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Home > Category Index for Science Quotations > Category Index S > Category: Separate

Separate Quotes (143 quotes)
Separated Quotes, Separating Quotes

Engineering, too, owes its most useful materials to the achievements of chemists in identifying, separating, and transforming materials: structural steel for the framework of bridges and buildings, portland cement for roadways and aqueducts, pure copper for the electrical industries, aluminum alloys for automobiles and airplanes, porcelain for spark plugs and electrical insulators. The triumphs of engineering skill rest on a chemical foundation.
In Fundamental Chemistry, and Elementary Textbook for College Classes (1936), 8.
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Mi è impossibile cingere i fianchi di una ragazza con il mio braccio destro e serrare il suo sorriso nella mia mano sinistra, per poi tentare di studiare i due oggetti separatamente. Allo stesso modo, non ci è possibile separare la vita dalla materia vivente, allo scopo di studiare la sola materia vivente e le sue reazioni. Inevitabilmente, studiando la materia vivente e le sue reazioni, studiamo la vita stessa.
It is impossible to encircle the hips of a girl with my right arm and hold her smile in my left hand, then proceed to study the two items separately. Similarly, we can not separate life from living matter, in order to study only living matter and its reactions. Inevitably, studying living matter and its reactions, we study life itself
In The Nature of Life (1948).
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Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se colorer d'une teinte rose uniforme et à partir de ce moment on aura beau agiter le vase, le vin et l'eau ne partaîtront plus pouvoir se séparer. Tout cela, Maxwell et Boltzmann l'ont expliqué, mais celui qui l'a vu plus nettement, dans un livre trop peu lu parce qu'il est difficile à lire, c'est Gibbs dans ses principes de la Mécanique Statistique.
Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from th at moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 3.
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That the general characters of the big group to which the embryo belongs appear in development earlier than the special characters. In agreement with this is the fact that the vesicular form is the most general form of all; for what is common in a greater degree to all animals than the opposition of an internal and an external surface?
The less general structural relations are formed after the more general, and so on until the most special appear.
The embryo of any given form, instead of passing through the state of other definite forms, on the contrary separates itself from them.

Fundamentally the embryo of a higher animal form never resembles the adult of another animal form, but only its embryo.
Über Entwicklungsgeschichte der Thiere: Beobachtung und Reflexion (1828), 224. Trans. E. S. Russell, Form and Function: A Contribution to the History of Animal Morphology (1916), 125-6.
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A century ago astronomers, geologists, chemists, physicists, each had an island of his own, separate and distinct from that of every other student of Nature; the whole field of research was then an archipelago of unconnected units. To-day all the provinces of study have risen together to form a continent without either a ferry or a bridge.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 182-183.
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A few days ago, a Master of Arts, who is still a young man, and therefore the recipient of a modern education, stated to me that until he had reached the age of twenty he had never been taught anything whatever regarding natural phenomena, or natural law. Twelve years of his life previously had been spent exclusively amongst the ancients. The case, I regret to say, is typical. Now we cannot, without prejudice to humanity, separate the present from the past.
'On the Study of Physics', From a Lecture delivered in the Royal Institution of Great Britain in the Spring of 1854. Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 1, 284-5.
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A human being is part of the whole, called by us “Universe”; a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest—a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. Nobody is able to achieve this completely but the striving for such achievement is, in itself, a part of the liberation and a foundation for inner security.
In Letter (4 Mar 1950), replying to a grieving father over the loss of a young son. In Dear Professor Einstein: Albert Einstein’s Letters to and from Children (2002), 184.
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A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
War and Peace (1869), Book 11, Chap. 1.
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A pair of Siamese twins in Australia, surgically separated six months ago, has been sewn back together. Apparently, each of them could remember only half the combination to their locker.
In Napalm and Silly Putty (2002), 104.
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A research journal serves that narrow borderland which separates the known from the unknown.
Editorial, Vol. 1, Part 1, in the new statistics journal of the Indian Statistical Institute, Sankhayā (1933), as quoted and cited by MacTutor webpage for Mahalanobis. Also reprinted in Sankhyā: The Indian Journal of Statistics (Feb 2003), 65, No. 1, xii.
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A time will come when science will transform [our bodies] by means which we cannot conjecture... And then, the earth being small, mankind will migrate into space, and will cross the airless Saharas which separate planet from planet, and sun from sun. The earth will become a Holy Land which will be visited by pilgrims from all quarters of the universe.
…...
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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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Alchemy is the art that separates what is useful from what is not by transforming it into its ultimate matter and essence.
In Labyrinthus Medicorum. Cap. V. Von dem Buch der alchimei, wie on dasselbig der arzt kein arzt sein mag. Ed. Sudhoff, vol. XI, 188-189. As cited in Walter Pagel, Paracelsus: An Introduction to Philosophical Medicine in the Era of the Renaissance (2nd rev. ed., 1982), 113.
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All that Anatomie can doe is only to shew us the gross and sensible parts of the body, or the vapid and dead juices all which, after the most diligent search, will be noe more able to direct a physician how to cure a disease than how to make a man; for to remedy the defects of a part whose organicall constitution and that texture whereby it operates, he cannot possibly know, is alike hard, as to make a part which he knows not how is made. Now it is certaine and beyond controversy that nature performs all her operations on the body by parts so minute and insensible that I thinke noe body will ever hope or pretend, even by the assistance of glasses or any other intervention, to come to a sight of them, and to tell us what organicall texture or what kinde offerment (for whether it be done by one or both of these ways is yet a question and like to be soe always notwithstanding all the endeavours of the most accurate dissections) separate any part of the juices in any of the viscera, or tell us of what liquors the particles of these juices are, or if this could be donne (which it is never like to be) would it at all contribute to the cure of the diseases of those very parts which we so perfectly knew.
'Anatomie' (1668). Quoted in Kenneth Dewhurst (ed.), Dr. Thomas Sydenham (1624-1689): His Life and Original Writings (1966), 85-6.
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And God said, Let there be lights in the firmament of the heavens to separate the day from the night; and let them be for signs and for seasons and for days and years, and let them be lights in the firmament of the heavens to give light upon the earth.” And it was so. And God made the two great lights, the greater light to rule the day, and the lesser light to rule the night; he made the stars also.
Bible
(circa 725 B.C.)
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Apparently separate parts of the world would be deeply and conspiratorially entangled, and our apparent free will would be entangled with them.
In 'Bertlmann's Socks and the Nature of Reality', Journal de physique (1981), 42, No.3, Supplement, C2-57.
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As I looked down, I saw a large river meandering slowly along for miles, passing from one country to another without stopping. I also saw huge forests, extending along several borders. And I watched the extent of one ocean touch the shores of separate continents. Two words leaped to mind as I looked down on all this: commonality and interdependence. We are one world.
…...
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As in the domains of practical life so likewise in science there has come about a division of labor. The individual can no longer control the whole field of mathematics: it is only possible for him to master separate parts of it in such a manner as to enable him to extend the boundaries of knowledge by creative research.
In Die reine Mathematik in den Jahren 1884-99, 10. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 94.
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As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection.
In Leçons Élémentaires sur la Mathematiques, Leçon cinquième. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 81.
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As our researches have made clear, an animal high in the organic scale only reaches this rank by passing through all the intermediate states which separate it from the animals placed below it. Man only becomes man after traversing transitional organisatory states which assimilate him first to fish, then to reptiles, then to birds and mammals.
Annales des Sciences Naturelles (1834), 2 (ii), 248. Trans. in E. S. Russell, Form and Function (1916), 82.
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As we were flying over the Mozambique Channel, which separates the island of Madagascar from the continent of Africa, we could clearly see the transverse sand bars at its bottom. It was just like a brook one waded in childhood.
Lev Demin
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Between this body [the earth] and the heavens there are suspended, in this aerial spirit, seven stars, separated by determinate spaces, which, on account of their motion, we call wandering.
In The Natural History of Pliny (1855), Vol. 1, 19-20.
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Biological evolution is a system of constant divergence without subsequent joining of branches. Lineages, once distinct, are separate forever. In human history, transmission across lineages is, perhaps, the major source of cultural change. Europeans learned about corn and potatoes from Native Americans and gave them smallpox in return.
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Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.
The Anatomy of Science (1926), 158-9.
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But come, hear my words, for truly learning causes the mind to grow. For as I said before in declaring the ends of my words … at one time there grew to be the one alone out of many, and at another time it separated so that there were many out of the one; fire and water and earth and boundless height of air, and baneful Strife apart from these, balancing each of them, and Love among them, their equal in length and breadth.
From The Fragments, Bk. 1, line 74. In Arthur Fairbanks (ed., trans.), Quotations from The First Philosophers of Greece (1898), 167-168.
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But concerning vision alone is a separate science formed among philosophers, namely, optics, and not concerning any other sense ... It is possible that some other science may be more useful, but no other science has so much sweetness and beauty of utility. Therefore it is the flower of the whole of philosophy and through it, and not without it, can the other sciences be known.
Opus Majus [1266-1268], Part V, distinction I, chapter I, trans. R. B. Burke, The Opus Maius of Roger Bacon (1928), Vol. 2, 420.
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Can we separate object and subject? Myself is nothing but a part of my body, my body is nothing but a part of my food, my food is nothing but a part of the earth, the earth is nothing but a part of the solar system.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), lii.
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Complexes are psychic contents which are outside the control of the conscious mind. They have been split off from consciousness and lead a separate existence in the unconscious, being at all times ready to hinder or to reinforce the conscious intentions.
Carl Jung
A Psychological Theory of Types (1931), 79.
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Could the waters of the Atlantic be drawn off so as to expose to view this great seagash which separates continents, and extends from the Arctic to the Antarctic, it would present a scene the most rugged, grand and imposing. The very ribs of the solid earth, with the foundations of the sea, would be brought to light.
(1860)
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Deaths, births, and marriages, considering how much they are separately dependent on the freedom of the human will, should seem to be subject to no law according to which any calculation could be made beforehand of their amount; and yet the yearly registers of these events in great countries prove that they go on with as much conformity to the laws of nature as the oscillations of the weather.
'Idea of a Universal history on a Cosmo-Political Plan' (1784). As translated by Thomas De Quinsey in The London Magazine (Oct 1824), 10, 385. Reprinted in 1859 by De Quincey in Vol. 8 of his Collective Edition of his writings.
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Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”
In article 'Mathematics', Encyclopedia Britannica (1911, 11th ed.), Vol. 17, 880. In the 2006 DVD edition of the encyclopedia, the definition of mathematics is given as “The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects.” [Premiss is a variant form of “premise”. —Webmaster]
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Each worldview was a cultural product, but evolution is true and separate creation is not ... Worldviews are social constructions, and they channel the search for facts. But facts are found and knowledge progresses, however fitfully. Fact and theory are intertwined, and all great scientists understand the interaction.
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Evolution is a process which favors cooperating rather than disoperating groups and that “fitness” is a function of the group as a whole than of separate individuals. The fitness of the individual is largely derived from his membership on a group.
In On Being Human (1950), 45.
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Explanation separates us from astonishment, which is the only gateway to the incomprehensible.
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Extinction has only separated groups: it has by no means made them; for if every form which has ever lived on this earth were suddenly to reappear, though it would be quite impossible to give definitions by which each group could be distinguished from other groups, as all would blend together by steps as fine as those between the finest existing varieties, nevertheless a natural classification, or at least a natural arrangement, would be possible.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1860), 431.
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For us, an atom shall be a small, spherical, homogeneous body or an essentially indivisible, material point, whereas a molecule shall be a separate group of atoms in any number and of any nature.
Annales de Chimie 1833, 52, 133. Trans. W. H. Brock.
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Force is no impelling god, no entity separate from the material substratum ; it is inseparable from matter, is one of its eternal indwelling properties.
As quoted in Ludwig Büchner, Force and Matter: Or, Principles of the Natural Order of the Universe (1891), 1.
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Fortunately Nature herself seems to have prepared for us the means of supplying that want which arises from the impossibility of making certain experiments on living bodies. The different classes of animals exhibit almost all the possible combinations of organs: we find them united, two and two, three and three, and in all proportions; while at the same time it may be said that there is no organ of which some class or some genus is not deprived. A careful examination of the effects which result from these unions and privations is therefore sufficient to enable us to form probable conclusions respecting the nature and use of each organ, or form of organ. In the same manner we may proceed to ascertain the use of the different parts of the same organ, and to discover those which are essential, and separate them from those which are only accessory. It is sufficient to trace the organ through all the classes which possess it, and to examine what parts constantly exist, and what change is produced in the respective functions of the organ, by the absence of those parts which are wanting in certain classes.
Letter to Jean Claude Mertrud. In Lectures on Comparative Anatomy (1802), Vol. I, xxiii--xxiv.
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Four college students taking a class together, had done so well through the semester, and each had an “A”. They were so confident, the weekend before finals, they went out partying with friends. Consequently, on Monday, they overslept and missed the final. They explained to the professor that they had gone to a remote mountain cabin for the weekend to study, but, unfortunately, they had a flat tire on the way back, didn’t have a spare, and couldn’t get help for a long time. As a result, they missed the final. The professor kindly agreed they could make up the final the following day. When they arrived the next morning, he placed them each in separate rooms, handed each one a test booklet, and told them to begin. The the first problem was simple, worth 5 points. Turning the page they found the next question, written: “(For 95 points): Which tire?”
Anonymous
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Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have [played] … an historical role … in the development of pure mathematics. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. Modern mathematics began with Cantor’s set theory and Peano’s space-filling curve. Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. These new structures were regarded … as “pathological,” .… as a “gallery of monsters,” akin to the cubist paintings and atonal music that were upsetting established standards of taste in the arts at about the same time. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in Nature. Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins.
Now, as Mandelbrot points out, … Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.
From 'Characterizing Irregularity', Science (12 May 1978), 200, No. 4342, 677-678. Quoted in Benoit Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 3-4.
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Fractals are patterns which occur on many levels. This concept can be applied to any musical parameter. I make melodic fractals, where the pitches of a theme I dream up are used to determine a melodic shape on several levels, in space and time. I make rhythmic fractals, where a set of durations associated with a motive get stretched and compressed and maybe layered on top of each other. I make loudness fractals, where the characteristic loudness of a sound, its envelope shape, is found on several time scales. I even make fractals with the form of a piece, its instrumentation, density, range, and so on. Here I’ve separated the parameters of music, but in a real piece, all of these things are combined, so you might call it a fractal of fractals.
Interview (1999) on The Discovery Channel. As quoted by Benoit B. Manelbrot and Richard Hudson in The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward (2010), 133.
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From the infinitely great down to the infinitely small, all things are subject to [the laws of nature]. The sun and the planets follow the laws discovered by Newton and Laplace, just as the atoms in their combinations follow the laws of chemistry, as living creatures follow the laws of biology. It is only the imperfections of the human mind which multiply the divisions of the sciences, separating astronomy from physics or chemistry, the natural sciences from the social sciences. In essence, science is one. It is none other than the truth.
In Cours d’Economie Politique (1896-97).
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Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison which we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome, but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.
From Essai d’une nouvelle théorie de la résistance des fluides (1752), translated as an epigram in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics (1990), Vol. 1, 33.
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However far the calculating reason of the mathematician may seem separated from the bold flight of the artist’s phantasy, it must be remembered that these expressions are but momentary images snatched arbitrarily from among the activities of both. In the projection of new theories the mathematician needs as bold and creative a phantasy as the productive artist, and in the execution of the details of a composition the artist too must calculate dispassionately the means which are necessary for the successful consummation of the parts. Common to both is the creation, the generation, of forms out of mind.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 185. From the original German, “Wie weit auch der rechnende Verstand des Mathematikers von dem kühnen Fluge der Phantasie des Künstlers getrennt zu sein scheint, so bezeichnen diese Ausdrücke doch blosse Augenblicksbilder, die willkürlich aus der Thätigkeit Beider herausgerissen sind. Bei dem Entwurfe neuer Theorieen bedarf der Mathematiker einer ebenso kühnen und schöpferischen Phantasie wie der schaffende Künstler, und bei der Ausführung der Einzelheiten eines Werkes muss auch der Künstler kühl alle Mittel berechnen, welche zum Gelingen der Theile erforderlich sind. Gemeinsam ist Beiden die Hervorbringung, die Erzeugung der Gebilde aus dem Geiste.”
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However far the mathematician’s calculating senses seem to be separated from the audacious flight of the artist’s imagination, these manifestations refer to mere instantaneous images, which have been arbitrarily torn from the operation of both. In designing new theories, the mathematician needs an equally bold and inspired imagination as creative as the artist, and in carrying out the details of a work the artist must unemotionally reckon all the resources necessary for the success of the parts. Common to both is the fabrication, the creation of the structure from the intellect.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. Translated by Webmaster using online resources. From the original German, “Wie weit auch der rechnende Verstand des Mathematikers von dem kühnen Fluge der Phantasie des Künstlers getrennt zu sein scheint, so bezeichnen diese Ausdrücke doch blosse Augenblicksbilder, die willkürlich aus der Thätigkeit Beider herausgerissen sind. Bei dem Entwurfe neuer Theorieen bedarf der Mathematiker einer ebenso kühnen und schöpferischen Phantasie wie der schaffende Künstler, und bei der Ausführung der Einzelheiten eines Werkes muss auch der Künstler kühl alle Mittel berechnen, welche zum Gelingen der Theile erforderlich sind. Gemeinsam ist Beiden die Hervorbringung, die Erzeugung der Gebilde aus dem Geiste.”
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I am more and more convinced that the ant colony is not so much composed of separate individuals as that the colony is a sort of individual, and each ant like a loose cell in it. Our own blood stream, for instance, contains hosts of white corpuscles which differ little from free-swimming amoebae. When bacteria invade the blood stream, the white corpuscles, like the ants defending the nest, are drawn mechanically to the infected spot, and will die defending the human cell colony. I admit that the comparison is imperfect, but the attempt to liken the individual human warrior to the individual ant in battle is even more inaccurate and misleading. The colony of ants with its component numbers stands half way, as a mechanical, intuitive, and psychical phenomenon, between our bodies as a collection of cells with separate functions and our armies made up of obedient privates. Until one learns both to deny real individual initiative to the single ant, and at the same time to divorce one's mind from the persuasion that the colony has a headquarters which directs activity … one can make nothing but pretty fallacies out of the polity of the ant heap.
In An Almanac for Moderns (1935), 121
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I cannot separate land and sea: to me they interfinger like a pattern in a moss agate, positive and negative shapes irrevocably interlocked. My knowledge of this peninsula depends on that understanding: of underwater canyons that are continuations of the land, of the shell fossils far inland that measure continuations of the sea in eons past.
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I do not think that, practically or morally, we can defend a policy of saving every distinctive local population of organisms. I can cite a good rationale for the preservation of species, for each species is a unique and separate natural object that, once lost, can never be reconstituted. But subspecies are distinctive local populations of species with broader geographic range. Subspecies are dynamic, interbreedable, and constantly changing: what then are we saving by declaring them all inviolate?
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I must beg leave to propose a separate technical name ‘chromosome’ for those things which have been called by Boveri ‘chromatic elements’, in which there occurs one of the most important acts in karyokinesis, viz. the longitudinal splitting.
[Coining the word ‘chromosome,’ or ‘chromosom’ in the original German.]
Original German text by Waldeyer in Archiv für Mikroskopische Anatomie (1888), 27, translated by W.B. Benham in Quarterly Journal of Microscopical Science (1889), 30, 181.
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I think that a particle must have a separate reality independent of the measurements. That is an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it.
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If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
In Gottfried Wilhelm Leibnitz and Alfred Gideon Langley (trans.), New Essays Concerning Human Understanding (1896), 413-414.
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If there is any kind of animal which is female and has no male separate from it, it is possible that this may generate a young one from itself. No instance of this worthy of any credit has been observed up to the present at any rate, but one case in the class of fishes makes us hesitate. No male of the so-called erythrinus has ever yet been seen, but females, and specimens full of roe, have been seen. Of this, however, we have as yet no proof worthy of credit.
Aristotle
Generation of Animals, 741a, 32-8. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 1150.
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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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If you had come to me a hundred years ago, do you think I should have dreamed of the telephone? Why, even now I cannot understand it! I use it every day, I transact half my correspondence by means of it, but I don’t understand it. Thnk of that little stretched disk of iron at the end of a wire repeating in your ear not only sounds, but words—not only words, but all the most delicate and elusive inflections and nuances of tone which separate one human voice from another! Is not that something of a miracle?
Quoted in Harold Begbie in Pall Mall magazine (Jan 1903). In Albert Shaw, The American Monthly Review of Reviews (1903), 27, 232.
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In defining an element let us not take an external boundary, Let us say, e.g., the smallest ponderable quantity of yttrium is an assemblage of ultimate atoms almost infinitely more like each other than they are to the atoms of any other approximating element. It does not necessarily follow that the atoms shall all be absolutely alike among themselves. The atomic weight which we ascribe to yttrium, therefore, merely represents a mean value around which the actual weights of the individual atoms of the “element” range within certain limits. But if my conjecture is tenable, could we separate atom from atom, we should find them varying within narrow limits on each side of the mean.
Address to Annual General Meeting of the Chemical Society (28 Mar 1888), printed in Journal of the Chemical Society (1888), 491.
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In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.
In 'Geometry', Encyclopedia Britannica (9th edition).
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In general the position as regards all such new calculi is this That one cannot accomplish by them anything that could not be accomplished without them. However, the advantage is, that, provided such a calculus corresponds to the inmost nature of frequent needs, anyone who masters it thoroughly is able—without the unconscious inspiration of genius which no one can command—to solve the respective problems, yea, to solve them mechanically in complicated cases in which, without such aid, even genius becomes powerless. Such is the case with the invention of general algebra, with the differential calculus, and in a more limited region with Lagrange’s calculus of variations, with my calculus of congruences, and with Möbius’s calculus. Such conceptions unite, as it were, into an organic whole countless problems which otherwise would remain isolated and require for their separate solution more or less application of inventive genius.
Letter (15 May 1843) to Schumacher, collected in Carl Friedrich Gauss Werke (1866), Vol. 8, 298, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 197-198. From the original German, “Überhaupt verhält es sich mit allen solchen neuen Calculs so, dass man durch sie nichts leisten kann, was nicht auch ohne sie zu leisten wäre; der Vortheil ist aber der, dass, wenn ein solcher Calcul dem innersten Wesen vielfach vorkommender Bedürfnisse correspondirt, jeder, der sich ihn ganz angeeignet hat, auch ohne die gleichsam unbewussten Inspirationen des Genies, die niemand erzwingen kann, die dahin gehörigen Aufgaben lösen, ja selbst in so verwickelten Fällen gleichsam mechanisch lösen kann, wo ohne eine solche Hülfe auch das Genie ohnmächtig wird. So ist es mit der Erfindung der Buchstabenrechnung überhaupt; so mit der Differentialrechnung gewesen; so ist es auch (wenn auch in partielleren Sphären) mit Lagranges Variationsrechnung, mit meiner Congruenzenrechnung und mit Möbius' Calcul. Es werden durch solche Conceptionen unzählige Aufgaben, die sonst vereinzelt stehen, und jedesmal neue Efforts (kleinere oder grössere) des Erfindungsgeistes erfordern, gleichsam zu einem organischen Reiche.”
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In my opinion there is no other salvation for civilization and even for the human race than the creation of a world government with security on the basis of law. As long as there are sovereign states with their separate armaments and armament secrets, new world wars cannot be avoided.
Interview comment reported in 'For a World Government: Einstein Says This is Only Way to Save Mankind', New York Times (15 Sep 1945), 11.
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In the animal world, on the other hand, the process of evolution is characterised by the progressive discrimination of the animal and vegetative functions, and a consequent differentiation of these two great provinces into their separate departments.
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In the beginning of the year 1800 the illustrious professor conceived the idea of forming a long column by piling up, in succession, a disc of copper, a disc of zinc, and a disc of wet cloth, with scrupulous attention to not changing this order. What could be expected beforehand from such a combination? Well, I do not hesitate to say, this apparently inert mass, this bizarre assembly, this pile of so many couples of unequal metals separated by a little liquid is, in the singularity of effect, the most marvellous instrument which men have yet invented, the telescope and the steam engine not excepted.
In François Arago, 'Bloge for Volta' (1831), Oeuvres Completes de François Arago (1854), Vol. 1, 219-20.
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In the pursuit of the physical sciences, the imagination supplies the hypothesis which bridges over the gulf that separates the known from the unknown.
Presidential Address to Anniversary meeting of the Royal Society (30 Nov 1859), Proceedings of the Royal Society of London (1860), 10, 165-166.
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Inasmuch as science represents one way of dealing with the world, it does tend to separate its practitioners from the rest. Being a scientist resembles membership of a religious order and a scientist usually finds that he has more in common with a colleague on the other side of the world than with his next-door neighbor.
In A Dictionary of Scientific Quotations (1991).
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It is most interesting to observe into how small a field the whole of the mysteries of nature thus ultimately resolve themselves. The inorganic has one final comprehensive law, GRAVITATION. The organic, the other great department of mundane things, rests in like manner on one law, and that is,—DEVELOPMENT. Nor may even these be after all twain, but only branches of one still more comprehensive law, the expression of that unity which man's wit can scarcely separate from Deity itself.
Vestiges of the Natural History of Creation (1844), 360.
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It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
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It is through it [intuition] that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality.
…...
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It [science] must be amoral by its very nature: the minute it begins separating facts into the two categories of good ones and bad ones it ceases to be science and becomes a mere nuisance, like theology.
From American Mercury (Sep 1927). Collected in A Mencken Chrestomathy (1949, 1956), 331.
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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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Journalism must find the facts, it must not prejudge things in terms of conservatism or liberalism or radicalism; it must not decide in advance that it is to be conformist or non-conformist; it cannot fly in the face of facts without courting ultimate disaster.
Journalism must focus the facts; facts are not important for their own sake; they are important only as a basis for action; journalism must focus the facts it finds upon the issues its readers face.
Journalism must filter the facts; it must with conscientious care separate the facts from admixtures of prejudice, passion, partisanship, and selfish interest; facts that are diluted, colored, or perverted are valueless as a basis for action.
Journalism must face the facts; it must learn that the energy spent in trying to find ways to get around, under, or over the facts is wasted energy; facts have a ruthless way of winning the day sooner or later.
Journalism must follow the facts; journalism must say of facts as Job said, of God: though they slay us, yet shall we trust them; if the facts threaten to upset a paper's cherished policy, it always pays the journalist to re-examine his policy; that way lies realism, and realism is the ultimate good.
From address as president of the Wisconsin local chapter of Theta Sigma Phi, at its first annual Matrix Table (9 Jan 1926). quoted in 'Journalism News and Notes', in Robert S. Crawford (ed.), The Wisconsin Alumni Magazine (Feb 1926), 27, No. 4, 101. If you know any other example of Glenn Frank speaking about his five themes on facts, please contact Webmaster.
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Language is simply alive, like an organism. We all tell each other this, in fact, when we speak of living languages, and I think we mean something more than an abstract metaphor. We mean alive. Words are the cells of language, moving the great body, on legs. Language grows and evolves, leaving fossils behind. The individual words are like different species of animals. Mutations occur. Words fuse, and then mate. Hybrid words and wild varieties or compound words are the progeny. Some mixed words are dominated by one parent while the other is recessive. The way a word is used this year is its phenotype, but it has deeply immutable meanings, often hidden, which is its genotype.... The separate languages of the Indo-European family were at one time, perhaps five thousand years ago, maybe much longer, a single language. The separation of the speakers by migrations had effects on language comparable to the speciation observed by Darwin on various islands of the Galapagos. Languages became different species, retaining enough resemblance to an original ancestor so that the family resemblance can still be seen.
in 'Living Language,' The Lives of a Cell: Notes of a Biology Watcher, (1974, 1984), 106.
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Listen now for the sound that forevermore separates the old from the new.
[Introducing the beep-beep chirp transmitted by the Sputnik satellite.]
NBC Radio
NBC radio announcer on the night of 4 Oct 1957. In 'The Nation: Red Moon Over the U.S.', Time (14 Oct 1957), 70, 27.
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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 is occupied and has been persistently occupied since his separate evolution, with three kinds of struggle: first with the massive unintelligent forces of nature, heat and cold, winds, rivers, matter and energy; secondly, with the things closer to him, animals and plants, his own body, its health and disease; and lastly, with his desires and fears, his imaginations and stupidities.
In The World, the Flesh and the Devil (1929).
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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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One of the earliest questions asked by an intelligent child is: “What is this made of?” “What is that made of?” And the answer is generally more or less satisfactory. For example, if the question relates to butter, the reply may be, “From cream.” It may be explained, besides, that when cream is beaten up, or churned, the butter separates, leaving skim-milk behind. But the question has not been answered. The child may ask, “Was the butter in the milk before it was churned? or has it been made out of the milk by the churning?” Possibly the person to whom the question is addressed may know that the milk contained the butter in the state of fine globules, and that the process of churning breaks up the globules, and causes them to stick together. The original question has not really been answered; and indeed it is not an easy one to reply to. Precisely such questions suggested themselves to the people of old, and they led to many speculations.
Opening paragraph of Modern Chemistry (1900, rev. 1907), 1.
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Picture yourself during the early 1920's inside the dome of the [Mount Wilson Observatory]. … [Milton] Humason is showing [Harlow] Shapley stars he had found in the Andromeda Nebula that appeared and disappeared on photographs of that object. The famous astronomer very patiently explains that these objects could not be stars because the Nebula was a nearby gaseous cloud within our own Milky Way system. Shapley takes his handkerchief from his pocket and wipes the identifying marks off the back of the photographic plate.
Of course, Hubble came along in 1924 and showed that it was just these Cepheid variable stars in the Andromeda Nebula which proved it was a separate galaxy system.
In Quasars, Redshifts and Controversies (1998), 168. Arp writes that this was “a piece of real history which I happen to know because it was told to me by one of the participants. It dramatically illustrate the critical role of discordant evidence.”
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Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.
Malay Archipelago
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Science is neither a single tradition, nor the best tradition there is, except for people who have become accustomed to its presence, its benefits and its disadvantages. In a democracy it should be separated from the state just as churches are now separated from the state.
Against Method, p. 238 (1975).The author's warning against allowing scientists to become the new 'high priests' of society.
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Secondly, the study of mathematics would show them the necessity there is in reasoning, to separate all the distinct ideas, and to see the habitudes that all those concerned in the present inquiry have to one another, and to lay by those which relate not to the proposition in hand, and wholly to leave them out of the reckoning. This is that which, in other respects besides quantity is absolutely requisite to just reasoning, though in them it is not so easily observed and so carefully practised. In those parts of knowledge where it is thought demonstration has nothing to do, men reason as it were in a lump; and if upon a summary and confused view, or upon a partial consideration, they can raise the appearance of a probability, they usually rest content; especially if it be in a dispute where every little straw is laid hold on, and everything that can but be drawn in any way to give color to the argument is advanced with ostentation. But that mind is not in a posture to find truth that does not distinctly take all the parts asunder, and, omitting what is not at all to the point, draws a conclusion from the result of all the particulars which in any way influence it.
In Conduct of the Understanding, Sect. 7.
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Some of my cousins who had the great advantage of University education used to tease me with arguments to prove that nothing has any existence except what we think of it. … These amusing mental acrobatics are all right to play with. They are perfectly harmless and perfectly useless. ... I always rested on the following argument. … We look up to the sky and see the sun. Our eyes are dazzled and our senses record the fact. So here is this great sun standing apparently on no better foundation than our physical senses. But happily there is a method, apart altogether from our physical senses, of testing the reality of the sun. It is by mathematics. By means of prolonged processes of mathematics, entirely separate from the senses, astronomers are able to calculate when an eclipse will occur. They predict by pure reason that a black spot will pass across the sun on a certain day. You go and look, and your sense of sight immediately tells you that their calculations are vindicated. So here you have the evidence of the senses reinforced by the entirely separate evidence of a vast independent process of mathematical reasoning. We have taken what is called in military map-making “a cross bearing.” When my metaphysical friends tell me that the data on which the astronomers made their calculations, were necessarily obtained originally through the evidence of the senses, I say, “no.” They might, in theory at any rate, be obtained by automatic calculating-machines set in motion by the light falling upon them without admixture of the human senses at any stage. When it is persisted that we should have to be told about the calculations and use our ears for that purpose, I reply that the mathematical process has a reality and virtue in itself, and that onie discovered it constitutes a new and independent factor. I am also at this point accustomed to reaffirm with emphasis my conviction that the sun is real, and also that it is hot— in fact hot as Hell, and that if the metaphysicians doubt it they should go there and see.
In My Early Life (1930).
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Sometimes I wonder whether there is any such thing as biology. The word was invented rather late—in 1809—and other words like botany, zoology, physiology, anatomy, have much longer histories and in general cover more coherent and unified subject matters. … I would like to see the words removed from dictionaries and college catalogues. I think they do more harm than good because they separate things that should not be separated…
In The Forest and the Sea (1960), 6-7.
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South America must have lain alongside Africa and formed a unified block which was split in two in the Cretaceous; the two parts must then have become increasingly separated over a period of millions of years like pieces of a cracked ice floe in water.
In The Origins of Continents and Oceans (4th ed. 1929), trans. John Biram (1966), 17.
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Tapestries are made by many artisans working together. The contributions of separate workers cannot be discerned in the completed work, and the loose and false threads have been covered over. So it is in our picture of particle physics.
In 'Towards a Unified Theory—Threads in a Tapestry', Nobel Lecture, 8 Dec 1979. In Nobel Lectures: Physics 1971-1980 (1992), 494. Also reproduced in Science (19 Dec 1980), New Series 210, No. 4476, 1319.
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The action of the mind in the acquisition of knowledge of any sort is synthetic-analytic; that is, uniting and separating. These are the two sides, or aspects, of the one process. … There is no such thing as a synthetic activity that is not accompanied by the analytic; and there is no analytic activity that is not accompanied by the synthetic. Children cannot be taught to perform these knowing acts. It is the nature of the mind to so act when it acts at all.
In The Public-School Journal (Jan 1895), Vol. 14, 281-282.
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The aim of science is to discover and illuminate truth. And that, I take it, is the aim of literature, whether biography or history or fiction. It seems to me, then, that there can be no separate literature of science.
Address upon receiving National Book Award at reception, Hotel Commodore, New York (27 Jan 1952). As cited in Linda Lear, Rachel Carson: Witness for Nature (1997), 219.
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The Atoms or Particles, which now constitute Heaven and Earth, being once separate and diffused in the Mundane Space, like the supposed Chaos, could never without a God by their Mechanical affections have convened into this present Frame of Things or any other like it.
A Confutation of Atheism from the Origin and Frame of the World. (1693), Part II, 7.
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The basic thesis of gestalt theory might be formulated thus: there are contexts in which what is happening in the whole cannot be deduced from the characteristics of the separate pieces, but conversely; what happens to a part of the whole is, in clearcut cases, determined by the laws of the inner structure of its 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, 84.
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The bird which is drawn to the water by its need of finding there the prey on which it lives, separates the digits of its feet in trying to strike the water and move about on the surface. The skin which unites these digits at their base acquires the habit of being stretched by these continually repeated separations of the digits; thus in course of time there are formed large webs which unite the digits of ducks, geese, etc., as we actually find them. In the same way efforts to swim, that is to push against the water so as to move about in it, have stretched the membranes between the digits of frogs, sea-tortoises, the otter, beaver, etc.
On the other hand, a bird which is accustomed to perch on trees and which springs from individuals all of whom had acquired this habit, necessarily has longer digits on its feet and differently shaped from those of the aquatic animals that I have just named. Its claws in time become lengthened, sharpened and curved into hooks, to clasp the branches on which the animal so often rests.
We find in the same way that the bird of the water-side which does not like swimming and yet is in need of going to the water's edge to secure its prey, is continually liable to sink into the mud. Now this bird tries to act in such a way that its body should not be immersed in the liquid, and hence makes its best efforts to stretch and lengthen its legs. The long-established habit acquired by this bird and all its race of continually stretching and lengthening its legs, results in the individuals of this race becoming raised as though on stilts, and gradually obtaining long, bare legs, denuded of feathers up to the thighs and often higher still.
Philosophie Zoologique (1809), Vol. 1, 249-50, trans. Hugh Elliot (1914), 119-20.
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The cause of nutrition and growth resides not in the organism as a whole but in the separate elementary parts—the cells.
Mikroskopische Untersuchungen über die Uebereinstimmung in der Struktur und dem Wachsthum der Thiere und Pflanzen (1839). Microscopic Researches into the Accordance in the Structure and Growth of Animals and Plants, trans. Henry Smith (1847), 192.
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The development of the Vertebrate proceeds from an axis upward, in two layers, which coalesce at the edges, and also downward, in two layers, which likewise coalesce at the edges. Thus two main tubes are formed, one above the other. During the formation of these, the embryo separates into strata, so that the two main tubes are composed of subordinate tubes which enclose each other as fundamental organs, and are capable of developing into all the organs.
As translated and quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 10, The History of Creation (1886), Vol. 1, 244. Alternate translation: “Vertebrate development consists in the formation, in the median plane, of four leaflets two of which are above the axis and two below. During this evolution the germ subdivides in layers, and this has the effect of dividing the primordial tubes into secondary masses. The latter, included in the other masses, are the fundamental organs with the faculty of forming all the other organs.” in François Jacob, The Logic of Life (1993), 121-122.
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The energy liberated when substrates undergo air oxidation is not liberated in one large burst, as was once thought, but is released in stepwise fashion. At least six separate steps seem to be involved. The process is not unlike that of locks in a canal. As each lock is passed in the ascent from a lower to a higher level a certain amount of energy is expended. Similarly, the total energy resulting from the oxidation of foodstuffs is released in small units or parcels, step by step. The amount of free energy released at each step is proportional to the difference in potential of the systems comprising the several steps.
'Oxidative Mechanisms in Animal Tissues', A Symposium on Respiratory Enzymes (1942), 22.
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The entire cosmos is made out of one and the same world-stuff, operated by the same energy as we ourselves. “Mind” and “matter” appears as two aspects of our unitary mind-bodies. There is no separate supernatural realm: all phenomena are part of one natural process of evolution. There is no basic cleavage between science and religion; they are both organs of evolving humanity.
In essay, 'The New Divinity', originally published in The Twentieth Century (1962), 170, 9. Collected in Essays of a Humanist (1964), 218.
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The essential character of a species in biology is, that it is a group of living organisms, separated from all other such groups by a set of distinctive characters, having relations to the environment not identical with those of any other group of organisms, and having the power of continuously reproducing its like. Genera are merely assemblages of a number of these species which have a closer resemblance to each other in certain important and often prominent characters than they have to any other species.
In 'The Method of Organic Evolution', Fortnightly Review (1895), 57, 441.
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The farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479.
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The fertilized germ of one of the higher animals … is perhaps the most wonderful object in nature… . On the doctrine of reversion [atavism] … the germ becomes a far more marvelous object, for, besides the visible changes which it undergoes, we must believe that it is crowded with invisible characters … separated by hundreds or even thousands of generations from the present time: and these characters, like those written on paper with invisible ink, lie ready to be evolved whenever the organization is disturbed by certain known or unknown conditions.
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The full story of successful organ transplantation in man weaves together three separate pathways: the study of renal disease, skin grafting in twins, and surgical determination. A leitmotif permeates each of these pathways, i.e. a single event or report was critical for medical progress.
In Tore Frängsmyr and Jan E. Lindsten (eds.), Nobel Lectures: Physiology Or Medicine: 1981-1990 (1993), 558.
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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 heart is an exceedingly strong muscle. … It contains two separate cavities.
As translated by E.T. Withington in 'The Heart', Hippocratic Writings (1978), 348.
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The human senses (above all, that of hearing) do not possess one set of constant parameters, to be measured independently, one at a time. It is even questionable whether the various 'senses' are to be regarded as separate, independent detectors. The human organism is one integrated whole, stimulated into response by physical signals; it is not to be thought of as a box, carrying various independent pairs of terminals labeled 'ears', 'eyes', 'nose', et cetera.
On Human Communication: A Review, A Survey and a Criticism (1957), 127-8.
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The humanities and science are not in inherent conflict but have become separated in the twentieth century. Now their essential unity must be re-emphasized so that 20th Century multiplicity may become 20th Century unity.
As quoted in 'Humanities Head', Time (8 Jun 1942), 39, No. 23, 63.
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The inhibitory nerves are of as fundamental importance in the economy of the body as the motor nerves. No evidence exists that the same nerve fibre is sometimes capable of acting as a motor nerve, sometimes as a nerve of inhibition, but on the contrary the latter nerves form a separate and complete nervous system subject to as definite anatomical and histological laws as the former.
'On the Structure, Distribution and Function of the Nerves which Innervate the Visceral and Vascular Systems', The Journal of Physiology, 1886, 7, 40.
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The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.
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The material universe must consist ... of bodies ... such that each of them exercises its own separate, independent, and invariable effect, a change of the total state being compounded of a number of separate changes each of which is solely due to a separate portion of the preceding state.
A Treatise on Probability (), 249. In Antony Flew, A Dictionary of Philosophy (1984), 30.
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The maxim of science is simply that of common sense—simple cases first; begin with seeing how the main force acts when there is as little as possible to impede it, and when you thoroughly comprehend that, add to it in succession the separate effects of each of the incumbering and interfering agencies.
Collected in The Works of Walter Bagehot (1889), Vol. 5, 319-320.
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The method of producing these numbers is called a sieve by Eratosthenes, since we take the odd numbers mingled and indiscriminate and we separate out of them by this method of production, as if by some instrument or sieve, the prime and incomposite numbers by themselves, and the secondary and composite numbers by themselves, and we find separately those that are mixed.
Nicomachus, Introduction to Arithmetic, 1.13.2. Quoted in Morris R. Cohen and I. E. Drabkin, A Sourcebook in Greek Science (1948), 19-20.
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The Microbe is so very small,
You cannot make him out at all.
But many sanguine people hope
To see him down a microscope.
His jointed tongue that lies beneath
A hundred curious rows of teeth;
His seven tufted tails with lots
Of lovely pink and purple spots
On each of which a pattern stands,
Composed of forty separate bands;
His eyebrows of a tender green;
All these have never yet been seen
But Scientists, who ought to know,
Assure us they must be so ...
Oh! let us never, never doubt
What nobody is sure about!
In More Beasts for Worse Children (1897), 47-8.
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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The occurrence of an internal skeleton, in definite relations to the other organ systems, and the articulation of the body into homologous segments, are points in the general organization of Vertebrates to which especial weight must be given. This metameric structure is more or less definitely expressed in most of the organs, and as it extends to the axial skeleton, the latter also gradually articulates into separate segments, the vertebrae. The latter, however, must be regarded only as the partial expression of a general articulation of the body which is all the more important in consequence of its appearing prior to the articulation of the originally inarticulate axial skeleton. Hence this general articulation may be considered as a primitive vertebral structure, to which the articulation of the axial skeleton is related as a secondary process of the same sort.
As translated and quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 11, The History of Creation (1886), Vol. 1, 328-329.
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The one who stays in my mind as the ideal man of science is, not Huxley or Tyndall, Hooker or Lubbock, still less my friend, philosopher and guide Herbert Spencer, but Francis Galton, whom I used to observe and listen to—I regret to add, without the least reciprocity—with rapt attention. Even to-day. I can conjure up, from memory’s misty deep, that tall figure with its attitude of perfect physical and mental poise; the clean-shaven face, the thin, compressed mouth with its enigmatical smile; the long upper lip and firm chin, and, as if presiding over the whole personality of the man, the prominent dark eyebrows from beneath which gleamed, with penetrating humour, contemplative grey eyes. Fascinating to me was Francis Galton’s all-embracing but apparently impersonal beneficence. But, to a recent and enthusiastic convert to the scientific method, the most relevant of Galton’s many gifts was the unique contribution of three separate and distinct processes of the intellect; a continuous curiosity about, and rapid apprehension of individual facts, whether common or uncommon; the faculty for ingenious trains of reasoning; and, more admirable than either of these, because the talent was wholly beyond my reach, the capacity for correcting and verifying his own hypotheses, by the statistical handling of masses of data, whether collected by himself or supplied by other students of the problem.
In My Apprenticeship (1926), 134-135.
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The peculiar taste both in pure and in mixed nature of those relations about which it is conversant, from its simple and definite phraseology, and from the severe logic so admirably displayed in the concatenation of its innumerable theorems, are indeed immense, and well entitled to separate and ample illustration.
In Philosophy of the Human Mind (1816), Vol. 2, Chap. 2, Sec. 3, 157.
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The phrase 'nature and nurture' is a convenient jingle of words, for it separates under two distinct heads the innumerable elements of which personality is composed. Nature is all that a man brings with himself into the world; nurture is every influence without that affects him after his birth.
English Men of Science: Their Nature and Nurture (1874), 12.
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The sciences have sworn among themselves an inviolable partnership; it is almost impossible to separate them, for they would rather suffer than be torn apart; and if anyone persists in doing so, he gets for his trouble only imperfect and confused fragments. Yet they do not arrive all together, but they hold each other by the hand so that they follow one another in a natural order which it is dangerous to change, because they refuse to enter in any other way where they are called. ...
Les Préludes de l'Harmonie Universelle (1634), 135-139. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 316.
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The separate atoms of a molecule are not connected all with all, or all with one, but, on the contrary, each one is connected only with one or with a few neighbouring atoms, just as in a chain link is connected with link.
'The Scientific Aims and Achievements of Chemistry', Nature (1878), 18, 212.
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The solution, as all thoughtful people recognize, must lie in properly melding the themes of inborn predisposition and shaping through life’s experiences. This fruitful joining cannot take the false form of percentages adding to 100–as in ‘intelligence is 80 percent nature and 20 percent nurture,’ or ‘homosexuality is 50 percent inborn and 50 percent learned,’ and a hundred other harmful statements in this foolish format. When two ends of such a spectrum are commingled, the result is not a separable amalgam (like shuffling two decks of cards with different backs), but an entirely new and higher entity that cannot be decomposed (just as adults cannot be separated into maternal and paternal contributions to their totality).
…...
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The universe seems to me infinitely strange and foreign. At such a moment I gaze upon it with a mixture of anguish and euphoria; separate from the universe, as though placed at a certain distance outside it; I look and I see pictures, creatures that move in a kind of timeless time and spaceless space, emitting sounds that are a kind of language I no longer understand or ever register.
‘Interviews: Brief Notes for Radio’, Notes and Counter-Notes: Writings on the Theatre (1964), 136.
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The whole subject of the X rays is opening out wonderfully, Bragg has of course got in ahead of us, and so the credit all belongs to him, but that does not make it less interesting. We find that an X ray bulb with a platinum target gives out a sharp line spectrum of five wavelengths which the crystal separates out as if it were a diffraction grating. In this way one can get pure monochromatic X rays. Tomorrow we search for the spectra of other elements. There is here a whole new branch of spectroscopy, which is sure to tell one much about the nature of an atom.
Letter to his mother (18 May 1913). In J. L. Heilbron (ed.), H. G. J. Moseley: The Life and Letters of an English Physicist 1887-1915 (1974), 205.
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The world is the geologist’s great puzzle-box; he stands before it like the child to whom the separate pieces of his puzzle remain a mystery till he detects their relation and sees where they fit, and then his fragments grow at once into a connected picture beneath his hand.
Geological Sketches (1866), II.
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There are something like ten million million million million million million million million million million million million million million (1 with eighty zeroes after it) particles in the region of the universe that we can observe. Where did they all come from? The answer is that, in quantum theory, particles can be created out of energy in the form of particle/antiparticle pairs. But that just raises the question of where the energy came from. The answer is that the total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.
A Brief History of Time: From the Big Bang to Black Holes (1988), 129.
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There are three leading objects in the study of truth:—one, to discover it; another, to demonstrate it when discovered; the last, to separate it from all admixture of falsehood.
As translated in Blaise Pascal and M.P. Faugère (trans.), 'On The Geometrical Spirit', collected in The Miscellaneous Writings of Pascal; Consisting of Letters, Essays, Conversations, and Miscellaneous Thoughts (1849), 73. From the original French, “On peut avoir trois principaux objets dans l’etude de la vérité: l’un, de la découvrir quand on la cherche; l’autre, de la démontrer quand on la possède; le dernier, de la discerner d'avec le faux quand on l’examine,” in 'De l'Esprit Géométrique', Pascal: Opuscules Philosophiques (1887), 82. For an alternative translation, see the quote beginning, “We may have three principal objects…” on the Blaise Pascal Quotes page of this website.
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There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
'The Study of the Natural Sciences: An Introductory Lecture to the Course of Experimental Chemistry in the University of Munich, for the Winter Session of 1852-53,' as translated and republished in The Medical Times and Gazette (22 Jan 1853), N.S. Vol. 6, 82.
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There is perhaps no science of which the development has been carried so far, which requires greater concentration and will power, and which by the abstract height of the qualities required tends more to separate one from daily life.
In 'Provisional Report of the American Subcommittee of the International Commission on Teaching of Mathematics', Bulletin American Society (Nov 1910), 97.
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There must be some bond of union between mass and the chemical elements; and as the mass of a substance is ultimately expressed (although not absolutely, but only relatively) in the atom, a functional dependence should exist and be discoverable between the individual properties of the elements and their atomic weights. But nothing, from mushrooms to a scientific dependence can be discovered without looking and trying. So I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and soon this convinced me that the properties of the elements are in periodic dependence upon their atomic weights; and although I had my doubts about some obscure points, yet I have never doubted the universality of this law, because it could not possibly be the result of chance.
Principles of Chemistry (1905), Vol. 2, 18.
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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This integrative action in virtue of which the nervous system unifies from separate organs an animal possessing solidarity, an individual, is the problem before us.
The Integrative Action of the Nervous System (1906), 2.
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This means that we have here an entirely separate kind of chemistry for which the current tool we use is the electrometer, not the balance, and which we might well call the chemistry of the imponderable.
(11 Dec 1911) As quoted in Marie and Pierre Curie and the Discovery of Polonium and Radium, Nobel Lecture
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This new force, which was unknown until now, is common to organic and inorganic nature. I do not believe that this is a force entirely independent of the electrochemical affinities of matter; I believe, on the contrary, that it is only a new manifestation, but since we cannot see their connection and mutual dependence, it will be easier to designate it by a separate name. I will call this force catalytic force. Similarly, I will call the decomposition of bodies by this force catalysis, as one designates the decomposition of bodies by chemical affinity analysis.
In'Some Ideas on a New Force which Acts in Organic Compounds', Annales chimie physiques, 1836, 61, 146. Translated in Henry M. Leicester and Herbert S. Klickstein, A Source Book in Chemistry 1400-1900 (1952), 267.
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This notion that “science” is something that belongs in a separate compartment of its own, apart from everyday life, is one that I should like to challenge. We live in a scientific age; yet we assume that knowledge of science is the prerogative of only a small number of human beings, isolated and priest-like in their laboratories. This is not true. It cannot be true. The materials of science are the materials of life itself. Science is part of the reality of living; it is the what, the how, and the why of everything in our experience. It is impossible to understand man without understanding his environment and the forces that have molded him physically and mentally.
Address upon receiving National Book Award at reception, Hotel Commodore, New York (27 Jan 1952). As cited in Linda Lear, Rachel Carson: Witness for Nature (1997), 218-219.
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This theme of mutually invisible life at widely differing scales bears an important implication for the ‘culture wars’ that supposedly now envelop our universities and our intellectual discourse in general ... One side of this false dichotomy features the postmodern relativists who argue that all culturally bound modes of perception must be equally valid, and that no factual truth therefore exists. The other side includes the benighted, old-fashioned realists who insist that flies truly have two wings, and that Shakespeare really did mean what he thought he was saying. The principle of scaling provides a resolution for the false parts of this silly dichotomy. Facts are facts and cannot be denied by any rational being. (Often, facts are also not at all easy to determine or specify–but this question raises different issues for another time.) Facts, however, may also be highly scale dependent–and the perceptions of one world may have no validity or expression in the domain of another. The one-page map of Maine cannot recognize the separate boulders of Acadia, but both provide equally valid representations of a factual coastline.
The World as I See It (1999)
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To be whole. To be complete. Wildness reminds us what it means to be human, what we are connected to rather than what we are separate from.
Testimony before the Senate Subcommittee on Forest & Public Lands Management regarding the Utah Public Lands Management Act of 1995, Washington, D.C. (13 Jul 1995).
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To be worthy of the name, an experimenter must be at once theorist and practitioner. While he must completely master the art of establishing experimental facts, which are the materials of science, he must also clearly understand the scientific principles which guide his reasoning through the varied experimental study of natural phenomena. We cannot separate these two things: head and hand. An able hand, without a head to direct it, is a blind tool; the head is powerless without its executive hand.
In Claude Bernard and Henry Copley Greene (trans.), An Introduction to the Study of Experimental Medicine (1927, 1957), 3.
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We may regard [Scheele] not only as having given the first indication of the rich harvest to be reaped by the investigation of the compounds of organic chemistry, but as having been the first to discover and make use of characteristic reactions by which closely allied substances can be detected and separated, so that he must be considered one of the chief founders of analytical chemistry.
In Treatise on Chemistry (1877, 1890), Vol. 1, 23.
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We see a universe marvelously arranged and obeying certain laws, but only dimly understand these laws. Our limited minds cannot grasp the mysterious force that moves the constellations. I am fascinated by Spinoza’s pantheism, but admire even more his contributions to modern thought because he is the first philosopher to deal with the soul and the body as one, not two separate things.
…...
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We set out, therefore, with the supposition that an organised body is not produced by a fundamental power which is guided in its operation by a definite idea, but is developed, according to blind laws of necessity, by powers which, like those of inorganic nature, are established by the very existence of matter. As the elementary materials of organic nature are not different from those of the inorganic kingdom, the source of the organic phenomena can only reside in another combination of these materials, whether it be in a peculiar mode of union of the elementary atoms to form atoms of the second order, or in the arrangement of these conglomerate molecules when forming either the separate morphological elementary parts of organisms, or an entire organism.
Mikroskopische Untersuchungen über die Uebereinstimmung in der Struktur und dem Wachsthum der Thiere und Pflanzen (1839). Microscopic Researches into the Accordance in the Structure and Growth of Animals and Plants, trans. Henry Smith (1847), 190-1.
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We shall therefore take an appropriately correct view of the origin of our life, if we consider our own embryos to have sprung immediately from those embryos whence our parents were developed, and these from the embryos of their parents, and so on for ever. We should in this way look on the nature of mankind, and perhaps on that of the whole animated creation, as one Continuous System, ever pushing out new branches in all directions, that variously interlace, and that bud into separate lives at every point of interlacement.
'Hereditary Talent and Character', Macmillan's Magazine, 1865, 12, 322.
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We should therefore, with grace and optimism, embrace NOMA’s tough-minded demand: Acknowledge the personal character of these human struggles about morals and meanings, and stop looking for definite answers in nature’s construction. But many people cannot bear to surrender nature as a ‘transitional object’–a baby’s warm blanket for our adult comfort. But when we do (for we must) , nature can finally emerge in her true form: not as a distorted mirror of our needs, but as our most fascinating comp anion. Only then can we unite the patches built by our separate magisteria into a beautiful and coherent quilt called wisdom.
…...
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What clearer evidence could we have had of the different formation of these rocks, and of the long interval which separated their formation, had we actually seen them emerging from the bosom of the deep? … The mind seemed to grow giddy by looking so far into the abyss of time.
As quoted in Dennis R. Dean, James Hutton and the History of Geology (1992), 122.
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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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When you can dump a load of bricks on a corner lot, and let me watch them arrange themselves into a house — when you can empty a handful of springs and wheels and screws on my desk, and let me see them gather themselves together into a watch — it will be easier for me to believe that all these thousands of worlds could have been created, balanced, and set to moving in their separate orbits, all without any directing intelligence at all.
In 'If A Man Die, Shall He Live again?', More Power To You: Fifty Editorials From Every Week (1917), 218-219.
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Where the untrained eye will see nothing but mire and dirt, Science will often reveal exquisite possibilities. The mud we tread under our feet in the street is a grimy mixture of clay and sand, soot and water. Separate the sand, however, as Ruskinn observes—let the atoms arrange themselves in peace according to their nature—and you have the opal. Separate the clay, and it becomes a white earth, fit for the finest porcelain; or if it still further purifies itself, you have a sapphire. Take the soot, and it properly treated it will give you a diamond. While lastly, the water, purified and distilled, will become a dew-drop, or crystallize into a lovely star. Or, again, you may see as you will in any shallow pool either the mud lying at the bottom, or the image of the heavens above.
The Pleasures of Life (1887, 2007), 63.
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Without preparing fluorine, without being able to separate it from the substances with which it is united, chemistry has been able to study and to analyze a great number of its compounds. The body was not isolated, and yet its place was marked in our classifications. This well demonstrates the usefulness of a scientific theory, a theory which is regarded as true during a certain time, which correlates facts and leads the mind to new hypotheses, the first causes of experimentation; which, little by little, destroy the theory itself, in order to replace it by another more in harmony with the progress of science.
[Describing the known history of fluorine compounds before his isolation of the element.]
'Fluorine', lecture at the Royal Institution (28 May 1897), translated from the French, in Proceedings of the Royal Institution (1897). In Annual Report of the Board of Regents of the Smithsonian Institution to July 1897 (1898), 262.
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You look at science (or at least talk of it) as some sort of demoralising invention of man, something apart from real life, and which must be cautiously guarded and kept separate from everyday existence. But science and everyday life cannot and should not be separated.
Letter to her father, Ellis Franklin (undated, summer 1940? while she was an undergraduate at Cambridge). Excerpted in Brenda Maddox, The Dark Lady of DNA (2002), 60-61.
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[The new term] Physicist is both to my mouth and ears so awkward that I think I shall never use it. The equivalent of three separate sounds of i in one word is too much.
Quoted in Sydney Ross, Nineteenth-Century Attitudes: Men of Science (1991), 10.
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[The purpose of flight research] is to separate the real from the imagined problems and to make known the overlooked and the unexpected.
Description of the purpose of the X-15 program given in a meeting at the Langley Research Center (Oct 1956). Quoted in Michael H. Gorn, Expanding the Envelope (2001), 3.
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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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- 90 -
Antoine Lavoisier
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Euclid
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- 80 -
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- 70 -
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- 60 -
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- 50 -
Stephen Hawking
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Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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