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

Function Quotes (127 quotes)

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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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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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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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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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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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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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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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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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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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.
In Terry Pratchett, Ian Stewart and Jack Cohen, The Science of Discworld (2014), 218.
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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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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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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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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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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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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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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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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 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 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 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 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 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 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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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 [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... [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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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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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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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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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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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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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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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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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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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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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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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 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 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 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 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 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 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 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 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 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 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 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 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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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 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 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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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 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 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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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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[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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“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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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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Sophie Germain
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Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
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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
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Bible
Thomas Huxley
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Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
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Robert Fulton
Pierre Laplace
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Thomas Edison
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Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
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Avicenna
James Watson
William Shakespeare
- 50 -
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- 40 -
Pierre Fermat
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- 30 -
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- 20 -
Carl Sagan
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- 10 -
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