The Sun, thus seated, by Mechanic Laws,
The Earth, and every distant Planet draws;
By which Attraction all the Planets found
Within his reach, are turn'd in Ether round.
In Creation: A Philosophical Poem in Seven Books (1712), book 2, l. 430-53, p.78-9.
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Dogbert (gazing at night sky) No matter how bad the day is, the stars are always there.
Dilbert Actually, many of them burned out years ago, but their light is just now reaching earth.
DogbertThank you for shattering my comfortable misconception.
DilbertIt's the miracle of science.
Dilbert comic strip (21 Nov 1990).
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Wilst du ins Unendliche schreiten, Geh nur im Endlichen nach allen Seiten.
If you want to reach the infinite, explore every aspect of the finite.
Jeremy Naydler (ed.), Goethe On Science: An Anthology of Goethe’s Scientific Writings (1996), 37.
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[Students or readers about teachers or authors.] They will listen with both ears to what is said by the men just a step or two ahead of them, who stand nearest to them, and within arm’s reach. A guide ceases to be of any use when he strides so far ahead as to be hidden by the curvature of the earth.
From Lecture (5 Apr 1917) at Hackley School, Tarrytown, N.Y., 'Choosing Books', collected in Canadian Stories (1918), 150.
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A child’s world is fresh and new and beautiful, full of wonder and excitement. It is our misfortune that for most of us that clear-eyed vision, that true instinct for what is beautiful and awe-inspiring, is dimmed and even lost before we reach adulthood.
In The Sense of Wonder (1956, 1998), 54.
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A discovery is like falling in love and reaching the top of a mountain after a hard climb all in one, an ecstasy not induced by drugs but by the revelation of a face of nature that no one has seen before and that often turns out to be more subtle and wonderful than anyone had imagined.
'True Science', review of Peter Medawar, Advice to a Young Scientist (1980). In The London Review of Books (Mar 1981), 6.
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A few days ago, a Master of Arts, who is still a young man, and therefore the recipient of a modern education, stated to me that until he had reached the age of twenty he had never been taught anything whatever regarding natural phenomena, or natural law. Twelve years of his life previously had been spent exclusively amongst the ancients. The case, I regret to say, is typical. Now we cannot, without prejudice to humanity, separate the present from the past.
'On the Study of Physics', From a Lecture delivered in the Royal Institution of Great Britain in the Spring of 1854. Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 1, 284-5.
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A mile and a half from town, I came to a grove of tall cocoanut trees, with clean, branchless stems reaching straight up sixty or seventy feet and topped with a spray of green foliage sheltering clusters of cocoanuts—not more picturesque than a forest of colossal ragged parasols, with bunches of magnified grapes under them, would be. I once heard a grouty northern invalid say that a cocoanut tree might be poetical, possibly it was; but it looked like a feather-duster struck by lightning. I think that describes it better than a picture—and yet, without any question, there is something fascinating about a cocoanut tree—and graceful, too.
In Roughing It (1913), 184-85.
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A mind not wholly wishful to reach the truth, or to rest it in or obey it when found, is to that extent a mind impervious to truth an incapable of unbiased belief.
Recent Theistic Discussion: the twentieth series of Croall Lectures (1921), 78. In The Homiletic Review, Vol. 83-84 (1922), Vol. 84, 290.
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A science is any discipline in which the fool of this generation can go beyond the point reached by the genius of the last generation.
Politics, Law and Ritual in Tribal Society (1965), 32.
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A troubling question for those of us committed to the widest application of intelligence in the study and solution of the problems of men is whether a general understanding of the social sciences will be possible much longer. Many significant areas of these disciplines have already been removed by the advances of the past two decades beyond the reach of anyone who does not know mathematics; and the man of letters is increasingly finding, to his dismay, that the study of mankind proper is passing from his hands to those of technicians and specialists. The aesthetic effect is admittedly bad: we have given up the belletristic “essay on man” for the barbarisms of a technical vocabulary, or at best the forbidding elegance of mathematical syntax.
Opening paragraph of 'The Study of Man: Sociology Learns the Language of Mathematics' in Commentary (1 Sep 1952). Reprinted in James Roy Newman, The World of Mathematics (1956), Vol. 2, 1294.
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About ten months ago [1609] a report reached my ears that a certain Fleming [Hans Lippershey] had constructed a spyglass, by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby... Of this truly remarkable effect several experiences were related, to which some persons gave credence while others denied them. A few days later the report was confirmed to me in a letter from a noble Frenchman at Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to enquire into the means by which I might arrive at the invention of a similar instrument. This I did shortly afterwards, my basis being the theory of refraction. First I prepared a tube of lead, at the ends of which I fitted two glass lenses, both plane on one side while on the other side one was spherically convex and the other concave.
The Starry Messenger (1610), trans. Stillman Drake, Discoveries and Opinions of Galileo (1957), 28-9.
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After an orange cloud—formed as a result of a dust storm over the Sahara and caught up by air currents—reached the Philippines and settled there with rain, I understood that we are all sailing in the same boat.
In Jack Hassard and Julie Weisberg , Environmental Science on the Net: The Global Thinking Project (1999), 40.
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All of us are interested in our roots. Generally this interest is latent in youth, and grows with age. Until I reached fifty I thought that history of science was a refuge for old scientists whose creative juices had dried up. Now of course I know that I was wrong! As we grow older, we become more interested in the past, in family history, local history, etc. Astronomy is, or was when I started in it, almost a family.
In Organizations and Strategies in Astronomy (2002), Vol. 3, 206.
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All our knowledge merely helps us to die a more painful death than the animals that know nothing. A day will come when science will turn upon its error and no longer hesitate to shorten our woes. A day will come when it will dare and act with certainty; when life, grown wiser, will depart silently at its hour, knowing that it has reached its term.
Our Eternity, translated by Alexander Teixeira de Mattos (1913), 24.
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America has always been greatest when we dared to be great. We can reach for greatness again. We can follow our dreams to distant stars, living and working in space for peaceful, economic, and scientific gain. Tonight, I am directing NASA to develop a permanently manned space station and to do it within a decade.
From State of the Union Address (25 Jan 1984).
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An example of such emergent phenomena is the origin of life from non-living chemical compounds in the oldest, lifeless oceans of the earth. Here, aided by the radiation energy received from the sun, countless chemical materials were synthesized and accumulated in such a way that they constituted, as it were, a primeval “soup.” In this primeval soup, by infinite variations of lifeless growth and decay of substances during some billions of years, the way of life was ultimately reached, with its metabolism characterized by selective assimilation and dissimilation as end stations of a sluiced and canalized flow of free chemical energy.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 458.
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Another great and special excellence of mathematics is that it demands earnest voluntary exertion. It is simply impossible for a person to become a good mathematician by the happy accident of having been sent to a good school; this may give him a preparation and a start, but by his own individual efforts alone can he reach an eminent position.
In Conflict of Studies (1873), 2.
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Anthropology has reached that point of development where the careful investigation of facts shakes our firm belief in the far-reaching theories that have been built up. The complexity of each phenomenon dawns on our minds, and makes us desirous of proceeding more cautiously. Heretofore we have seen the features common to all human thought. Now we begin to see their differences. We recognize that these are no less important than their similarities, and the value of detailed studies becomes apparent. Our aim has not changed, but our method must change. We are still searching for the laws that govern the growth of human culture, of human thought; but we recognize the fact that before we seek for what is common to all culture, we must analyze each culture by careful and exact methods, as the geologist analyzes the succession and order of deposits, as the biologist examines the forms of living matter. We see that the growth of human culture manifests itself in the growth of each special culture. Thus we have come to understand that before we can build up the theory of the growth of all human culture, we must know the growth of cultures that we find here and there among the most primitive tribes of the Arctic, of the deserts of Australia, and of the impenetrable forests of South America; and the progress of the civilization of antiquity and of our own times. We must, so far as we can, reconstruct the actual history of mankind, before we can hope to discover the laws underlying that history.
The Jesup North Pacific Expedition: Memoir of the American Museum of Natural History (1898), Vol. 1, 4.
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Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.
From Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838), as translated by Nathaniel T. Bacon in 'Preface', Researches Into Mathematical Principles of the Theory of Wealth (1897), 4. From the original French, “Quiconque connaît la notation algébrique, lit d'un clin-d'œil dans une équation le résultat auquel on parvient péniblement par des règles de fausse position, dans l'arithmétique de Banque.”
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Architects who have aimed at acquiring manual skill without scholarship have never been able to reach a position of authority to correspond to their pains, while those who relied only upon theories and scholarship were obviously hunting the shadow, not the substance. But those who have a thorough knowledge of both, like men armed at all points, have the sooner attained their object and carried authority with them.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 3.
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As a scientist and geneticist I started to feel that science would probably soon reach the point where its interference into the life processes would be counterproductive if a properly designed governing policy was not implemented. A heavily overcrowded planet, ninety-five percent urbanized with nuclear energy as the main source of energy and with all aspects of life highly computerized, is not too pleasant a place for human life. The life of any individual soon will be predictable from birth to death. Medicine, able to cure almost everything, will make the load of accumulated defects too heavy in the next two or three centuries. The artificial prolongation of life, which looked like a very bright idea when I started research in aging about twenty-five years ago, has now lost its attractiveness for me. This is because I now know that the aging process is so multiform and complex that the real technology and chemistry of its prevention by artificial interference must be too complex and expensive. It would be the privilege of a few, not the method for the majority. I also was deeply concerned about the fact that most research is now either directly or indirectly related to military projects and objectives for power.
Quoted in 'Zhores A(leksandrovich) Medvedev', Contemporary Authors Online, Gale, 2002.
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As geologists, we learn that it is not only the present condition of the globe that has been suited to the accommodation of myriads of living creatures, but that many former states also have been equally adapted to the organization and habits of prior races of beings. The disposition of the seas, continents, and islands, and the climates have varied; so it appears that the species have been changed, and yet they have all been so modelled, on types analogous to those of existing plants and animals, as to indicate throughout a perfect harmony of design and unity of purpose. To assume that the evidence of the beginning or end of so vast a scheme lies within the reach of our philosophical inquiries, or even of our speculations, appears to us inconsistent with a just estimate of the relations which subsist between the finite powers of man and the attributes of an Infinite and Eternal Being.
Concluding remark, Principles of Geology(1833), Vol. 3, 384-5.
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As man advances in civilisation, and small tribes are united into larger communities, the simplest reason would tell each individual that he ought to extend his social instincts and sympathies to all the members of the same nation, though personally unknown to him. This point being once reached, there is only an artificial barrier to prevent his sympathies extending to the men of all nations and races.
…...
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As new areas of the world came into view through exploration, the number of identified species of animals and plants grew astronomically. By 1800 it had reached 70,000. Today more than 1.25 million different species, two-thirds animal and one-third plant, are known, and no biologist supposes that the count is complete.
In The Intelligent Man's Guide to Science: The Biological Sciences (1960), 654. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 320.
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As our researches have made clear, an animal high in the organic scale only reaches this rank by passing through all the intermediate states which separate it from the animals placed below it. Man only becomes man after traversing transitional organisatory states which assimilate him first to fish, then to reptiles, then to birds and mammals.
Annales des Sciences Naturelles (1834), 2 (ii), 248. Trans. in E. S. Russell, Form and Function (1916), 82.
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As our technology evolves, we will have the capacity to reach new, ever-increasing depths. The question is: What kind of technology, in the end, do we want to deploy in the far reaches of the ocean? Tools of science, ecology and documentation, or the destructive tools of heavy industry? Some parts of our oceans, like the rich and mysterious recesses of our Atlantic submarine canyons and seamounts, are so stunning and sensitive they deserve to be protected from destructive activities.
In 'Ocean Oases: Protecting Canyons & Seamounts of the Atlantic Coast', The Huffington Post (8 Jun 2011).
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Astronomers and physicists, dealing habitually with objects and quantities far beyond the reach of the senses, even with the aid of the most powerful aids that ingenuity has been able to devise, tend almost inevitably to fall into the ways of thinking of men dealing with objects and quantities that do not exist at all, e.g., theologians and metaphysicians. Thus their speculations tend almost inevitably to depart from the field of true science, which is that of precise observation, and to become mere soaring in the empyrean. The process works backward, too. That is to say, their reports of what they pretend actually to see are often very unreliable. It is thus no wonder that, of all men of science, they are the most given to flirting with theology. Nor is it remarkable that, in the popular belief, most astronomers end by losing their minds.
Minority Report: H. L. Mencken’s Notebooks (1956), Sample 74, 60.
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Astronomers have built telescopes which can show myriads of stars unseen before; but when a man looks through a tear in his own eye, that is a lens which opens reaches into the unknown, and reveals orbs which no telescope, however skilfully constructed, could do.
Life Thoughts (1858), 20.
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At first sight nothing seems more obvious than that everything has a beginning and an end, and that everything can be subdivided into smaller parts. Nevertheless, for entirely speculative reasons the philosophers of Antiquity, especially the Stoics, concluded this concept to be quite unnecessary. The prodigious development of physics has now reached the same conclusion as those philosophers, Empedocles and Democritus in particular, who lived around 500 B.C. and for whom even ancient man had a lively admiration.
'Development of the Theory of Electrolytic Dissociation', Nobel Lecture, 11 December 1903. In Nobel Lectures: Chemistry 1901-1921 (1966), 45.
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At length being at Clapham where there is, on the common, a large pond which, I observed to be one day very rough with the wind, I fetched out a cruet of oil and dropt a little of it on the water. I saw it spread itself with surprising swiftness upon the surface; but the effect of smoothing the waves was not produced; for I had applied it first on the leeward side of the pond, where the waves were largest, and the wind drove my oil back upon the shore. I then went to the windward side, where they began to form; and there the oil, though not more than a tea-spoonful, produced an instant calm over a space several yards square, which spread amazingly, and extended itself gradually till it reached the leeside, making all that quarter of the pond, perhaps half an acre, as smooth as a looking-glass.
[Experiment to test an observation made at sea in 1757, when he had seen the wake of a ship smoothed, explained by the captain as presumably due to cooks emptying greasy water in to the sea through the scuppers.]
Letter, extract in 'Of the still of Waves by Means of Oil The Gentleman's Magazine (1775), Vol. 45, 82.
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At night I would return home, set out a lamp before me, and devote myself to reading and writing. Whenever sleep overcame me or I became conscious of weakening, I would turn aside to drink a cup of wine, so that my strength would return to me. Then I would return to reading. And whenever sleep seized me I would see those very problems in my dream; and many questions became clear to me in my sleep. I continued in this until all of the sciences were deeply rooted within me and I understood them as is humanly possible. Everything which I knew at the time is just as I know it now; I have not added anything to it to this day. Thus I mastered the logical, natural, and mathematical sciences, and I had now reached the science.
Avicenna
W. E. Gohhnan, The Life of Ibn Sina: A Critical Edition and Annotated Translation (1974), 29-31.
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Boundaries which mark off one field of science from another are purely artificial, are set up only for temporary convenience. Let chemists and physicists dig deep enough, and they reach common ground.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 183.
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By the end of the next century, the “greenhouse effect” may increase temperatures worldwide to levels that have not been reached for at least 100,000 years. And the effects on sea level and on agriculture and other human activities are likely to be so profound that we should be planning for them now.
In 'Temperatures Rise in the Global Greenhouse', New Scientist (15 May 1986), 110, No. 1508, 32.
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Can I pay any higher tribute to a man [George Gaylord Simpson] than to state that his work both established a profession and sowed the seeds for its own revision? If Simpson had reached final truth, he either would have been a priest or would have chosen a dull profession. The history of life cannot be a dull profession.
From 'G.G. Simpson, Paleontology, and the Modern Synthesis', collected in Ernst Mayr, William B. Provine (eds.), The Evolutionary Synthesis: Perspectives on the Unification of Biology (1998), 171.
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Can the cause be reached from knowledge of the effect with the same certainty as the effect can be shown to follow from its cause? Is it possible for one effect to have many causes? If one determinate cause cannot be reached from the effect, since there is no effect which has not some cause, it follows that an effect, when it has one cause, may have another, and so that there may be several causes of it.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 81.
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Chemical analysis and synthesis go no farther than to the separation of particles one from another, and to their reunion. No new creation or destruction of matter is within the reach of chemical agency. We might as well attempt to introduce a new planet into the solar system, or to annihilate one already in existence, as to create or destroy a particle of hydrogen.
A New System of Chemical Philosophy (1808), Vol. 1, 212.
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Clearly it is not reason that has failed. What has failed—as it has always failed—is the attempt to achieve certainty, to reach an absolute, to find the course of human events to a final end. ... It is not reason that has promised to eliminate risk in human undertakings; it is the emotional needs of men.
In The Quest For Identity (1958), 135.
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Decades spent in contact with science and its vehicles have directed my mind and senses to areas beyond their reach. I now see scientific accomplishments as a path, not an end; a path leading to and disappearing in mystery. Science, in fact, forms many paths branching from the trunk of human progress; and on every periphery they end in the miraculous. Following these paths far enough, one must eventually conclude that science itself is a miracle—like the awareness of man arising from and then disappearing in the apparent nothingness of space. Rather than nullifying religion and proving that “God is dead,” science enhances spiritual values by revealing the magnitudes and minitudes—from cosmos to atom—through which man extends and of which he is composed.
A Letter From Lindbergh', Life (4 Jul 1969), 60B. In Eugene C. Gerhart, Quote it Completely! (1998), 409.
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Do not expect to be hailed as a hero when you make your great discovery. More likely you will be a ratbag—maybe failed by your examiners. Your statistics, or your observations, or your literature study, or your something else will be patently deficient. Do not doubt that in our enlightened age the really important advances are and will be rejected more often than acclaimed. Nor should we doubt that in our own professional lifetime we too will repudiate with like pontifical finality the most significant insight ever to reach our desk.
Theories of the Earth and Universe (1988), 365.
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Does it not seem as if Algebra had attained to the dignity of a fine art, in which the workman has a free hand to develop his conceptions, as in a musical theme or a subject for a painting? It has reached a point where every properly developed algebraical composition, like a skillful landscape, is expected to suggest the notion of an infinite distance lying beyond the limits of the canvas.
In 'Lectures on the Theory of Reciprocants', Lecture XXI, American Journal of Mathematics (Jul 1886), 9, No. 3, 136.
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Each human life is unique, born of a miracle that reaches beyond laboratory science.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 42
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Egypt has been called the Gift of the Nile. Once every year the river overflows its banks, depositing a layer of rich alluvial soil on the parched ground. Then it recedes and soon the whole countryside, as far as the eye can reach, is covered with Egyptologists.
In 'Cheops, or Khufu', The Decline and Fall of Practically Everybody (1950), 7.
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Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special eory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes no authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.
Variety of Men (1966), 100-1.
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Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached.
In Physics and Philosophy: The Revolution in Modern Science (1958, 1962), 168.
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Even in populous districts, the practice of medicine is a lonely road which winds up-hill all the way and a man may easily go astray and never reach the Delectable Mountains unless he early finds those shepherd guides of whom Bunyan tells, Knowledge, Experience, Watchful, and Sincere.
In Aequanimitas (1904), 299.
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Even mistaken hypotheses and theories are of use in leading to discoveries. This remark is true in all the sciences. The alchemists founded chemistry by pursuing chimerical problems and theories which are false. In physical science, which is more advanced than biology, we might still cite men of science who make great discoveries by relying on false theories. It seems, indeed, a necessary weakness of our mind to be able to reach truth only across a multitude of errors and obstacles.
An Introduction to the Study of Experimental Medicine (1865, translation 1927, 1957), 170.
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Eventually, we reach … the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial.
In Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202. The lecture series was delivered at Yale University in Fall 1935. Part of a longer quote on this page that begins: “The explorations of space…”.
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Every instant she commences an immense journey, and every instant she has reached her goal.
As quoted by T.H. Huxley, in Norman Lockyer (ed.), 'Nature: Aphorisms by Goethe', Nature (1870), 1, 10.
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Every rule has its limits, and every concept its ambiguities. Most of all is this true in the science of life, where nothing quite corresponds to our ideas; similar ends are reached by varied means, and no causes are simple.
In Internal Factors in Evolution (1965), 13.
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Faith is a knowledge within the heart, beyond the reach of proof.
In The Kahlil Gibran Reader: Inspirational Writings (2006), 38.
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For we are dwelling in a hollow of the earth, and fancy that we are on the surface… . But the fact is, that owing to our feebleness and sluggishness we are prevented from reaching the surface of the air.
Plato
In Plato and B. Jowett (trans.), The Dialogues of Plato: Republic (2nd ed., 1875), Vol. 1, 490.
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Form your life humanly, and you have done enough: but you will never reach the height of art and the depth of science without something divine.
Idea 68. In Friedrich Schlegel, translated by Ernst Behler and Roman Struc, Dialogue on Poetry and Literary Aphorisms (trans. 1968), 155.
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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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Gauss [replied], when asked how soon he expected to reach certain mathematical conclusions, “that he had them long ago, all he was worrying about was how to reach them.”
In Louis Pasteur, Free Lance of Science (1950), 365. Also excerpted in 'Mechanisms of Discovery', collected in I.S. Gordon and S. Sorkin (eds.) The Armchair Science Reader (1959), 336.
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Genius is supposed to be a power of producing excellences which are put of the reach of the rules of art: a power which no precepts can teach, and which no industry can acquire.
From 'A Discourse Delivered to the Students of the Royal Academy, on the Distribution of Prizes' (10 Dec 1774), in Seven Discourses Delivered in the Royal Academy (1778), 202-203.
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God has not revealed all things to man and has entrusted us with but a fragment of His mighty work. But He who directs all things, who has established and laid the foundation of the world, who has clothed Himself with Creation, He is greater and better than that which He has wrought. Hidden from our eyes, He can only be reached by the spirit.
From Quaestiones Naturales as translated in Charles Singer, From Magic to Science (1958), 57.
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Good applied science in medicine, as in physics, requires a high degree of certainty about the basic facts at hand, and especially about their meaning, and we have not yet reached this point for most of medicine.
The Medusa and the Snail (1979), 143.
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He seemed to approach the grave as an hyperbolic curve approaches a line, less directly as he got nearer, till it was doubtful if he would ever reach it at all.
In Far from the Madding Crowd (1874, 1909), Chap. 15, 117. In the 1874 edition, “—sheering off” were the original words, replaced by “less directly” by the 1909 edition.
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How near one Species to the next is join'd,
The due Gradations please a thinking Mind;
and there are Creatures which no eye can see,
That for a Moment live and breathe like me:
Whom a small Fly in bulk as far exceeds,
As yon tall Cedar does the waving Reeds:
These we can reach—and may we not suppose
There still are Creatures more minute than those.
'The Enquiry'. In Poems Upon Several Occasions (1748), 198.
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How twins are born my discourse will explain thus. The cause is chiefly the nature of the womb in woman. For if it has grown equally on either side of its mouth, and if it opens equally, and also dries equally after menstruation, it can give nourishment, if it conceive the secretion of the man so that it immediately divides into both parts of the womb equally. Now if the seed secreted from both parents be abundant and strong, it can grow in both places, as it masters the nourishment that reaches it. In all other cases twins are not formed. Now when the secretion from both parents is male, of necessity boys are begotten in both places; but when from both it is female, girls are begotten. But when one secretion is female and the other male, whichever masters the other gives the embryo its sex. Twins are like one another for the following reasons. First, the places are alike in which they grow; then they were secreted together; then they grow by the same nourishment, and at birth they reach together the light of day.
Regimen, in Hippocrates, trans. W. H. S. Jones (1931), Vol. 4, 273.
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I always keep two legs going, with one trying to reach ahead.
Quoted in James Gleick, Genius: the Life and Science of Richard Feynman (1993), 93.
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I am convinced that an important stage of human thought will have been reached when the physiological and the psychological, the objective and the subjective, are actually united, when the tormenting conflicts or contradictions between my consciousness and my body will have been factually resolved or discarded.
Physiology of the Higher Nervous Activity (1932), 93-4.
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I am reminded of the great French Marshal Lyautey, who once asked his gardener to plant a tree. The gardener objected that the tree was slow-growing and would not reach maturity for a hundred years. The Marshal replied, “In that case, there is no time to lose, plant it this afternoon.”
Address at the University of California, Berkeley, California (23 March 1962), in Public Papers of the Presidents of the United States: John F. Kennedy (1962), 266. Kennedy used this story several times. The indicated source, Marshal Lyautey, has not been verified. Contact Webmaster if you know a primary source.
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I became expert at dissecting crayfish. At one point I had a crayfish claw mounted on an apparatus in such a way that I could operate the individual nerves. I could get the several-jointed claw to reach down and pick up a pencil and wave it around. I am not sure that what I was doing had much scientific value, although I did learn which nerve fiber had to be excited to inhibit the effects of another fiber so that the claw would open. And it did get me interested in robotic instrumentation, something that I have now returned to. I am trying to build better micromanipulators for surgery and the like.
In Jeremy Bernstein, 'A.I.', The New Yorker (14 Dec 1981).
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I believed that, instead of the multiplicity of rules that comprise logic, I would have enough in the following four, as long as I made a firm and steadfast resolution never to fail to observe them.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 16.
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I can’t change the direction of the wind, but I can adjust my sails to always reach my destination.
…...
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I feel a desperation to make people see what we are doing to the environment, what a mess we are making of our world. At this point, the more people I reach, the more I accomplish. … I miss Gombe and my wonderful years in the forest But if I were to go back to that, I wouldn’t feel I was doing what I should be doing.
Answering the question, “Why have you transferred your energies from animal research to activism?” From interview by Tamar Lewin, 'Wildlife to Tireless Crusader, See Jane Run', New York Times (20 Nov 2000), F35.
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I have looked further into space than ever human being did before me. I have observed stars of which the light, it can be proved, must take two million years to reach the earth.
Having identified Uranus (1781), the first planet discovered since antiquity. Quoted in Constance Anne Lubbock, The Herschel Chronicle: the Life-story of William Herschel and his Sister, Caroline Herschel (1933), 336.
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I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain … But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.
(1891) As quoted in translation in Leo Koenigsberger and Frances A. Welby (trans.), Hermann von Helmholtz (1906), 180-181.
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I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations. … For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it.
Although this preface would have been assumed by contemporary readers to be written by Copernicus, it was unsigned. It is now believed to have been written and added at press time by Andreas Osiander (who was then overseeing the printing of the book). It suggests the earth’s motion as described was merely a mathematical device, and not to be taken as absolute reality. Text as given in 'To the Reader on the Hypotheses in this Work', Copernicus: On the Revolutions of the Heavenly Spheres (1543), translated by ‎Alistair Matheson Duncan (1976), 22-3. By adding this preface, Osiander wished to stave off criticism by theologians. See also the Andreas Osiander Quotes page of this website.
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I have now reached the point where I may indicate briefly what to me constitutes the essence of the crisis of our time. It concerns the relationship of the individual to society. The individual has become more conscious than ever of his dependence upon society. But he does not experience this dependence as a positive asset, as an organic tie, as a protective force, but rather as a threat to his natural rights, or even to his economic existence. Moreover, his position in society is such that the egotistical drives of his make-up are constantly being accentuated, while his social drives, which are by nature weaker, progressively deteriorate. All human beings, whatever their position in society, are suffering from this process of deterioration. Unknowingly prisoners of their own egotism, they feel insecure, lonely, and deprived of the naive, simple, and unsophisticated enjoyment of life. Man can find meaning in life, short and perilous as it is, only through devoting himself to society.
…...
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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 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 never could do anything with figures, never had any talent for mathematics, never accomplished anything in my efforts at that rugged study, and to-day the only mathematics I know is multiplication, and the minute I get away up in that, as soon as I reach nine times seven— [He lapsed into deep thought, trying to figure nine times seven. Mr. McKelway whispered the answer to him.] I’ve got it now. It’s eighty-four. Well, I can get that far all right with a little hesitation. After that I am uncertain, and I can’t manage a statistic.
Speech at the New York Association for Promoting the Interests of the Blind (29 Mar 1906). In Mark Twain and William Dean Howells (ed.), Mark Twain’s Speeches? (1910), 323.
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I should rejoice to see … Euclid honourably shelved or buried “deeper than did ever plummet sound” out of the schoolboys’ reach; morphology introduced into the elements of algebra; projection, correlation, and motion accepted as aids to geometry; the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrines of the imaginary and inconceivable.
From Presidential Address (1869) to the British Association, Exeter, Section A, collected in Collected Mathematical Papers of Lames Joseph Sylvester (1908), Vol. 2, 657. Also in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 93. [Note: “plummet sound” refers to ocean depth measurement (sound) from a ship using a line dropped with a weight (plummet). —Webmaster]
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I tell young people to reach for the stars. And I can't think of a greater high than you could possibly get than by inventing something.
From audio on MIT video '1999 Lemelson-MIT Lifetime Achievement Award Winner', on 'Innovative Lives: Stephanie Kwolek and Kevlar, The Wonder Fiber' on the Smithsonian website.
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I think that space flight is a condition of Nature that comes into effect when an intelligent species reaches the saturation point of its planetary habitat combined with a certain level of technological ability... I think it is a built-in gene-directed drive for the spreading of the species and its continuation.
…...
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I've found out so much about electricity that I've reached the point where I understand nothing and can explain nothing.
[Describing his experiments with the Leyden jar.]
Letter to Réamur (20 Jan 1746), in AS. Proc. verb., LXV (1746), 6. Cited in J. L. Heilbron, Electricity in the 17th and 18th Centuries: a Study of Early Modern Physics (1979), 314.
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Ideas are like stars: You will not succeed in touching them with your hands, but like the seafaring man on the ocean desert of waters, you choose them as your guides, and following them, you reach your destiny.
…...
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If all economists were laid end to end, they would not reach a conclusion.
Anonymous
Often seen misattributed (?) to George Bernard Shaw, but there appears to be no source in the writings of Shaw. However, the theme "laid end to end, they would not" has long been used humorously in various incarnations. For example, “If all the arguments in the world were placed end to end, they would not reach any conclusion”, as used by Tom Sims in 'Tom Sims Says', Brownwood Bulletin (18 Jul 1925), 4. The subject quote was attributed to Shaw by George Soule in 'Bridges to the Unknown', in The Saturday Review of Literature (20 May 1933), 9, No. 44, 601. See discussion on the quoteinvestigator.com website.
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If and when all the laws governing physical phenomena are finally discovered, and all the empirical constants occurring in these laws are finally expressed through the four independent basic constants, we will be able to say that physical science has reached its end, that no excitement is left in further explorations, and that all that remains to a physicist is either tedious work on minor details or the self-educational study and adoration of the magnificence of the completed system. At that stage physical science will enter from the epoch of Columbus and Magellan into the epoch of the National Geographic Magazine!
'Any Physics Tomorrow', Physics Today, January 1949, 2, 17.
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If any one should ask me what I consider the most distinctive, progressive feature of California, I should answer promptly, its cable-car system. And it is not alone its system which seems to have reached a point of perfection, but the amazing length of the ride that is given you for the chink of a nickel. I have circled this city of San Francisco, … for this smallest of Southern coins.
In Letters from California (1888), 33.
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If one in twenty does not seem high enough odds, we may, if we prefer it, draw the line at one in fifty (the 2 per cent. point), or one in a hundred (the 1 per cent. point). Personally, the writer prefers to set a low standard of significance at the 5 per cent. point, and ignore entirely all results which fail to reach this level. A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance.
'The Arrangement of Field Experiments', The Journal of the Ministry of Agriculture, 1926, 33, 504.
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If one of these people, in whom the chance-worship of our remoter ancestors thus strangely survives, should be within reach of the sea when a heavy gale is blowing, let him betake himself to the shore and watch the scene. Let him note the infinite variety of form and size of the tossing waves out at sea; or against the curves of their foam-crested breakers, as they dash against the rocks; let him listen to the roar and scream of the shingle as it is cast up and torn down the beach; or look at the flakes of foam as they drive hither and thither before the wind: or note the play of colours, which answers a gleam of sunshine as it falls upon their myriad bubbles. Surely here, if anywhere, he will say that chance is supreme, and bend the knee as one who has entered the very penetralia of his divinity. But the man of science knows that here, as everywhere, perfect order is manifested; that there is not a curve of the waves, not a note in the howling chorus, not a rainbow-glint on a bubble, which is other than a necessary consequence of the ascertained laws of nature; and that with a sufficient knowledge of the conditions, competent physico-mathematical skill could account for, and indeed predict, every one of these 'chance' events.
In 'On the Reception of the Origin of Species'. In Francis Darwin (ed.), The Life and Letters of Charles Darwin, Including an Autobiographical Chapter (1888), Vol. 2, 200-1.
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If the atoms in [a] decimetre cube of lead were all put into a chain side by side the same distance apart as they are in the normal lead, the strings of atoms so formed would reach over six million million miles.
In Lecture (1936) on 'Forty Years of Atomic Theory', collected in Needham and Pagel (eds.) in Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 99.
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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 the finding of Coines, Medals, Urnes, and other Monuments of famous Persons, or Towns, or Utensils, be admitted for unquestionable Proofs, that such Persons or things have, in former Times, had a being, certainly those Petrifactions may be allowed to be of equal Validity and Evidence, that there have been formerly such Vegetables or Animals. These are truly Authentick Antiquity not to be counterfeited, the Stamps, and Impressions, and Characters of Nature that are beyond the Reach and Power of Humane Wit and Invention, and are true universal Characters legible to all rational Men.
Lectures and Discourses of Earthquakes (1668). In The Posthumous Works of Robert Hooke, containing his Cutlerian Lectures and other Discourses read at the Meetings of the Illustrious Royal Society (1705), 449.
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If the world may be thought of as a certain definite quantity of force and as a certain definite number of centers of force—and every other representation remains indefinite and therefore useless—it follows that, in the great dice game of existence, it must pass through calculable number of combinations. In infinite time, every possible combination would at some time or another be realized; more: it would be realized an infinite number of times. And since between every combination and its next recurrence all other possible combinations would have to take place, and each of these combination conditions of the entire sequence of combinations in the same series, a circular movement of absolutely identical series is thus demonstrated: the world as a circular movement that has already repeated itself infinitely often and plays its game in infinitum. This conception is not simply a mechanistic conception; for if it were that, it would not condition an infinite recurrence of identical cases, but a final state. Because the world has not reached this, mechanistic theory must be considered an imperfect and merely provisional hypothesis.
The Will to Power (Notes written 1883-1888), book 4, no. 1066. Trans. W. Kaufmann and R. J. Hollingdale and ed. W. Kaufmann (1968), 549.
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If you stacked all the US currency together, you could probably reach the moon, but I bet the Apollo programme was still more economical.
In Geoff Tibballs, The Mammoth Book of Zingers, Quips, and One-Liners (2004), 502. If you know the primary source, please contact Webmaster.
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In 1768, some peasants, near Luce in France, heard a thunderclap and saw a large stone fall from the sky. Reports of this strange phenomenon reached the French Academy of Sciences. The Academy asked Lavoisier, the premier chemist, to investigate. Lavoisier knew that stones do not fall out of the sky; so, in his knowledgeable arrogance, he reported that the witnesses were either lying or mistaken. The academy did not accept the fact of meteorites until the following century.
In 'Forum: A Case of Spontaneous Human Combustion', New Scientist (15 May 1986), 70.
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In a University we are especially bound to recognise not only the unity of science itself, but the communion of the workers in science. We are too apt to suppose that we are congregated here merely to be within reach of certain appliances of study, such as museums and laboratories, libraries and lecturers, so that each of us may study what he prefers. I suppose that when the bees crowd round the flowers it is for the sake of the honey that they do so, never thinking that it is the dust which they are carrying from flower to flower which is to render possible a more splendid array of flowers, and a busier crowd of bees, in the years to come. We cannot, therefore, do better than improve the shining hour in helping forward the cross-fertilization of the sciences.
'The Telephone', Nature, 15, 1878. In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 743-4.
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In early times, when the knowledge of nature was small, little attempt was made to divide science into parts, and men of science did not specialize. Aristotle was a master of all science known in his day, and wrote indifferently treatises on physics or animals. As increasing knowledge made it impossible for any one man to grasp all scientific subjects, lines of division were drawn for convenience of study and of teaching. Besides the broad distinction into physical and biological science, minute subdivisions arose, and, at a certain stage of development, much attention was, given to methods of classification, and much emphasis laid on the results, which were thought to have a significance beyond that of the mere convenience of mankind.
But we have reached the stage when the different streams of knowledge, followed by the different sciences, are coalescing, and the artificial barriers raised by calling those sciences by different names are breaking down. Geology uses the methods and data of physics, chemistry and biology; no one can say whether the science of radioactivity is to be classed as chemistry or physics, or whether sociology is properly grouped with biology or economics. Indeed, it is often just where this coalescence of two subjects occurs, when some connecting channel between them is opened suddenly, that the most striking advances in knowledge take place. The accumulated experience of one department of science, and the special methods which have been developed to deal with its problems, become suddenly available in the domain of another department, and many questions insoluble before may find answers in the new light cast upon them. Such considerations show us that science is in reality one, though we may agree to look on it now from one side and now from another as we approach it from the standpoint of physics, physiology or psychology.
In article 'Science', Encyclopedia Britannica (1911), 402.
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In India we have clear evidence that administrative statistics had reached a high state of organization before 300 B.C. In the Arthasastra of Kautilya … the duties of the Gopa, the village accountant, [include] “by setting up boundaries to villages, by numbering plots of grounds as cultivated, uncultivated, plains, wet lands, gardens, vegetable gardens, fences (váta), forests altars, temples of gods, irrigation works, cremation grounds, feeding houses (sattra), places where water is freely supplied to travellers (prapá), places of pilgrimage, pasture grounds and roads, and thereby fixing the boundaries of various villages, of fields, of forests, and of roads, he shall register gifts, sales, charities, and remission of taxes regarding fields.”
Editorial, introducing the new statistics journal of the Indian Statistical Institute, Sankhayā (1933), 1, No. 1. Also reprinted in Sankhyā: The Indian Journal of Statistics (Feb 2003), 65, No. 1, viii.
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In mathematics it is notorious that we start from absurdities to reach a realm of law, and our whole (mathematical) conception of the world is based on a foundation which we believe to have no existence.
In The Dance of Life (1923), 86.
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In my opinion instruction is very purposeless for such individuals who do no want merely to collect a mass of knowledge, but are mainly interested in exercising (training) their own powers. One doesn't need to grasp such a one by the hand and lead him to the goal, but only from time to time give him suggestions, in order that he may reach it himself in the shortest way.
Letter to Heinrich Schumacher (2 Oct 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
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In our day grand generalizations have been reached. The theory of the origin of species is but one of them. Another, of still wider grasp and more radical significance, is the doctrine of the Conservation of Energy, the ultimate philosophical issues of which are as yet but dimly seem-that doctrine which “binds nature fast in fate” to an extent not hitherto recognized, exacting from every antecedent its equivalent consequent, and bringing vital as well as physical phenomena under the dominion of that law of causal connexion which, so far as the human understanding has yet pierced, asserts itself everywhere in nature.
'Address Delivered Before The British Association Assembled at Belfast', (19 Aug 1874). Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 1801.
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In scientific matters ... the greatest discoverer differs from the most arduous imitator and apprentice only in degree, whereas he differs in kind from someone whom nature has endowed for fine art. But saying this does not disparage those great men to whom the human race owes so much in contrast to those whom nature has endowed for fine art. For the scientists' talent lies in continuing to increase the perfection of our cognitions and on all the dependent benefits, as well as in imparting that same knowledge to others; and in these respects they are far superior to those who merit the honour of being called geniuses. For the latter's art stops at some point, because a boundary is set for it beyond which it cannot go and which has probably long since been reached and cannot be extended further.
The Critique of Judgement (1790), trans. J. C. Meredith (1991), 72.
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In the conception of a machine or the product of a machine there is a point where one may leave off for parsimonious reasons, without having reached aesthetic perfection; at this point perhaps every mechanical factor is accounted for, and the sense of incompleteness is due to the failure to recognize the claims of the human agent. Aesthetics carries with it the implications of alternatives between a number of mechanical solutions of equal validity; and unless this awareness is present at every stage of the process … it is not likely to come out with any success in the final stage of design.
From 'The Esthetic Assimilation of the Machine', Technics and Civilization (1934), 349.
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In the infancy of physical science, it was hoped that some discovery might be made that would enable us to emancipate ourselves from the bondage of gravity, and, at least, pay a visit to our neighbour the moon. The poor attempts of the aeronaut have shewn the hopelessness of the enterprise. The success of his achievement depends on the buoyant power of the atmosphere, but the atmosphere extends only a few miles above the earth, and its action cannot reach beyond its own limits. The only machine, independent of the atmosphere, we can conceive of, would be one on the principle of the rocket. The rocket rises in the air, not from the resistance offered by the atmosphere to its fiery stream, but from the internal reaction. The velocity would, indeed, be greater in a vacuum than in the atmosphere, and could we dispense with the comfort of breathing air, we might, with such a machine, transcend the boundaries of our globe, and visit other orbs.
God's Glory in the Heavens (1862, 3rd Ed. 1867) 3-4.
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In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.
Letter to Ernst Weber (21 May 1843). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
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In the sense that [truth] means the reality about a human being it is probably impossible for a biographer to achieve. In the sense that it means a reasonable presentation of all the available facts it is more nearly possible, but even this limited goal is harder to reach than it appears to be. A biographer needs to be both humble and cautious.
Describing the difficulty of historical sources giving conflicting facts. From 'Getting at the Truth', The Saturday Review (19 Sep 1953), 36, No. 38, 11. Excerpted in Meta Riley Emberger and Marian Ross Hall, Scientific Writing (1955), 399.
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Invention is an Heroic thing, and plac'd above the reach of a low, and vulgar Genius. It requires an active, a bold, a nimble, a restless mind: a thousand difficulties must be contemn'd with which a mean heart would be broken: many attempts must be made to no purpose: much Treasure must sometimes be scatter'd without any return: much violence, and vigour of thoughts must attend it: some irregularities, and excesses must be granted it, that would hardly be pardon'd by the severe Rules of Prudence.
The History of the Royal Society (1667), 392.
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It has been just so in all my inventions. The first step is an intuition—and comes with a burst, then difficulties arise. This thing that gives out and then that—“Bugs”as such little faults and difficulties are called show themselves and months of anxious watching, study and labor are requisite before commercial success—or failure—is certainly reached.
[Describing his invention of a storage battery that involved 10,296 experiments. Note Edison's use of the term “Bug” in the engineering research field for a mechanical defect greatly predates the use of the term as applied by Admiral Grace Murray Hopper to a computing defect upon finding a moth in the electronic mainframe.]
Letter to Theodore Puskas (18 Nov 1878). In The Yale Book of Quotations (2006), 226.
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It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophising? Such might indeed be the right thing to do a time when the physicist believes he has at his disposal a rigid system of fundamental laws which are so well that waves of doubt can't reach them; but it cannot be right at a time when the very foundations of physics itself have become problematic as they are now … when experience forces us to seek a newer and more solid foundation.
‘Physics and Reality’, Franklin Institute Journal (Mar 1936). Collected in Out of My Later Years (1950), 58.
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It is an irony of fate that I myself have been the recipient of excessive admiration and reverence from my fellow-beings, through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the few ideas to which I have with my feeble powers attained through ceaseless struggle. I am quite aware that for any organisation to reach its goals, one man must do the thinking and directing and generally bear the responsibility. But the led must not be coerced, they must be able to choose their leader.
In 'What I Believe', Forum and Century (1930), 84, 193-194.
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It is 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 interesting to observe the result of habit in the peculiar shape and size of the giraffe (Camelo-pardalis): this animal, the largest of the mammals, is known to live in the interior of Africa in places where the soil is nearly always arid and barren, so that it is obliged to browse on the leaves on the trees and to make constant efforts to reach them. From this habit long maintained in all its race, it has resulted that the animal's fore-legs have become longer than its hind legs, and that its neck is lengthened to such a degree that the giraffe, without standing up on its hind legs, attains a height of six metres (nearly 20 feet).
Philosophie Zoologique (1809), Vol. 1, 256, trans. Hugh Elliot (1914), 122.
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It is not failure but success that is forcing man off this earth. It is not sickness but the triumph of health... Our capacity to survive has expanded beyond the capacity of Earth to support us. The pains we are feeling are growing pains. We can solve growth problems in direct proportion to our capacity to find new worlds... If man stays on Earth, his extinction is sure even if he lasts till the sun expands and destroys him... It is no longer reasonable to assume that the meaning of life lies on this earth alone. If Earth is all there is for man, we are reaching the foreseeable end of man.
…...
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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 is the individual only who is timeless. Societies, cultures, and civilizations - past and present - are often incomprehensible to outsiders, but the individual’s hunger, anxieties, dreams, and preoccupations have remained unchanged through the millennia. Thus, we are up against the paradox that the individual who is more complex, unpredictable, and mysterious than any communal entity is the one nearest to our understanding; so near that even the interval of millennia cannot weaken our feeling of kinshiIf in some manner the voice of an individual reaches us from the remotest distance of time, it is a timeless voice speaking about ourselves.
In Reflections on the Human Condition (1973), 97.
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It is, as Schrödinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 537.
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It must be borne in mind that the tragedy of life doesn’t lie in not reaching your goal. The tragedy lies in having no goal to reach. It isn’t a calamity to die with dreams unfulfilled, but it is a calamity not to dream. It is not a disaster to be unable to capture your idea, but it is disaster to have no idea to capture. It is not a disgrace not to reach for the stars, but it is a disgrace to have no stars to reach for. Not failure, but low aim is a sin.
…...
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It must not be thought that it is ever possible to reach the interior earth by any perseverance in mining: both because the exterior earth is too thick, in comparison with human strength; and especially because of the intermediate waters, which would gush forth with greater impetus, the deeper the place in which their veins were first opened; and which would drown all miners.
Principles of Philosophy (1644), trans. V. R. and R. P. Miller (1983), 217-8.
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It sometimes strikes me that the whole of science is a piece of impudence; that nature can afford to ignore our impertinent interference. If our monkey mischief should ever reach the point of blowing up the earth by decomposing an atom, and even annihilated the sun himself, I cannot really suppose that the universe would turn a hair.
The Confessions of Aleister Crowley, ch. 14 (1929, rev 1970).
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It took hundreds of millions of years to produce the life that now inhabits the earth–eons of time in which that developing and evolving and diversifying life reached a state of adjustment and balance with its surroundings.
In Silent Spring (1962), 6.
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It was a dark and stormy night, so R. H. Bing volunteered to drive some stranded mathematicians from the fogged-in Madison airport to Chicago. Freezing rain pelted the windscreen and iced the roadway as Bing drove on—concentrating deeply on the mathematical theorem he was explaining. Soon the windshield was fogged from the energetic explanation. The passengers too had beaded brows, but their sweat arose from fear. As the mathematical description got brighter, the visibility got dimmer. Finally, the conferees felt a trace of hope for their survival when Bing reached forward—apparently to wipe off the moisture from the windshield. Their hope turned to horror when, instead, Bing drew a figure with his finger on the foggy pane and continued his proof—embellishing the illustration with arrows and helpful labels as needed for the demonstration.
In 'R. H. Bing', Biographical Memoirs: National Academy of Sciences (2002), 49. Anecdote based on the recollections of Bing's colleagues, Steve Armentrout and C. E. Burgess. The narrative was given in a memorial tribute at the University of Texas at Austin.
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It will be a vast boon to mankind when we learn to prophesy the precise dates when cycles of various kinds will reach definite stages.
Mainsprings of Civilization (1945), 458.
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It would be wrong to assume that one must stay with a research programme until it has exhausted all its heuristic power, that one must not introduce a rival programme before everybody agrees that the point of degeneration has probably been reached.
In Radio Lecture (30 Jun 1973) broadcast by the Open University, collected in Imre Lakatos, John Worrall (ed.) and Gregory Currie (ed.), 'Introduction: Science and Pseudoscience', The Methodology of Scientific Research Programmes (1978, 1980), Vol. 1, 68.
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It would, of course, be a poor lookout for the advancement of science if young men started believing what their elders tell them, but perhaps it is legitimate to remark that young Turks look younger, or more Turkish ... if the conclusions they eventually reach are different from what anyone had said before.
In Nature, 1969.
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I’ve learned that every day you should reach out and touch someone. People love a warm hug, or just a friendly pat on the back.
Ninth stanza of poem 'On Turning 70'. The poem is printed in Michigan Office of Services to the Aging, Annual Report 2004 (2005), no page number.
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J. J. Sylvester was an enthusiastic supporter of reform [in the teaching of geometry]. The difference in attitude on this question between the two foremost British mathematicians, J. J. Sylvester, the algebraist, and Arthur Cayley, the algebraist and geometer, was grotesque. Sylvester wished to bury Euclid “deeper than e’er plummet sounded” out of the schoolboy’s reach; Cayley, an ardent admirer of Euclid, desired the retention of Simson’s Euclid. When reminded that this treatise was a mixture of Euclid and Simson, Cayley suggested striking out Simson’s additions and keeping strictly to the original treatise.
In History of Elementary Mathematics (1910), 285.
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John Young and Bob Crippen have made us very proud. Their deeds reminded us that we as a free people can accomplish whatever we set out to do. Nothing binds our abilities except our expectations, and, given that, the farthest star is within our reach.
At Oval Office ceremony (20 May 1981) awarding NASA Distinguished Service medals to Young and Crippen, and a Congressional Space Medal of Honor to Young.
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Just as in the animal and vegetable kingdoms, an individual comes into being, so to speak, grows, remains in being, declines and passes on, will it not be the same for entire species? If our faith did not teach us that animals left the Creator's hands just as they now appear and, if it were permitted to entertain the slightest doubt as to their beginning and their end, may not a philosopher, left to his own conjectures, suspect that, from time immemorial, animal life had its own constituent elements, scattered and intermingled with the general body of matter, and that it happened when these constituent elements came together because it was possible for them to do so; that the embryo formed from these elements went through innumerable arrangements and developments, successively acquiring movement, feeling, ideas, thought, reflection, consciousness, feelings, emotions, signs, gestures, sounds, articulate sounds, language, laws, arts and sciences; that millions of years passed between each of these developments, and there may be other developments or kinds of growth still to come of which we know nothing; that a stationary point either has been or will be reached; that the embryo either is, or will be, moving away from this point through a process of everlasting decay, during which its faculties will leave it in the same way as they arrived; that it will disappear for ever from nature-or rather, that it will continue to exist there, but in a form and with faculties very different from those it displays at this present point in time? Religion saves us from many deviations, and a good deal of work. Had religion not enlightened us on the origin of the world and the universal system of being, what a multitude of different hypotheses we would have been tempted to take as nature's secret! Since these hypotheses are all equally wrong, they would all have seemed almost equally plausible. The question of why anything exists is the most awkward that philosophy can raise- and Revelation alone provides the answer.
Thoughts on the Interpretation of Nature and Other Philosophical Works (1753/4), ed. D. Adams (1999), Section LVIII, 75-6.
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Just as, in civil History, one consults title-deeds, one studies coins, one deciphers ancient inscriptions, in order to determine the epochs of human revolutions and to fix the dates of moral [i.e. human] events; so, in Natural History, one must excavate the archives of the world, recover ancient monuments from the depths of the earth, collect their remains, and assemble in one body of proofs all the evidence of physical changes that enable us to reach back to the different ages of Nature. This, then, is the order of the times indicated by facts and monuments: these are six epochs in the succession of the first ages of Nature; six spaces of duration, the limits of which although indeterminate are not less real; for these epochs are not like those of civil History ... that we can count and measure exactly; nevertheless we can compare them with each other and estimate their relative duration.
'Des Époques de la Nature', Histoire Naturelle, Générale et Particulière contenant les Époques de la Nature (1778), Supplement Vol. 9, 1-2, 41. Trans. Martin J. Rudwick.
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Laplace considers astronomy a science of observation, because we can only observe the movements of the planets; we cannot reach them, indeed, to alter their course and to experiment with them. “On earth,” said Laplace, “we make phenomena vary by experiments; in the sky, we carefully define all the phenomena presented to us by celestial motion.” Certain physicians call medicine a science of observations, because they wrongly think that experimentation is inapplicable to it.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 18. A footnote cites Laplace, Système du monde, Chap. 2.
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Laws of Thermodynamics
1) You cannot win, you can only break even.
2) You can only break even at absolute zero.
3) You cannot reach absolute zero.
Anonymous
Folklore amongst physicists.
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Leo Szilard’s Ten Commandments:
1. Recognize the connections of things and the laws of conduct of men, so that you may know what you are doing.
2. Let your acts be directed towards a worthy goal, but do not ask if they will reach it; they are to be models and examples, not means to an end.
3. Speak to all men as you do to yourself, with no concern for the effect you make, so that you do not shut them out from your world; lest in isolation the meaning of life slips out of sight and you lose the belief in the perfection of the creation.
4. Do not destroy what you cannot create.
5. Touch no dish, except that you are hungry.
6. Do not covet what you cannot have.
7. Do not lie without need.
8. Honor children. Listen reverently to their words and speak to them with infinite love.
9. Do your work for six years; but in the seventh, go into solitude or among strangers, so that the memory of your friends does not hinder you from being what you have become.
10. Lead your life with a gentle hand and be ready to leave whenever you are called.
Circulated by Mrs. Szilard in July 1964, in a letter to their friends (translated by Dr. Jacob Bronowski). As printed in Robert J. Levine, Ethics and Regulation of Clinical Research (1988), 431.
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Logic has borrowed the rules of geometry without understanding its power. … I am far from placing logicians by the side of geometers who teach the true way to guide the reason. … The method of avoiding error is sought by every one. The logicians profess to lead the way, the geometers alone reach it, and aside from their science there is no true demonstration.
From De l’Art de Persuader, (1657). Pensées de Pascal (1842), Part 1, Article 3, 41-42. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202. From the original French, “La logique a peut-être emprunté les règles de la géométrie sans en comprendre la force … je serai bien éloigné de les mettre en parallèle avec les géomètres, qui apprennent la véritable méthode de conduire la raison. … La méthode de ne point errer est recherchée de tout le monde. Les logiciens font profession d'y conduire, les géomètres seuls y arrivent; et, hors de leur science …, il n'y a point de véritables démonstrations ….”
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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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Man is slightly nearer to the atom than to the star. … From his central position man can survey the grandest works of Nature with the astronomer, or the minutest works with the physicist. … [K]nowledge of the stars leads through the atom; and important knowledge of the atom has been reached through the stars.
Lecture 1. Stars and Atoms (1928, 2007), 9.
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Mars is there, waiting to be reached.
…...
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Mathematicians assume the right to choose, within the limits of logical contradiction, what path they please in reaching their results.
In A Letter to American Teachers of History (1910), Introduction, v.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics in gross, it is plain, are a grievance in natural philosophy, and with reason…Mathematical proofs are out of the reach of topical arguments, and are not to be attacked by the equivocal use of words or declamation, that make so great a part of other discourses; nay, even of controversies.
In 'Mr Locke’s Reply to the Bishop of Worcester’s Answer to his Second Letter', collected in The Works of John Locke (1824), Vol. 3, 428.
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Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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May the conscience and the common sense of the peoples be awakened, so that we may reach a new stage in the life of nations, where people will look back on war as an incomprehensible aberration of their forefathers!
…...
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Men are weak now, and yet they transform the Earth's surface. In millions of years their might will increase to the extent that they will change the surface of the Earth, its oceans, the atmosphere, and themselves. They will control the climate and the Solar System just as they control the Earth. They will travel beyond the limits of our planetary system; they will reach other Suns, and use their fresh energy instead of the energy of their dying luminary.
In Plan of Space Exploration (1926). Quote as translated in Vitaliĭ Ivanovich Sevastʹi︠a︡nov, Arkadiĭ Dmitrievich Ursul, I︠U︡riĭ Andreevich Shkolenko, The Universe and Civilisation (1981), 104.
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Men who do not know the truth of things try to reach certainty about them, so that, if they cannot satisfy their intellects by science, their wills at least may rest on conscience.
In The New Science (3rd ed., 1744), Book 1, Para. 137, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948), 56.
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Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.
In 'A Plea for the Mathematician', Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.
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My view of the matter, for what it is worth, is that there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process. My view may be expressed by saying that every discovery contains an “irrational element,” or “a creative intuition,” in Bergson's sense. In a similar way Einstein speaks of the “search for those highly universal laws … from which a picture of the world can be obtained by pure deduction. There is no logical path.” he says, “leading to these … laws. They can only be reached by intuition, based upon something like an intellectual love (Einfühlung) of the objects of experience.”
In The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 8.
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Neither art nor science knows anything of moral approval or disapproval. Science is out of the reach of morals, for her eyes are fixed upon eternal truths. Art is out of the reach of morals, for her eyes are fixed upon things beautiful and immortal and ever-changing.
In his dialogue 'The Critic As Artist', collected in Intentions (1891), 156. Also collected in Oscariana: Epigrams (1895), 27.
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Now and then, in the course of the century, a great man of science, like Darwin; a great poet, like Keats; a fine critical spirit, like M. Renan; a supreme artist, like Flaubert, has been able to isolate himself, to keep himself out of reach of the clamorous claims of others, to stand “under the shelter of the wall,” as Plato puts it, and so to realise the perfection of what was in him, to his own incomparable gain, and to the incomparable and lasting gain of the whole world.
In Sebastian Melmoth (1908), 133-134.
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Now Freud may be right or he may be wrong in the place he gives to biology in human fate, but I think we must stop to consider whether this emphasis on biology, whether correct or incorrect, is not so far from being a reactionary idea that it is actually a liberating idea. It proposes to us that culture is not all-powerful. It suggests that there is a residue of human quality beyond the reach of cultural control, and that this residue of human quality, elemental as it may be, serves to bring culture itself under criticism and keeps it from being absolute.
In Freud and the Crisis of our Culture (1955), 48.
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Now, when all these studies reach the point of inter-communion and connection with one another, and come to be considered in their mutual affinities, then, I think, but not till then, will the pursuit of them have a value for our objects: otherwise there is no profit in them.
Plato
From The Republic, Book 7, Chap. 7, 531. As translated in The Dialogues of Plato (1871), Vol. 2, 367.
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October 9, 1863
Always, however great the height of the balloon, when I have seen the horizon it has roughly appeared to be on the level of the car though of course the dip of the horizon is a very appreciable quantity or the same height as the eye. From this one might infer that, could the earth be seen without a cloud or anything to obscure it, and the boundary line of the plane approximately the same height as the eye, the general appearance would be that of a slight concavity; but I have never seen any part of the surface of the earth other than as a plane.
Towns and cities, when viewed from the balloon are like models in motion. I shall always remember the ascent of 9th October, 1863, when we passed over London about sunset. At the time when we were 7,000 feet high, and directly over London Bridge, the scene around was one that cannot probably be equalled in the world. We were still so low as not to have lost sight of the details of the spectacle which presented itself to our eyes; and with one glance the homes of 3,000,000 people could be seen, and so distinct was the view, that every large building was easily distinguishable. In fact, the whole of London was visible, and some parts most clearly. All round, the suburbs were also very distinct, with their lines of detached villas, imbedded as it were in a mass of shrubs; beyond, the country was like a garden, its fields, well marked, becoming smaller and smaller as the eye wandered farther and farther away.
Again looking down, there was the Thames, throughout its whole length, without the slightest mist, dotted over its winding course with innumerable ships and steamboats, like moving toys. Gravesend was visible, also the mouth of the Thames, and the coast around as far as Norfolk. The southern shore of the mouth of the Thames was not so clear, but the sea beyond was seen for many miles; when at a higher elevation, I looked for the coast of France, but was unable to see it. On looking round, the eye was arrested by the garden-like appearance of the county of Kent, till again London claimed yet more careful attention.
Smoke, thin and blue, was curling from it, and slowly moving away in beautiful curves, from all except one part, south of the Thames, where it was less blue and seemed more dense, till the cause became evident; it was mixed with mist rising from the ground, the southern limit of which was bounded by an even line, doubtless indicating the meeting of the subsoils of gravel and clay. The whole scene was surmounted by a canopy of blue, everywhere free from cloud, except near the horizon, where a band of cumulus and stratus extended all round, forming a fitting boundary to such a glorious view.
As seen from the earth, the sunset this evening was described as fine, the air being clear and the shadows well defined; but, as we rose to view it and its effects, the golden hues increased in intensity; their richness decreased as the distance from the sun increased, both right and left; but still as far as 90º from the sun, rose-coloured clouds extended. The remainder of the circle was completed, for the most part, by pure white cumulus of well-rounded and symmetrical forms.
I have seen London by night. I have crossed it during the day at the height of four miles. I have often admired the splendour of sky scenery, but never have I seen anything which surpassed this spectacle. The roar of the town heard at this elevation was a deep, rich, continuous sound the voice of labour. At four miles above London, all was hushed; no sound reached our ears.
Travels in the Air (1871), 99-100.
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On a huge hill, Cragged, and steep, Truth stands, and hee that will
Reach her, about must, and about must goo.
Satyre, III, I. 79-81. The Works of John Donne (Wordsworth edition 1994), 113.
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On a perfect planet such as might be acceptable to a physicist, one might predict that from its origin the diversity of life would grow exponentially until the carrying capacity, however defined, was reached. The fossil record on Earth, however, tells a very different story.
In 'The Evolution of Diversity in AAncient Ecosystems: a Review', Philosophical Transactions of the Royal Society B (28 Feb 1998), 353, No. 1366, 327.
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Once we have judged a thing a work of art, we have judged it ethically of the first importance and put it beyond the reach of the moralist.
In Art (1913), 20.
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One is constantly reminded of the infinite lavishness and fertility of Nature—inexhaustible abundance amid what seems enormous waste. And yet when we look into any of her operations that lie within reach of our minds, we learn that no particle of her material is wasted or worn out. It is eternally flowing from use to use, beauty to yet higher beauty; and we soon cease to lament waste and death, and rather rejoice and exult in the imperishable, unspendable wealth of the universe.
John Muir
In My First Summer in the Sierra (1911), 325. Based on Muir's original journals and sketches of his 1869 stay in the Sierra.
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Our aim is not to make poets, but to allow people to express themselves in a meaningful and appropriate way. We try to get them to enjoy and open up to a point where they can relate—anything to reach the level of their feeling and understanding.
As given in obituary, Myrna Oliver, 'Arthur Lerner; Promoted Use of Poetry in Therapy', Los Angeles Times (8 Apr 1998).
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Philosophy would long ago have reached a high level if our predecessors and fathers had put this into practice; and we would not waste time on the primary difficulties, which appear now as severe as in the first centuries which noticed them. We would have the experience of assured phenomena, which would serve as principles for a solid reasoning; truth would not be so deeply sunken; nature would have taken off most of her envelopes; one would see the marvels she contains in all her individuals. ...
Les Préludes de l'Harmonie Universelle (1634), 135-139. In Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 316.
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Physics, owing to the simplicity of its subject matter, has reached a higher state of development than any other science. (1931)
In The Scientific Outlook (1931, 2009), 42.
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Qualified scientists in Washington believe that the atom-blasting of Japan is the start toward heating plants the size of telephone booths for great factories, and motor-car trips of 1,000 hours on one gram of fuel. One expert estimated that with a few grams of uranium it might be possible to power the Queen Mary from Europe to the U.S. and back again. One of America’s leading scientists, Doctor Vollrath, said that the new discovery brings man’s attempt to reach the moon within bounds of possibility.
Newspaper
The Maple Leaf (8 Aug 1945), 4.
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Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
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Reach high, for stars lie hidden in your soul. Dream deep, for every dream precedes the goal.
…...
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Reaching the Moon by three-man vessels in one long bound from Earth is like casting a thin thread across space. The main effort, in the coming decades, will be to strengthen this thread; to make it a cord, a cable, and, finally, a broad highway.
In 'The Coming Decades in Space', Boy’s Life (Jun 1972), 8. Reprinted in The Beginning and the End (1977), 203.
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Religion and science ... constitute deep-rooted and ancient efforts to find richer experience and deeper meaning than are found in the ordinary biological and social satisfactions. As pointed out by Whitehead, religion and science have similar origins and are evolving toward similar goals. Both started from crude observations and fanciful concepts, meaningful only within a narrow range of conditions for the people who formulated them of their limited tribal experience. But progressively, continuously, and almost simultaneously, religious and scientific concepts are ridding themselves of their coarse and local components, reaching higher and higher levels of abstraction and purity. Both the myths of religion and the laws of science, it is now becoming apparent, are not so much descriptions of facts as symbolic expressions of cosmic truths.
'On Being Human,' A God Within, Scribner (1972).
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Religions, in fact, like castles, sunsets and women, never reach their maximum of beauty until they are touched by decay.
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Science advances through tentative answers to a series of more and more subtle questions which reach deeper and deeper into the essence of natural phenomena.
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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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Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.
Letter collected in Tamworth Reading Room: Letters on an Address Delivered by Sir Robert Peel, Bart., M.P. on the Establishment of a Reading Room at Tamworth (1841), 32. Excerpted in John Henry Newman, An Essay in Aid of a Grammar of Assent (1870), 89 & 94 footnote.
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Science is like society and trade, in resting at bottom upon a basis of faith. There are some things here, too, that we can not prove, otherwise there would be nothing we can prove. Science is busy with the hither-end of things, not the thither-end. It is a mistake to contrast religion and science in this respect, and to think of religion as taking everything for granted, and science as doing only clean work, and having all the loose ends gathered up and tucked in. We never reach the roots of things in science more than in religion.
From 'Walking by Faith', The Pattern in the Mount: And Other Sermons (1885), 49. The sentence “Science is busy with the hither-end of things, not the thither-end” is quoted alone in collections such as James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 382:35.
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Science is the topography of ignorance. From a few elevated points we triangulate vast spaces, inclosing infinite unknown details. We cast the lead, and draw up a little sand from abysses we may never reach with our dredges.
'Border Lines of Knowledge in Some Provinces of Medical Science', an introductory lecture to the Medical Class of Harvard University (6 Nov 1861). In Works of Oliver Wendell Holmes (1892), 211.
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Science makes people reach selflessly for truth and objectivity; it teaches people to accept reality, with wonder and admiration, not to mention the deep awe and joy that the natural order of things brings to the true scientist.
Lecture, Austrian UNESCO Commision (30 Mar 1953), in Atomenergie und Frieden: Lise Meitner und Otto Hahn (1953), 23-4. Trans. Ruth Sime, Lise Meitner: A Life in Physics (1996), 375.
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Science, in the immediate, produces knowledge and, indirectly, means of action. It leads to methodical action if definite goals are set up in advance. For the function of setting up goals and passing statements of value transcends its domain. While it is true that science, to the extent of its grasp of causative connections, may reach important conclusions as to the compatibility and incompatibility of goals and evaluations, the independent and fundamental definitions regarding goals and values remain beyond science’s reach.
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Scientists still do not appear to understand sufficiently that all earth sciences must contribute evidence toward unveiling the state of our planet in earlier times, and that the truth of the matter can only be reached by combing all this evidence. ... It is only by combing the information furnished by all the earth sciences that we can hope to determine 'truth' here, that is to say, to find the picture that sets out all the known facts in the best arrangement and that therefore has the highest degree of probability. Further, we have to be prepared always for the possibility that each new discovery, no matter what science furnishes it, may modify the conclusions we draw.
The Origins of Continents and Oceans
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See, thro' this air, this ocean, and this earth,
All matter quick, and bursting into birth.
Above, how high progressive life may go!
Around, how wide! how deep extend below!
Vast chain of being, which from God began,
Natures ethereal, human, angel, man,
Beast, bird, fish, insect! what no eye can see,
No glass can reach! from Infinite to thee,
From thee to Nothing—On superior pow'rs
Were we to press, inferior might on ours:
Or in the full creation leave a void,
Where, one step broken, the great scale's destroy'd:
From Nature's chain whatever link you strike,
Tenth or ten thousandth, breaks the chain alike.
'An Essay on Man' (1733-4), Epistle I. In John Butt (ed.), The Poems of Alexander Pope (1965), 513.
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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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Sheppey hath long been noted for producing large quantities of Sheep (whence probably its name is derived) as well as Corn; and exhibits to the Curious Naturalist a most desirable Spot, by affording many rare Plants, and more especially in the of its Northern Cliffs, so great a Quantity and Variety of Fossils, both native and extraneous are scarcely to be paralleled. These Cliffs length about six miles; Minster, Shurland and Warden are the Manors to which they appertain, the more elevated parts whereof reach about thirds of their extension, and are at the very highest of them not less than fifty yards perpendicular height above the Beach and Shore.
Quoted in Augustus A. Daly, History of the Isle of Sheppey (1975), 247.
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Since as the Creation is, so is the Creator also magnified, we may conclude in consequence of an infinity, and an infinite all-active power, that as the visible creation is supposed to be full of siderial systems and planetary worlds, so on, in like similar manner, the endless Immensity is an unlimited plenum of creations not unlike the known Universe.… That this in all probability may be the real case, is in some degree made evident by the many cloudy spots, just perceivable by us, as far without our starry Regions, in which tho’ visibly luminous spaces, no one Star or particular constituent body can possibly be distinguished; those in all likelyhood may be external creation, bordering upon the known one, too remote for even our Telescopes to reach.
In The Universe and the Stars: Being an Original Theory on the Visible Creation, Founded on the Laws of Nature (1750, 1837), 143-144.
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Sir,—The Planet [Neptune] whose position you marked out actually exists. On the day on which your letter reached me, I found a star of the eighth magnitude, which was not recorded in the excellent map designed by Dr. Bremiker, containing the twenty-first hour of the collection published by the Royal Academy of Berlin. The observation of the succeeding day showed it to be the Planet of which we were in quest.
Letter, from Berlin (25 Sep 1846). In John Pringle Nichol, The Planet Neptune: An Exposition and History (1848), 89. Galle thus confirmed the existence of the planet Neptune, found at the position predicted in a letter he had just received from Urbain Le Verrier.
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So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us.
To the German Society of Scientists and Physicists, Braunschweig, Germany (Sep 1896). As quoted in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 20. Wiechert was reporting his measurement of the mass of the moving particles in a cathode ray beam (electrons).
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So long as new ideas are created, sales will continue to reach new highs.
In Forbes (1946), 57, 46.
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Some writers, rejecting the idea which science had reached, that reefs of rocks could be due in any way to “animalcules,” have talked of electrical forces, the first and last appeal of ignorance.
In Corals and Coral Islands (1879), 17.
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Somewhere in the arrangement of this world there seems to be a great concern about giving us delight, which shows that, in the universe, over and above the meaning of matter and forces, there is a message conveyed through the magic touch of personality. ...
Is it merely because the rose is round and pink that it gives me more satisfaction than the gold which could buy me the necessities of life, or any number of slaves. ... Somehow we feel that through a rose the language of love reached our hearts.
The Religion of Man (1931), 102. Quoted in H. E. Hunter, The Divine Proportion (1970), 6.
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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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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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Take risks. Ask big questions. Don't be afraid to make mistakes; if you don't make mistakes, you're not reaching far enough.
In Monterey Bay Aquarium Research Institute, MBARI's First Decade: A Retrospective (1997), 3, withoug citation. If you know the primary source, please contact Webmaster.
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Telescopes are in some ways like time machines. They reveal galaxies so far away that their light has taken billions of years to reach us. We in astronomy have an advantage in studying the universe, in that we can actually see the past.
We owe our existence to stars, because they make the atoms of which we are formed. So if you are romantic you can say we are literally starstuff. If you’re less romantic you can say we’re the nuclear waste from the fuel that makes stars shine.
We’ve made so many advances in our understanding. A few centuries ago, the pioneer navigators learnt the size and shape of our Earth, and the layout of the continents. We are now just learning the dimensions and ingredients of our entire cosmos, and can at last make some sense of our cosmic habitat.
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That radioactive elements created by us are found in nature is an astounding event in the history of the earth. And of the Human race. To fail to consider its importance and its consequences would be a folly for which humanity would have to pay a terrible price. When public opinion has been created in the countries concerned and among all the nations, an opinion informed of the dangers involved in going on with the tests and led by the reason which this information imposes, then the statesmen may reach an agreement to stop the experiments.
In 'Excerpts from Message by Schweitzer', New York Times (24 Apr 1957), 4, translated from a letter issued by Schweitzer through the Nobel Committee, asking that public opinion demand an end to nuclear tests.
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That the great majority of those who leave school should have some idea of the kind of evidence required to substantiate given types of belief does not seem unreasonable. Nor is it absurd to expect that they should go forth with a lively interest in the ways in which knowledge is improved and a marked distaste for all conclusions reached in disharmony with the methods of scientific inquiry.
Address to Section L, Education, of the American Association for the Advancement of Science, at Boston (1909), 'Science as Subject-Matter and as Method'. Published in Science (28 Jan 1910), N.S. Vol. 31, No. 787, 126.
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The American, by nature, is optimistic. He is experimental, an inventor and a builder who builds best when called upon to build greatly. Arouse his will to believe in himself, give him a great goal to believe in, and he will create the means to reach it.
Given with date 1 Jan 1960 in Brian M. Thomsen, The Dream That Will Not Die: Inspiring Words of John, Robert, and Edward Kennedy (2010), 79. Webmaster has not seen a primary document for this quote. Although it is widely circulated, the origin is usually never cited. If you know the primary source, please contact Webmaster.
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The child asks, “What is the moon, and why does it shine?” “What is this water and where does it run?” “What is this wind?” “What makes the waves of the sea?” “Where does this animal live, and what is the use of this plant?” And if not snubbed and stunted by being told not to ask foolish questions, there is no limit to the intellectual craving of a young child; nor any bounds to the slow, but solid, accretion of knowledge and development of the thinking faculty in this way. To all such questions, answers which are necessarily incomplete, though true as far as they go, may be given by any teacher whose ideas represent real knowledge and not mere book learning; and a panoramic view of Nature, accompanied by a strong infusion of the scientific habit of mind, may thus be placed within the reach of every child of nine or ten.
In 'Scientific Education', Lay Sermons, Addresses, and Reviews (1870), 71. https://books.google.com/books?id=13cJAAAAIAAJ Thomas Henry Huxley - 1870
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The desire to reach for the sky runs deep in our human psyche.
…...
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The earth was covered by a huge ice sheet which buried the Siberian mammoths, and reached just as far south as did the phenomenon of erratic boulders. This ice sheet filled all the irregularities of the surface of Europe before the uplift of the Alps, the Baltic Sea, all the lakes of Northern Germany and Switzerland. It extended beyond the shorelines of the Mediterranean and of the Atlantic Ocean, and even covered completely North America and Asiatic Russia. When the Alps were uplifted, the ice sheet was pushed upwards like the other rocks, and the debris, broken loose from all the cracks generated by the uplift, fell over its surface and, without becoming rounded (since they underwent no friction), moved down the slope of the ice sheet.
From Études sur Les Glaciers (1840), as translated by Albert V. Carozzi in Studies on Glaciers: Preceded by the Discourse of Neuchâtel (1967), 166.
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The empirical basis of objective science has nothing “absolute” about it. Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or “given” base; and when we cease our attempts to drive our piles into a deeper layer, it is not because we have reached firm ground. We simply stop when we are satisfied that they are firm enough to carry the structure, at least for the time being.
The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 94.
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The Excellence of Modern Geometry is in nothing more evident, than in those full and adequate Solutions it gives to Problems; representing all possible Cases in one view, and in one general Theorem many times comprehending whole Sciences; which deduced at length into Propositions, and demonstrated after the manner of the Ancients, might well become the subjects of large Treatises: For whatsoever Theorem solves the most complicated Problem of the kind, does with a due Reduction reach all the subordinate Cases.
In 'An Instance of the Excellence of Modern Algebra, etc', Philosophical Transactions, 1694, 960.
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The experiences are so innumerable and varied, that the journey appears to be interminable and the Destination is ever out of sight. But the wonder of it is, when at last you reach your Destination you find that you had never travelled at all! It was a journey from here to Here.
Meher Bab
In 'A Journey Without Journeying', The Everything and the Nothing (1963), 11.
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The explorations of space end on a note of uncertainty. And necessarily so. … We know our immediate neighborhood rather intimately. With increasing distance our knowledge fades, and fades rapidly. Eventually, we reach the dim boundary—the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial. The search will continue. Not until the empirical resources are exhausted, need we pass on to the dreamy realms of speculation.
From conclusion of The Silliman Memorial Lectures Series delivered at Yale University (Fall 1935). Collected in The Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202.
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The fact that man produces a concept ‘I’ besides the totality of his mental and emotional experiences or perceptions does not prove that there must be any specific existence behind such a concept. We are succumbing to illusions produced by our self-created language, without reaching a better understanding of anything. Most of so-called philosophy is due to this kind of fallacy.
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The future … [is] something which everyone reaches at the rate of sixty minutes an hour, whatever he does, whoever he is.
In The Screwtape Letters & Screwtape Proposes a Toast (1961), 130.
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The goal of science is clear—it is nothing short of the complete interpretation of the universe. But the goal is an ideal one—it marks the direction in which we move and strive, but never the point we shall actually reach.
From The Grammar of Science (1892), 17.
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The great age of the earth will appear greater to man when he understands the origin of living organisms and the reasons for the gradual development and improvement of their organization. This antiquity will appear even greater when he realizes the length of time and the particular conditions which were necessary to bring all the living species into existence. This is particularly true since man is the latest result and present climax of this development, the ultimate limit of which, if it is ever reached, cannot be known.
Hydrogéologie (1802), trans. A. V. Carozzi (1964), 77.
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The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
In History of Mathematics (3rd Ed., 1901), 468.
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The great object of all knowledge is to enlarge and purify the soul, to fill the mind with noble contemplations, to furnish a refined pleasure, and to lead our feeble reason from the works of nature up to its great Author and Sustainer. Considering this as the ultimate end of science, no branch of it can surely claim precedence of Astronomy. No other science furnishes such a palpable embodiment of the abstractions which lie at the foundation of our intellectual system; the great ideas of time, and space, and extension, and magnitude, and number, and motion, and power. How grand the conception of the ages on ages required for several of the secular equations of the solar system; of distances from which the light of a fixed star would not reach us in twenty millions of years, of magnitudes compared with which the earth is but a foot-ball; of starry hosts—suns like our own—numberless as the sands on the shore; of worlds and systems shooting through the infinite spaces.
Oration at Inauguration of the Dudley Astronomical Observatory, Albany (28 Jul 1856). Text published as The Uses of Astronomy (1856), 36.
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The greatest achievements in the science of this [twentieth] century are themselves the sources of more puzzlement than human beings have ever experienced. Indeed, it is likely that the twentieth century will be looked back at as the time when science provided the first close glimpse of the profundity of human ignorance. We have not reached solutions; we have only begun to discover how to ask questions.
In 'On Science and Certainty', Discover Magazine (Oct 1980).
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The greatest possibility of evil in self-medication [with penicillin] is the use of too-small doses, so that, instead of clearing up the infection, the microbes are educated to resist penicillin and a host of penicillin-fast organisms is bred out which can be passed on to other individuals and perhaps from there to others until they reach someone who gets a septicemia or a pneumonia which penicillin cannot save. In such a case the thoughtless person playing with penicillin treatment is morally responsible for the death of the man who finally succumbs to infection with the penicillin-resistant organism. I hope this evil can be averted.
In 'Penicillin’s Finder Assays Its Future: Sir Alexander Fleming Says Improved Dosage Method is Needed to Extend Use', New York Times (26 Jun 1945), 21.
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The highest object at which the natural sciences are constrained to aim, but which they will never reach, is the determination of the forces which are present in nature, and of the state of matter at any given moment—in one word, the reduction of all the phenomena of nature to mechanics.
In Über das Ziel der Naturwissenschaften (1865), 9. As translated in John Bernhard Stallo, The Concepts and Theories of Modern Physics (1882), 18. From the original German, “Das höchste Ziel, welches die Naturwissenschaften zu erstreben haben, ist die Verwirklichung der eben gemachten Voraussetzung, also die Ermittelung der Kräfte, welche in der Natur vorhanden sind, und des Zustandes, in dem die Materie in einem Augenblicke sich befindet, mit einem Worte, die Zurückführung aller Naturerscheinungen auf die Mechanik.”
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The highest principles for our aspirations and judgments are given to us in the Jewish-Christian religious tradition. It is a very high goal which, with our weak powers, we can reach only very inadequately, but which gives a sure foundation to our aspirations and valuations.
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The highest reach of human science is the recognition of human ignorance.
In Discussions on Philosophy and Literature, Education and University Reform (1866), 629.
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The highest reach of science is, one may say, an inventive power, a faculty of divination, akin to the highest power exercised in poetry; therefore, a nation whose spirit is characterised by energy may well be eminent in science; and we have Newton. Shakspeare [sic] and Newton: in the intellectual sphere there can be no higher names. And what that energy, which is the life of genius, above everything demands and insists upon, is freedom; entire independence of all authority, prescription and routine, the fullest room to expand as it will.
'The Literary Influence of Acadennes' Essays in Criticism (1865), in R.H. Super (ed.) The Complete Prose Works of Matthew Arnold: Lectures and Essays in Criticism (1962), Vol. 3, 238.
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The history of acceptance of new theories frequently shows the following steps: At first the new idea is treated as pure nonsense, not worth looking at. Then comes a time when a multitude of contradictory objections are raised, such as: the new theory is too fancy, or merely a new terminology; it is not fruitful, or simply wrong. Finally a state is reached when everyone seems to claim that he had always followed this theory. This usually marks the last state before general acceptance.
In 'Field Theory and the Phase Space', collected in Melvin Herman Marx, Psychological Theory: Contemporary Readings (1951), 299.
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The human race has reached a turning point. Man has opened the secrets of nature and mastered new powers. If he uses them wisely, he can reach new heights of civilization. If he uses them foolishly, they may destroy him. Man must create the moral and legal framework for the world which will insure that his new powers are used for good and not for evil.
State of the Union Address (4 Jan 1950). In William J. Federer, A Treasury of Presidential Quotations (2004), 291.
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The last few meters up to the summit no longer seem so hard. On reaching the top, I sit down and let my legs dangle into space. I don’t have to climb anymore. I pull my camera from my rucksack and, in my down mittens, fumble a long time with the batteries before I have it working properly. Then I film Peter. Now, after the hours of torment, which indeed I didn’t recognize as torment, now, when the monotonous motion of plodding upwards is at an end, and I have nothing more to do than breathe, a great peace floods my whole being. I breathe like someone who has run the race of his life and knows that he may now rest forever. I keep looking all around, because the first time I didn’t see anything of the panorama I had expected from Everest, neither indeed did I notice how the wind was continually chasing snow across the summit. In my state of spiritual abstraction, I no longer belong to myself and to my eyesight. I am nothing more than a single, narrow, gasping lung, floating over the mists and the summits.
…...
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The manner of Demoivre’s death has a certain interest for psychologists. Shortly before it, he declared that it was necessary for him to sleep some ten minutes or a quarter of an hour longer each day than the preceding one: the day after he had thus reached a total of something over twenty-three hours he slept up to the limit of twenty-four hours, and then died in his sleep.
In History of Mathematics (3rd Ed., 1901), 394.
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The mathematician has reached the highest rung on the ladder of human thought.
In The Dance of Life (1923), 140.
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The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.
In The Grammar of Science (1900), 505.
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The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracl