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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Special Quotes (184 quotes)


...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
I Want to be a Mathematician: an Automathography in Three Parts (1985), 324.
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Blut ist ein ganz besondrer Saft.
Blood is a very special juice.
In Faust, Part I (1808), scene in Faust’s study, line 1740. As translated by Stuart Atkins in Faust I & II, (1984, 1994), 45. Said by Mephistopheles, as Faust pledges his soul with his blood on the devil’s pact. Also translated by Bayard Taylor as “Blood is a juice of rarest quality,” in Faust: A Tragedy (1872), Part 1, 62. Also seen as “Blood is a very unusual fluid.”
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Branches or types are characterized by the plan of their structure,
Classes, by the manner in which that plan is executed, as far as ways and means are concerned,
Orders, by the degrees of complication of that structure,
Families, by their form, as far as determined by structure,
Genera, by the details of the execution in special parts, and
Species, by the relations of individuals to one another and to the world in which they live, as well as by the proportions of their parts, their ornamentation, etc.
Essay on Classification (1857). Contributions to the Natural History of the United States of America (1857), Vol. I, 170.
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That the general characters of the big group to which the embryo belongs appear in development earlier than the special characters. In agreement with this is the fact that the vesicular form is the most general form of all; for what is common in a greater degree to all animals than the opposition of an internal and an external surface?
The less general structural relations are formed after the more general, and so on until the most special appear.
The embryo of any given form, instead of passing through the state of other definite forms, on the contrary separates itself from them.

Fundamentally the embryo of a higher animal form never resembles the adult of another animal form, but only its embryo.
Über Entwicklungsgeschichte der Thiere: Beobachtung und Reflexion (1828), 224. Trans. E. S. Russell, Form and Function: A Contribution to the History of Animal Morphology (1916), 125-6.
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[Responding to a student whose friend asked about studying Agricultural Chemistry at Johns Hopkins:]
We would be glad to have your friend come here to study, but tell him that we teach Chemistry here and not Agricultural Chemistry, nor any other special kind of chemistry. ... We teach Chemistry.
In Frederick Hutton Getman, The Life of Ira Remsen, 71.
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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 137-138. (Note that Bernard overlooks how the statistical method can be useful: a surgeon announcing a mortality rate of 40% invites comparison. A surgeon with worse outcomes should adopt this method. If a surgeon has a better results, that method should be adopted.)
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A parable: A man was examining the construction of a cathedral. He asked a stone mason what he was doing chipping the stones, and the mason replied, “I am making stones.” He asked a stone carver what he was doing. “I am carving a gargoyle.” And so it went, each person said in detail what they were doing. Finally he came to an old woman who was sweeping the ground. She said. “I am helping build a cathedral.”
...Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture.
[For example, in education, a teacher might say in the next class he was going to “explain Young's modulus and how to measure it,” rather than, “I am going to educate the students and prepare them for their future careers.”]
In The Art of Doing Science and Engineering: Learning to Learn (1975, 2005), 195.
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A story about the Jack Spratts of medicine [was] told recently by Dr. Charles H. Best, co-discoverer of insulin. He had been invited to a conference of heart specialists in North America. On the eve of the meeting, out of respect for the fat-clogs-the-arteries theory, the delegates sat down to a special banquet served without fats. It was unpalatable but they all ate it as a duty. Next morning Best looked round the breakfast room and saw these same specialists—all in the 40-60 year old, coronary age group—happily tucking into eggs, bacon, buttered toast and coffee with cream.
'Objections To High-Fat Diets', Eat Fat And Grow Slim (1958), Ch. 3.
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Absorbed in the special investigation, I paid no heed to the edifice which was meanwhile unconsciously building itself up. Having however completed the comparison of the fossil species in Paris, I wanted, for the sake of an easy revision of the same, to make a list according to their succession in geological formations, with a view of determining the characteristics more exactly and bringing them by their enumeration into bolder relief. What was my joy and surprise to find that the simplest enumeration of the fossil fishes according to their geological succession was also a complete statement of the natural relations of the families among themselves; that one might therefore read the genetic development of the whole class in the history of creation, the representation of the genera and species in the several families being therein determined; in one word, that the genetic succession of the fishes corresponds perfectly with their zoological classification, and with just that classification proposed by me.
Quoted in Elizabeth Cary Agassiz (ed.), Louis Agassiz: His Life and Correspondence (1885), Vol. I, 203-4.
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According to the older view, for every single effect of a serum, there was a separate substance, or at least a particular chemical group... A normal serum contained as many different haemagglutinins as it agglutinated different cells. The situation was undoubtedly made much simpler if, to use the Ehrlich terminology... the separate haptophore groups can combine with an extremely large number of receptors in stepwise differing quantities as a stain does with different animal tissues, though not always with the same intensity. A normal serum would therefore visibly affect such a large number of different blood cells... not because it contained countless special substances, but because of the colloids of the serum, and therefore of the agglutinins by reason of their chemical constitution and the electrochemical properties resulting from it. That this manner of representation is a considerable simplification is clear; it also opens the way to direct experimental testing by the methods of structural chemistry.
'Die Theorien der Antikorperbildung ... ', Wiener klinische Wöchenschrift (1909), 22, 1623-1631. Trans. Pauline M. H. Mazumdar.
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After 16 months of teaching, consulting, fellowship, and special project activities on matters ranging from conservation to healthcare to international trade, Gov. Ventura appointed me to the Minnesota Court of Appeals.
…...
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All appearances to the contrary, the only watchmaker in nature is the blind forces of physics, albeit deployed in very special way. A true watchmaker has foresight: he designs his cogs springs, and plans their interconnections, with a future purpose in his mind's eye. Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind's eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of watchmaker in nature, it is the blind watchmaker.
The Blind Watchmaker (1986), 5.
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All known living bodies are sharply divided into two special kingdoms, based upon the essential differences which distinguish animals from plants, and in spite of what has been said, I am convinced that these two kingdoms do not really merge into one another at any point.
Attributed.
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All of our experience indicates that life can manifest itself only in a concrete form, and that it is bound to certain substantial loci. These loci are cells and cell formations. But we are far from seeking the last and highest level of understanding in the morphology of these loci of life. Anatomy does not exclude physiology, but physiology certainly presupposes anatomy. The phenomena that the physiologist investigates occur in special organs with quite characteristic anatomical arrangements; the various morphological parts disclosed by the anatomist are the bearers of properties or, if you will, of forces probed by the physiologist; when the physiologist has established a law, whether through physical or chemical investigation, the anatomist can still proudly state: This is the structure in which the law becomes manifest.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 19, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 84.
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Among your pupils, sooner or later, there must be one. who has a genius for geometry. He will be Sylvester’s special pupil—the one pupil who will derive from his master, knowledge and enthusiasm—and that one pupil will give more reputation to your institution than the ten thousand, who will complain of the obscurity of Sylvester, and for whom you will provide another class of teachers.
Letter (18 Sep 1875) recommending the appointment of J.J. Sylvester to Daniel C. Gilman. In Daniel C. Gilman Papers, Ms. 1, Special Collections Division, Milton S. Eisenhower Library, Johns Hopkins University. As quoted in Karen Hunger Parshall, 'America’s First School of Mathematical Research: James Joseph Sylvester at The Johns Hopkins University 1876—1883', Archive for History of Exact Sciences (1988), 38, No. 2, 167.
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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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Any country that wants to make full use of all its potential scientists and technologists … must not expect to get the women quite so simply as it gets the men. It seems to me that marriage and motherhood are at least as socially important as military service. Government regulations are framed to ensure (in the United Kingdom) that a man returning to work from military service is not penalized by his absence. Is it utopian, then, to suggest that any country that really wants a woman to return to a scientific career when her children no longer need her physical presence should make special arrangements to encourage her to do so?
In Impact of Science on Society (1970), 20 58. Commenting how for men who went to war, their jobs were held for them pending their return.
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Anyone of common mental and physical health can practice scientific research. … Anyone can try by patient experiment what happens if this or that substance be mixed in this or that proportion with some other under this or that condition. Anyone can vary the experiment in any number of ways. He that hits in this fashion on something novel and of use will have fame. … The fame will be the product of luck and industry. It will not be the product of special talent.
In Essays of a Catholic Layman in England (1931).
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As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.
Collected Works (1877), Vol. 5, 25-26. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 412.
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As language-using organisms, we participate in the evolution of the Universe most fruitfully through interpretation. We understand the world by drawing pictures, telling stories, conversing. These are our special contributions to existence. It is our immense good fortune and grave responsibility to sing the songs of the Cosmos.
Epigraph, without citation, in Michael Dowd, Thank God for Evolution: How the Marriage of Science and Religion Will Transform Your Life and Our World (2008), 103.
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Before the promulgation of the periodic law the chemical elements were mere fragmentary incidental facts in nature; there was no special reason to expect the discovery of new elements, and the new ones which were discovered from time to time appeared to be possessed of quite novel properties. The law of periodicity first enabled us to perceive undiscovered elements at a distance which formerly were inaccessible to chemical vision, and long ere they were discovered new elements appeared before our eyes possessed of a number of well-defined properties.
In Faraday Lecture, delivered before the Fellows of the Chemical Society in the Theatre of the Royal Institution (4 Jun 1889), printed in Professor Mendeléeff, 'The Periodic Law of the Chemical Elements', Transactions of the Chemical Society (1889), 55, 648.
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Beta decay was … like a dear old friend. There would always be a special place in my heart reserved especially for it.
In paper presented to the International Conference on the History of Original Ideas and Basic Discoveries, Erice, Sicily (27 Jul-4 Aug 1994), 'Parity Violation' collected in Harvey B. Newman, Thomas Ypsilantis History of Original Ideas and Basic Discoveries in Particle Physics (1996), 390-391.
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Biology as a discipline would benefit enormously if we could bring together the scientists working at the opposite ends of the biological spectrum. Students of organisms who know natural history have abundant questions to offer the students of molecules and cells. And molecular and cellular biologists with their armory of techniques and special insights have much to offer students of organisms and ecology.
In 'The role of natural history in contemporary biology', BioScience (1986), 36, 328-329.
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Biology occupies a position among the sciences both marginal and central. Marginal because, the living world, constituting only a tiny and very “special” part of the universe, it does not seem likely that the study of living beings will ever uncover general laws applicable outside the biosphere. But if the ultimate aim of the whole of science is indeed, as I believe, to clarify man's relationship to the universe, then biology must be accorded a central position, since of all the disciplines it is the one that endeavours to go most directly to the heart of the problems that must be resolved before that of “human nature” can even be framed in other than metaphysical terms.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), xi.
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But there is another alchemy, operative and practical, which teaches how to make the noble metals and colours and many other things better and more abundantly by art than they are made in nature. And science of this kind is greater than all those preceding because it produces greater utilities. For not only can it yield wealth and very many other things for the public welfare, but it also teaches how to discover such things as are capable of prolonging human life for much longer periods than can be accomplished by nature … Therefore this science has special utilities of that nature, while nevertheless it confirms theoretical alchemy through its works.
Opus Tertium [1266-1268], chapter 12, quoted in A. C. Crombie, Augustine to Galileo (1959), Vol. I, 69.
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Can one think that because we are engineers, beauty does not preoccupy us or that we do not try to build beautiful, as well as solid and long lasting structures? Aren’t the genuine functions of strength always in keeping with unwritten conditions of harmony? … Besides, there is an attraction, a special charm in the colossal to which ordinary theories of art do not apply.
As translated in Henry Petroski, Remaking the World: Adventures in Engineering (1998), 173. From the original French in interview of Eiffel by Paul Bourde, in the newspaper Le Temps (14 Feb 1887). Quoted in 'Au Jour le Jour: Les Artistes Contre la Tour Eiffel', Gazette Anecdotique, Littéraire, Artistique et Bibliographique (Feb 1887), 126, and in Gustave Eiffel, Travaux Scientifiques Exécutés à la Tour de 300 Mètres de 1889 à 1900 (1900), 14. “Parce que nous sommes des ingénieurs, croit-on donc que la beauté ne nous préoccupe pas dans nos constructions et qu'en même temps que nous faisons solide et durable nous ne nous efforçons pas rletfaire élégant? Est-ce que les véritables conditions de la force ne sont pas toujours conformes aux conditions secrètes de l'harmonie?.… Il y a du reste dans le colossal une attraction, un charme propre auxquels les théories d'art ordinaires ne sont guère applicables.
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Chance throws peculiar conditions in everyone's way. If we apply intelligence, patience and special vision, we are rewarded with new creative breakthroughs.
Told to his Harvard students. As quoted, without citation, by Marcus Bach, 'Serendiptiy in the Business World', in The Rotarian (Oct 1981), 139, No. 4, 40. If you know a primary source, please contact Webmaster.
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Coming to the question of life being found on other planets, Professor Haldane apologized for discoursing, as a mere biologist, on a subject on which we had been expecting a lecture by a physicist [J. D. Bernal]. He mentioned three hypotheses:
(a) That life had a supernatural origin,
(b) That it originated from inorganic materials, and (c) That life is a constituent of the Universe and can only arise from pre-existing life. The first hypothesis, he said, should be taken seriously, and he would proceed to do so. From the fact that there are 400,000 species of beetle on this planet, but only 8,000 species of mammals, he concluded that the Creator, if he exists, has a special preference for beetles, and so we might be more likely to meet them than any other type of animal on a planet which would support life.
In Mark Williamson, 'Haldane’s Special Preference', The Linnean, 1992, 8, 14.
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Culture is activity of thought, and receptiveness to beauty and humane feeling. Scraps of information have nothing to do with it. A merely well informed man is the most useless bore on God’s earth. What we should aim at producing is men who possess both culture and expert knowledge in some special direction.
Opening sentences of Chapter 1,'The Aims of Education', in Aims of Education and Other Essays (1917), 1.
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Darwin abolished special creations, contributed the Origin of Species and hitched all life together in one unbroken procession of Siamese Twins, the whole evolved by natural and orderly processes from one microscopic parent germ.
'The Secret History of Eddypus', in Mark Twain and David Ketterer (ed.), Tales of Wonder (2003), 223.
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Disease is not something personal and special, but only a manifestation of life under modified conditions, operating according to the same laws as apply to the living body at all times, from the first moment until death.
In Ian F. McNeely, Medicine on a Grand Scale: Rudolf Virchow, Liberalism, and the Public Health (2002), 26.
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Each species has evolved a special set of solutions to the general problems that all organisms must face. By the fact of its existence, a species demonstrates that its members are able to carry out adequately a series of general functions. … These general functions offer a framework within which one can integrate one’s view of biology and focus one’s research. Such a view helps one to avoid becoming lost in a morass of unstructured detail—even though the ways in which different species perform these functions may differ widely. A few obvious examples will suffice. Organisms must remain functionally integrated. They must obtain materials from their environments, and process and release energy from these materials. … They must differentiate and grow, and they must reproduce. By focusing one’s questions on one or another of these obligatory and universal capacities, one can ensure that one’s research will not be trivial and that it will have some chance of achieving broad general applicability.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 331.
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Each volcano is an independent machine—nay, each vent and monticule is for the time being engaged in its own peculiar business, cooking as it were its special dish, which in due time is to be separately served. We have instances of vents within hailing distance of each other pouring out totally different kinds of lava, neither sympathizing with the other in any discernible manner nor influencing other in any appreciable degree.
In Report on the Geology of the High Plateaus of Utah (1880), 115.
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Effective science began when it passed from the occasional amateur into the hands of men who made the winning of knowledge their special function or profession.
Address to 48th annual summer convention of the American Institute of Electriccal Engineers, Cleveland (21 Jun 1932), abridged in 'The Rôle of the Engineer', The Electrical Journal (1932), 109, 223.
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Effects vary with the conditions which bring them to pass, but laws do not vary. Physiological and pathological states are ruled by the same forces; they differ only because of the special conditions under which the vital laws manifest themselves.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957),10.
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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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Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.
Ampère gives this example drawn from geometry to illustrate his meaning for “direct synthesis” when deductions following from more simple, already-known theorems leads to a new discovery. In James R. Hofmann, André-Marie Ampère (1996), 159. Cites Académie des Sciences Ampère Archives, box 261.
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Every creature has its own food, and an appropriate alchemist with the task of dividing it ... The alchemist takes the food and changes it into a tincture which he sends through the body to become blood and flesh. This alchemist dwells in the stomach where he cooks and works. The man eats a piece of meat, in which is both bad and good. When the meat reaches the stomach, there is the alchemist who divides it. What does not belong to health he casts away to a special place, and sends the good wherever it is needed. That is the Creator's decree... That is the virtue and power of the alchemist in man.
Volumen Medicinae Paramirum (c. 1520), in Paracelsus: Essential Readings, edited by Nicholas Goodrick-Clarke (1990), 50-1.
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Every natural scientist who thinks with any degree of consistency at all will, I think, come to the view that all those capacities that we understand by the phrase psychic activities (Seelenthiitigkeiten) are but functions of the brain substance; or, to express myself a bit crudely here, that thoughts stand in the same relation to the brain as gall does to the liver or urine to the kidneys. To assume a soul that makes use of the brain as an instrument with which it can work as it pleases is pure nonsense; we would then be forced to assume a special soul for every function of the body as well.
Carl Vogt
In Physiologische Briefe für Gelbildete aIle Stünde (1845-1847), 3 parts, 206. as translated in Frederick Gregory, Scientific Materialism in Nineteenth Century Germany (1977), 64.
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For in disease the most voluntary or most special movements, faculties, etc., suffer first and most, that is in an order the exact opposite of evolution. Therefore I call this the principle of Dissolution.
'On the Anatomical and Physiological Localisation of Movements in the Brain' (1875), Preface. In James Taylor (ed.), Selected Writings of John Hughlings Jackson, Vol. 1 (1931), 38.
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For Linnaeus, Homo sapiens was both special and not special ... Special and not special have come to mean nonbiological and biological, or nurture and nature. These later polarizations are nonsensical. Humans are animals and everything we do lies within our biological potential ... the statement that humans are animals does not imply that our specific patterns of behavior and social arrangements are in any way directly determined by our genes. Potentiality and determination are different concepts.
…...
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For the evolution of science by societies the main requisite is the perfect freedom of communication between each member and anyone of the others who may act as a reagent.
The gaseous condition is exemplified in the soiree, where the members rush about confusedly, and the only communication is during a collision, which in some instances may be prolonged by button-holing.
The opposite condition, the crystalline, is shown in the lecture, where the members sit in rows, while science flows in an uninterrupted stream from a source which we take as the origin. This is radiation of science. Conduction takes place along the series of members seated round a dinner table, and fixed there for several hours, with flowers in the middle to prevent any cross currents.
The condition most favourable to life is an intermediate plastic or colloidal condition, where the order of business is (1) Greetings and confused talk; (2) A short communication from one who has something to say and to show; (3) Remarks on the communication addressed to the Chair, introducing matters irrelevant to the communication but interesting to the members; (4) This lets each member see who is interested in his special hobby, and who is likely to help him; and leads to (5) Confused conversation and examination of objects on the table.
I have not indicated how this programme is to be combined with eating.
Letter to William Grylls Adams (3 Dec 1873). In P. M. Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 949-50.
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For the past 10 years I have had the interesting experience of observing the development of Parkinson's syndrome on myself. As a matter of fact, this condition does not come under my special medical interests or I would have had it solved long ago. … The condition has its compensations: one is not yanked from interesting work to go to the jungles of Burma ... one avoids all kinds of deadly committee meetings, etc.
Article for his 25th anniversary class report. In Barry G. Firkin, Judith A. Whitworth, Dictionary of Medical Eponyms (1996), 5.
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Gauss was not the son of a mathematician; Handel’s father was a surgeon, of whose musical powers nothing is known; Titian was the son and also the nephew of a lawyer, while he and his brother, Francesco Vecellio, were the first painters in a family which produced a succession of seven other artists with diminishing talents. These facts do not, however, prove that the condition of the nerve-tracts and centres of the brain, which determine the specific talent, appeared for the first time in these men: the appropriate condition surely existed previously in their parents, although it did not achieve expression. They prove, as it seems to me, that a high degree of endowment in a special direction, which we call talent, cannot have arisen from the experience of previous generations, that is, by the exercise of the brain in the same specific direction.
In 'On Heredity', Essays upon Heredity and Kindred Biological Problems (1889), Vol. 1, 96.
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General practice is at least as difficult, if it is to be carried on well and successfully, as any special practice can be, and probably more so; for the G.P. has to live continually, as it were, with the results of his handiwork.
The Corner of Harley Street: Being Some Familiar Correspondence of Peter Harding, M. D., Ch. 26.
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Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
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Genuine religion has its root deep down in the heart of humanity and in the reality of things. It is not surprising that by our methods we fail to grasp it: the actions of the Deity make no appeal to any special sense, only a universal appeal; and our methods are, as we know, incompetent to detect complete uniformity. There is a principle of Relativity here, and unless we encounter flaw or jar or change, nothing in us responds; we are deaf and blind therefore to the Immanent Grandeur, unless we have insight enough to recognise in the woven fabric of existence, flowing steadily from the loom in an infinite progress towards perfection, the ever-growing garment of a transcendent God.
Continuity: The Presidential Address to the British Association (1913), 92-93.
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Geometric writings are not rare in which one would seek in vain for an idea at all novel, for a result which sooner or later might be of service, for anything in fact which might be destined to survive in the science; and one finds instead treatises on trivial problems or investigations on special forms which have absolutely no use, no importance, which have their origin not in the science itself but in the caprice of the author; or one finds applications of known methods which have already been made thousands of times; or generalizations from known results which are so easily made that the knowledge of the latter suffices to give at once the former. Now such work is not merely useless; it is actually harmful because it produces a real incumbrance in the science and an embarrassment for the more serious investigators; and because often it crowds out certain lines of thought which might well have deserved to be studied.
From 'On Some Recent Tendencies in Geometric Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
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How hard to realize that every camp of men or beast has this glorious starry firmament for a roof! In such places standing alone on the mountain-top it is easy to realize that whatever special nests we make - leaves and moss like the marmots and birds, or tents or piled stone - we all dwell in a house of one room - the world with the firmament for its roof - and are sailing the celestial spaces without leaving any track.
John Muir
…...
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However, before we come to [special] creation, which puts an end to all discussion: I think we should try everything else.
De Stella Nova, On the New Star (1606), Chapter 22, in Johannes Kepler Gesammelte Werke (1937-), Vol. 1, 257, ll. 23-4.
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However, if we consider that all the characteristics which have been cited are only differences in degree of structure, may we not suppose that this special condition of organization of man has been gradually acquired at the close of a long period of time, with the aid of circumstances which have proved favorable? What a subject for reflection for those who have the courage to enter into it!
In Recherches sur l'Organization des corps vivans (1802), as translated in Alpheus Spring Packard, Lamarck, the Founder of Evolution: His Life and Work (1901), 363. Packard's italics.
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Humanity, in the course of time, had to endure from the hands of science two great outrages against its naive self-love. The first was when humanity discovered that our earth was not the center of the universe…. The second occurred when biological research robbed man of his apparent superiority under special creation, and rebuked him with his descent from the animal kingdom, and his ineradicable animal nature.
From a series of 28 lectures for laymen, Part Three, 'General Theory of the Neurons', Lecture 18, 'Traumatic Fixation—the Unconscious' collected in Sigmund Freud and G. Stanley Hall (trans.), A General Introduction to Psychoanalysis (1920), 246-247.
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I am by heritage a Jew, by citizenship a Swiss, and by makeup a human being, and only a human being, without any special attachment to any state or national entity whatsoever.
…...
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I believe … that we can still have a genre of scientific books suitable for and accessible alike to professionals and interested laypeople. The concepts of science, in all their richness and ambiguity, can be presented without any compromise, without any simplification counting as distortion, in language accessible to all intelligent people … I hope that this book can be read with profit both in seminars for graduate students and–if the movie stinks and you forgot your sleeping pills–on the businessman’s special to Tokyo.
In Wonderful Life: The Burgess Shale and the Nature of History (1990), Preface, 16.
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I believe—and human psychologists, particularly psychoanalysts should test this—that present-day civilized man suffers from insufficient discharge of his aggressive drive. It is more than probable that the evil effects of the human aggressive drives, explained by Sigmund Freud as the results of a special death wish, simply derive from the fact that in prehistoric times intra-specific selection bred into man a measure of aggression drive for which in the social order today he finds no adequate outlet.
On Aggression, trans. M. Latzke (1966), 209.
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I cannot find anything showing early aptitude for acquiring languages; but that he [Clifford] had it and was fond of exercising it in later life is certain. One practical reason for it was the desire of being able to read mathematical papers in foreign journals; but this would not account for his taking up Spanish, of which he acquired a competent knowledge in the course of a tour to the Pyrenees. When he was at Algiers in 1876 he began Arabic, and made progress enough to follow in a general way a course of lessons given in that language. He read modern Greek fluently, and at one time he was furious about Sanskrit. He even spent some time on hieroglyphics. A new language is a riddle before it is conquered, a power in the hand afterwards: to Clifford every riddle was a challenge, and every chance of new power a divine opportunity to be seized. Hence he was likewise interested in the various modes of conveying and expressing language invented for special purposes, such as the Morse alphabet and shorthand. … I have forgotten to mention his command of French and German, the former of which he knew very well, and the latter quite sufficiently; …
In paper, 'William Kingdon Clifford', The Fortnightly Review (1879), 31, 671. Published in advance of Leslie Stephen and Frederick Pollock (eds.), Clifford’s Lectures and Essays (1879), Vol. 1, Introduction, 9. The 'Introduction' was written by Pollock.
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I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified. The comparative smallness of what we know today as gravitational effects is not a conclusive reason for ignoring the principle of general relativity in theoretical investigations of a fundamental character. In other words, I do not believe that it is justifiable to ask: What would physics look like without gravitation?
…...
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I had at one time a very bad fever of which I almost died. In my fever I had a long consistent delirium. I dreamt that I was in Hell, and that Hell is a place full of all those happenings that are improbable but not impossible. The effects of this are curious. Some of the damned, when they first arrive below, imagine that they will beguile the tedium of eternity by games of cards. But they find this impossible, because, whenever a pack is shuffled, it comes out in perfect order, beginning with the Ace of Spades and ending with the King of Hearts. There is a special department of Hell for students of probability. In this department there are many typewriters and many monkeys. Every time that a monkey walks on a typewriter, it types by chance one of Shakespeare's sonnets. There is another place of torment for physicists. In this there are kettles and fires, but when the kettles are put on the fires, the water in them freezes. There are also stuffy rooms. But experience has taught the physicists never to open a window because, when they do, all the air rushes out and leaves the room a vacuum.
'The Metaphysician's Nightmare', Nightmares of Eminent Persons and Other Stories (1954), 38-9.
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I have no special talents. I am only passionately curious.
Letter to Carl Seelig (11 Mar 1952), AEA 39-013. As cited in Walter Isaacson, Einstein: His Life and Universe (2008), 548.
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Srinivasa Ramanujan quote: I have not trodden through a conventional university course, but I am striking out a new path for mys
I have not trodden through a conventional university course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling.”
First letter to G.H. Hardy (16 Jan 1913). In Collected Papers of Srinivasa Ramanujan (1927), xxiii. Hardy notes he did “seem to remember his telling me that his friends had given him some assistance” in writing the letter because Ramanujan's “knowledge of English, at that stage of his life, could scarcely have been sufficient.”
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I have often thought that an interesting essay might be written on the influence of race on the selection of mathematical methods. methods. The Semitic races had a special genius for arithmetic and algebra, but as far as I know have never produced a single geometrician of any eminence. The Greeks on the other hand adopted a geometrical procedure wherever it was possible, and they even treated arithmetic as a branch of geometry by means of the device of representing numbers by lines.
In A History of the Study of Mathematics at Cambridge (1889), 123
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I have paid special attention to those Properties of the Positive Rays which seem to throw light on the problems of the structure of molecules and atoms and the question of chemical combination … I am convinced that as yet we are only at the beginning of the harvest of results which will elucidate the process of chemical combination, and thus bridge over the most serious gap which now exists between Physics and Chemistry.
Rays of Positive Electricity and their Application to Chemical Analyses (1921), v.
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I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially [science] of nature, requires a pure portion, lying at the foundation of the empirical, and based upon a priori knowledge of natural things. … To the possibility of a determinate natural thing, and therefore to cognise it à priori, is further requisite that the intuition corresponding à priori to the conception should be given; in other words, that the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.
From Preface to The Metaphysical Foundations of Natural Science (1786), as translated by Ernest Belford Boax, in Kant’s Prolegomena: And The Metaphysical Foundations of Natural Science (1883), 140.
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I propose to provide proof... that just as always an alcoholic ferment, the yeast of beer, is found where sugar is converted into alcohol and carbonic acid, so always a special ferment, a lactic yeast, is found where sugar is transformed into lactic acid. And, furthermore, when any plastic nitrogenated substance is able to transform sugar into that acid, the reason is that it is a suitable nutrient for the growth of the [lactic] ferment.
Comptes Rendus (1857), 45, 913.
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I think people get it upside down when they say the unambiguous is the reality and the ambiguous is merely uncertainty about what is really unambiguous. Let’s turn it around the other way: the ambiguous is the reality and the unambiguous is merely a special case of it, where we finally manage to pin down some very special aspect.
In William Byers, How Mathematicians Think (2007), 25.
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I venture to maintain, that, if the general culture obtained in the Faculty of Arts were what it ought to be, the student would have quite as much knowledge of the fundamental principles of Physics, of Chemistry, and of Biology, as he needs, before he commenced his special medical studies. Moreover, I would urge, that a thorough study of Human Physiology is, in itself, an education broader and more comprehensive than much that passes under that name. There is no side of the intellect which it does not call into play, no region of human knowledge into which either its roots, or its branches, do not extend; like the Atlantic between the Old and the New Worlds, its waves wash the shores of the two worlds of matter and of mind; its tributary streams flow from both; through its waters, as yet unfurrowed by the keel of any Columbus, lies the road, if such there be, from the one to the other; far away from that Northwest Passage of mere speculation, in which so many brave souls have been hopelessly frozen up.
'Universities: Actual and Ideal' (1874). In Collected Essays (1893), Vol. 3, 220.
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I wish people would more generally bring back the seeds of pleasing foreign plants and introduce them broadcast, sowing them by our waysides and in our fields, or in whatever situation is most likely to suit them. It is true, this would puzzle botanists, but there is no reason why botanists should not be puzzled. A botanist is a person whose aim is to uproot, kill and exterminate every plant that is at all remarkable for rarity or any special virtue, and the rarer it is the more bitterly he will hunt it down.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 281.
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I wish the lecturers to treat their subject as a strictly natural science, the greatest of all possible sciences, indeed, in one sense, the only science, that of Infinite Being, without reference to or reliance upon any supposed special exception or so-called miraculous revelation. I wish it considered just as astronomy or chemistry is.
Statement in deed of foundation of the Gifford Lectures on natural theology (1885).
Quoted in Michael A. Arbib and Mary B. Hesse, The Construction of Reality (1986), 1.
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I would like to be rather more special, and I would like to be understood in an honest way rather than in a vague way.
In The Character of Physical Law (1965, 2001), 13.
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If any spiritualistic medium can do stunts, there is no more need for special conditions than there is for a chemist to turn down lights, start operations with a hymn, and ask whether there's any chemical present that has affinity with something named Hydrogen.
Lo! (1932). In The Complete Books of Charles Fort (1975), 575.
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If we define 'thought collective' as a community of persons mutually exchanging ideas or maintaining intellectual interaction, we will find by implication that it also provides the special 'carrier' for the historical development of any field of thought, as well as for the given stock of knowledge and level of culture. This we have designated thought style.
Genesis and the Development of a Scientific Fact (1935), 39.
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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 scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.
The Ethical Functions of Scientific Study: An Address Delivered at the Annual Commencement of the University of Michigan, 28 June 1888, 7-8.
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In the temple of science are many mansions, and various indeed are they that dwell therein and the motives that have led them thither. Many take to science out of a joyful sense of superior intellectual power; science is their own special sport to which they look for vivid experience and the satisfaction of ambition; many others are to be found in the temple who have offered the products of their brains on this altar for purely utilitarian purposes. Were an angel of the Lord to come and drive all the people belonging to these two categories out of the temple, the assemblage would be seriously depleted, but there would still be some men, of both present and past times, left inside. Our Planck is one of them, and that is why we love him.
Address at Physical Society, Berlin (1918), for Max Planck’s 60th birthday, 'Principles of Research' in Essays in Science (1934, 2004), 1.
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Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain. “Omne exit in infinitum” is their favorite motto and accepted axiom.
In 'A Plea for the Mathematician', Nature, Vol. 1, 861. [The Latin phrase “Omne exit in infinitum” means “Everything goes to infinity”.
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It has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have “collected data” that the mathematician is able to deduce the required generalisation. Thus a Maxwell followed Faraday and a Newton completed Kepler.
In Higher Mathematics for Students of Chemistry and Physics (1902), 3.
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It is a delusion that the use of reason is easy and needs no training or special caution.
In The Art of Scientific Investigation (1950), 85.
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It is a matter of primary importance in the cultivation of those sciences in which truth is discoverable by the human intellect that the investigator should be free, independent, unshackled in his movement; that he should be allowed and enabled to fix his mind intently, nay, exclusively, on his special object, without the risk of being distracted every other minute in the process and progress of his inquiry by charges of temerariousness, or by warnings against extravagance or scandal.
In The Idea of a University Defined and Illustrated (1905), 471.
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It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes, but that we were somehow built in from the beginning.
The First Three Minutes: A Modern View of the Origin of the Universe (1977), 154.
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It is customary to connect Medicine with Botany, yet scientific treatment demands that we should consider each separately. For the fact is that in every art, theory must be disconnected and separated from practice, and the two must be dealt with singly and individually in their proper order before they are united. And for that reason, in order that Botany, which is, as it were, a special branch of Natural Philosophy [Physica], may form a unit by itself before it can be brought into connection with other sciences, it must be divided and unyoked from Medicine.
Methodi herbariae libri tres (1592), translated in Agnes Arber, Herbals: Their Origin and Evolution, 2nd edition (1938), 144.
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It is ironical that, in the very field in which Science has claimed superiority to Theology, for example—in the abandoning of dogma and the granting of absolute freedom to criticism—the positions are now reversed. Science will not tolerate criticism of special relativity, while Theology talks freely about the death of God, religionless Christianity, and so on.
In 'Preface', Science at the Crossroads (1972), 13.
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It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through feedback. Both of them have sensory receptors as one stage in their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended aetion, is reported back to the central regulatory apparatus.
In The Human Use of Human Beings: Cybernetics and Society (1954), 26-27.
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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 told of Faraday that he refused to be called a physicist; he very much disliked the new name as being too special and particular and insisted on the old one, philosopher, in all its spacious generality: we may suppose that this was his way of saying that he had not over-ridden the limiting conditions of class only to submit to the limitation of a profession.
Commentary (Jun 1962), 33, 461-77. Cited by Sydney Ross in Nineteenth-Century Attitudes: Men of Science (1991), 11.
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It needs scarcely be pointed out that in placing Mathematics at the head of Positive Philosophy, we are only extending the application of the principle which has governed our whole Classification. We are simply carrying back our principle to its first manifestation. Geometrical and Mechanical phenomena are the most general, the most simple, the most abstract of all,— the most irreducible to others, the most independent of them; serving, in fact, as a basis to all others. It follows that the study of them is an indispensable preliminary to that of all others. Therefore must Mathematics hold the first place in the hierarchy of the sciences, and be the point of departure of all Education whether general or special.
In Auguste Comte and Harriet Martineau (trans.), The Positive Philosophy (1858), Introduction, Chap. 2, 50.
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It seems to me that the view toward which we are tending is that the specificity in gene action is always a chemical specificity, probably the production of enzymes which guide metabolic processes along particular channels. A given array of genes thus determines the production of a particular kind of protoplasm with particular properties—such, for example, as that of responding to surface forces by the formation of a special sort of semipermeable membrane, and that of responding to trivial asymmetries in the play of external stimuli by polarization, with consequent orderly quantitative gradients in all physiologic processes. Different genes may now be called into play at different points in this simple pattern, either through the local formation of their specific substrates for action, or by activation of a mutational nature. In either case the pattern becomes more complex and qualitatively differentiated. Successive interactions of differentiated regions and the calling into play of additional genes may lead to any degree of complexity of pattern in the organism as a largely self-contained system. The array of genes, assembled in the course of evolution, must of course be one which determines a highly self­regulatory system of reactions. On this view the genes are highly specific chemically, and thus called into play only under very specific conditions; but their morphological effects, if any, rest on quantitative influences of immediate or remote products on growth gradients, which are resultants of all that has gone on before in the organism.
In 'Genetics of Abnormal Growth in the Guinea Pig', Cold Spring Harbor Symposia on Quantitative Biology (1934), 2, 142.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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It would be interesting to inquire how many times essential advances in science have first been made possible by the fact that the boundaries of special disciplines were not respected… Trespassing is one of the most successful techniques in science.
Dynamics in Psychology (1940), 115-116
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Just as a tree constitutes a mass arranged in a definite manner, in which, in every single part, in the leaves as in the root, in the trunk as in the blossom, cells are discovered to be the ultimate elements, so is it also with the forms of animal life. Every animal presents itself as a sum of vital unities, every one of which manifests all the characteristics of life. The characteristics and unity of life cannot be limited to anyone particular spot in a highly developed organism (for example, to the brain of man), but are to be found only in the definite, constantly recurring structure, which every individual element displays. Hence it follows that the structural composition of a body of considerable size, a so-called individual, always represents a kind of social arrangement of parts, an arrangement of a social kind, in which a number of individual existences are mutually dependent, but in such a way, that every element has its own special action, and, even though it derive its stimulus to activity from other parts, yet alone effects the actual performance of its duties.
In Lecture I, 'Cells and the Cellular Theory' (1858), Rudolf Virchow and Frank Chance (trans.) ,Cellular Pathology (1860), 13-14.
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Let me describe briefly how a black hole might be created. Imagine a star with a mass 10 times that of the sun. During most of its lifetime of about a billion years the star will generate heat at its center by converting hydrogen into helium. The energy released will create sufficient pressure to support the star against its own gravity, giving rise to an object with a radius about five times the radius of the sun. The escape velocity from the surface of such a star would be about 1,000 kilometers per second. That is to say, an object fired vertically upward from the surface of the star with a velocity of less than 1,000 kilometers per second would be dragged back by the gravitational field of the star and would return to the surface, whereas an object with a velocity greater than that would escape to infinity.
When the star had exhausted its nuclear fuel, there would be nothing to maintain the outward pressure, and the star would begin to collapse because of its own gravity. As the star shrank, the gravitational field at the surface would become stronger and the escape velocity would increase. By the time the radius had got down to 10 kilometers the escape velocity would have increased to 100,000 kilometers per second, the velocity of light. After that time any light emitted from the star would not be able to escape to infinity but would be dragged back by the gravitational field. According to the special theory of relativity nothing can travel faster than light, so that if light cannot escape, nothing else can either. The result would be a black hole: a region of space-time from which it is not possible to escape to infinity.
'The Quantum Mechanics of Black Holes', Scientific American, 1977, 236, 34-40.
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Let the surgeon take care to regulate the whole regimen of the patient's life for joy and happiness by promising that he will soon be well, by allowing his relatives and special friends to cheer him and by having someone tell him jokes, and let him be solaced also by music on the viol or psaltery. The surgeon must forbid anger, hatred, and sadness in the patient, and remind him that the body grows fat from joy and thin from sadness.
In James Joseph Walsh, Old-Time Makers of Medicine (1911), 270.
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Mathematical knowledge is not—as all Cambridge men are surely aware—the result of any special gift. It is merely the development of those conceptions of form and number which every human being possesses; and any person of average intellect can make himself a fair mathematician if he will only pay continuous attention; in plain English, think enough about the subject.
'Science', a lecture delivered at the Royal Institution. The Works of Charles Kingsley (1880), 241.
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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 has often been characterized as the most conservative of all sciences. This is true in the sense of the immediate dependence of new upon old results. All the marvellous new advancements presuppose the old as indispensable steps in the ladder. … Inaccessibility of special fields of mathematics, except by the regular way of logically antecedent acquirements, renders the study discouraging or hateful to weak or indolent minds.
In Number and its Algebra (1896), 136.
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Montaigne simply turns his mind loose and writes whatever he feels like writing. Mostly, he wants to say that reason is not a special, unique gift of human beings, marking us off from the rest of nature.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1979), 147.
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Nature! … Each of her works has an essence of its own; each of her phenomena a special characterisation: and yet their diversity is in unity.
As quoted by T.H. Huxley, in Norman Lockyer (ed.), 'Nature: Aphorisms by Goethe', Nature (1870), 1, 10.
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Nevertheless, scientific method is not the same as the scientific spirit. The scientific spirit does not rest content with applying that which is already known, but is a restless spirit, ever pressing forward towards the regions of the unknown, and endeavouring to lay under contribution for the special purpose in hand the knowledge acquired in all portions of the wide field of exact science. Lastly, it acts as a check, as well as a stimulus, sifting the value of the evidence, and rejecting that which is worthless, and restraining too eager flights of the imagination and too hasty conclusions.
'The Scientific Spirit in Medicine: Inaugural Sessional Address to the Abernethian Society', St. Bartholomew's Hospital Journal, 1912, 20, 19.
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Next came the patent laws. These began in England in 1624, and in this country with the adoption of our Constitution. Before then any man [might] instantly use what another man had invented, so that the inventor had no special advantage from his own invention. The patent system changed this, secured to the inventor for a limited time exclusive use of his inventions, and thereby added the fuel of interest to the fire of genius in the discovery and production of new and useful things.
Lecture 'Discoveries, Inventions and Improvements' (22 Feb 1860) in John George Nicolay and John Hay (eds.), Complete Works of Abraham Lincoln (1894), Vol. 5, 113. In Eugene C. Gerhart, Quote it Completely! (1998), 802.
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Nirvana is a state of pure blissful knowledge ... It has nothing to do with the individual. The ego or its separation is an illusion. Indeed in a certain sense two ‘I’s are identical namely when one disregards all special contents–their Karma. The goal of man is to preserve his Karma and to develop it further ... when man dies his Karma lives and creates for itself another carrier.
…...
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No nation can be really great unless it is great in peace, in industry, integrity, honesty. Skilled intelligence in civic affairs and industrial enterprises alike; the special ability of the artist, the man of letters, the man of science, and the man of business; the rigid determination to wrong no man, and to stand for righteousness—all these are necessary in a great nation.
Address (2 Jun 1897) at U.S. Naval War College, Newport, Rhode Island. In 'Washington's Forgotten Maxim', United States Naval Institute Proceedings (1897), 23, 450.
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Nothing travels faster than the speed of light, with the possible exception of bad news, which obeys its own special laws.
In Mostly Harmless (1992), 1.
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One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
In Albert Einstein, translated by G.B. Jeffery and W. Perrett, 'Geometry and Experience',Sidelights on Relativity (1922), 27.
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Our eyes are special detectors. They allows us to register information not only from across the room but from across the universe.
In magazine article, 'Coming to our Senses', Natural History Magazine (Mar 2001). Collected in Death by Black Hole: And Other Cosmic Quandaries (2007), 25. This is Tyson’s respectful update of a quote by Edwin P. Hubble in 1954: “Equipped with his five senses, man explores the universe around him and calls the adventure science.” (See Science Quotations by Edwin Hubble.)
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Quantum mechanics and relativity, taken together, are extraordinarily restrictive, and they therefore provide us with a great logical machine. We can explore with our minds any number of possible universes consisting of all kinds of mythical particles and interactions, but all except a very few can be rejected on a priori grounds because they are not simultaneously consistent with special relativity and quantum mechanics. Hopefully in the end we will find that only one theory is consistent with both and that theory will determine the nature of our particular universe.
…...
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Scheele, it was said, never forgot anything if it had to do with chemistry. He never forgot the look, the feel, the smell of a substance, or the way it was transformed in chemical reactions, never forgot anything he read, or was told, about the phenomena of chemistry. He seemed indifferent, or inattentive, to most things else, being wholly dedicated to his single passion, chemistry. It was this pure and passionate absorption in phenomena—noticing everything, forgetting nothing—that constituted Scheele's special strength.
Uncle Tungsten: Memories of a Chemical Boyhood (2001), 44.
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Science and technology, and the various forms of art, all unite humanity in a single and interconnected system. As science progresses, the worldwide cooperation of scientists and technologists becomes more and more of a special and distinct intellectual community of friendship, in which, in place of antagonism, there is growing up a mutually advantageous sharing of work, a coordination of efforts, a common language for the exchange of information, and a solidarity, which are in many cases independent of the social and political differences of individual states.
In The Medvedev Papers (1970).
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Science, though apparently transformed into pure knowledge, has yet never lost its character of being a craft; and that it is not the knowledge itself which can rightly be called science, but a special way of getting and of using knowledge. Namely, science is the getting of knowledge from experience on the assumption of uniformity in nature, and the use of such knowledge to guide the actions of men.
In 'On The Scientific Basis of Morals', Contemporary Review (Sep 1875), collected in Leslie Stephen and Frederick Pollock (eds.), Lectures and Essays: By the Late William Kingdon Clifford, F.R.S. (1886), 289.
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So in regard to mental qualities, their transmission is manifest in our dogs, horses and other domestic animals. Besides special tastes and habits, general intelligence, courage, bad and good tempers. etc., are certainly transmitted.
The Descent of Man
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Society will pardon much to genius and special gifts; but, being in its nature conventional, it loves what is conventional, or what belongs to coming together.
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Study actively. Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
In I Want to be a Mathematician: An Automathography (1985), 69.
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Suicide is merely the product of the general condition of society, and that the individual felon only carries into effect what is a necessary consequence of preceding circumstances. In a given state of society, a certain number of persons must put an end to their own life. This is the general law; and the special question as to who shall commit the crime depends of course upon special laws; which, however, in their total action, must obey the large social law to which they are all subordinate. And the power of the larger law is so irresistible, that neither the love of life nor the fear of another world can avail any thing towards even checking its operation.
In History of Civilization in England (1857, 1904), 15-16.
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Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]
In Darwinism, chap. 15.
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That special substance according to whose mass and degree of development all the creatures of this world take rank in the scale of creation, is not bone, but brain.
The Foot-prints of the Creator: Or, The Asterolepis of Stromness (1850, 1859), 160.
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The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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The apodictic quality of mathematical thought, the certainty and correctness of its conclusions, are due, not to a special mode of ratiocination, but to the character of the concepts with which it deals. What is that distinctive characteristic? I answer: precision, sharpness, completeness,* of definition. But how comes your mathematician by such completeness? There is no mysterious trick involved; some ideas admit of such precision, others do not; and the mathematician is one who deals with those that do.
In 'The Universe and Beyond', Hibbert Journal (1904-1905), 3, 309. An editorial footnote indicates “precision, sharpness, completeness” — i.e., in terms of the absolutely clear and indefinable.
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The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Attributed, perhaps apocryphal. As given in Felix E. Browder, Norbert Wiener (1966), 65.
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The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Stated without quotation marks, as “attributed apocryphally perhaps”, in M. Kac, 'Wiener and Integration in Function Spaces', Bulletin of the American Mathematical Society (Jan 1966), 72, No. 1, Part 2, 65.
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The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Attributed (apocryphally perhaps). As cited in Bulletin of the American Mathematical Society (1966), 72, 65.
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The capacity to blunder slightly is the real marvel of DNA. Without this special attribute, we would still be anaerobic bacteria and there would be no music.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1979), 28.
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The chances for favorable serendipity are increased if one studies an animal that is not one of the common laboratory species. Atypical animals, or preparations, force one to use non-standard approaches and non-standard techniques, and even to think nonstandard ideas. My own preference is to seek out species which show some extreme of adaptation. Such organisms often force one to abandon standard methods and standard points of view. Almost inevitably they lead one to ask new questions, and most importantly in trying to comprehend their special and often unusual adaptations one often serendipitously stumbles upon new insights.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 234.
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The chemist works along his own brilliant line of discovery and exposition; the astronomer has his special field to explore; the geologist has a well-defined sphere to occupy. It is manifest, however, that not one of these men can tell the whole tale, and make a complete story of creation. Another man is wanted. A man who, though not necessarily going into formal science, sees the whole idea, and speaks of it in its unity. This man is the theologian. He is not a chemist, an astronomer, a geologist, a botanist——he is more: he speaks of circles, not of segments; of principles, not of facts; of causes and purposes rather than of effects and appearances. Not that the latter are excluded from his study, but that they are so wisely included in it as to be put in their proper places.
In The People's Bible: Discourses Upon Holy Scripture: Vol. 1. Genesis (1885), 120.
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The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Aristotle
As translated in Book 13, 1078.a3, Aristotle’s Metaphysics, a Revised Text with Introduction and Commentary by W. D. Ross (1924), Vol. 2, 416.
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The constant conditions which are maintained in the body might be termed equilibria. That word, however, has come to have fairly exact meaning as applied to relatively simple physico-chemical states, in closed systems, where known forces are balanced. The coordinated physiological processes which maintain most of the steady states in the organism are so complex and so peculiar to living beings—involving, as they may, the brain and nerves, the heart, lungs, kidneys and spleen, all working cooperatively—that I have suggested a special designation for these states, homeostasis. The word does not imply something set and immobile, a stagnation. It means a condition—a condition which may vary, but which is relatively constant.
In The Wisdom of the Body (1932), 24.
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The difficulties connected with my criterion of demarcation (D) are important, but must not be exaggerated. It is vague, since it is a methodological rule, and since the demarcation between science and nonscience is vague. But it is more than sharp enough to make a distinction between many physical theories on the one hand, and metaphysical theories, such as psychoanalysis, or Marxism (in its present form), on the other. This is, of course, one of my main theses; and nobody who has not understood it can be said to have understood my theory.
The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the 'means of production' would lead to social, political, and ideological developments, rather than the other way round.
But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin's and Stalin's ideology that Russia must push forward with its industrialization ('Socialism is dictatorship of the proletariat plus electrification') which promoted the new development of the means of production.
Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).
However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.
Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler's break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)
The point is very clear. Neither Freud nor Adler excludes any particular person's acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud's theory; the theory was compatible with everything that could happen—even without any special immunization treatment.
Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.
'The Problem of Demarcation' (1974). Collected in David Miller (ed.) Popper Selections (1985), 127-128.
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The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
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The doctrine of evolution implies the passage from the most organised to the least organised, or, in other terms, from the most general to the most special. Roughly, we say that there is a gradual 'adding on' of the more and more special, a continual adding on of new organisations. But this 'adding on' is at the same time a 'keeping down'. The higher nervous arrangements evolved out of the lower keep down those lower, just as a government evolved out of a nation controls as well as directs that nation.
'Evolution and Dissolution of the Nervous System', British Medical Journal (1884), I, 662.
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The efforts of most human-beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. Beneath the effort directed toward the accumulation of worldly goods lies all too frequently the illusion that this is the most substantial and desirable end to be achieved; but there is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual's own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.
In letter (1 May 1935), Letters to the Editor, 'The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician', New York Times (4 May 1935), 12.
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The elements of human nature are the learning rules, emotional reinforcers, and hormonal feedback loops that guide the development of social behaviour into certain channels as opposed to others. Human nature is not just the array of outcomes attained in existing societies. It is also the potential array that might be achieved through conscious design by future societies. By looking over the realized social systems of hundreds of animal species and deriving the principles by which these systems have evolved, we can be certain that all human choices represent only a tiny subset of those theoretically possible. Human nature is, moreover, a hodgepodge of special genetic adaptations to an environment largely vanished, the world of the Ice­Age hunter-gatherer.
In On Human Nature (1978), 196.
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The experience and behaviour that gets labelled schizophrenic is a special strategy that a person invents in order to live in an unlivable situation.
Politics of Experience (1967), 95.
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The first fundamental rule of historical science and research, when by these is sought a knowledge of the general destinies of mankind, is to keep these and every object connected with them steadily in view, without losing ourselves in the details of special inquiries and particular facts, for the multitude and variety of these subjects is absolutely boundless; and on the ocean of historical science the main subject easily vanishes from the eye.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 8.
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The Geometer has the special privilege to carry out, by abstraction, all constructions by means of the intellect.
In Paolo Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (1999), 138-139.
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The great rule: If the little bit you have is nothing special in itself, at least find a way of saying it that is a little bit special.
Aphorism 55 in Notebook E, as translated by R.J. Hollingdale in Aphorisms (1990).
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The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics.
In The Philosophy of the Inductive Sciences (1868), Part 1, Bk. 2, chap. 1, sect. 4.
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The important thing in any science is to do the things that can be done. Scientists naturally have a right and a duty to have opinions. But their science gives them no special insight into public affairs. There is a time for scientists and movie stars and people who have flown the Atlantic to restrain their opinions lest they be taken more seriously than they should be.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 69.
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The lives of scientists, considered as Lives, almost always make dull reading. For one thing, the careers of the famous and the merely ordinary fall into much the same pattern, give or take an honorary degree or two, or (in European countries) an honorific order. It could be hardly otherwise. Academics can only seldom lead lives that are spacious or exciting in a worldly sense. They need laboratories or libraries and the company of other academics. Their work is in no way made deeper or more cogent by privation, distress or worldly buffetings. Their private lives may be unhappy, strangely mixed up or comic, but not in ways that tell us anything special about the nature or direction of their work. Academics lie outside the devastation area of the literary convention according to which the lives of artists and men of letters are intrinsically interesting, a source of cultural insight in themselves. If a scientist were to cut his ear off, no one would take it as evidence of a heightened sensibility; if a historian were to fail (as Ruskin did) to consummate his marriage, we should not suppose that our understanding of historical scholarship had somehow been enriched.
'J.B.S: A Johnsonian Scientist', New York Review of Books (10 Oct 1968), reprinted in Pluto's Republic (1982), and inThe Strange Case of the Spotted Mice and Other Classic Essays on Science (1996), 86.
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The maintenance of biological diversity requires special measures that extend far beyond the establishment of nature reserves. Several reasons for this stand out. Existing reserves have been selected according to a number of criteria, including the desire to protect nature, scenery, and watersheds, and to promote cultural values and recreational opportunities. The actual requirements of individual species, populations, and communities have seldom been known, nor has the available information always been employed in site selection and planning for nature reserves. The use of lands surrounding nature reserves has typically been inimical to conservation, since it has usually involved heavy use of pesticides, industrial development, and the presence of human settlements in which fire, hunting, and firewood gathering feature as elements of the local economy.
The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), xii.
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The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube for three. Two men cooperating with two different pieces of apparatus, say a special furnace and a pyrometer or a hydraulic press and new chemical substances, are more powerful than their arithmetical sum. These facts doubtless assist as assets of a research laboratory.
Quoted from a speech delivered at the fiftieth anniversary of granting of M.I.T's charter, in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 352.
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The meaning of human life and the destiny of man cannot be separable from the meaning and destiny of life in general. 'What is man?' is a special case of 'What is life?' Probably the human species is not intelligent enough to answer either question fully, but even such glimmerings as are within our powers must be precious to us. The extent to which we can hope to understand ourselves and to plan our future depends in some measure on our ability to read the riddles of the past. The present, for all its awesome importance to us who chance to dwell in it, is only a random point in the long flow of time. Terrestrial life is one and continuous in space and time. Any true comprehension of it requires the attempt to view it whole and not in the artificial limits of any one place or epoch. The processes of life can be adequately displayed only in the course of life throughout the long ages of its existence.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 9.
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The most fundamental difference between compounds of low molecular weight and macromolecular compounds resides in the fact that the latter may exhibit properties that cannot be deduced from a close examination of the low molecular weight materials. Not very different structures can be obtained from a few building blocks; but if 10,000 or 100,000 blocks are at hand, the most varied structures become possible, such as houses or halls, whose special structure cannot be predicted from the constructions that are possible with only a few building blocks... Thus, a chromosome can be viewed as a material whose macromolecules possess a well defined arrangement, like a living room in which each piece of furniture has its place and not, as in a warehouse, where the pieces of furniture are placed together in a heap without design.
Quoted, without citation, in Ralph E. Oesper (ed.), The Human Side of Scientists (1975), 175.
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The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics “knows nothing of causation” could only be taken to express the whole truth, if by the term “causation” is understood “efficient causation.” The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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The participation in the general development of the mental powers without special reference to his future vocation must be recognized as the essential aim of mathematical instruction.
In Anleitung zum Mathematischen Unterricht an höheren Schulen (1906), 12.
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The particular ‘desire’ of the Eregion Elves—an ‘allegory’ if you like of a love of machinery, and technical devices—is also symbolised by their special friendship with the Dwarves of Moria.
From Letter draft to Peter Hastings (manager of a Catholic bookshop in Oxford, who wrote about his enthusiasm for Lord of the Rings) (Sep 1954). In Humphrey Carpenter (ed.) assisted by Christopher Tolkien, The Letters of J.R.R. Tolkien (1995, 2014), 190, Letter No. 153.
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The patient has two sleeves, one containing a diagnostic and the other a therapeutic armamentarium; these sleeves should rarely be emptied in one move; keep some techniques in reserve; time your manoeuvres to best serve the status and special needs of your patient.
Chinese proverb.
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The powerful notion of entropy, which comes from a very special branch of physics … is certainly useful in the study of communication and quite helpful when applied in the theory of language.
From 'The Growth of Science and the Structure of Culture', Daedalus (Winter 1958), 87, No. 1, 67.
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The process of natural selection has been summed up in the phrase “survival of the fittest.” This, however, tells only part of the story. “Survival of the existing” in many cases covers more of the truth. For in hosts of cases the survival of characters rests not on any special usefulness or fitness, but on the fact that individuals possessing these characters have inhabited or invaded a certain area. The principle of utility explains survivals among competing structures. It rarely accounts for qualities associated with geographic distribution.
The nature of animals which first colonize a district must determine what the future fauna will be. From their specific characters, which are neither useful nor harmful, will be derived for the most part the specific characters of their successors.
It is not essential to the meadow lark that he should have a black blotch on the breast or the outer tail-feather white. Yet all meadow larks have these characters just as all shore larks have the tiny plume behind the ear. Those characters of the parent stock, which may be harmful in the new relations, will be eliminated by natural selection. Those especially helpful will be intensified and modified, but the great body of characters, the marks by which we know the species, will be neither helpful nor hurtful. These will be meaningless streaks and spots, variations in size of parts, peculiar relations of scales or hair or feathers, little matters which can neither help nor hurt, but which have all the persistence heredity can give.
Foot-notes to Evolution. A Series of Popular Addresses on the Evolution of Life (1898), 218.
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The prominent reason why a mathematician can be judged by none but mathematicians, is that he uses a peculiar language. The language of mathesis is special and untranslatable. In its simplest forms it can be translated, as, for instance, we say a right angle to mean a square corner. But you go a little higher in the science of mathematics, and it is impossible to dispense with a peculiar language. It would defy all the power of Mercury himself to explain to a person ignorant of the science what is meant by the single phrase “functional exponent.” How much more impossible, if we may say so, would it be to explain a whole treatise like Hamilton’s Quaternions, in such a wise as to make it possible to judge of its value! But to one who has learned this language, it is the most precise and clear of all modes of expression. It discloses the thought exactly as conceived by the writer, with more or less beauty of form, but never with obscurity. It may be prolix, as it often is among French writers; may delight in mere verbal metamorphoses, as in the Cambridge University of England; or adopt the briefest and clearest forms, as under the pens of the geometers of our Cambridge; but it always reveals to us precisely the writer’s thought.
In North American Review (Jul 1857), 85, 224-225.
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The psychoanalysis of individual human beings, however, teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father.
(Originally published 1913). Totem and Taboo, vol. 13, pt. 4, sct. 6, Complete Works, Standard Edition, eds. James Strachey and Anna Freud (1953).
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The psychology of committees is a special case of the psychology of mobs.
In The Decline and Fall of Science (1976), 3.
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The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. [But] precise language is not precise in any sense if you deal with the real objects of the world, and is overly pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.
Criticizing “overly pedantic” language in proposed textbooks for a modified arithmetic course for grades 1-8 in California schools. In article, 'New Textbooks for the ‘New’ Mathematics', Engineering and Science (Mar 1965), 28, No. 6. Collected in Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard Feynman (2008), 454. He was writing as a member of the California State Curriculum Committee
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The special vital forces that distinguish living things from the nonliving are emergent, holistic properties, not properties of their physiochemical components. Nor can they be explained in mechanistic terms.
Interview in 'Vital Holistic Phenomena and Properties of Living', The World & I (1986), 1, No. 5-6, 265.
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The steady states of the fluid matrix of the body are commonly preserved by physiological reactions, i.e., by more complicated processes than are involved in simple physico-chemical equilibria. Special designations, therefore, are appropriate:—“homeostasis” to designate stability of the organism; “homeostatic conditions,” to indicate details of the stability; and “homeostatic reactions,” to signify means for maintaining stability.
'Physiological Regulation of Normal States: Some Tentative Postulates Concerning Biological Homeostatics', 1926. Reprinted in L. L. Langley (ed.), Homeostasis: Origins of the Concept (1973), 246.
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The total number of people who understand relativistic time, even after eighty years since the advent of special relativity, is still much smaller than the number of people who believe in horoscopes.
'Classical to Quantum: A Generalized Phase Transition', in A. van der Merwe et al. (eds.) Microphysical Reality and Quantum Formalism (1987), 145.
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The traditional boundaries between various fields of science are rapidly disappearing and what is more important science does not know any national borders. The scientists of the world are forming an invisible network with a very free flow of scientific information - a freedom accepted by the countries of the world irrespective of political systems or religions. ... Great care must be taken that the scientific network is utilized only for scientific purposes - if it gets involved in political questions it loses its special status and utility as a nonpolitical force for development.
Banquet speech accepting Nobel Prize in Physiology or Medicine (10 Dec 1982). In Wilhelm Odelberg (editor) Les Prix Nobel. The Nobel Prizes 1982 (1983)
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The words are strung together, with their own special grammar—the laws of quantum theory—to form sentences, which are molecules. Soon we have books, entire libraries, made out of molecular “sentences.” The universe is like a library in which the words are atoms. Just look at what has been written with these hundred words! Our own bodies are books in that library, specified by the organization of molecules—but the universe and literature are organizations of identical, interchangeable objects; they are information systems.
In The Cosmic Code: Quantum Physics as the Language of Nature (1983), 255.
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The world of mathematics, which you condemn, is really a beautiful world; it has nothing to do with life and death and human sordidness, but is eternal, cold and passionless. To me, pure, mathematics is one of the highest forms of art; it has a sublimity quite special to itself, and an immense dignity derived, from the fact that its world is exempt I, from change and time. I am quite serious in this. The only difficulty is that none but mathematicians can enter this enchanted region, and they hardly ever have a sense of beauty. And mathematics is the only thing we know of that is capable of perfection; in thinking about it we become Gods.
Letter to Helen Thomas (30 Dec 1901). Quoted in Nicholas Griffin (ed.), The Selected Letters of Bertrand Russell (1992), Vol. 1, 224.
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There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes.
From letter to his professor Christoffer Hansteen (1826) in Oeuvres, 2, 263-65. In Morris Kline, Mathematical Thought from Ancient to Modern Times (1990), Vol. 3, 947.
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There is a science which investigates being as being and the attributes which belong to this in virtue of its own nature. Now this is not the same as any of the so-called special sciences; for none of these treats universally of being as being. They cut off a part of being and investigate the attribute of this part; this is what the mathematical sciences for instance do. Now since we are seeking the first principles and the highest causes, clearly there must be some thing to which these belong in virtue of its own nature. If then those who sought the elements of existing things were seeking these same principles, it is necessary that the elements must be elements of being not by accident but just because it is being. Therefore it is of being as being that we also must grasp the first causes.
Aristotle
'Book Gamma (1003a17-1011b23' in Metaphysics, trans. W.D. Ross (1924). Excerpt 'Being Qua Being', in Joseph Margolis and Jacques Catudal, The Quarrel between Invariance and Flux (2001), 18-19.
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There is no such thing as a special category of science called applied science; there is science and its applications, which are related to one another as the fruit is related to the tree that has borne it.
In Pasteur Vallery-Radot (ed.), Correspondance de Pasteur 1840-1895 (1940), Vol. 1, 315. Quoted in Patrice Debré and Elborg Forster (trans.), Louis Pasteur, (1994), 84.
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There was one quality of mind which seemed to be of special and extreme advantage in leading him [Charles Darwin] to make discoveries. It was the power of never letting exceptions pass unnoticed. Everybody notices a fact as an exception when it is striking or frequent, but he had a special instinct for arresting an exception. A point apparently slight and unconnected with his present work is passed over by many a man almost unconsciously with some half-considered explanation, which is in fact no explanation. It was just these things that he seized on to make a start from. In a certain sense there is nothing special in this procedure, many discoveries being made by means of it. I only mention it because, as I watched him at work, the value of this power to an experimenter was so strongly impressed upon me.
In Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of his Published Letters (1908), 94-95.
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Till the fifteenth century little progress appears to have been made in the science or practice of music; but since that era it has advanced with marvelous rapidity, its progress being curiously parallel with that of mathematics, inasmuch as great musical geniuses appeared suddenly among different nations, equal in their possession of this special faculty to any that have since arisen. As with the mathematical so with the musical faculty it is impossible to trace any connection between its possession and survival in the struggle for existence.
In 'Darwinism Applied to Man', Darwinism: An Exposition of the Theory of Natural Selection with Some of Its Applications (1901), Chap. 15, 468.
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To be creative, scientists need libraries and laboratories and the company of other scientists; certainly a quiet and untroubled life is a help. A scientist's work is in no way deepened or made more cogent by privation, anxiety, distress, or emotional harassment. To be sure, the private lives of scientists may be strangely and even comically mixed up, but not in ways that have any special bearing on the nature and quality of their work. If a scientist were to cut off an ear, no one would interpret such an action as evidence of an unhappy torment of creativity; nor will a scientist be excused any bizarrerie, however extravagant, on the grounds that he is a scientist, however brilliant.
In Advice to a Young Scientist (1979), 40.
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Very old and wide-spread is the opinion that forests have an important impact on rainfall. ... If forests enhance the amount and frequency of precipitation simply by being there, deforestation as part of agricultural expansion everywhere, must necessarily result in less rainfall and more frequent droughts. This view is most poignantly expressed by the saying: Man walks the earth and desert follows his steps! ... It is not surprising that under such circumstances the issue of a link between forests and climate has ... been addressed by governments. Lately, the Italian government has been paying special attention to reforestation in Italy and its expected improvement of the climate. ... It must be prevented that periods of heavy rainfall alternate with droughts. ...In the Unites States deforestation plays an important role as well and is seen as the cause for a reduction in rainfall. ... committee chairman of the American Association for Advancement of Science demands decisive steps to extend woodland in order to counteract the increasing drought. ... some serious concerns. In 1873, in Vienna, the congress for agriculture and forestry discussed the problem in detail; and when the Prussian house of representatives ordered a special commission to examine a proposed law pertaining to the preservation and implementation of forests for safeguarding, it pointed out that the steady decrease in the water levels of Prussian rivers was one of the most serious consequences of deforestation only to be rectified by reforestation programs. It is worth mentioning that ... the same concerns were raised in Russia as well and governmental circles reconsidered the issue of deforestation.
as quoted in Eduard Brückner - The Sources and Consequences of Climate Change and Climate Variability in Historical Times editted by N. Stehr and H. von Storch (2000)
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Water is the most precious, limited natural resource we have in this country… But because water belongs to no one—except the people—special interests, including government polluters, use it as their private sewers.
In Nader’s Foreword to David Zwick, Marcy Benstock and Ralph Nader, Water wasteland: Ralph Nader's Study Group Report on Water Pollution (1971), xiii.
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We are having wool pulled over our eyes if we let ourselves be convinced that scientists, taken as a group, are anything special in the way of brains. They are very ordinary professional men, and all they know is their own trade, just like all other professional men. There are some geniuses among them, just as there are mental giants in any other field of endeavor.
In Science is a Sacred Cow (1950), 23-24.
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We are the only species that can destroy the Earth or take care of it and nurture all that live on this very special planet. I’m urging you to look on these things. For whatever reason, this planet was built specifically for us. Working on this planet is an absolute moral code. … Let’s go out and do what we were put on Earth to do.
Address at Tuskegee University, 79th Annual Scholarship Convocation/Parents Recognition Program. Published in News Release (3 Oct 2004). Previously on the university website.
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We can allow satellites, planets, suns, universe, nay whole systems of universe[s,] to be governed by laws, but the smallest insect, we wish to be created at once by special act.
In Notebook N (1838), 36. Excerpted in Charles Darwin, Thomas F. Glick (ed.) and David Kohn (ed.) On Evolution: The Development of the Theory of Natural Selection (1996), 80.
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We expect that the study of lunar geology will help to answer some longstanding questions about the early evolution of the earth. The moon and the earth are essentially a two-planet system, and the two bodies are probably closely related in origin. In this connection the moon is of special interest because its surface has not been subjected to the erosion by running water that has helped to shape the earth's surface.
In Scientific American (Sep 1964). As cited in '50, 100 & 150 Years Ago', Scientific American (Dec 2014), 311, No. 6, 98.
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We have corrupted the term research to mean study and experiment and development toward selected objectives, and we have even espoused secret and classified projects. This was not the old meaning of university research. We need a new term, or the revival of a still older one, to refer to the dedicated activities of the scholar, the intensive study of special aspects of a subject for its own sake, motivated by the love of knowledge and truth.
In 'Technology and National Research Policy', Bulletin of the Atomic Scientists (Oct 1953), 292.
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We may regard the cell quite apart from its familiar morphological aspects, and contemplate its constitution from the purely chemical standpoint. We are obliged to adopt the view, that the protoplasm is equipped with certain atomic groups, whose function especially consists in fixing to themselves food-stuffs, of importance to the cell-life. Adopting the nomenclature of organic chemistry, these groups may be designated side-chains. We may assume that the protoplasm consists of a special executive centre (Leistungs-centrum) in connection with which are nutritive side-chains… The relationship of the corresponding groups, i.e., those of the food-stuff, and those of the cell, must be specific. They must be adapted to one another, as, e.g., male and female screw (Pasteur), or as lock and key (E. Fischer).
Croonian Lecture, 'On Immunity with Special Reference to Cell Life', Proceedings of the Royal Society of London, 1900, 66, 433-434.
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We must infer that a plant or animal of any species, is made up of special units, in all of which there dwells the intrinsic aptitude to aggregate into the form of that species: just as in the atoms of a salt, there dwells the intrinsic aptitude to crystallize in a particular way.
In The Principles of Biology (1872), Vol. 1, 181.
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We now realize with special clarity, how much in error are those theorists who believe that theory comes inductively from experience.
In section 3, 'The Field Concept', Physics and Reality (1936), collected in Essays in Physics (1950), 28.
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What, then, is it in particular that can be learned from teachers of special distinction? Above all, what they teach is high standards. We measure everything, including ourselves, by comparisons; and in the absence of someone with outstanding ability there is a risk that we easily come to believe that we are excellent and much better than the next man. Mediocre people may appear big to themselves (and to others) if they are surrounded by small circumstances. By the same token, big people feel dwarfed in the company of giants, and this is a most useful feeling. So what the giants of science teach us is to see ourselves modestly and not to overrate ourselves.
Reminiscences and Reflections (1981), 175.
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When chemists have brought their knowledge out of their special laboratories into the laboratory of the world, where chemical combinations are and have been through all time going on in such vast proportions,—when physicists study the laws of moisture, of clouds and storms, in past periods as well as in the present,—when, in short, geologists and zoologists are chemists and physicists, and vice versa,—then we shall learn more of the changes the world has undergone than is possible now that they are separately studied.
Geological Sketches (1866), 73.
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When first I applied my mind to Mathematics I read straight away most of what is usually given by the mathematical writers, and I paid special attention to Arithmetic and Geometry because they were said to be the simplest and so to speak the way to all the rest. But in neither case did I then meet with authors who fully satisfied me. I did indeed learn in their works many propositions about numbers which I found on calculation to be true. As to figures, they in a sense exhibited to my eyes a great number of truths and drew conclusions from certain consequences. But they did not seem to make it sufficiently plain to the mind itself why these things are so, and how they discovered them. Consequently I was not surprised that many people, even of talent and scholarship, should, after glancing at these sciences, have either given them up as being empty and childish or, taking them to be very difficult and intricate, been deterred at the very outset from learning them. … But when I afterwards bethought myself how it could be that the earliest pioneers of Philosophy in bygone ages refused to admit to the study of wisdom any one who was not versed in Mathematics … I was confirmed in my suspicion that they had knowledge of a species of Mathematics very different from that which passes current in our time.
In Elizabeth S. Haldane (trans.) and G.R.T. Ross (trans.), 'Rules for the Direction of the Mind', The Philosophical Works of Descartes (1911, 1973), Vol. 1, Rule 4, 11.
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When not protected by law, by popular favor or superstition, or by other special circumstances, [birds] yield very readily to the influences of civilization, and, though the first operations of the settler are favorable to the increase of many species, the great extension of rural and of mechanical industry is, in a variety of ways, destructive even to tribes not directly warred upon by man.
In Man and Nature, (1864), 93-93.
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When one studies strongly radioactive substances special precautions must be taken if one wishes to be able to take delicate measurements. The various objects used in a chemical laboratory and those used in a chemical laboratory, and those which serve for experiments in physics, become radioactive in a short time and act upon photographic plates through black paper. Dust, the air of the room, and one's clothes all become radioactive.
Notebook entry. In Eve Curie, Madame Curie: a Biography by Eve Curie (1937, 2007), 196.
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When we think of giving a child a mathematical education we are apt to ask whether he has special aptitudes fitting him to receive it. Do we ask any such questions when we talk of teaching him to read and write?
In 'Mathematics for Children', Popular Science Monthly (Oct 1899), 187, citing “translated for the Popular Science Monthly from the Revue Scientifique. Also seen paraphrased as “To ask whether a child has an aptitude for mathematics is equivalent to asking whether he has an aptitude for reading and writing,” in William L. Schaaf, 'Memorabilia Mathematica', The Mathematics Teacher (Mar 1957), 50, No. 3, 231.
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Whenever … a controversy arises in mathematics, the issue is not whether a thing is true or not, but whether the proof might not be conducted more simply in some other way, or whether the proposition demonstrated is sufficiently important for the advancement of the science as to deserve especial enunciation and emphasis, or finally, whether the proposition is not a special case of some other and more general truth which is as easily discovered.
In Mathematical Essays and Recreations (1898), 88.
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[Defining Life] The special activity of organized beings.
Duges, "Physiologie Comparée." In The British Controversialist and Literary Magazine (1865), 234.
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[It has been ascertained by statistical observation that in engineering enterprises one man is killed for every million francs that is spent on the works.] Supposing you have to build a bridge at an expense of one hundred million francs, you must be prepared for the death of one hundred men. In building the Eiffel Tower, which was a construction costing six million and a half, we only lost four men, thus remaining below the average. In the construction of the Forth Bridge, 55 men were lost in over 45,000,000 francs’ worth of work. That would appear to be a large number according to the general rule, but when the special risks are remembered, this number shows as a very small one.
As quoted in 'M. Eiffel and the Forth Bridge', The Tablet (15 Mar 1890), 75, 400. Similarly quoted in Robert Harborough Sherard, Twenty Years in Paris: Being Some Recollections of a Literary Life (1905), 169, which adds to the end “, and reflects very great credit on the engineers for the precautions which they took on behalf of their men.” Sherard gave the context that Eiffel was at the inauguration [4 Mar 1890] of the Forth Bridge, and gave this compliment when conversing there with the Prince of Wales.
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[Student:} I only use my math book on special equations.
From movie Rock 'n' Roll High School (1979). Writers, Richard Whitley, Russ Dvonch and Joseph McBride. In Larry Langman and Paul Gold, Comedy Quotes from the Movies (2001), 359.
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[We] can easily distinguish what relates to Mathematics in any question from that which belongs to the other sciences. But as I considered the matter carefully it gradually came to light that all those matters only were referred to Mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called “Universal Mathematics,” not a far-fetched asignation, but one of long standing which has passed into current use, because in this science is contained everything on account of which the others are called parts of Mathematics.
Rules for the Direction of the Mind (written 1628). As translated by Elizabeth Sanderson Haldane and George Robert Thomson Ross in The Philosophical Works of Descartes (1911, 1931), 13.
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…The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein’s special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein’s amazing revelations have likewise sunk into the commonplaces of educated thought.
In The Theory of Relativity and its Influence on Scientific Thought (1922), 31-32
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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