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Home > Category Index for Science Quotations > Category Index F > Category: Function

Function Quotes (235 quotes)

... I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
Quoted in Sir Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), 541. Science and Method (1908) 51-52, 392.
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... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself … A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.
'Operational Definition and Analogy in Physical Theories', British Journal for the Philosophy of Science (Feb 1952), 2, No. 8, 291.
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“Any specialty, if important, is too important to be left to the specialists.” After all, the specialist cannot function unless he concentrates more or less entirely on his specialty and, in doing so, he will ignore the vast universe lying outside and miss important elements that ought to help guide his judgment. He therefore needs the help of the nonspecialist, who, while relying on the specialist for key information, can yet supply the necessary judgment based on everything else… Science, therefore, has become too important to be left to the scientists.
In 'The Fascination of Science', The Roving Mind (1983), 123. Asimov begins by extending a quote by George Clemenceau: “War is too important to be left to the generals.”
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“It's absolutely clear that the function of the world is to declare the glory of God.” I thought, what does that sentence mean?!
Quoting and reacting to a letter he saw in a newspaper about Stephen Hawking’s comments on the nonexistence of God. From 'Interview: Of Mind and Matter: David Attenborough Meets Richard Dawkins', The Guardian (11 Sep 2010).
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“These changes in the body,” he wrote in the review paper he sent to the American Journal of Physiology late in 1913, “are, each one of them, directly serviceable in making the organism more efficient in the struggle which fear or rage or pain may involve; for fear and rage are organic preparations for action, and pain is the most powerful known stimulus to supreme exertion. The organism which with the aid of increased adrenal secretion can best muster its energies, can best call forth sugar to supply the labouring muscles, can best lessen fatigue, and can best send blood to the parts essential in the run or the fight for life, is most likely to survive. Such, according to the view here propounded, is the function of the adrenal medulla at times of great emergency.”
Quoted in S. Benison, A. C. Barger and E. L. Wolfe, Walter B Cannon: The Life and Times of a Young Scientist (1987), 311.
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[Magic] enables man to carry out with confidence his important tasks, to maintain his poise and his mental integrity in fits of anger, in the throes of hate, of unrequited love, of despair and anxiety. The function of magic is to ritualize man's optimism, to enhance his faith in the victory of hope over fear. Magic expresses the greater value for man of confidence over doubt, of steadfastness over vacillation, of optimism over pessimism.
Magic, Science and Religion (1925), 90.
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[Molecular biology] is concerned particularly with the forms of biological molecules and with the evolution, exploitation and ramification of these forms in the ascent to higher and higher levels of organisation. Molecular biology is predominantly three-dimensional and structural—which does not mean, however, that it is merely a refinement of morphology. It must at the same time inquire into genesis and function.
From Harvey lecture (1951). As cited by John Law in 'The Case of X-ray Protein Crystallography', collected in Gerard Lemaine (ed.), Perspectives on the Emergence of Scientific Disciplines, 1976, 141.
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[The heart is] really a fascinating organ. It's about the only organ in the body that you can really witness its function. Doing things. And so on. Some of the other organs you can witness, like the intestines, will have this sort of peristaltic motion. But nothing that can compare with the activity of the human heart.
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Natura non facit saltum or, Nature does not make leaps… If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
From Benoit B. Mandelbrot and Richard Hudson, The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward (2004,2010), 85-86.
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The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiassed by personal feeling is characteristic of what may be termed the scientific frame of mind.
From The Grammar of Science (1892), 8.
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A function to each organ, and each organ to its own function, is the law of all organization.
Social Statics: Or, The Conditions Essential to Human Happiness Specified, and the First of them Developed (1851), 274.
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A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 140-141.
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Adrenalin does not excite sympathetic ganglia when applied to them directly, as does nicotine. Its effective action is localised at the periphery. The existence upon plain muscle of a peripheral nervous network, that degenerates only after section of both the constrictor and inhibitory nerves entering it, and not after section of either alone, has been described. I find that even after such complete denervation, whether of three days' or ten months' duration, the plain muscle of the dilatator pupillae will respond to adrenalin, and that with greater rapidity and longer persistence than does the iris whose nervous relations are uninjured. Therefore it cannot be that adrenalin excites any structure derived from, and dependent for its persistence on, the peripheral neurone. But since adrenalin does not evoke any reaction from muscle that has at no time of its life been innervated by the sympathetic, the point at which the stimulus of the chemical excitant is received, and transformed into what may cause the change of tension of the muscle fibre, is perhaps a mechanism developed out of the muscle cell in response to its union with the synapsing sympathetic fibre, the function of which is to receive and transform the nervous impulse. Adrenalin might then be the chemical stimulant liberated on each occasion when the impulse arrives at the periphery.
'On the Action of Adrenalin', Proceedings of the Physiological Society, 21 May 1904, in The Journal of Physiology 1904, 31, xxi.
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All living organisms are but leaves on the same tree of life. The various functions of plants and animals and their specialized organs are manifestations of the same living matter. This adapts itself to different jobs and circumstances, but operates on the same basic principles. Muscle contraction is only one of these adaptations. In principle it would not matter whether we studied nerve, kidney or muscle to understand the basic principles of life. In practice, however, it matters a great deal.
'Muscle Research', Scientific American, 1949, 180 (6), 22.
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All schools, all colleges have two great functions: to confer, and to conceal valuable knowledge.
(5 Nov 1908). 'More Maxims of Mark,' Mark Twain Collected Tales, Sketches, Speeches, & Essays, 1891-1910 (1992), 941. In Mark Twain and Brian Collins (ed.), When in Doubt, Tell the Truth: and Other Quotations from Mark Twain (1996), 43.
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All the properties that we designate as activity of the soul, are only the functions of the cerebral substance, and to express ourselves in a coarser way, thought is just about to the brain what bile is to the liver and urine to the kidney. It is absurd to admit an independent soul who uses the cerebellum as an instrument with which he would work as he pleases.
Carl Vogt
As quoted in William Vogt, La Vie d'un Homme, Carl Vogt (1896), 48. Translated by Webmaster, from the original French, “Toutes les propriétés que nous designons sous le nom d’activité de l’âme, ne sont que les fonctions de la substance cérébrale, et pour nous exprimer d’ une façon plus grossière, la pensée est à peu près au cerveau ce que la bile est au foie et l’urine au rein. Il est absurde d’ admettre une âme indépendante qui se serve du cervelet comme d’un instrument avec lequelle travaillerait comme il lui plait.”
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Although man is not armed by nature nor is naturally swiftest in flight, yet he has something better by far—reason. For by the possession of this function he exceeds the beasts to such a degree that he subdues. … You see, therefore, how much the gift of reason surpasses mere physical equipment.
As given in Toby E. Huff, The Rise of Early Modern Science: Islam, China and the West (2003), 102, citing Tina Stiefel, Science, Reason, and Faith in the Twelfth Century (1976), 3.
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An engineer [is] one of those people who make things work without even understanding how they function. … Today I would add: one of those people who are unable to make anything work, but think they know why it doesn’t function!
In 'Sundays in a Quantum Engineer’s Life', collected in Reinhold A. Bertlmann, A. Zeilinger (eds.),Quantum (Un)speakables: From Bell to Quantum Information (2002), 199.
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An immune system of enormous complexity is present in all vertebrate animals. When we place a population of lymphocytes from such an animal in appropriate tissue culture fluid, and when we add an antigen, the lymphocytes will produce specific antibody molecules, in the absence of any nerve cells. I find it astonishing that the immune system embodies a degree of complexity which suggests some more or less superficial though striking analogies with human language, and that this cognitive system has evolved and functions without assistance of the brain.
'The Generative Grammar of the Immune System', Nobel Lecture, 8 Dec 1984. In Nobel Lectures: Physiology or Medicine 1981-1990 (1993), 223.
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Analogue. A part or organ in one animal which has the same function as another part or organ in a different animal.
'Glossary', Lectures on the Comparative Anatomy and Physiology of the Invertebrate Animals Delivered at the Royal College of Surgeons in 1843 (1843), 374.
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André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That’s one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity.
In I Want to be a Mathematician: an Automathography (1985), 123.
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Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definition of a group of mathematical conceptions. Interdependence and mutual logical consistency among the members of the group are postulated, otherwise the group would either have to be treated as several distinct groups, or would lie beyond the sphere of mathematics.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
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Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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As I have already mentioned, wherever cells are formed, this tough fluid precedes the first solid structures that indicate the presence of future cells. Moreover, we must assume that this substance furnishes the material for the formation of the nucleus and of the primitive sac, not only because these structures are closely apposed to it, but also because,they react to iodine in the same way. We must assume also that the organization of this substance is the process that inaugurates the formation of new cells. It therefore seems justifiable for me to propose a name that refers to its physiological function: I propose the word protoplasma.
H. Mohl, Botanisch Zeitung (1846), 4, col. 73, trans. Henry Harris, The Birth of the Cell (1999), 75.
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As was predicted at the beginning of the Human Genome Project, getting the sequence will be the easy part as only technical issues are involved. The hard part will be finding out what it means, because this poses intellectual problems of how to understand the participation of the genes in the functions of living cells.
Loose Ends from Current Biology (1997), 71.
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At the beginning of this debate Stephen [Hawking] said that he thinks that he is a positivist, whereas I am a Platonist. I am happy with him being a positivist, but I think that the crucial point here is, rather, that I am a realist. Also, if one compares this debate with the famous debate of Bohr and Einstein, some seventy years ago, I should think that Stephen plays the role of Bohr, whereas I play Einstein's role! For Einstein argued that there should exist something like a real world, not necessarily represented by a wave function, whereas Bohr stressed that the wave function doesn't describe a 'real' microworld but only 'knowledge' that is useful for making predictions.
Debate at the Isaac Newton Institute of the Mathematical Sciences, Cambridge University (1994), transcribed in Stephen Hawking and Roger Penrose, The Nature of Space and Time (1996), 134-135.
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At this point, however, I have no intention whatever of criticizing the false teachings of Galen, who is easily first among the professors of dissection, for I certainly do not wish to start off by gaining a reputation for impiety toward him, the author of all good things, or by seeming insubordinate to his authority. For I am well aware how upset the practitioners (unlike the followers of Aristotle) invariably become nowadays, when they discover in the course of a single dissection that Galen has departed on two hundred or more occasions from the true description of the harmony, function, and action of the human parts, and how grimly they examine the dissected portions as they strive with all the zeal at their command to defend him. Yet even they, drawn by their love of truth, are gradually calming down and placing more faith in their own not ineffective eyes and reason than in Galen’s writings.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, iv, as translated by William Frank Richardson, in On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), Preface, liv.
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Bacteria are highly adaptable. They frequently change both morphologically and functionally. Their virulence is also an essentially fluctuating property, that increases or diminishes according to the conditions to which the pathogenic organism is subjected.
In Studies in Immunity (1909), 1.
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Biologists have long attempted by chemical means to induce in higher organisms predictable and specific changes which thereafter could be transmitted in series as hereditary characters. Among microorganisms the most striking example of inheritable and specific alterations in cell structure and function that can be experimentally induced and are reproducible under well defined and adequately controlled conditions is the transformation of specific types of Pneumococcus.
Oswald T. Avery (1877-1955), Colin Macleod (1909-72) and Maclyn McCarty (1911-2005), 'Studies on the Chemical Nature of the Substance Inducing Transformation of Pneumococcal Types', Journal of Experimental Medicine 1944, 79, 137.
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But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
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But science is the great instrument of social change, all the greater because its object is not change but knowledge, and its silent appropriation of this dominant function, amid the din of political and religious strife, is the most vital of all the revolutions which have marked the development of modern civilisation.
Decadence: Henry Sidgwick Memorial Lecture (1908), 55-6.
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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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Can the cultural evolution of higher ethical values gain a direction and momentum of its own and completely replace genetic evolution? I think not. The genes hold culture an a leash. The leash is very long, but inevitably values will be constrained in accordance with their effects in the human gene pool. The brain is a product of evolution. Human behaviour—like the deepest capacities for emotional response which drive and guide it—is the circuitous technique by which human genetic material has been and will be kept intact. Morality has no other demonstrable ultimate function.
In On Human Nature (1978), 167. In William Andrew Rottschaefer, The Biology and Psychology of Moral Agency (1998), 58.
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Chromosomes … [contain] some kind of code-script the entire pattern of the individual’s future development and of its functioning in the mature state. Every complete set of chromosomes contains the full code.
In What is Life? : The Physical Aspect of the Living Cell (1944), 20.
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Concentrate only on the achievements, and ignore the mistakes. When judging a mathematician you should only integrate f+ (the positive part of his function) and ignore the negative part. Perhaps this should apply more generally to all evaluations of your fellow men.
On his philosophy of writing letters of recommendation. As given in essay, Ronald Coifman and Robert S. Strichartz, 'The School of Antoni Zygmund', collected in Peter Duren (ed.), A Century of Mathematics in America (1989), 348. The authors acknowledge students of Zygmund provided personal recollections to them for the essay in general. Webmaster speculates the quote is from a student recollection, and not necessarily verbatim.
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Constant, or free, life is the third form of life; it belongs to the most highly organized animals. In it, life is not suspended in any circumstance, it unrolls along a constant course, apparently indifferent to the variations in the cosmic environment, or to the changes in the material conditions that surround the animal. Organs, apparatus, and tissues function in an apparently uniform manner, without their activity undergoing those considerable variations exhibited by animals with an oscillating life. This because in reality the internal environment that envelops the organs, the tissues, and the elements of the tissues does not change; the variations in the atmosphere stop there, so that it is true to say that physical conditions of the environment are constant in the higher animals; it is enveloped in an invariable medium, which acts as an atmosphere of its own in the constantly changing cosmic environment. It is an organism that has placed itself in a hot-house. Thus the perpetual changes in the cosmic environment do not touch it; it is not chained to them, it is free and independent.
Lectures on the Phenomena of Life Common to Animals and Plants (1878), trans. Hebbel E. Hoff, Roger Guillemin and Lucienne Guillemin (1974), 83.
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Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
(1906). As quoted “in free translation” in Benoit B. Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 7.
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Descriptive anatomy is to physiology what geography is to history, and just as it is not enough to know the typography of a country to understand its history, so also it is not enough to know the anatomy of organs to understand their functions.
Lectures on the Phenomena of Life Common to Animals and Plants (1878), trans. Hebbel E. Hoff, Roger Guillemin and Lucienne Guillemin (1974), 7.
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Disease is an abnormal state of the body which primarily and independently produces a disturbance in the normal functions of the body. It may be an abnormality of temperament or form (structure). Symptom is a manifestation of some abnormal state in the body. It may be harmful as a colic pain or harmless as the flushing of cheeks in peripneumonia.
Avicenna
'A Discussion of the Cause of Disease and Symptoms', in The Canon of Medicine, adapted by L. Bakhtiar (1999), 171.
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DNA that used to have some function way back in evolution but currently does not (and might possibly be revived if, say, an ancient parasite reappeared), DNA that controls how genes switch their protein manufacturing on and off, DNA that controls those, and so on. Some may actually be genuine junk. And some (so the joke goes) may encode a message like ‘It was me, I’m God, I existed all along, ha ha.’
With co-author Jack Cohen. In Terry Pratchett, Ian Stewart and Jack Cohen, Chap. 26, 'The Descent of Darwin', The Science of Discworld (1999), 193. Pratchett wrote the fantasy story told in the odd-numbered chapters. Following each, relevant real science is provided by his co-authors, Stewart and Cohen, in the even-numbered chapters (such as Chap. 26), but which of the two wrote which lines, is not designated. As the biologist, perhaps it was Jack Cohen who wrote this.
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Dr. Wallace, in his Darwinism, declares that he can find no ground for the existence of pure scientists, especially mathematicians, on the hypothesis of natural selection. If we put aside the fact that great power in theoretical science is correlated with other developments of increasing brain-activity, we may, I think, still account for the existence of pure scientists as Dr. Wallace would himself account for that of worker-bees. Their function may not fit them individually to survive in the struggle for existence, but they are a source of strength and efficiency to the society which produces them.
In Grammar of Science (1911), Part, 1, 221.
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During my span of life science has become a matter of public concern and the l'art pour l'art standpoint of my youth is now obsolete. Science has become an integral and most important part of our civilization, and scientific work means contributing to its development. Science in our technical age has social, economic, and political functions, and however remote one's own work is from technical application it is a link in the chain of actions and decisions which determine the fate of the human race. I realized this aspect of science in its full impact only after Hiroshima.
Max Born
My Life & My Views (1968), 49.
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During the half-century that has elapsed since the enunciation of the cell-theory by Schleiden and Schwann, in 1838-39, it has became ever more clearly apparent that the key to all ultimate biological problems must, in the last analysis, be sought in the cell. It was the cell-theory that first brought the structure of plants and animals under one point of view by revealing their common plan of organization. It was through the cell-theory that Kolliker and Remak opened the way to an understanding of the nature of embryological development, and the law of genetic continuity lying at the basis of inheritance. It was the cell-­theory again which, in the hands of Virchaw and Max Schultze, inaugurated a new era in the history of physiology and pathology, by showing that all the various functions of the body, in health and in disease, are but the outward expression of cell­-activities. And at a still later day it was through the cell-theory that Hertwig, Fol, Van Beneden, and Strasburger solved the long-standing riddle of the fertilization of the egg, and the mechanism of hereditary transmission. No other biological generalization, save only the theory of organic evolution, has brought so many apparently diverse phenomena under a common point of view or has accomplished more far the unification of knowledge. The cell-theory must therefore be placed beside the evolution-theory as one of the foundation stones of modern biology.
In The Cell in Development and Inheritance (1896), 1.
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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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EAT, v.i. To perform successively (and successfully) the functions of mastication, humectation, and deglutition.
The Cynic's Word Book (1906), 82. Also published later as The Devil's Dictionary.
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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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Engineers at General Motors have developed a revolutionary new engine whose only function is to lubricate itself.
In Napalm and Silly Putty (2002), 105.
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Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members. On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112-113.
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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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Evolution is a process which favors cooperating rather than disoperating groups and that “fitness” is a function of the group as a whole than of separate individuals. The fitness of the individual is largely derived from his membership on a group.
In On Being Human (1950), 45.
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Experiments may be of two kinds: experiments of simple fact, and experiments of quantity. ...[In the latter] the conditions will ... vary, not in quality, but quantity, and the effect will also vary in quantity, so that the result of quantitative induction is also to arrive at some mathematical expression involving the quantity of each condition, and expressing the quantity of the result. In other words, we wish to know what function the effect is of its conditions. We shall find that it is one thing to obtain the numerical results, and quite another thing to detect the law obeyed by those results, the latter being an operation of an inverse and tentative character.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 1892), 439.
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For if medicine is really to accomplish its great task, it must intervene in political and social life. It must point out the hindrances that impede the normal social functioning of vital processes, and effect their removal.
In Die einheitsrebungen in der wissenschaftlichen medicin (1849), 48. As quoted and citefd in Paul Farmer, Pathologies of Power (2004), 323.
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For, every time a certain portion is destroyed, be it of the brain or of the spinal cord, a function is compelled to cease suddenly, and before the time known beforehand when it would stop naturally, it is certain that this function depends upon the area destroyed. It is in this way that I have recognized that the prime motive power of respiration has its seat in that part of the medulla oblongata that gives rise to the nerves of the eighth pair [vagi]; and it is by this method that up to a certain point it will be possible to discover the use of certain parts of the brain.
Expériences sur le Principe de la Vie, Notamment sur celui des Mouvements du Coeur, et sur le Siege de ce Principe (1812), 148-149. Translated in Edwin Clarke and L. S. Jacyna, Nineteenth Century Origins of Neuroscientific Concepts (1987), 247.
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Fortunately Nature herself seems to have prepared for us the means of supplying that want which arises from the impossibility of making certain experiments on living bodies. The different classes of animals exhibit almost all the possible combinations of organs: we find them united, two and two, three and three, and in all proportions; while at the same time it may be said that there is no organ of which some class or some genus is not deprived. A careful examination of the effects which result from these unions and privations is therefore sufficient to enable us to form probable conclusions respecting the nature and use of each organ, or form of organ. In the same manner we may proceed to ascertain the use of the different parts of the same organ, and to discover those which are essential, and separate them from those which are only accessory. It is sufficient to trace the organ through all the classes which possess it, and to examine what parts constantly exist, and what change is produced in the respective functions of the organ, by the absence of those parts which are wanting in certain classes.
Letter to Jean Claude Mertrud. In Lectures on Comparative Anatomy (1802), Vol. I, xxiii--xxiv.
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Genetics has enticed a great many explorers during the past two decades. They have labored with fruit-flies and guinea-pigs, with sweet peas and corn, with thousands of animals and plants in fact, and they have made heredity no longer a mystery but an exact science to be ranked close behind physics and chemistry in definiteness of conception. One is inclined to believe, however, that the unique magnetic attraction of genetics lies in the vision of potential good which it holds for mankind rather than a circumscribed interest in the hereditary mechanisms of the lowly species used as laboratory material. If man had been found to be sharply demarcated from the rest of the occupants of the world, so that his heritage of physical form, of physiological function, and of mental attributes came about in a superior manner setting him apart as lord of creation, interest in the genetics of the humbler organisms—if one admits the truth—would have flagged severely. Biologists would have turned their attention largely to the ways of human heredity, in spite of the fact that the difficulties encountered would have rendered progress slow and uncertain. Since this was not the case, since the laws ruling the inheritance of the denizens of the garden and the inmates of the stable were found to be applicable to prince and potentate as well, one could shut himself up in his laboratory and labor to his heart's content, feeling certain that any truth which it fell to his lot to discover had a real human interest, after all.
Mankind at the Crossroads (1923), v-vi.
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Has anyone ever given credit to the Black Death for the Renaissance—in other words, for modern civilization? … [It] exterminated such huge masses of the European proletariat that the average intelligence and enterprise of the race were greatly lifted, and that this purged and improved society suddenly functioned splendidly. … The best brains of the time, thus suddenly emancipated, began to function freely and magnificently. There ensued what we call the Renaissance.
From American Mercury (Jun 1924), 188-189. Collected in 'Eugenic Note', A Mencken Chrestomathy (1949, 1956), 376-377.
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Historically [chemistry] arose from a constellation of interests: the empirically based technologies of early metallurgists, brewers, dyers, tanners, calciners and pharmacists; the speculative Greek philosphers' concern whether brute matter was invariant or transformable; the alchemists' real or symbolic attempts to achieve the transmutation of base metals into gold; and the iatrochemists' interst in the chemistry and pathology of animal and human functions. Partly because of the sheer complexity of chemical phenomena, the absence of criteria and standards of purity, and uncertainty over the definition of elements ... but above all because of the lack of a concept of the gaseous state of matter, chemistry remained a rambling, puzzling and chaotic area of natural philosophy until the middle of the eighteenth century.
The Chemical Tree: A History of Chemistry (2000), xxii.
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Homologue. The same organ in different animals under every variety of form and function.
'Glossary', Lectures on the Comparative Anatomy and Physiology of the Invertebrate Animals Delivered at the Royal College of Surgeons in 1843 (1843), 379.
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How can cosmic religious feeling be communicated from one person to another, if it can give rise to no definite notion of a God and no theology? In my view, it is the most important function of art and science to awaken this feeling and keep it alive in those who are receptive to it.
…...
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However much the pits may be apparent, yet none, as far as can be comprehended by the senses, passes through the septum of the heart from the right ventricle into the left. I have not seen even the most obscure passages by which the septum of the ventricles is pervious, although they are mentioned by professors of anatomy since they are convinced that blood is carried from the right ventricle into the left. As a result—as I shall declare more openly elsewhere—I am in no little doubt regarding the function of the heart in this part.
In De Humani Corporis Fabrica Libri Septem [Seven Books on the Structure of the Human Body] (revised ed. 1555), 734. Quoted and trans. in Charles Donald O'Malley, Andreas Vesalius of Brussels, 1514-1564 (1964), 281.
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Human societies are glued together with conversation and friendship. Conversation is the natural and characteristic activity of human beings. Friendship is the milieu within which we function.
In From Eros to Gaia (1992), 197.
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Hypothesis is the most important mental technique of the investigator, and its main function is to suggest new experiments or new observations. Indeed, most experiments and many observations are carried out with the deliberate object of testing an hypothesis. Another function is to help one see the significance of an object or event that otherwise would mean nothing. For instance, a mind prepared by the hypothesis of evolution would make many more significant observations on a field excursion than one not so prepared. Hypotheses should be used as tools to uncover new facts rather than as ends in themselves.
The Art of Scientific Investigation (1953), 46.
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I am more and more convinced that the ant colony is not so much composed of separate individuals as that the colony is a sort of individual, and each ant like a loose cell in it. Our own blood stream, for instance, contains hosts of white corpuscles which differ little from free-swimming amoebae. When bacteria invade the blood stream, the white corpuscles, like the ants defending the nest, are drawn mechanically to the infected spot, and will die defending the human cell colony. I admit that the comparison is imperfect, but the attempt to liken the individual human warrior to the individual ant in battle is even more inaccurate and misleading. The colony of ants with its component numbers stands half way, as a mechanical, intuitive, and psychical phenomenon, between our bodies as a collection of cells with separate functions and our armies made up of obedient privates. Until one learns both to deny real individual initiative to the single ant, and at the same time to divorce one's mind from the persuasion that the colony has a headquarters which directs activity … one can make nothing but pretty fallacies out of the polity of the ant heap.
In An Almanac for Moderns (1935), 121
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our “creations,” are simply the notes of our observations.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 113.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I consider the differences between man and animals in propensities, feelings, and intellectual faculties, to be the result of the same cause as that which we assign for the variations in other functions, viz. difference of organization; and that the superiority of man in rational endowments is not greater than the more exquisite, complicated, and perfectly developed structure of his brain, and particularly of his ample cerebral hemispheres, to which the rest of the animal kingdom offers no parallel, nor even any near approximation, is sufficient to account for.
Lectures on Physiology, Zoology, and the Natural History of Man (1819), 237.
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I have never had reason, up to now, to give up the concept which I have always stressed, that nerve cells, instead of working individually, act together, so that we must think that several groups of elements exercise a cumulative effect on the peripheral organs through whole bundles of fibres. It is understood that this concept implies another regarding the opposite action of sensory functions. However opposed it may seem to the popular tendency to individualize the elements, I cannot abandon the idea of a unitary action of the nervous system, without bothering if, by that, I approach old conceptions.
'The Neuron Doctrine-Theory and Facts', Nobel Lecture 11 Dec 1906. In Nobel Lectures: Physiology or Medicine 1901-1921 (1967), 216.
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I propose to substitute the word 'autonomic'. The word implies a certain degree of independent action, but exercised under control of a higher power. The 'autonomic' nervous system means the nervous system of the glands and of the involuntary muscle; it governs the 'organic' functions of the body.
'On the Union of Cranial Autonomic (Visceral) Fibres w;th the Nerve Cells of the Superior Cervical Ganglion', The Journal of Physiology, 1898-99, 23, 241.
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I want to put in something about Bernoulli’s numbers, in one of my Notes, as an example of how the implicit function may be worked out by the engine, without having been worked out by human head & hands first. Give me the necessary data & formulae.
Lovelace Papers, Bodleian Library, Oxford University, 42, folio 12 (6 Feb 1841). As quoted and cited in Dorothy Stein (ed.), 'This First Child of Mine', Ada: A Life and a Legacy (1985), 106-107.
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I will try to account for the degree of my aesthetic emotion. That, I conceive, is the function of the critic.
In Art (1913), 169.
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I wish that one would be persuaded that psychological experiments, especially those on the complex functions, are not improved [by large studies]; the statistical method gives only mediocre results; some recent examples demonstrate that. The American authors, who love to do things big, often publish experiments that have been conducted on hundreds and thousands of people; they instinctively obey the prejudice that the persuasiveness of a work is proportional to the number of observations. This is only an illusion.
L' Études expérimentale de l'intelligence (1903), 299.
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I would clarify that by ‘animal’ I understand a being that has feeling and that is capable of exercising life functions through a principle called soul; that the soul uses the body's organs, which are true machines, by virtue of its being the principal cause of the action of each of the machine's parts; and that although the placement that these parts have with respect to one another does scarcely anything else through the soul's mediation than what it does in pure machines, the entire machine nonetheless needs to be activated and guided by the soul in the same way as an organ, which, although capable of rendering different sounds through the placement of the parts of which it is composed, nonetheless never does so except through the guidance of the organist.
'La Mechanique des Animaux', in Oeuvres Diverses de Physique et de Mechanique (1721), Vol. 1, 329. Quoted in Jacques Roger, Keith R. Benson (ed.), Robert Ellrich (trans.), The Life Sciences in Eighteenth-Century French Thought, (1997), 273-4.
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I would rather be ashes than dust!
I would rather that my spark should burn out in a brilliant blaze than it should be stifled by dry-rot.
I would rather be a superb meteor, every atom of me in magnificent glow, than a sleepy and permanent planet.
The proper function of man is to live, not to exist.
I shall not waste my days in trying to prolong them.
I shall use my time.
'Jack London Credo' quoted, without citing a source, in Irving Shepard (ed.), Jack London’s Tales of Adventure (1956), Introduction, vii. (Irving Shepard was London's literary executor.) This sentiment, expressed two months before his death, was quoted by journalist Ernest J. Hopkins in the San Francisco Bulletin (2 Dec 1916), Pt. 2, 1. No direct source in London's writings has been found, though he wrote “I would rather be ashes than dust&rdquo. as an inscription in an autograph book. Biographer Clarice Stasz cautions that although Hopkins had visited the ranch just weeks before London's death, the journalist's quote (as was not uncommon in his time) is not necessarily reliable, or may be his own invention. See this comment in 'Apocrypha' appended to Jack London, The Call Of The Wild (eBookEden.com).
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If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
…...
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If sleeping and dreaming do not perform vital biological functions, then they must represent nature's most stupid blunder and most colossal waste of time.
Private Myths: Dreams and Dreaming (1995, 1997), 91.
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If we assume that there is only one enzyme present to act as an oxidizing agent, we must assume for it as many different degrees of activity as are required to explain the occurrence of the various colors known to mendelize (three in mice, yellow, brown, and black). If we assume that a different enzyme or group of enzymes is responsible for the production of each pigment we must suppose that in mice at least three such enzymes or groups of enzymes exist. To determine which of these conditions occurs in mice is not a problem for the biologist, but for the chemist. The biologist must confine his attention to determining the number of distinct agencies at work in pigment formation irrespective of their chemical nature. These agencies, because of their physiological behavior, the biologist chooses to call 'factors,' and attempts to learn what he can about their functions in the evolution of color varieties.
Experimental Studies of the Inheritance of Color in Mice (1913), 17-18.
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If we survey the mathematical works of Sylvester, we recognize indeed a considerable abundance, but in contradistinction to Cayley—not a versatility toward separate fields, but, with few exceptions—a confinement to arithmetic-algebraic branches. …
The concept of Function of a continuous variable, the fundamental concept of modern mathematics, plays no role, is indeed scarcely mentioned in the entire work of Sylvester—Sylvester was combinatorist [combinatoriker].
In Mathematische Annalen (1898), Bd.50, 134-135. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 173.
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In geologists’ own lives, the least effect of time is that they think in two languages, function on two different scales. … “A million years is a short time—the shortest worth messing with for most problems.”
In Basin and Range (1981), 134.
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In my personal view, a failure to discover unimagined objects and answer unasked questions, once HST functions properly, would indicate a lack of imagination in stocking the Universe on the part of the Deity.
In Hubble Space Telescope flaw: hearing before the Committee on Science, Space, and Technology, U.S. House of Representatives, One Hundred First Congress, second session, July 13, 1990 (1990), 105.
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In the animal world, on the other hand, the process of evolution is characterised by the progressive discrimination of the animal and vegetative functions, and a consequent differentiation of these two great provinces into their separate departments.
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In the course of normal speaking the inhibitory function of the will is continuously directed to bringing the course of ideas and the articulatory movements into harmony with each other. If the expressive movement which which follows the idea is retarded through mechanical causes, as is the case in writing ... such anticipations make their appearance with particular ease.
Folk Psychology (1900)
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In the dog two conditions were found to produce pathological disturbances by functional interference, namely, an unusually acute clashing of the excitatory and inhibitory processes, and the influence of strong and extraordinary stimuli. In man precisely similar conditions constitute the usual causes of nervous and psychic disturbances. Different conditions productive of extreme excitation, such as intense grief or bitter insults, often lead, when the natural reactions are inhibited by the necessary restraint, to profound and prolonged loss of balance in nervous and psychic activity.
Ivan Pavlov and G. V. Anrep (ed., trans.), Conditioned Reflexes—An Investigation of the Physiological Activity of the Cerebral Cortex (1927), 397.
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In the endeavor to clearly comprehend and explain the functions of the combination of forces called “brain,” the physiologist is hindered and troubled by the views of the nature of those cerebral forces which the needs of dogmatic theology have imposed on mankind.
In 'General Conclusions, Anatomy of the Vertebrates (1868, 2011), Vol. 3, Chap 40, 823. Excerpt in Noah Porter (ed.), Half Hours with Modern Scientists (1872), 71.
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In the last fifteen years we have witnessed an event that, I believe, is unique in the history of the natural sciences: their subjugation to and incorporation into the whirls and frenzies of disgusting publicity and propaganda. This is no doubt symptomatic of the precarious position assigned by present-day society to any form of intellectual activity. Such intellectual pursuits have at all times been both absurd and fragile; but they become ever more ludicrous when, as is now true of science, they become mass professions and must, as homeless pretentious parasites, justify their right to exist in a period devoted to nothing but the rapid consumption of goods and amusements. These sciences were always a divertissement in the sense in which Pascal used the word; but what is their function in a society living under the motto lunam et circenses? Are they only a band of court jesters in search of courts which, if they ever existed, have long lost their desire to be amused?
Voices in the Labyrinth: Nature, Man, and Science (1979), 27.
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In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.
In Adventure of Ideas (1933), 91.
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In trying to evaluate Hopkins' unique contribution to biochemistry it may perhaps be said that he alone amongst his contemporaries succeeded in formulating the subject. Among others whose several achievements in their own fields may have surpassed his, no one has ever attempted to unify and correlate biochemical knowledge so as to form a comprehensible picture of the cell and its relation to life, reproduction and function.
'Sir F. G. Hopkins' Teaching and Scientific Influence'. In J. Needham and E. Baldwin (eds.), Hopkins and Biochemistry, 1861-1947 (1949), 36.
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It [analysis] lacks at this point such plan and unity that it is really amazing that it can be studied by so many people. The worst is that it has not at all been treated with rigor. There are only a few propositions in higher analysis that have been demonstrated with complete rigor. Everywhere one finds the unfortunate manner of reasoning from the particular to the general, and it is very unusual that with such a method one finds, in spite of everything, only a few of what many be called paradoxes. It is really very interesting to seek the reason.
In my opinion that arises from the fact that the functions with which analysis has until now been occupied can, for the most part, be expressed by means of powers. As soon as others appear, something that, it is true, does not often happen, this no longer works and from false conclusions there flow a mass of incorrect propositions.
From a letter to his professor Hansteen in Christiania, Oslo in Correspondence (1902), 23 . In Umberto Bottazzini and Warren Van Egmond, The Higher Calculus (1986), 87-88.
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It is a melancholy experience for a professional mathematician to find him writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings; there is no scorn more profound, or on the whole more justifiable, than that of men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 61 (Hardy's opening lines after Snow's foreward).
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It is distinctly proved, by this series of observations, that the reflex function exists in the medulla independently of the brain; in the medulla oblongata independently of the medulla spinalis; and in the spinal marrow of the anterior extremities, of the posterior extremities, and of the tail, independently of that of each other of these parts, respectively. There is still a more interesting and satisfactory mode of performing the experiment: it is to divide the spinal marrow between the nerves of the superior and inferior extremities. We have then two modes of animal life : the first being the assemblage of the voluntary and respiratory powers with those of the reflex function and irritability; the second, the two latter powers only: the first are those which obtain in the perfect animal, the second those which animate the foetus. The phenomena are precisely what might have been anticipated. If the spinal marrow be now destroyed, the irritability alone remains,—all the other phenomena having ceased.
'On the Reflex Function of the Medulla Oblongata and Medulla Spinalis,' Philosophical Transactions of the Royal Society, 1833, 123, 650.
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It is in this mutual dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws, since it is evident that the seemly harmony between organs which interact is a necessary condition of existence of the creature to which they belong and that if one of these functions were modified in a manner incompatible with the modifications of the others the creature could no longer continue to exist.
Leçons d' anatomie comparée, Vol. I, 47. Trans. William Coleman, Georges Cuvier Zoologist: A Study in the History of Evolution Theory (1964), 67-8.
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It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 37-38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112.
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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 not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is tautological to say that an organism is adapted to its environment. It is even tautological to say that an organism is physiologically adapted to its environment. However, just as in the case of many morphological characters, it is unwarranted to conclude that all aspects of the physiology of an organism have evolved in reference to a specific milieu. It is equally gratuitous to assume that an organism will inevitably show physiological specializations in its adaptation to a particular set of conditions. All that can be concluded is that the functional capacities of an organism are sufficient to have allowed persistence within its environment. On one hand, the history of an evolutionary line may place serious constraints upon the types of further physiological changes that are readily feasible. Some changes might require excessive restructuring of the genome or might involve maladaptive changes in related functions. On the other hand, a taxon which is successful in occupying a variety of environments may be less impressive in individual physiological capacities than one with a far more limited distribution.
In W.R. Dawson, G.A. Bartholomew, and A.F. Bennett, 'A Reappraisal of the Aquatic Specializations of the Galapagos Marine Iguana (Amblyrhynchus cristatus)', Evolution (1977), 31, 891.
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It is the function of notions in science to be useful, to be interesting, to be verifiable and to acquire value from anyone of these qualities. Scientific notions have little to gain as science from being forced into relation with that formidable abstraction, “general truth.”
In paper delivered before the Royal College of Surgeons of England (15 Feb 1932), in 'The Commemoration of Great Men', British Medical Journal (1932), 1, 32. Collected in The Collected Papers of Wilfred Trotter, FRS (1941), 29.
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It is the intact and functioning organism on which natural selection operates. Organisms are therefore the central element of concern to the biologist who aspires to a broad and integrated understanding of biology.
From 'Interspecific comparison as a tool for ecological physiologists', collected in M.E. Feder, A.F. Bennett, W.W. Burggren, and R.B. Huey, (eds.), New Directions in Ecological Physiology (1987), 15.
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It is true that I am the father [of the H-bomb] in the biological sense that I performed a necessary function and let nature take its course. After that a child had to be born. It might he robust or it might be stillborn, but something had to be born. The process of conception was by no means a pleasure: it was filled with difficulty and anxiety….
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 72.
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It seems reasonable to envision, for a time 10 or 15 years hence, a “thinking center” that will incorporate the functions of present-day libraries together with anticipated advances in information storage and retrieval and ... a network of such centers, connected to one another by wide-band communication lines and to individual users by leased-wire services.
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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It should be the function of medicine to have people die young as late as possible.
…...
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It would seem that more than function itself, simplicity is the deciding factor in the aesthetic equation. One might call the process beauty through function and simplification.
As quoted in Christian Science Monitor (7 May 1952).
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It... [can] be easily shown:
1. That all present mountains did not exist from the beginning of things.
2. That there is no growing of mountains.
3. That the rocks or mountains have nothing in common with the bones of animals except a certain resemblance in hardness, since they agree in neither matter nor manner of production, nor in composition, nor in function, if one may be permitted to affirm aught about a subject otherwise so little known as are the functions of things.
4. That the extension of crests of mountains, or chains, as some prefer to call them, along the lines of certain definite zones of the earth, accords with neither reason nor experience.
5. That mountains can be overthrown, and fields carried over from one side of a high road across to the other; that peaks of mountains can be raised and lowered, that the earth can be opened and closed again, and that other things of this kind occur which those who in their reading of history wish to escape the name of credulous, consider myths.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 232-4.
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Just as mathematics aims to study such entities as numbers, functions, spaces, etc., the subject matter of metamathematics is mathematics itself.
In 'Mathematics: A Non-Technical Exposition', American Scientist (3 Jul 1954), 42, No. 3, 490.
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Leaving aside genetic surgery applied humans, I foresee that the coming century will place in our hands two other forms of biological technology which are less dangerous but still revolutionary enough to transform the conditions of our existence. I count these new technologies as powerful allies in the attack on Bernal's three enemies. I give them the names “biological engineering” and “self-reproducing machinery.” Biological engineering means the artificial synthesis of living organisms designed to fulfil human purposes. Self-reproducing machinery means the imitation of the function and reproduction of a living organism with non-living materials, a computer-program imitating the function of DNA and a miniature factory imitating the functions of protein molecules. After we have attained a complete understanding of the principles of organization and development of a simple multicellular organism, both of these avenues of technological exploitation should be open to us.
From 3rd J.D. Bernal Lecture, Birkbeck College London (16 May 1972), The World, the Flesh and the Devil (1972), 6. Collected in The Scientist as Rebel (2006), 292. (The World, the Flesh & the Devil: An Enquiry into the Future of the Three Enemies of the Rational Soul is the title of a book by J. D Bernal, a scientist who pioneered X-ray crystallography.)
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Life consists in the sum of the functions, by which death is resisted.
[Also translated as: Life is the ensemble of functions that resist death.]
Recherches physiologiques sur la vie et la mort (1800), trans. P. Gold, Physiological Researches on Life and Death (1815), 21.
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Logic it is called [referring to Whitehead and Russell’s Principia Mathematica] and logic it is, the logic of propositions and functions and classes and relations, by far the greatest (not merely the biggest) logic that our planet has produced, so much that is new in matter and in manner; but it is also mathematics, a prolegomenon to the science, yet itself mathematics in its most genuine sense, differing from other parts of the science only in the respects that it surpasses these in fundamentally, generality and precision, and lacks traditionality. Few will read it, but all will feel its effect, for behind it is the urgence and push of a magnificent past: two thousand five hundred years of record and yet longer tradition of human endeavor to think aright.
In Science (1912), 35, 110, from his book review on Alfred North Whitehead and Bertrand Russell, Principia Mathematica.
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Man is not only part of a field, but a part and member of his group. When people are together, as when they are at work, then the most unnatural behavior, which only appears in late stages or abnormal cases, would be to behave as separate Egos. Under normal circumstances they work in common, each a meaningfully functioning part of the whole.
Lecture at the Kantgesellschaft (Kant Society), Berlin (17 Dec 1924), 'Über Gestalttheorie', as taken down in shorthand. Translated by N. Nairn-Allison in Social Research (1944), 11, 91.
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Man not only survives and functions in his environment, he shapes it and he is shaped by it.
In Barbara Ward and René Jules Dubos, Only One Earth: the Care and Maintenance of a Small Planet: an unofficial report commissioned by the Secretary-General of the United Nations Conference on the Human Environment (1972), 30. This is similar to the quote, “Man shapes himself through decisions that shape his environment,” which is commonly seen attributed to Dubos, but without citation. If you know the primary source of this wording of that quote, please contact webmaster.
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Man's health and well-being depends upon, among many things, the proper functioning of the myriad proteins that participate in the intricate synergisms of living systems.
Nobel Prize Banquet Speech (10 Dec 1972).
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Mankind lies groaning, half-crushed beneath the weight of its own progress. Men do not sufficiently realize that their future is in their own hands. Theirs is the task of determining first of all whether they want to go on living or not. Theirs the responsibility, then, for deciding if they want merely to live, or intend to make just the extra effort required for fulfilling, even on their refractory planet, the essential function of the universe, which is a machine for the making of gods.
The Two Sources of Morality and Religion, trans. by R. Ashley Audra and Cloudesley Brereton (1935), 275.
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Mathematicians … believed that prediction was just a function of keeping track of things. If you knew enough, you could predict anything. … Chaos theory throws it right out the window because … in fact there are great categories of phenomena that are inherently unpredictable.
In novel, Jurassic Park (1990, 1991), 158.
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Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skilful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures.
In Werke [Kehrbach] (1890), Bd. 5, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
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Matter and mind are not separate, they are aspects of one energy. Look at the mind as a function of matter and you have science; look at matter as the product of the mind and you have religion.
…...
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Models so constructed, though of no practical value, serve a useful academic function. The oldest problem in economic education is how to exclude the incompetent. The requirement that there be an ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.
In Economics, Peace, and Laughter (1981), 40-41.
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My own prejudices are exactly the opposite of the functionalists’: “If you want to understand function, study structure.” I was supposed to have said in my molecular biology days. (I believe I was sailing at the time.)
What Mad Pursuit: A Personal View of Scientific Discovery (1988), 150.
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My reading of Aristotle leads me to believe that in all his work he had always before him the question; What light does this throw on man? But the question was not phrased in his mind—at least, so it appears to me—in the sense of “What light does this throw upon the origin of man,” but rather in the sense “What light does this throw on the way in which man functions and behaves here and now?”
Considering Aristotle as an anthropologist. In 'Review: The Discovery of Man by Stanley Casson', Isis (Jun 1941), 33, No. 2, 303.
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Myths and science fulfill a similar function: they both provide human beings with a representation of the world and of the forces that are supposed to govern it. They both fix the limits of what is considered as possible.
The Possible and the Actual (1982), 9.
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Natural selection produces systems that function no better than necessary. It results in ad hoc adaptive solutions to immediate problems. Whatever enhances fitness is selected. The product of natural selection is not perfection but adequacy, not final answers but limited, short-term solutions.
In 'The role of natural history in contemporary biology', BioScience (1986), 36, 325.
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Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does.
In Day the Universe Changed (1985), 11.
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No knowledge can be more satisfactory to a man than that of his own frame, its parts, their functions and actions.
Letter (7 Oct 1814) to Thomas Cooper. Collected in The Writings of Thomas Jefferson: Correspondence (1854), 390.
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No occupation is more worthy of an intelligent and enlightened mind, than the study of Nature and natural objects; and whether we labour to investigate the structure and function of the human system, whether we direct our attention to the classification and habits of the animal kingdom, or prosecute our researches in the more pleasing and varied field of vegetable life, we shall constantly find some new object to attract our attention, some fresh beauties to excite our imagination, and some previously undiscovered source of gratification and delight.
In A Practical Treatise on the Cultivation of the Dahlia (1838), 1-2.
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No physiologist who calmly considers the question in connection with the general truths of his science, can long resist the conviction that different parts of the cerebrum subserve different kinds of mental action. Localization of function is the law of all organization whatever: separateness of duty is universally accompanied with separateness of structure: and it would be marvellous were an exception to exist in the cerebral hemispheres.
The Principles of Psychology (1855), 607.
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Nothing in our experience suggests the introduction of [complex numbers]. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 537.
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Nursing at its highest level encompasses the teaching of the individual to know his body and its functions for the maintenance and promotion of health and prevention of disease. Self-care can be, and is, very efficacious when people are encouraged and guided to learn to care for themselves, whenever possible.
As quoted in American Nurses’ Association, Contemporary Minority Leaders in Nursing: Afro-American, Hispanic, Native American Perspectives (1983), 92.
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Objective conscience is the function of a normal being; the representative of God in the essence. Buried so deeply that it remains relatively indestructible.
In On Love & Psychological Exercises: With Some Aphorisms & Other Essays (1998), 52.
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Of all the constituents of the human body, bone is the hardest, the driest, the earthiest, and the coldest; and, excepting only the teeth, it is devoid of sensation. God, the great Creator of all things, formed its substance to this specification with good reason, intending it to be like a foundation for the whole body; for in the fabric of the human body bones perform the same function as do walls and beams in houses, poles in tents, and keels and ribs in boats.
Bones Differentiated by Function
Some bones, by reason of their strength, form as it were props for the body; these include the tibia, the femur, the spinal vertebrae, and most of the bony framework. Others are like bastions, defense walls, and ramparts, affording natural protection to other parts; examples are the skull, the spines and transverse processes of the vertebrae, the breast bone, the ribs. Others stand in front of the joints between certain bones, to ensure that the joint does not move too loosely or bend to too acute an angle. This is the function of the tiny bones, likened by the professors of anatomy to the size of a sesame seed, which are attached to the second internode of the thumb, the first internode of the other four fingers and the first internodes of the five toes. The teeth, on the other hand, serve specifically to cut, crush, pound and grind our food, and similarly the two ossicles in the organ of hearing perform a specifically auditory function.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, 1, as translated by William Frank Richardson, in 'Nature of Bone; Function of Bones', On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), 1.
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Old mathematicians never die; they just lose some of their functions.
Anonymous
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On the one hand, then, in the reproductive functions proper—menstruation, defloration, pregnancy and parturition—woman is biologically doomed to suffer. Nature seems to have no hesitation in administering to her strong doses of pain, and she can do nothing but submit passively to the regimen prescribed. On the other hand, as regards sexual attraction, which is necessary for the act of impregnation, and as regards the erotic pleasures experienced during the act itself, the woman may be on an equal footing with the man.
'Passivity, Masochism and Femininity', Journal of Psychoanalysis, 1935, 16, 327.
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One most necessary function of the brain is to exert an inhibitory power over the nerve centres that lie below it, just as man exercises a beneficial control over his fellow animals of a lower order of dignity; and the increased irregular activity of the lower centres surely betokens a degeneration: it is like the turbulent, aimless action of a democracy without a head.
The Physiology and Pathology of Mind (1868), 94.
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Organisms ... are directed and limited by their past. They must remain imperfect in their form and function, and to that extent unpredictable since they are not optimal machines. We cannot know their future with certainty, if only because a myriad of quirky functional shifts lie within the capacity of any feature, however well adapted to a present role.
…...
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Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archaeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.
From Address (1940), given at the Bicentennial Conference at the University of Pennsylvania, 'The Mathematical Way of Thinking'. Collected in Hermann Weyl and Peter Pesic (ed.), Levels of Infinity: Selected Writings on Mathematics and Philosophy (2012), 67.
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Physiology, in its analysis of the physiological functions of the sense organs, must use the results of subjective observation of sensations; and psychology, in its turn, needs to know the physiological aspects of sensory function, in order rightly to appreciate the psychological.
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Plants, again, inasmuch as they are without locomotion, present no great variety in their heterogeneous pacts. For, when the functions are but few, few also are the organs required to effect them. ... Animals, however, that not only live but perceive, present a great multiformity of pacts, and this diversity is greater in some animals than in others, being most varied in those to whose share has fallen not mere life but life of high degree. Now such an animal is man.
Aristotle
Parts of Animals, 655b, 37-656a, 7. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 1021-2.
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Plants, generally speaking, meet the impact of the terrestrial environment head on, although of course they in turn modify the physical environment by adventitious group activity. The individual plant cannot select its habitat; its location is largely determined by the vagaries of the dispersal of seeds or spores and is thus profoundly affected by chance. Because of their mobility and their capacity for acceptance or rejection terrestrial animals, in contrast, can and do actively seek out and utilize the facets of the environment that allow their physiological capacities to function adequately. This means that an animal by its behavior can fit the environment to its physiology by selecting situations in which its physiological capacities can cope with physical conditions. If one accepts this idea, it follows that there is no such thing as The Environment, for there exist as many different terrestrial environments as there are species of animals.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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Post-operatively the transplanted kidney functioned immediately with a dramatic improvement in the patient’s renal and cardiopulmonary status. This spectacular success was a clear demonstration that organ transplantation could be life-saving. In a way, it was spying into the future because we had achieved our long-term goal by bypassing, but not solving, the issue of biological incompatibility.
Referring to the pioneering first kidney transplant. It was well-matched since it was between twins. In Nobel Lecture (8 Dec 1990). Printed in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures, Physiology or Medicine 1981-1990 (1993).
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Psychogenesis has led to man. Now it effaces itself, relieved or absorbed by another and a higher function—the engendering and subsequent development of the mind, in one word noogenesis. When for the first time in a living creature instinct perceived itself in its own mirror, the whole world took a pace forward.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 181. Originally published in French as Le Phénomene Humain (1955).
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Psychology is a part of the science of life or biology. … As the physiologist inquires into the way in which the so-called “functions” of the body are performed, so the psychologist studies the so-called “faculties” of the mind.
In Hume (1879), 50.
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Reproduction is so primitive and fundamental a function of vital organisms that the mechanism by which it is assured is highly complex and not yet clearly understood. It is not necessarily connected with sex, nor is sex necessarily connected with reproduction.
Psychology of Sex (1933), 7.
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Returning to the moon is an important step for our space program. Establishing an extended human presence on the moon could vastly reduce the costs of further space exploration, making possible ever more ambitious missions. Lifting heavy spacecraft and fuel out of the Earth’s gravity is expensive. Spacecraft assembled and provisioned on the moon could escape its far lower gravity using far less energy, and thus, far less cost. Also, the moon is home to abundant resources. Its soil contains raw materials that might be harvested and processed into rocket fuel or breathable air. We can use our time on the moon to develop and test new approaches and technologies and systems that will allow us to function in other, more challenging environments. The moon is a logical step toward further progress and achievement.
Speech, NASA Headquarters (14 Jan 2004). In Office of the Federal Register (U.S.) Staff (eds.), Public Papers of the Presidents of the United States, George W. Bush (2007), 58.
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Science has fulfilled her function when she has ascertained and enunciated truth.
From Man’s Place in Nature (1894), 108-109.
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Science is able to make cooperate catholics and mechanics, students and Nobel prize winners, because a common faith distributes the functions of workmanship despite all differences of rational formulation.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 8.
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Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one other—only in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.
The Social System (1951, 1977), Chap. 8, 111. As a functionalist, Parsons argued that social practices had to be studied in terms of their function in maintaining society.
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Science, in the immediate, produces knowledge and, indirectly, means of action. It leads to methodical action if definite goals are set up in advance. For the function of setting up goals and passing statements of value transcends its domain. While it is true that science, to the extent of its grasp of causative connections, may reach important conclusions as to the compatibility and incompatibility of goals and evaluations, the independent and fundamental definitions regarding goals and values remain beyond science’s reach.
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Scientific physiology has the task of determining the functions of the animal body and deriving them as a necessary consequence from its elementary conditions.
Lehrbuch der Physiologie des Menschens (1852), Vol 1, 1. Trans. Paul F. Cranefield, 'The Organic Physics of 1847 and the Biophysics of Today', Journal of the History of Medicine and Allied Sciences (1957), 12, 410.
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Scientific practice is above all a story-telling practice. ... Biology is inherently historical, and its form of discourse is inherently narrative. ... Biology as a way of knowing the world is kin to Romantic literature, with its discourse about organic form and function. Biology is the fiction appropriate to objects called organisms; biology fashions the facts “discovered” about organic beings.
Primate Visions: Gender, Race and Nature in the World of Modern Science(1989), 4-5.
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Several times every day I observed the portions of the polyp with a magnifying glass. On the 4th December, that is to say on the ninth day after having cut the polyp, I seemed in the morning to be able to perceive, on the edges of the anterior end of the second part (the part that had neither head nor arms), three little points arising from those edges. They immediately made me think of the horns that serve as the legs and arms of the polyp. Nevertheless I did not want to decide at once that these were actually arms that were beginning to grow. Throughout the next day I continually observed these points: this excited me extremely, and awaited with impatience the moment when I should know with certainty what they were. At last, on the following day, they were so big that there was no longer any room for doubt that they were actually arms growing at the anterior extremity of this second part. The next day two more arms started to grow out, and a few days later three more. The second part thus had eight of them, and they were all in a short time as long as those of the first part, that is to say as long as those the polyp possessed before it was cut. I then no longer found any difference between the second part and a polyp that had never been cut. I had remarked the same thing about the first part since the day after the operation. When I observed them with the magnifying glass with all the attention of which I was capable, each of the two appeared perceptibly to be a complete polyp, and they performed all the functions that were known to me: they extended, contracted, and walked.
Mémoires, pour servir à l'histoire d'un genre de polyps d'eau douce à bras en forme de cornes (1744), 7-16. Trans. John R. Baker, in Abraham Trembley of Geneva: Scientist and Philosopher 1710-1784 (1952), 32.
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Sex is a natural function. You can’t make it happen, but you can teach people to let it happen.
NY Times 29 Oct 84
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Sexual instinct—as emotion, idea, and impulse—is a function of the cerebral cortex. Thus far no definite region of the cortex has been proved to be exclusively the seat of sexual sensations and impulses.
Psychopathia Sexualis: With Special Reference to Contrary Sexual Instinct: A Medico-Legal Study (1886), trans. Charles Gilbert Chaddock (1892), 24.
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Since disease originates in the elementary cell, the organization and microscopic functions of which reproduce the general organization exactly and in all its relationships, nothing is more suited to simplifying the work of classification and of systematic division than to take the elementary cell as the basis of division.
As quoted in article, Marc Klein,'François-Vincent Raspail', in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1975). Vol.11, 300-301.
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Since many cases are known in which the specificities of antigens and enzymes appear to bear a direct relation to gene specificities, it seems reasonable to suppose that the gene’s primary and possibly sole function is in directing the final configurations of protein molecules.
Assuming that each specific protein of the organism has its unique configuration copied from that of a gene, it follows that every enzyme whose specificity depends on a protein should be subject to modification or inactivation through gene mutation. This would, of course, mean that the reaction normally catalyzed by the enzyme in question would either have its rate or products modified or be blocked entirely.
Such a view does not mean that genes directly “make” proteins. Regardless of precisely how proteins are synthesized, and from what component parts, these parts must themselves be synthesized by reactions which are enzymatically catalyzed and which in turn depend on the functioning of many genes. Thus in the synthesis of a single protein molecule, probably at least several hundred different genes contribute. But the final molecule corresponds to only one of them and this is the gene we visualize as being in primary control.
In 'Genetics and Metabolism in Neurospora', Physiological Reviews, 1945, 25, 660.
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Some of the worst tyrannies of our day genuinely are ‘vowed’ to the service of mankind, yet can function only by pitting neighbor against neighbor. The all-seeing eye of a totalitarian regime is usually the watchful eye of the next-door neighbor. In a Communist state love of neighbor may be classed as counter-revolutionary.
In 'Brotherhood', The Ordeal of Change (1963), 91.
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Sometime in my early teens, I started feeling an inner urgency, ups and downs of excitement and frustration, caused by such unlikely occupations as reading Granville’s course of calculus ... I found this book in the attic of a friend’s apartment. Among other standard stuff, it contained the notorious epsilon-delta definition of continuous functions. After struggling with this definition for some time (it was the hot Crimean summer, and I was sitting in the shadow of a dusty apple tree), I got so angry that I dug a shallow grave for the book between the roots, buried it there, and left in disdain. Rain started in an hour. I ran back to the tree and exhumed the poor thing. Thus, I discovered that I loved it, regardless.
'Mathematics as Profession and vocation', in V. Arnold et al. (eds.), Mathematics: Frontiers and Perspectives (2000), 153. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 79.
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Superficially, it might be said that the function of the kidneys is to make urine; but in a more considered view one can say that the kidneys make the stuff of philosophy itself.
'The Evolution of the Kidney', Lectures on the Kidney (1943), 4.
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Sylvester was incapable of reading mathematics in a purely receptive way. Apparently a subject either fired in his brain a train of active and restless thought, or it would not retain his attention at all. To a man of such a temperament, it would have been peculiarly helpful to live in an atmosphere in which his human associations would have supplied the stimulus which he could not find in mere reading. The great modern work in the theory of functions and in allied disciplines, he never became acquainted with …
What would have been the effect if, in the prime of his powers, he had been surrounded by the influences which prevail in Berlin or in Gottingen? It may be confidently taken for granted that he would have done splendid work in those domains of analysis, which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.
In Address delivered at a memorial meeting at the Johns Hopkins University (2 May 1897), published in Bulletin of the American Mathematical Society (Jun 1897), 303. Also in Johns Hopkins University Circulars, 16 (1897), 54.
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Tait dubbed Maxwell dp/dt, for according to thermodynamics dp/dt = JCM (where C denotes Carnot’s function) the initials of (J.C.) Maxwell’s name. On the other hand Maxwell denoted Thomson by T and Tait by T'; so that it became customary to quote Thomson and Tait’s Treatise on Natural Philosophy as T and T'.
In Bibliotheca Mathematica (1903), 3, 187. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 178. [Note: Thomson is William Thomson, later Lord Kelvin. —Webmaster.]
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The actuality of us being cognizant and accepting of the fact we are but a speck of sand in a universe sized desert, whose existence is irrelevant to any facet of universal function is a hard pill to swallow. Knowing the world will go on for another billion years after death and you will have no recollection of anything, just as you have no recollection of the billion years before your birth is a mind-boggling intuition.
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The admirable perfection of the adaptations of organisms and of their parts to the functions they perform has detracted attention from the fact that adaptedness does not consist of perfect fit, but capacity to fit or to adapt in a variety of ways: only in this sense is adaptedness a guarantee of further survival and evolutionary progress, for too perfect a fit is fatal to the species if not to the individual. This, I think, sets phylogeny and ontogeny in the correct perspective. It is the genotype which bears the marks of past experience of the species and defines the range of possible fits. What fit is actually chosen, what phenotype is actually evolved, is determined by the ever renewed individual history.
'The Interplay of Heredity and Environment in the Synthesis of Respiratory Enzymes in Yeast', The Harvey Lectures: Delivered under the auspices of The Harvey Society of New York 1950-1951, 1951, 156, 45-6.
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The basic ideas and simplest facts of set-theoretic topology are needed in the most diverse areas of mathematics; the concepts of topological and metric spaces, of compactness, the properties of continuous functions and the like are often indispensable.
As co-author with H. Hopf, Topologie I (1935), 23. As quoted, translated and cited in Reinhold Remmert, Theory of Complex Functions (1991), 9-10. From the original German, “Die Grundbegriffe und die einfachsten Tatsachen aus der mengentheoretischen Topologie braucht man in sehr verschiedenen Gebieten der Mathematik; die Begriffe des topologischen und des metrischen Raumes, der Kompaktheit, die Eigenschaften stetiger Abbildungen u. dgl. sind oft unentbehrlich.”
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The chemical differences among various species and genera of animals and plants are certainly as significant for the history of their origins as the differences in form. If we could define clearly the differences in molecular constitution and functions of different kinds of organisms, there would be possible a more illuminating and deeper understanding of question of the evolutionary reactions of organisms than could ever be expected from morphological considerations.
'Uber das Vorkommen von Haemoglobin in den Muskeln der Mollusken und die Verbreitung desselben in den lebenden Organismen', Pflügers Archiv für die gesamte Physiologie des Menschen und der Tiere, 1871, 4, 318-9. Trans. Joseph S. Fruton, Proteins, Enzymes, Genes: The Interplay of Chemistry and Biology (1999), 270.
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The choice of zoology as a main subject [at university] was to follow up my childhood love of nature. … My animal studies never became quite what I had hoped for. We hardly heard of wild beasts and the way they lived in the wilderness. We sliced up intestines and looked at them under the microscope … but their life and function in the environment was ignored in favor of their Latin names. … Was our knowledge of nature superior to, or only different from, that of the eagle-eyed Polynesian islanders, who specialized in appraising nature the way it could best benefit man? I had to think as a scientist now. Not as a Polynesian yet. Knowledge was to be sought independently of its purpose.
In Ch. 1, 'Farewell to Civilization', Fatu-Hiva (1974), 9-10.
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The energy of a covalent bond is largely the energy of resonance of two electrons between two atoms. The examination of the form of the resonance integral shows that the resonance energy increases in magnitude with increase in the overlapping of the two atomic orbitals involved in the formation of the bond, the word ‘overlapping” signifying the extent to which regions in space in which the two orbital wave functions have large values coincide... Consequently it is expected that of two orbitals in an atom the one which can overlap more with an orbital of another atom will form the stronger bond with that atom, and, moreover, the bond formed by a given orbital will tend to lie in that direction in which the orbital is concentrated.
Nature of the Chemical Bond and the Structure of Molecules and Crystals (1939), 76.
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The essence of religion is inertia; the essence of science is change. It is the function of the one to preserve, it is the function of the other to improve. If, as in Egypt, they are firmly chained together, either science will advance, in which case the religion will be altered, or the religion will preserve its purity, and science will congeal.
In The Martyrdom of Man (1876), 41.
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The events of the past few years have led to a critical examination of the function of science in society. It used to be believed that the results of scientific investigation would lead to continuous progressive improvements in conditions of life; but first the War and then the economic crisis have shown that science can be used as easily for destructive and wasteful purposes, and voices have been raised demanding the cessation of scientific research as the only means of preserving a tolerable civilization. Scientists themselves, faced with these criticisms, have been forced to consider, effectively for the first time, how the work they are doing is connected around them. This book is an attempt to analyse this connection; to investigate how far scientists, individually and collectively, are responsible for this state of affairs, and to suggest what possible steps could be taken which would lead to a fruitful and not to a destructive utilization of science.
The Social Function of Science (1939), xlii.
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The existence of life must be considered as an elementary fact that can not be explained, but must be taken as a starting point in biology, in a similar way as the quantum of action, which appears as an irrational element from the point of view of classical mechanical physics, taken together with the existence of elementary particles, forms the foundation of atomic physics. The asserted impossibility of a physical or chemical explanation of the function peculiar to life would in this sense be analogous to the insufficiency of the mechanical analysis for the understanding of the stability of atoms.
'Light and Life', Nature, 1933, 131, 458.
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The fact is that up to now the free society has not been good for the intellectual. It has neither accorded him a superior status to sustain his confidence nor made it easy for him to acquire an unquestioned sense of social usefulness. For he derives his sense of usefulness mainly from directing, instructing, and planning-from minding other people’s business-and is bound to feel superfluous and neglected where people believe themselves competent to manage individual and communal affairs, and are impatient of supervision and regulation. A free society is as much a threat to the intellectual’s sense of worth as an automated economy is to the workingman’s sense of worth. Any social order that can function with a minimum of leadership will be anathema to the intellectual.
In 'Concerning Individual Freedom', The Ordeal of Change (1963), 141.
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The fate of the physiology of the brain is independent of the truth and falsity of my assertions relative to the laws of the organization of the nervous system, in general, and of the brain in particular, just as the knowledge of the functions of a sense is independent of the knowledge of the structure of its apparatus.
Critical Review of Some Anatomical- Physiological Works; With an Explanation of a New Philosophy of the Moral Qualities and Intellectual Faculties (1835), 237-8.
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The following theorem can be found in the work of Mr. Cauchy: If the various terms of the series u0 + u1 + u2 +... are continuous functions,… then the sum s of the series is also a continuous function of x. But it seems to me that this theorem admits exceptions. For example the series
sin x - (1/2)sin 2x + (1/3)sin 3x - …
is discontinuous at each value (2m + 1)π of x,…
In Oeuvres (1826), Vol. 1, 224-225. As quoted and cited in Ernst Hairer and Gerhard Wanner Analysis by Its History (2008), 213.
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The function of Art is to imitate Nature in her manner of operation. Our understanding of “her manner of operation” changes according to advances in the sciences.
John Cage
A Year from Monday (1969), 31.
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The function of geometry is to draw us away from the sensible and the perishable to the intelligible and the eternal.
Plutarch
As quoted in Benjamin Farrington, Greek Science: Its Meaning for Us (Thales to Aristotle) (1944), 38-39.
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The function of ignoring, of inattention, is as vital a factor in mental progress as the function of attention itself.
In The Principles of Psychology (1918), Vol. 2, 371.
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The function of Latin literature is its expression of Rome. When to England and France your imagination can add Rome in the background, you have laid firm the foundations of culture. The understanding of Rome leads back to the Mediterranean civilisation of which Rome was the last phase, and it automatically exhibits the geography of Europe, and the functions of seas and rivers and mountains and plains. The merit of this study in the education of youth is its concreteness, its inspiration to action, and the uniform greatness of persons, in their characters and their staging. Their aims were great, their virtues were great, and their vices were great. They had the saving merit of sinning with cart ropes.
In 'The Place of Classics in Education', The Aims of Education: & Other Essays (1917), 106.
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The function of mutation is to maintain the stock of genetic variance at a high level.
(1930).
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The function of prayer is not to influence God, but rather to change the nature of the one who prays.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 179
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The function of science fiction is not always to predict the future but sometimes to prevent it.
…...
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The History of Evolution of Organisms consists of two kindred and closely connected parts: Ontogeny, which is the history of the evolution of individual organisms, and Phylogeny, which is the history of the evolution of organic tribes. Ontogency is a brief and rapid recapitulation of Phylogeny, dependent on the physiological functions of Heredity (reproduction) and Adaptation (nutrition). The individual organism reproduces in the rapid and short course of its own evolution the most important of the changes in form through which its ancestors, according to laws of Heredity and Adaptation, have passed in the slow and long course of their palaeontological evolution.
Translated from his Generelle Morphologie (1866) as an epigraph to Chap. 1, The Evolution of Man, (1886), Vol 1, 1-2.
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The human brain became large by natural selection (who knows why, but presumably for good cause). Yet surely most ‘things’ now done by our brains, and essential both to our cultures and to our very survival, are epiphenomena of the computing power of this machine, not genetically grounded Darwinian entities created specifically by natural selection for their current function.
…...
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The law of the heart is thus the same as the law of muscular tissue generally, that the energy of contraction, however measured, is a function of the length of the muscle fibre.
The Linacre Lecture on the Law of the Heart (1918), 142.
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The laws of Coexistence;—the adaptation of structure to function; and to a certain extent the elucidation of natural affinities may be legitimately founded upon the examination of fully developed species;—But to obtain an insight into the laws of development,—the signification or bedeutung, of the parts of an animal body demands a patient examination of the successive stages of their development, in every group of Animals.
'Lecture Four, 9 May 1837', The Hunterian Lectures in Comparative Anatomy, May-June 1837, ed. Phillip Reid Sloan (1992), 191.
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The microbial global brain—gifted with long-range transport, data trading, genetic variants … and the ability to reinvent genomes—began its operations some 91 trillion bacterial generations before the birth of the Internet. Ancient bacteria, if they functioned like those today, had mastered the art of worldwide information exchange. … The earliest microorganisms would have used planet-sweeping currents of wind and water to carry the scraps of genetic code…
In 'Creative Nets in the Precambrian Era', Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 18-19.
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The mind has an outlook which transcends the natural law by which it functions.
Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 56.
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The Modern Theory of Functions—that stateliest of all the pure creations of the human intellect.
In Lectures on Science, Philosophy and Art (1908), 16.
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The more I meditate on the principles of the theory of functions—and I do this unremittingly the stronger becomes my conviction that the foundations upon which these must be built are the truths of Algebra…
From Letter (3 Oct 1875), to Professor Schwartz. As quoted and translated in Ernst Hairer and Gerhard Wanner, Analysis by Its History (2008), 177. From the original German in Mathematische Werke (1875, 1895), Vol. 2, 235, “Je mehr ich über die Principien der Functionentheorie nachdenke—und ich thue dies unablässig—, um so fester wird meine Überzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss…”
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The name chronic alcoholism applies to the collective symptoms of a disordered condition of the mental, motor, and sensory functions of the nervous system, these symptoms assuming a chronic form, and without their being immediately connected with any of those (organic) modifications of the central or peripheric portions of the nervous system which may be detected during life, or discovered after death by ocular inspection; such symptoms, moreover, affecting individuals who have persisted for a considerable length of time in the abuse of alcoholic liquors.
Published in Swedish in 1849. Translation quoted in William Marcet On Chronic Alcoholic Intoxication (1868), 21.
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The neuro-physiological organization which we call instinct functions in a blindly mechanical way, particularly apparent when its function goes wrong.
On Aggression, trans. M. Latzke (1966), 73.
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The new appears as a minority point of view, and hence is unpopular. The function of a university is to give it a sanctuary.
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The night before Easter Sunday of that year (1920) I awoke, turned on the light, and jotted down a few notes on a tiny slip of thin paper. Then I fell asleep again. It occurred to me at six o’clock in the morning that during the night I had written down something most important, but I was unable to decipher the scrawl. The next night, at three o’clock, the idea returned. It was the design of an experiment to determine whether the hypothesis of chemical transmission that I had uttered seventeen years ago was correct. I got up immediately, went to the laboratory, and performed a simple experiment on a frog heart according to the nocturnal design. I have to describe this experiment briefly since its results became the foundation of the theory of chemical transmission of the nervous impulse. The hearts of two frogs were isolated, the first with its nerves, the second without. Both hearts were attached to Straub cannulas filled with a little Ringer solution. The vagus nerve of the first heart was stimulated for a few minutes. Then the Ringer solution that had been in the first heart during the stimulation of the vagus was transferred to the second heart. It slowed and its beats diminished just as if its vagus had been stimulated. Similarly, when the accelerator nerve was stimulated and the Ringer from this period transferred, the second heart speeded up and its beats increased. These results unequivocally proved that the nerves do not influence the heart directly but liberate from their terminals specific chemical substances which, in their turn, cause the well-known modifications of the function of the heart characteristic of the stimulation of its nerves.
'An Autobiographic Sketch', Perspectives in Biology and Medicine (1960), 4, 17.
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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 same thing may have all the kinds of causes, e.g. the moving cause of a house is the art or the builder, the final cause is the function it fulfils, the matter is earth and stones, and the form is the definitory formula.
Aristotle
Metaphysics, 996b, 5-8. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1574.
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The saying often quoted from Lord Kelvin… that “where you cannot measure your knowledge is meagre and unsatisfactory,” as applied in mental and social science, is misleading and pernicious. This is another way of saying that these sciences are not science in the sense of physical science and cannot attempt to be such without forfeiting their proper nature and function. Insistence on a concretely quantitative economics means the use of statistics of physical magnitudes, whose economic meaning and significance is uncertain and dubious. (Even wheat is approximately homogeneous only if measured in economic terms.) And a similar statement would even apply more to other social sciences. In this field, the Kelvin dictum very largely means in practice, “if you cannot measure, measure anyhow!”
'What is Truth' in Economics? (1956), 166.
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The soul of man is—objectively considered—essentially similar to that of all other vertebrates; it is the physiological action or function of the brain.
In Wonders of Life (1904), 12.
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The test of a first-rate intelligence is the ability to hold two opposed ideas in mind at the same time and still retain the ability to function.
The Crack-Up (1936, 1993), 69.
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The ultimate function of prophecy is not to tell the future, but to make it. Your successful past will block your visions of the future.
…...
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The universe is an asymmetrical entity. I am inclined to believe that life as it is manifested to us must be a function of the asymmetry of the universe or of the consequence of this fact. The universe is asymmetrical; for if one placed the entire set of bodies that compose the solar system, each moving in its own way, before a mirror, the image shown would not be superimposable on the reality.
Rene Vallery-Radot, Vie de Pasteur (1900), 79. Quoted in Patrice Debre, Louis Pasteur, trans. Elborg Forster (1994), 78.
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The university imparts information, but it imparts it imaginatively. At least, this is the function which it should perform for society. A university which fails in this respect has no reason for existence. This atmosphere of excitement, arising from imaginative consideration, transforms knowledge. A fact is no longer a bare fact: it is invested with all its possibilities. It is no longer a bur. den on the memory: it is energising as the poet of our dreams, and as the architect of our purposes.
In 'Universities and Their Function', The Aims of Education: & Other Essays (1917), 139.
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There are many occasions when the muscles that form the lips of the mouth move the lateral muscles that are joined to them, and there are an equal number of occasions when these lateral muscles move the lips of this mouth, replacing it where it cannot return of itself, because the function of muscle is to pull and not to push except in the case of the genitals and the tongue.
'Anatomy', in The Notebooks of Leonardoda Vinci, trans. E. MacCurdy (1938), Vol. 1, 152.
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There are those who say that the human kidney was created to keep the blood pure, or more precisely, to keep our internal environment in an ideal balanced state. This I must deny. I grant that the human kidney is a marvelous organ, but I cannot grant that it was purposefully designed to excrete urine or to regulate the composition of the blood or to subserve the physiological welfare of Homo sapiens in any sense. Rather I contend that the human kidney manufactures the kind of urine that it does, and it maintains the blood in the composition which that fluid has, because this kidney has a certain functional architecture; and it owes that architecture not to design or foresight or to any plan, but to the fact that the earth is an unstable sphere with a fragile crust, to the geologic revolutions that for six hundred million years have raised and lowered continents and seas, to the predacious enemies, and heat and cold, and storms and droughts; to the unending succession of vicissitudes that have driven the mutant vertebrates from sea into fresh water, into desiccated swamps, out upon the dry land, from one habitation to another, perpetually in search of the free and independent life, perpetually failing, for one reason or another, to find it.
From Fish to Philosopher (1953), 210-1.
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There are three ways to encourage initiative. One is to cut off people’s heads as they do in Russia. Another is to subject people to public criticism, which is impossible in such secret work as this. A third way is to set up competition. This is Livermore’s most valuable function: simply to be a competitor.
Explaining the merit in setting up a second laboratory, at Livermore, California, to continue his thermonuclear research after he left Los Alamos due to disagreements he had there. As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 70-72.
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There is no end of hypotheses about consciousness, particularly by philosophers. But most of these are not what we might call principled scientific theories, based on observables and related to the functions of the brain and body. Several theories of consciousness based on functionalism and on the machine model of the mind... have recently been proposed. These generally come in two flavors: one in which consciousness is assumed to be efficacious, and another in which it is considered an epiphenomenon. In the first, consciousness is likened to the executive in a computer systems program, and in the second, to a fascinating but more or less useless by-product of computation.
Bright and Brilliant Fire, On the Matters of the Mind (1992), 112.
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There is plenty of room left for exact experiment in art, and the gate has been opened for some time. What had been accomplished in music by the end of the eighteenth century has only begun in the fine arts. Mathematics and physics have given us a clue in the form of rules to be strictly observed or departed from, as the case may be. Here salutary discipline is come to grips first of all with the function of forms, and not with form as the final result … in this way we learn how to look beyond the surface and get to the root of things.
Paul Klee
Quoted in The Bulletin of the Atomic Scientists (Feb 1959), 59, citing Bauhaus-Zeitschrijt (1928).
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There is thus a possibility that the ancient dream of philosophers to connect all Nature with the properties of whole numbers will some day be realized. To do so physics will have to develop a long way to establish the details of how the correspondence is to be made. One hint for this development seems pretty obvious, namely, the study of whole numbers in modern mathematics is inextricably bound up with the theory of functions of a complex variable, which theory we have already seen has a good chance of forming the basis of the physics of the future. The working out of this idea would lead to a connection between atomic theory and cosmology.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 129.
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They hold that the function of universities is to make learning repellent and thus to prevent its becoming dangerously common. And they discharge this beneficent function all the more efficiently because they do it unconsciously and automatically. The professors think they are advancing healthy intellectual assimilation and digestion when they are in reality little better than cancer on the stomach.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 32.
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This is only one step in a much larger project. I discovered (no, not me: my team) the function of sugar nucleotides in cell metabolism. I want others to understood this, but it is not easy to explain: this is not a very noteworthy deed, and we hardly know even a little.
[replying when asked about the significance of his Nobel prize-winning achievement.]
As quoted in John H. Exto, Crucible of Science: The Story of the Cori Laboratory (2013), 52.
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This organ deserves to be styled the starting point of life and the sun of our microcosm just as much as the sun deserves to be styled the heart of the world. For it is by the heart's vigorous beat that the blood is moved, perfected, activated, and protected from injury and coagulation. The heart is the tutelary deity of the body, the basis of life, the source of all things, carrying out its function of nourishing, warming, and activating body as a whole. But we shall more fittingly speak of these matters when we consider the final cause of this kind of movement.
De Motu Cordis (1628), The Circulation of the Blood and Other Writings, trans. Kenneth J. Franklin (1957), Chapter 8, 59. Alternate translation: “The heart is the beginning of life; the sun of the microcosm, even as the sun in his turn might well be designated the heart of the world; for it is the heart by whose virtue and pulse the blood is moved, perfected, made apt to nourish, and is preserved from corruption and coagulation; it is the household divinity which, discharging its function, nourishes, cherishes, quickens the whole body, and is indeed the foundation of life, the source of all action. … The heart, like the prince in a kingdom, in whose hands lie the chief highest authority, rules over all; it is the original and foundation from which all power is derived, on which all power depends in the animal body.” In translation by Geoffrey Keynes (1953), 59.
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This relation logical implication is probably the most rigorous and powerful of all the intellectual enterprises of man. From a properly selected set of the vast number of prepositional functions a set can be selected from which an infinitude of prepositional functions can be implied. In this sense all postulational thinking is mathematics. It can be shown that doctrines in the sciences, natural and social, in history, in jurisprudence and in ethics are constructed on the postulational thinking scheme and to that extent are mathematical. Together the proper enterprise of Science and the enterprise of Mathematics embrace the whole knowledge-seeking activity of mankind, whereby “knowledge” is meant the kind of knowledge that admits of being made articulate in the form of propositions.
In Mathematics as a Culture Clue: And Other Essays (1947), 127.
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Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.
In Antoine-Augustin Cournot and Nathaniel T. Bacon (trans.), Mathematical Theory of the Principles of Wealth (1897), Preface, 3.
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Thus a eukaryotic cell may be thought of as an empire directed by a republic of sovereign chromosomes in the nucleus. The chromosomes preside over the outlying cytoplasm in which formerly independent but now subject and degenerate prokaryotes carry out a variety of specialized service functions.
Molecular Genetics: An Introductory Narrative (1971), 622. Cell;Empire;Republic;Sovereign;Chromosome;Nucleus;Cytoplasm;Eukaryote;Prokaryote;Specialization;Service;Function
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Thus it might be said, that the vegetable is only the sketch, nor rather the ground-work of the animal; that for the formation of the latter, it has only been requisite to clothe the former with an apparatus of external organs, by which it might be connected with external objects.
From hence it follows, that the functions of the animal are of two very different classes. By the one (which is composed of an habitual succession of assimilation and excretion) it lives within itself, transforms into its proper substance the particles of other bodies, and afterwards rejects them when they are become heterogeneous to its nature. By the other, it lives externally, is the inhabitant of the world, and not as the vegetable of a spot only; it feels, it perceives, it reflects on its sensations, it moves according to their influence, and frequently is enabled to communicate by its voice its desires, and its fears, its pleasures, and its pains.
The aggregate of the functions of the first order, I shall name the organic life, because all organized beings, whether animal or vegetable, enjoy it more or less, because organic texture is the sole condition necessary to its existence. The sum of the functions of the second class, because it is exclusively the property of the animal, I shall denominate the animal life.
Physiological Researches on Life and Death (1815), trans. P. Gold, 22-3.
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Thus science strips off, one after the other, the more or less gross materialisations by which we endeavour to form an objective image of the soul, till men of science, speculating, in their non-scientific intervals, like other men on what science may possibly lead to, have prophesied that we shall soon have to confess that the soul is nothing else than a function of certain complex material systems.
Review of B. Stewart and P. G. Tait's book on Paradoxical Philosophy, in Nature, 19, 1878. In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 760.
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To discover and to teach are distinct functions; they are also distinct gifts, and are not commonly found united in the same person.
Discourses on the Scope and Nature of University Education. Addressed to the Catholics of Dublin (1852), Preface, xii.
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To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
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To function efficiently in today’s world, you need math. The world is so technical, if you plan to work in it, a math background will let you go farther and faster.
In 'Ross, Mary Golda :The Cherokee Nation Remembers the First Woman Engineer for Lockheed', Indian Country News, article published online (13 May 2008) on the indiancountrynews.com website.
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To look backward for a while is to refresh the eye, to restore it, and to render it more fit for its prime function of looking forward.
…...
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To say that mind is a product or function of protoplasm, or of its molecular changes, is to use words to which we can attach no clear conception. You cannot have, in the whole, what does not exist in any of the parts; and those who argue thus should put forth a definite conception of matter, with clearly enunciated properties, and show, that the necessary result of a certain complex arrangement of the elements or atoms of that matter, will be the production of self-consciousness. There is no escape from this dilemma—either all matter is conscious, or consciousness is something distinct from matter, and in the latter case, its presence in material forms is a proof of the existence of conscious beings, outside of, and independent of, what we term matter. The foregoing considerations lead us to the very important conclusion, that matter is essentially force, and nothing but force; that matter, as popularly understood, does not exist, and is, in fact, philosophically inconceivable. When we touch matter, we only really experience sensations of resistance, implying repulsive force; and no other sense can give us such apparently solid proofs of the reality of matter, as touch does. This conclusion, if kept constantly present in the mind, will be found to have a most important bearing on almost every high scientific and philosophical problem, and especially on such as relate to our own conscious existence.
In 'The Limits of Natural Selection as Applied to Man', last chapter of Contributions to the Theory of Natural Selection (1870), 365-366.
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To the extent that remaining old-growth Douglas fir ecosystems possess unique structural and functional characteristics distinct from surrounding managed forests, the analogy between forest habitat islands and oceanic islands applies. Forest planning decision variables such as total acreage to be maintained, patch size frequency distribution, spatial distribution of patches, specific locations, and protective measures all need to be addressed.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), 6.
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Today the function of the artist is to bring imagination to science and science to imagination, where they meet, in the myth.
…...
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We are all but recent leaves on the same old tree of life and if this life has adapted itself to new functions and conditions, it uses the same old basic principles over and over again. There is no real difference between the grass and the man who mows it.
In Free Radical by R.W. Moss (1988).
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We are now witnessing, after the slow fermentation of fifty years, a concentration of technical power aimed at the essential determinants of heredity, development and disease. This concentration is made possible by the common function of nucleic acids as the molecular midwife of all reproductive particles. Indeed it is the nucleic acids which, in spite of their chemical obscurity, are giving to biology a unity which has so far been lacking, a chemical unity.
Nucleic Acid (1947), 266-7.
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We are once for all adapted to the military status. A millennium of peace would not breed the fighting disposition out of our bone and marrow, and a function so ingrained and vital will never consent to die without resistance, and will always find impassioned apologists and idealizers.
From 'Remarks at The Peace Banquet' (7 Oct 1904), Boston, on the closing day of the World’s Peace Congress. Printed in Atlantic Monthly (Dec 1904), 845-846. Collected in Essays in Religion and Morality (1982), Vol. 9, 121.
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We come back then to our records of nervous messages with a reasonable assurance that they do tell us what the message is like. It is a succession of brief waves of surface breakdown, each allowing a momentary leakage of ions from the nerve fibre. The waves can be set up so that they follow one another in rapid or in slow succession, and this is the only form of gradation of which the message is capable. Essentially the same kind of activity is found in all sorts of nerve fibres from all sorts of animals and there is no evidence to suggest that any other kind of nervous transmission is possible. In fact we may conclude that the electrical method can tell us how the nerve fibre carries out its function as the conducting unit of the nervous system, and that it does so by reactions of a fairly simple type.
The Mechanism of Nervous Action (1932), 21.
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We have theories of races and of functions, but scarcely yet a remote approach to an idea of creation. We are now so far from the road to truth, that religious teachers dispute and hate each other, and speculative men are esteemed unsound and frivolous.
In 'Introduction', Nature: Addresses, and Lectures (1849), 2.
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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 never really see time. We see only clocks. If you say this object moves, what you really mean is that this object is here when the hand of your clock is here, and so on. We say we measure time with clocks, but we see only the hands of the clocks, not time itself. And the hands of a clock are a physical variable like any other. So in a sense we cheat because what we really observe are physical variables as a function of other physical variables, but we represent that as if everything is evolving in time.
Quoted by Tim Folger in 'Newsflash: Time May Not Exist', Discover Magazine (Jun 2007).
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Weeds function as an unseen tax on the crop harvest.
From 'War on Weeds', Science (19 Apr 1946), 103, No. 2677, 465.
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Whatever be the detail with which you cram your student, the chance of his meeting in after life exactly that detail is almost infinitesimal; and if he does meet it, he will probably have forgotten what you taught him about it. The really useful training yields a comprehension of a few general principles with a thorough grounding in the way they apply to a variety of concrete details. In subsequent practice the men will have forgotten your particular details; but they will remember by an unconscious common sense how to apply principles to immediate circumstances. Your learning is useless to you till you have lost your textbooks, burnt your lecture notes, and forgotten the minutiae which you learned by heart for the examination. What, in the way of detail, you continually require will stick in your memory as obvious facts like the sun and the moon; and what you casually require can be looked up in any work of reference. The function of a University is to enable you to shed details in favor of principles. When I speak of principles I am hardly even thinking of verbal formulations. A principle which has thoroughly soaked into you is rather a mental habit than a formal statement. It becomes the way the mind reacts to the appropriate stimulus in the form of illustrative circumstances. Nobody goes about with his knowledge clearly and consciously before him. Mental cultivation is nothing else than the satisfactory way in which the mind will function when it is poked up into activity.
In 'The Rhythm of Education', The Aims of Education: & Other Essays (1917), 41.
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Whatever State of the Human Body doth disorder the Vital, the natural, or even the Animal Functions of the same is call’d a Disease.
Aphorism No. 1 in Boerhaave’s Aphorisms: Concerning The Knowledge and Cure of Diseases (1715), 1
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When I listen to a soprano sing a Handel aria with an astonishing coloratura from that particular larynx, I say to myself, there has to be a biological reason that was useful at some stage. The larynx of a human being did not evolve without having some function. And the only function I can see is sexual attraction.
From 'Interview: Of Mind and Matter: David Attenborough Meets Richard Dawkins', The Guardian (11 Sep 2010).
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When in many dissections, carried out as opportunity offered upon living animals, I first addressed my mind to seeing how I could discover the function and offices of the heart’s movement in animals through the use of my own eyes instead of through the books and writings of others, I kept finding the matter so truly hard and beset with difficulties that I all but thought, with Fracastoro, that the heart's movement had been understood by God alone.
De Motu Cordis (1628), The Circulation of the Blood and Other Writings, trans. Kenneth J. Franklin (1957), Chapter 1, author's motives for writing, 23.
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When physiologists revealed the existence and functions of hormones they not only gave increased opportunities for the activities of biochemists but in particular gave a new charter to biochemical thought, and with the discovery of vitamins that charter was extended.
'Biological Thought and Chemical Thought: A Plea for Unification', Linacre Lecture, Cambridge (6 May 1938), published in Lancet (1938),2, 1201.
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While playing the part of the detective the investigator follows clues, but having captured his alleged fact, he turns judge and examines the case by means of logically arranged evidence. Both functions are equally essential but they are different.
In The Art of Scientific Investigation (1950, 1957), 92.
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Who has not be amazed to learn that the function y = ex, like a phoenix rising again from its own ashes, is its own derivative?
In François Le Lionnais (ed.), Great Currents of Mathematical Thought: Mathematics in the Arts and Sciences (1971), Vol. 2, 126.
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Whoever looks at the insect world, at flies, aphides, gnats and innumerable parasites, and even at the infant mammals, must have remarked the extreme content they take in suction, which constitutes the main business of their life. If we go into a library or newsroom, we see the same function on a higher plane, performed with like ardor, with equal impatience of interruption, indicating the sweetness of the act. In the highest civilization the book is still the highest delight.
In Lecture, second in a series given at Freeman Place Chapel, Boston (Mar 1859), 'Quotation and Originality', in Letters and Social Aims (1875, 1917), 177.
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Whoever would not remain in complete ignorance of the resources which cause him to act; whoever would seize, at a single philosophical glance, the nature of man and animals, and their relations to external objects; whoever would establish, on the intellectual and moral functions, a solid doctrine of mental diseases, of the general and governing influence of the brain in the states of health and disease, should know, that it is indispensable, that the study of the organization of the brain should march side by side with that of its functions.
On the Organ of the Moral Qualities and Intellectual Faculties, and the Plurality of the Cerebral Organs (1835), 45-6.
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Why it is that animals, instead of developing in a simple and straightforward way, undergo in the course of their growth a series of complicated changes, during which they often acquire organs which have no function, and which, after remaining visible for a short time, disappear without leaving a trace ... To the Darwinian, the explanation of such facts is obvious. The stage when the tadpole breathes by gills is a repetition of the stage when the ancestors of the frog had not advanced in the scale of development beyond a fish.
In The Works of Francis Maitland Balfour (1885), Vol. 1, 702.
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With reference to … dyspepsia, it is saddening to see the perpetuation of the term “functional” as shorthand for “I don’t know the nature of the problem.”
In Letters, British Medical Journal (9 Feb 2002), 324, No. 7333, 364.
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You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.
From the recollection of Claude Shannon given in discussion with Myron Tribus (Apr 1961) about the reason Shannon chose the word “entropy” for his information function (first used by Shannon in a 1945 memorandum at Bell Labs). The suggestion from Neumann to use “entropy” dates back to a Neumann-Shannon conversation c.1940. Shannon’s recollection of the Neumann’s recommendation was quoted as recollected by Tribus in Myron Tribus and Edward C. McIrving, 'Energy and Information', Scientific American (1971), 225, 179-88.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


by Ian Ellis
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