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Who said: “Nature does nothing in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superfluous causes.”
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Combine Quotes (58 quotes)


…comparing the capacity of computers to the capacity of the human brain, I’ve often wondered, where does our success come from? The answer is synthesis, the ability to combine creativity and calculation, art and science, into whole that is much greater than the sum of its parts.
In How Life Imitates Chess: Making the Right Moves, from the Board to the Boardroom (2007), 4.
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[Charles Kettering] is unique in that he combines in one individual the interest in pure science with the practical ability to apply knowledge in useful devices.
As quoted in book review, T.A. Boyd, 'Charles F. Kettering: Prophet of Progress', Science (30 Jan 1959), 256.
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A book should have either intelligibility or correctness; to combine the two is impossible, but to lack both is to be unworthy of a place as Euclid has occupied in education.
In essay, 'Mathematics and the Metaphysicians' (1901), collected in Mysticism and Logic: And Other Essays (1917), 73. The essay was also published as 'Recent Work in the Philosophy of Mathematics', in the American magazine, International Monthly.
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A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
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About eight days ago I discovered that sulfur in burning, far from losing weight, on the contrary, gains it; it is the same with phosphorus; this increase of weight arises from a prodigious quantity of air that is fixed during combustion and combines with the vapors. This discovery, which I have established by experiments, that I regard as decisive, has led me to think that what is observed in the combustion of sulfur and phosphorus may well take place in the case of all substances that gain in weight by combustion and calcination; and I am persuaded that the increase in weight of metallic calxes is due to the same cause... This discovery seems to me one of the most interesting that has been made since Stahl and since it is difficult not to disclose something inadvertently in conversation with friends that could lead to the truth I have thought it necessary to make the present deposit to the Secretary of the Academy to await the time I make my experiments public.
Sealed note deposited with the Secretary of the French Academy 1 Nov 1772. Oeuvres de Lavoisier, Correspondance, Fasc. II. 1770-75 (1957), 389-90. Adapted from translation by A. N. Meldrum, The Eighteenth-Century Revolution in Science (1930), 3.
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According to the older view, for every single effect of a serum, there was a separate substance, or at least a particular chemical group... A normal serum contained as many different haemagglutinins as it agglutinated different cells. The situation was undoubtedly made much simpler if, to use the Ehrlich terminology... the separate haptophore groups can combine with an extremely large number of receptors in stepwise differing quantities as a stain does with different animal tissues, though not always with the same intensity. A normal serum would therefore visibly affect such a large number of different blood cells... not because it contained countless special substances, but because of the colloids of the serum, and therefore of the agglutinins by reason of their chemical constitution and the electrochemical properties resulting from it. That this manner of representation is a considerable simplification is clear; it also opens the way to direct experimental testing by the methods of structural chemistry.
'Die Theorien der Antikorperbildung ... ', Wiener klinische Wöchenschrift (1909), 22, 1623-1631. Trans. Pauline M. H. Mazumdar.
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Aimed by us are futuristic humane machines wherein human level electronic intelligence and nerve system are combined to machines of ultraprecision capabilities.
In Marc J. Madou, Fundamentals of Microfabrication: the Science of Miniaturization (2nd ed., 2002), 467.
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Among the multitude of animals which scamper, fly, burrow and swim around us, man is the only one who is not locked into his environment. His imagination, his reason, his emotional subtlety and toughness, make it possible for him not to accept the environment, but to change it. And that series of inventions, by which man from age to age has remade his environment, is a different kind of evolution—not biological, but cultural evolution. I call that brilliant sequence of cultural peaks The Ascent of Man. I use the word ascent with a precise meaning. Man is distinguished from other animals by his imaginative gifts. He makes plans, inventions, new discoveries, by putting different talents together; and his discoveries become more subtle and penetrating, as he learns to combine his talents in more complex and intimate ways. So the great discoveries of different ages and different cultures, in technique, in science, in the arts, express in their progression a richer and more intricate conjunction of human faculties, an ascending trellis of his gifts.
The Ascent of Man (1973), 19-20.
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But in practical affairs, particularly in politics, men are needed who combine human experience and interest in human relations with a knowledge of science and technology. Moreover, they must be men of action and not contemplation. I have the impression that no method of education can produce people with all the qualities required. I am haunted by the idea that this break in human civilization, caused by the discovery of the scientific method, may be irreparable.
Max Born
My Life & My Views (1968), 57-8.
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By blending water and minerals from below with sunlight and CO2 from above, green plants link the earth to the sky. We tend to believe that plants grow out of the soil, but in fact most of their substance comes from the air. The bulk of the cellulose and the other organic compounds produced through photosynthesis consists of heavy carbon and oxygen atoms, which plants take directly from the air in the form of CO2. Thus the weight of a wooden log comes almost entirely from the air. When we burn a log in a fireplace, oxygen and carbon combine once more into CO2, and in the light and heat of the fire we recover part of the solar energy that went into making the wood.
The Web of Life: A New Scientific Understanding of Living Systems (1997), 178.
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Chess combines the beauty of mathematical structure with the recreational delights of a competitive game.
In 'Preface', Mathematics, Magic, and Mystery (1956), ix.
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Considered from the standpoint of chemistry, living bodies appear to us as laboratories of chemical processes, for they undergo perpetual changes in their material substrate. They draw materials from the outside world and combine them with the mass of their liquid and solid parts.
In 'Allgemeine Betrachtungen der orgauischen Korper', Physiologie des Menschen (1830), Vol. 1, 34. Trans. in Kenneth L. Caneva, Robert Mayer and the Conservation of Energy (1993), 7I.
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Her [Nettie Stevens] single-mindedness and devotion, combined with keen powers of observation; her thoughtfulness and patience, united to a well-balanced judgment, account, in part, for her remarkable accomplishment.
In obituary, 'The Scientific Work of Miss N.M. Steves', Science (11 Oct 1912), 36, No. 928, 470.
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I could clearly see that the blood is divided and flows through tortuous vessels and that it is not poured out into spaces, but is always driven through tubules and distributed by the manifold bendings of the vessels... [F]rom the simplicity Nature employs in all her works, we may conclude... that the network I once believed to be nervous [that is, sinewy] is really a vessel intermingled with the vesicles and sinuses and carrying the mass of blood to them or away from them... though these elude even the keenest sight because of their small size... From these considerations it is highly probable that the question about the mutual union and anastomosis of the vessels can be solved; for if Nature once circulates the blood within vessels and combines their ends in a network, it is probable that they are joined by anastomosis at other times too.
'The Return to Bologna 1659-1662', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 194-5.
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I think that space flight is a condition of Nature that comes into effect when an intelligent species reaches the saturation point of its planetary habitat combined with a certain level of technological ability... I think it is a built-in gene-directed drive for the spreading of the species and its continuation.
…...
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If atoms do, by chance, happen to combine themselves into so many shapes, why have they never combined together to form a house or a slipper? By the same token, why do we not believe that if innumerable letters of the Greek alphabet were poured all over the market-place they would eventually happen to form the text of the Iliad?
The Essays of Michel de Montaigne, Book 2, Chapter 12, 'Apology for Raymond Sebond', trans. M. A. Screech (1991), 612.
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If we can combine our knowledge of science with the wisdom of wildness, if we can nurture civilization through roots in the primitive, man’s potentialities appear to be unbounded, Through this evolving awareness, and his awareness of that awareness, he can emerge with the miraculous—to which we can attach what better name than “God”? And in this merging, as long sensed by intuition but still only vaguely perceived by rationality, experience may travel without need for accompanying life.
A Letter From Lindbergh', Life (4 Jul 1969), 61. In Eugene C. Gerhart, Quote it Completely! (1998), 409.
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In all chemical investigations, it has justly been considered an important object to ascertain the relative weights of the simples which constitute a compound. But unfortunately the enquiry has terminated here; whereas from the relative weights in the mass, the relative weights of the ultimate particles or atoms of the bodies might have been inferred, from which their number and weight in various other compounds would appear, in order to assist and to guide future investigations, and to correct their results. Now it is one great object of this work, to shew the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle.
If there are two bodies, A and B, which are disposed to combine, the following is the order in which the combinations may take place, beginning with the most simple: namely,
1 atom of A + 1 atom of B = 1 atom of C, binary
1 atom of A + 2 atoms of B = 1 atom of D, ternary
2 atoms of A + 1 atom of B = 1 atom of E, ternary
1 atom of A + 3 atoms of B = 1 atom of F, quaternary
3 atoms of A and 1 atom of B = 1 atom of G, quaternary
A New System of Chemical Philosophy (1808), Vol. 1, 212-3.
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In one person he [Isaac Newton] combined the experimenter, the theorist, the mechanic and, not least, the artist in exposition.
In 'Foreword' to Isaac Newton, Opticks (1952), lix.
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Incandescent carbon particles, by the tens of millions, leap free of the log and wave like banners, as flame. Several hundred significantly different chemical reactions are now going on. For example, a carbon atom and four hydrogen atoms, coming out of the breaking cellulose, may lock together and form methane, natural gas. The methane, burning (combining with oxygen), turns into carbon dioxide and water, which also go up the flue. If two carbon atoms happen to come out of the wood with six hydrogen atoms, they are, agglomerately, ethane, which bums to become, also, carbon dioxide and water. Three carbons and eight hydrogens form propane, and propane is there, too, in the fire. Four carbons and ten hydrogens—butane. Five carbons … pentane. Six … hexane. Seven … heptane. Eight carbons and eighteen hydrogens—octane. All these compounds come away in the breaking of the cellulose molecule, and burn, and go up the chimney as carbon dioxide and water. Pentane, hexane, heptane, and octane have a collective name. Logs burning in a fireplace are making and burning gasoline.
In 'Firewood', Pieces of the Frame (1975), 205-206.
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Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
…...
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Intelligence is an extremely subtle concept. It’s a kind of understanding that flourishes if it’s combined with a good memory, but exists anyway even in the absence of good memory. It’s the ability to draw consequences from causes, to make correct inferences, to foresee what might be the result, to work out logical problems, to be reasonable, rational, to have the ability to understand the solution from perhaps insufficient information. You know when a person is intelligent, but you can be easily fooled if you are not yourself intelligent.
In Irv Broughton (ed.), The Writer's Mind: Interviews with American Authors (1990), Vol. 2, 57.
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It cannot, of course, be stated with absolute certainty that no elements can combine with argon; but it appears at least improbable that any compounds will be formed.
As surmised in Gases of the Atmosphere (1896, 1905), 193. [The first argon compound was finally made a century later (Aug 2000), argon fluorohydride, HArF, but unstable above 40 K (–233 °C). —Webmaster]
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It is not Cayley’s way to analyze concepts into their ultimate elements. … But he is master of the empirical utilization of the material: in the way he combines it to form a single abstract concept which he generalizes and then subjects to computative tests, in the way the newly acquired data are made to yield at a single stroke the general comprehensive idea to the subsequent numerical verification of which years of labor are devoted. Cayley is thus the natural philosopher among mathematicians.
In Mathematische Annalen, Bd. 46 (1895), 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 146.
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It is still false to conclude that man is nothing but the highest animal, or the most progressive product of organic evolution. He is also a fundamentally new sort of animal and one in which, although organic evolution continues on its way, a fundamentally new sort of evolution has also appeared. The basis of this new sort of evolution is a new sort of heredity, the inheritance of learning. This sort of heredity appears modestly in other mammals and even lower in the animal kingdom, but in man it has incomparably fuller development and it combines with man's other characteristics unique in degree with a result that cannot be considered unique only in degree but must also be considered unique in kind.
In The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 286.
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Knowing what we know from X-ray and related studies of the fibrous proteins, how they are built from long polypeptide chains with linear patterns drawn to a grand scale, how these chains can contract and take up different configurations by intramolecular folding, how the chain- groups are penetrated by, and their sidechains react with, smaller co-operating molecules, and finally how they can combine so readily with nucleic acid molecules and still maintain the fibrous configuration, it is but natural to assume, as a first working hypothesis at least, that they form the long scroll on which is written the pattern of life. No other molecules satisfy so many requirements.
William Thomas Astbury and Florence O. Bell. 'Some Recent Developments in the X-Ray Study of Proteins and Related Structures', Cold Spring Harbor Symposia on Quantitative Biology, 1938, 6, 1144.
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Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.
In 'Preface', Mathematics, Magic, and Mystery (1956), ix. Webmaster checked the actual page, in the 1956 edition, and there Gardner plainly uses the beginning words “Mathematical magic.” On page 113, Gardner credits Royal V. Heath for originating the term “Mathemagic,” used as Heath’s book title in 1933. Anywhere you see the quote incorrectly beginning with “Mathemagical mathematics…” or saying Gardner coined the term “mathemagical” obviously did not check the primary source.
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Mathematics … above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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Mathematics because of its nature and structure is peculiarly fitted for high school instruction [Gymnasiallehrfach]. Especially the higher mathematics, even if presented only in its elements, combines within itself all those qualities which are demanded of a secondary subject.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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Mathematics is the study which forms the foundation of the course [at West Point Military Academy]. This is necessary, both to impart to the mind that combined strength and versatility, the peculiar vigor and rapidity of comparison necessary for military action, and to pave the way for progress in the higher military sciences.
In Congressional Committee on Military Affairs, 1834, United States Bureau of Education, Bulletin 1912, No. 2, 10.
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Nascent atoms are equipped with arms, with which they can combine with other atoms.
Blunder by an anonymous student. Collected in 'Classroom Emanations', Journal of Chemical Education, (Dec 1925), 2, No. 12, 1196. This is seen on the web incorrectly attributed to P. W. Adkins—who was born in 1940. The article in the 1925 Journal has no author credit. It is a collection of alleged student blunders submitted to the journal Editor. [Note: The list may unknowingly include undesired inauthentic contributions. —Webmaster.]
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New sources of power … will surely be discovered. Nuclear energy is incomparably greater than the molecular energy we use today. The coal a man can get in a day can easily do five hundred times as much work as himself. Nuclear energy is at least one million times more powerful still. If the hydrogen atoms in a pound of water could be prevailed upon to combine and form helium, they would suffice to drive a thousand-horsepower engine for a whole year. If the electrons, those tiny planets of the atomic systems, were induced to combine with the nuclei in hydrogen, the horsepower would be 120 times greater still. There is no question among scientists that this gigantic source of energy exists. What is lacking is the match to set the bonfire alight, or it may be the detonator to cause the dynamite to explode. The scientists are looking for this.
[In his last major speech to the House of Commons on 1 Mar 1955, Churchill quoted from his original printed article, nearly 25 years earlier.]
'Fifty Years Hence'. Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57:3, 395.
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Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to this idea in its elf, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?
…...
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Perhaps I may without immodesty lay claim to the appellation of Mathematical Adam, as I believe that I have given more names (passed into general circulation) of the creatures of the mathematical reason than all the other mathematicians of the age combined.
In Nature (1887-1888), 87, 162. As quoted and cited in As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 178
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Science is a collaborative effort. The combined results of several people working together is often much more effective than could be that of an individual scientist working alone.
From his second Nobel Prize Banquet speech (10 Dec 1972). In Wilhelm Odelberg (ed.), Les Prix Nobel en 1972 (1973).
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Science progresses by a series of combinations in which chance plays not the least role. Its life is rough and resembles that of minerals which grow by juxtaposition [accretion]. This applies not only to science such as it emerges [results] from the work of a series of scientists, but also to the particular research of each one of them. In vain would analysts dissimulate: (however abstract it may be, analysis is no more our power than that of others); they do not deduce, they combine, they compare: (it must be sought out, sounded out, solicited.) When they arrive at the truth it is by cannoning from one side to another that they come across it.
English translation from manuscript, in Évariste Galois and Peter M. Neumann, 'Dossier 12: On the progress of pure analysis', The Mathematical Writings of Évariste Galois (2011), 263. A transcription of the original French is on page 262. In the following quote from that page, indicated deletions are omitted, and Webmaster uses parentheses to enclose indications of insertions above the original written line. “La science progresse par une série de combinaisons où le hazard ne joue pas le moindre rôle; sa vie est brute et ressemble à celle des minéraux qui croissent par juxtà position. Cela s’applique non seulement à la science telle qu’elle résulte des travaux d’une série de savants, mais aussi aux recherches particulières à chacun d’eux. En vain les analystes voudraient-ils se le dissimuler: (toute immatérielle qu’elle wst analyse n’est pas pas plus en notre pouvoir que des autres); ils ne déduisent pas, ils combinent, ils comparent: (il faut l’epier, la sonder, la solliciter) quand ils arrivent à la vérité, c’est en heurtant de côté et d’autre qu’il y sont tombés.” Webmaster corrected from typo “put” to “but” in the English text.
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Simple molecules combine to make powerful chemicals. Simple cells combine to make powerful life-forms. Simple electronics combine to make powerful computers. Logically, all things are created by a combination of simpler, less capable components. Therefore, a supreme being must be in our future, not our origin. What if “God” is the consciousness that will be created when enough of us are connected by the Internet?!!
Thoughts by character Dogbert in Dilbert cartoon strip (11 Feb 1996).
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Subtlety is not a proof of wisdom. Fools and even madmen are at times extraordinarily subtle. One can add that subtlety rarely combines with genius, which is usually ingenuous, or with greatness of character, which is always frank.
(1827). In Aleksandr Sergeevich Pushkin, John Bayley (ed.), Pushkin on Literature (1986), 211.
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The chemists work with inaccurate and poor measuring services, but they employ very good materials. The physicists, on the other hand, use excellent methods and accurate instruments, but they apply these to very inferior materials. The physical chemists combine both these characteristics in that they apply imprecise methods to impure materials.
Quoted in Ralph Oesper, The Human Side of Scientists (1975), 116.
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The constructions of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow-mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth. Everybody who looks at the spectacle of modern algebra will be struck by this complementarity of freedom and necessity.
In 'A Half-Century of Mathematics',The American Mathematical Monthly (Oct 1951), 58, No. 8, 538-539.
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The dance is four-dimensional art in that it moves concretely in both space and time. For the onlooker, it is an art largely of visual space combined with time. But for the dancer, and this is more important, the dance is more a muscular than a visual space rhythm, a muscular time, a muscular movement and balance. Dancing is not animated sculpture, it is kinesthetic.
In Art Is Action: A Discussion of Nine Arts in a Modern World (1939), 56.
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The genuine spirit of Mathesis is devout. No intellectual pursuit more truly leads to profound impressions of the existence and attributes of a Creator, and to a deep sense of our filial relations to him, than the study of these abstract sciences. Who can understand so well how feeble are our conceptions of Almighty Power, as he who has calculated the attraction of the sun and the planets, and weighed in his balance the irresistible force of the lightning? Who can so well understand how confused is our estimate of the Eternal Wisdom, as he who has traced out the secret laws which guide the hosts of heaven, and combine the atoms on earth? Who can so well understand that man is made in the image of his Creator, as he who has sought to frame new laws and conditions to govern imaginary worlds, and found his own thoughts similar to those on which his Creator has acted?
In 'The Imagination in Mathematics', North American Review, 85, 226.
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The geometrical problems and theorems of the Greeks always refer to definite, oftentimes to rather complicated figures. Now frequently the points and lines of such a figure may assume very many different relative positions; each of these possible cases is then considered separately. On the contrary, present day mathematicians generate their figures one from another, and are accustomed to consider them subject to variation; in this manner they unite the various cases and combine them as much as possible by employing negative and imaginary magnitudes. For example, the problems which Apollonius treats in his two books De sectione rationis, are solved today by means of a single, universally applicable construction; Apollonius, on the contrary, separates it into more than eighty different cases varying only in position. Thus, as Hermann Hankel has fittingly remarked, the ancient geometry sacrifices to a seeming simplicity the true simplicity which consists in the unity of principles; it attained a trivial sensual presentability at the cost of the recognition of the relations of geometric forms in all their changes and in all the variations of their sensually presentable positions.
In 'Die Synthetische Geometrie im Altertum und in der Neuzeit', Jahresbericht der Deutschen Mathematiker Vereinigung (1902), 2, 346-347. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112. The spelling of the first “Apollonius” has been corrected from “Appolonius” in the original English text. From the original German, “Die geometrischen Probleme und Sätze der Griechen beziehen sich allemal auf bestimmte, oft recht komplizierte Figuren. Nun können aber die Punkte und Linien einer solchen Figur häufig sehr verschiedene Lagen zu einander annehmen; jeder dieser möglichen Fälle wird alsdann für sich besonders erörtert. Dagegen lassen die heutigen Mathematiker ihre Figuren aus einander entstehen und sind gewohnt, sie als veränderlich zu betrachten; sie vereinigen so die speziellen Fälle und fassen sie möglichst zusammen unter Benutzung auch negativer und imaginärer Gröfsen. Das Problem z. B., welches Apollonius in seinen zwei Büchern de sectione rationis behandelt, löst man heutzutage durch eine einzige, allgemein anwendbare Konstruktion; Apollonius selber dagegen zerlegt es in mehr als 80 nur durch die Lage verschiedene Fälle. So opfert, wie Hermann Hankel treffend bemerkt, die antike Geometrie einer scheinbaren Einfachheit die wahre, in der Einheit der Prinzipien bestehende; sie erreicht eine triviale sinnliche Anschaulichkeit auf Kosten der Erkenntnis vom Zusammenhang geometrischer Gestalten in aller Wechsel und in aller Veränderlichkeit ihrer sinnlich vorstellbaren Lage.”
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The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics.
In The Philosophy of the Inductive Sciences (1868), Part 1, Bk. 2, chap. 1, sect. 4.
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The instruction of children should aim gradually to combine knowing and doing [Wissen und Konnen]. Among all sciences mathematics seems to be the only one of a kind to satisfy this aim most completely.
In Werke, Bd. 9 (1888), 409.
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The most wonderful mystery of life may well be the means by which it created so much diversity from so little physical matter. The biosphere, all organisms combined, makes up only about one part in ten billion of the earth’s mass. … Yet life has divided into millions of species, the fundamental units, each playing a unique role in relation to the whole.
In 'The Most Fundamental Unit', The Diversity of Life (1992), 35.
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The real accomplishment of modern science and technology consists in taking ordinary men, informing them narrowly and deeply and then, through appropriate organization, arranging to have their knowledge combined with that of other specialized but equally ordinary men. This dispenses with the need for genius. The resulting performance, though less inspiring, is far more predictable.
In The New Industrial State (1967), 62.
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The science of medicine is a barbarous jargon and the effects of our medicine on the human system are in the highest degree uncertain, except indeed that they have already destroyed more lives than war, pestilence, and famine combined.
…...
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The study of economics does not seem to require any specialised gifts of an unusually high order. Is it not, intellectually regarded, a very easy subject compared with the higher branches of philosophy and pure science? Yet good, or even competent, economists are the rarest of birds. An easy subject, at which very few excel! The paradox finds its explanation, perhaps, in that the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood; as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician.
'Alfred Marshall: 1842-1924' (1924). In Geoffrey Keynes (ed.), Essays in Biography (1933), 170.
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The theory of quantum mechanics also explained all kinds of details, such as why an oxygen atom combines with two hydrogen atoms to make water, and so on. Quantum mechanics thus supplied the theory behind chemistry. So, fundamental theoretical chemistry is really physics.
In 'Introduction', QED: The Strange Theory of Light and Matter (1985), 5.
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There are three ruling ideas, three so to say, spheres of thought, which pervade the whole body of mathematical science, to some one or other of which, or to two or all three of them combined, every mathematical truth admits of being referred; these are the three cardinal notions, of Number, Space and Order.
Arithmetic has for its object the properties of number in the abstract. In algebra, viewed as a science of operations, order is the predominating idea. The business of geometry is with the evolution of the properties of space, or of bodies viewed as existing in space.
In 'A Probationary Lecture on Geometry, York British Association Report (1844), Part 2; Collected Mathematical Papers, Vol. 2, 5.
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This pure species of air [oxygen] has the property of combining with the blood and … this combination constitutes its red colour.
From 'Expériences sur la respiration des animaux, et sur les changemens qui arrivent à l’air en passant par leur poumon', Histoire de l’Académie Royale des Sciences for 1777 (1780) as translated by Thomas Henry in 'Experiments on the Respiration of Animals on the Changes effected on the Air passing through their Lungs', Essays, on the Effects Produced by Various Processes on Atmospheric Air, etc. (1783), 13-14. Also in John F. Fulton, Selected Readings in the History of Physiology (1930), 125.
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To behold is not necessarily to observe, and the power of comparing and combining is only to be obtained by education. It is much to be regretted that habits of exact observation are not cultivated in our schools; to this deficiency may be traced much of the fallacious reasoning, the false philosophy which prevails.
As quoted in Inaugural Address, Edward C.C. Stanford, 'Glasgow Philosophical Meeting' (8 Dec 1873), The Chemical News and Journal of Physical Science (2 Jan 1874), 7.
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We claim to be more moral than other nations, and to conquer and govern and tax and plunder weaker peoples for their good! While robbing them we actually claim to be benefactors! And then we wonder, or profess to wonder, why other Governments hate us! Are they not fully justified in hating us? Is it surprising that they seek every means to annoy us, that they struggle to get navies to compete with us, and look forward to a time when some two or three of them may combine together and thoroughly humble and cripple us? And who can deny that any just Being, looking at all the nations of the earth with impartiality and thorough knowledge, would decide that we deserve to be humbled, and that it might do us good?
In 'Practical Politics', The Clarion (30 Sep 1904), 1.
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We have three principal means: observation of nature, reflection, and experiment. Observation gathers the facts, reflection combines them, experiment verifies the result of the combination. It is essential that the observation of nature be assiduous, that reflection be profound, and that experimentation be exact. Rarely does one see these abilities in combination. And so, creative geniuses are not common.
In On the Interpretation of Nature (1753).
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What agencies of electricity, gravity, light, affinity combine to make every plant what it is, and in a manner so quiet that the presence of these tremendous powers is not ordinarily suspected. Faraday said, “A grain of water is known to have electric relations equivalent to a very powerful flash of lightning.”
In 'Perpetual Forces', North American Review (1877), No. 125. Collected in Ralph Waldo Emerson and James Elliot Cabot (ed.), Lectures and Biographical Sketches (1883), 60.
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What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property—the screw. The right line, the circle, the screw—the representations of translation, rotation, and the two combined—ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.
From Letter (15 Feb 1852) to W.R. Hamilton, collected in Robert Perceval Graves, Life of W.R. Hamilton (1889), Vol. 3, 343.
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What quality is shared by all objects that provoke our aesthetic emotions? Only one answer seems possible—significant form. In each, lines and colors combined in a particular way; certain forms and relations of forms, stir our aesthetic emotions. These relations and combinations of lines and colours, these æsthetically moving forms, I call “Significant Form”; and “Significant Form” is the one quality common to all works of visual art.
In Art (1913), 8.
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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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