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Home > Category Index for Science Quotations > Category Index A > Category: Applicable

Applicable Quotes (31 quotes)

...it is not to be taken in the sense of our day, which we reckon by the course of the sun; but it must have another meaning, applicable to the
three days mentioned before the creation of the heavenly bodies.
iv.26
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[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.
Quoted, without source, in The Grolier Library of Science Biographies (1996), Vol. 3, 191.
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[Pechblende] einer eigenthümlichen, selbstständigen metallischen Substanz bestehe. Es fallen folglich auch deren bisherige Benennungen, als: Ресhblende Eisenpecherz, hinweg, welche nun durch einen neuen ausschliessend bezeichnenden Namen zu ersetzen sind. Ich habe dazu den Namen: Uranerz (Uranium) erwählt; zu einigem Andenken, dass die chemische Ausfindung dieses neuen Metallkörpers in die Epoche der astronomischen. Entdeckung des Planeten Uranus gefallen sei.
[Pitchblende] consists of a peculiar, distinct, metallic substance. Therefore its former denominations, pitch-blende, pitch-iron-ore, &c. are no longer applicable, and must be supplied by another more appropriate name.—I have chosen that of uranite, (Uranium), as a kind of memorial, that the chemical discovery of this new metal happened in the period of the astronomical discovery of the new planet Uranus.
In original German edition, Beiträge Zur Chemischen Kenntniss Der Mineralkörper (1797), Vol. 2, 215. English edition, translator not named, Analytical Essays Towards Promoting the Chemical Knowledge of Mineral Substances (1801), 491. The new planet was discovered on 13 Mar 1781 by William Herschel, who originally named it Georgium Sidus (George's Star) to honour King George III.
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A living organism must be studied from two distinct aspects. One of these is the causal-analytic aspect which is so fruitfully applicable to ontogeny. The other is the historical descriptive aspect which is unravelling lines of phylogeny with ever-increasing precision. Each of these aspects may make suggestions concerning the possible significance of events seen under the other, but does not explain or translate them into simpler terms.
'Embryology and Evolution', in G. R. de Beer (ed.), Evolution: Essays on Aspects of Evolutionary Biology presented to Professor E. S. Goodrich on his Seventieth Birthday (1938), 76-7.
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Biology occupies a position among the sciences both marginal and central. Marginal because, the living world, constituting only a tiny and very “special” part of the universe, it does not seem likely that the study of living beings will ever uncover general laws applicable outside the biosphere. But if the ultimate aim of the whole of science is indeed, as I believe, to clarify man's relationship to the universe, then biology must be accorded a central position, since of all the disciplines it is the one that endeavours to go most directly to the heart of the problems that must be resolved before that of “human nature” can even be framed in other than metaphysical terms.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), xi.
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By destroying the biological character of phenomena, the use of averages in physiology and medicine usually gives only apparent accuracy to the results. From our point of view, we may distinguish between several kinds of averages: physical averages, chemical averages and physiological and pathological averages. If, for instance, we observe the number of pulsations and the degree of blood pressure by means of the oscillations of a manometer throughout one day, and if we take the average of all our figures to get the true or average blood pressure and to learn the true or average number of pulsations, we shall simply have wrong numbers. In fact, the pulse decreases in number and intensity when we are fasting and increases during digestion or under different influences of movement and rest; all the biological characteristics of the phenomenon disappear in the average. Chemical averages are also often used. If we collect a man's urine during twenty-four hours and mix all this urine to analyze the average, we get an analysis of a urine which simply does not exist; for urine, when fasting, is different from urine during digestion. A startling instance of this kind was invented by a physiologist who took urine from a railroad station urinal where people of all nations passed, and who believed he could thus present an analysis of average European urine! Aside from physical and chemical, there are physiological averages, or what we might call average descriptions of phenomena, which are even more false. Let me assume that a physician collects a great many individual observations of a disease and that he makes an average description of symptoms observed in the individual cases; he will thus have a description that will never be matched in nature. So in physiology, we must never make average descriptions of experiments, because the true relations of phenomena disappear in the average; when dealing with complex and variable experiments, we must study their various circumstances, and then present our most perfect experiment as a type, which, however, still stands for true facts. In the cases just considered, averages must therefore be rejected, because they confuse, while aiming to unify, and distort while aiming to simplify. Averages are applicable only to reducing very slightly varying numerical data about clearly defined and absolutely simple cases.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 134-135.
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For the better part of my last semester at Garden City High, I constructed a physical pendulum and used it to make a “precision” measurement of gravity. The years of experience building things taught me skills that were directly applicable to the construction of the pendulum. Twenty-five years later, I was to develop a refined version of this measurement using laser-cooled atoms in an atomic fountain interferometer.
[Outcome of high school physics teacher, Thomas Miner, encouraging Chu's ambitious laboratory project.]
Autobiography in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 116.
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Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
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Genetics has enticed a great many explorers during the past two decades. They have labored with fruit-flies and guinea-pigs, with sweet peas and corn, with thousands of animals and plants in fact, and they have made heredity no longer a mystery but an exact science to be ranked close behind physics and chemistry in definiteness of conception. One is inclined to believe, however, that the unique magnetic attraction of genetics lies in the vision of potential good which it holds for mankind rather than a circumscribed interest in the hereditary mechanisms of the lowly species used as laboratory material. If man had been found to be sharply demarcated from the rest of the occupants of the world, so that his heritage of physical form, of physiological function, and of mental attributes came about in a superior manner setting him apart as lord of creation, interest in the genetics of the humbler organisms—if one admits the truth—would have flagged severely. Biologists would have turned their attention largely to the ways of human heredity, in spite of the fact that the difficulties encountered would have rendered progress slow and uncertain. Since this was not the case, since the laws ruling the inheritance of the denizens of the garden and the inmates of the stable were found to be applicable to prince and potentate as well, one could shut himself up in his laboratory and labor to his heart's content, feeling certain that any truth which it fell to his lot to discover had a real human interest, after all.
Mankind at the Crossroads (1923), v-vi.
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I found the invention was applicable to painting, and would also contribute to facilitate the study of geography: for I have applied it to some maps, the rivers of which I represented in silver, and in the cities in gold. The rivers appearing, as it were, in silver streams, have a most pleasing effect on the sight, and relieve the eye of that painful search for the course, and origin, of rivers, the minutest branches of which can be splendidly represented this way.
Description of an outcome of her experiments originally investigating 'the possibility of making cloths of gold, silver and other metals by chemical processes.'
Preface to An Essay on Combustion with a View to a New Art of Dyeing and Painting (1794), iii-iv. In Marilyn Bailey Ogilvie and Joy Dorothy Harvey, The Biographical Dictionary of Women in Science (2000), 478.
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I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.
Max Born
My Life & My Views (1968), 48.
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I love mathematics not only because it is applicable to technology but also because it is beautiful.
In Eberhard Zeidler, Quantum Field Theory (2006), 955.
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I think we are living in a new time. I think that the ways of working when there was not the current widespread questioning of what science does are no longer applicable. Besides, there is a difference between the sort of research you do when you’re developing something for the first time and the sort of thing you have to do to make sure it continues to work—and the two different sorts of research are done best by different sorts of people. And, just as with basic science, one needs confirmatory experiments. One can’t just have one group saying “yes they’re safe, yes they’re safe, take our word for it, we made them and we know they’re safe”. Someone else, quite independent, needs to take a look, do the confirmatory experiment. Duplication in this case can do nothing but good.
From interview with Graham Chedd, 'The Lady Gets Her Way', New Scientist (5 Jul 1973), 59, No. 853, 16.
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Indeed, the aim of teaching [mathematics] should be rather to strengthen his [the pupil’s] faculties, and to supply a method of reasoning applicable to other subjects, than to furnish him with an instrument for solving practical problems.
In John Perry (ed.), Discussion on the Teaching of Mathematics (1901), 84. The discussion took place on 14 Sep 1901 at the British Association at Glasgow, during a joint meeting of the mathematics and physics sections with the education section. The proceedings began with an address by John Perry. Magnus spoke in the Discussion that followed.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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Mathematics is the language of languages, the best school for sharpening thought and expression, is applicable to all processes in nature; and Germany needs mathematical gymnasia. Mathematics is God’s form of speech, and simplifies all things organic and inorganic. As knowledge becomes real, complete and great it approximates mathematical forms. It mediates between the worlds of mind and of matter.
Summarizing the ideas presented by Christian Heinrich Dillmann in Die Mathematik die Fackelträgerin einer neuen Zeit (1889). From book review, 'Recent Literature on Arithmetic and Arithmetical Teaching', in Granville Stanley Hall (ed.), The Pedagogical Seminary (1892), 2, 168. Dillmann’s book title translates as “Mathematics the Torchbearer of a New Era”. (However, Conant concluded that it was a “loosely-written, vague and incoherent book, which belies every anticipation awakened by its attractive title.”)
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Natural law is not applicable to the unseen world behind the symbols, because it is unadapted to anything except symbols, and its perfection is a perfection of symbolic linkage. You cannot apply such a scheme to the parts of our personality which are not measurable by symbols any more than you can extract the square root of a sonnet.
Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 53.
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Nothing is less applicable to life than mathematical reasoning. A proposition in mathematics is decidedly false or true. Everywhere else the true is mingled with the false.
Quoted, without citation, in David Eugene Smith, The Teaching of Elementary Mathematics (1904), 170.
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That no generally applicable law of the formulation and development of hybrids has yet been successfully formulated can hardly astonish anyone who is acquainted with the extent of the task and who can appreciate the difficulties with which experiments of this kind have to contend.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 2.
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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 History of Evolution is the real source of light in the investigation of organic bodies. It is applicable at every step, and all our ideas of the correlation of organic bodies will be swayed by our knowledge of the history of evolution. To carry the proof of it into all branches of research would be an almost endless task. (1828)
Quoted as an epigraph to Chap. 3, in Ernst Haeckel, The Evolution of Man, (1886), Vol 1, 48.
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The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers.
Nobel Prize Banquet Speech (10 Dec1933). In Carl Gustaf Santesson (Ed.), Les Prix Nobel en 1933 (1935), 78
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The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.
In A Treatise on Projections (1880), Introduction, xi. Published as United States Coast and Geodetic Survey, Treasury Department Document, No. 61.
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The Primal Plant is going be the strangest creature in the world, which Nature herself must envy me. With this model and the key to it, it will be possible to go on for ever inventing plants and know that their existence is logical; that is to say, if they do not actually exist, they could, for they are not the shadowy phantoms of a vain imagination, but possess an inner necessity and truth. The same law will be applicable to all other living organisms.
To Herder, 17 May 1787. Italian Journey (1816-17), trans. W. H. Auden and Elizabeth Mayer (1970), 310-11.
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The scientific method of examining facts is not peculiar to one class of phenomena and to one class of workers; it is applicable to social as well as to physical problems, and we must carefully guard ourselves against supposing that the scientific frame of mind is a peculiarity of the professional scientist.
From The Grammar of Science (1892), 8.
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Though, probably, no competent geologist would contend that the European classification of strata is applicable to all other parts of the globe, yet most, if not all geologists, write as though it were so.
'Illogical Geology', The Universal Review (1859), 2, 54.
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To ask what qualities distinguish good from routine scientific research is to address a question that should be of central concern to every scientist. We can make the question more tractable by rephrasing it, “What attributes are shared by the scientific works which have contributed importantly to our understanding of the physical world—in this case the world of living things?” Two of the most widely accepted characteristics of good scientific work are generality of application and originality of conception. . These qualities are easy to point out in the works of others and, of course extremely difficult to achieve in one’s own research. At first hearing novelty and generality appear to be mutually exclusive, but they really are not. They just have different frames of reference. Novelty has a human frame of reference; generality has a biological frame of reference. Consider, for example, Darwinian Natural Selection. It offers a mechanism so widely applicable as to be almost coexistent with reproduction, so universal as to be almost axiomatic, and so innovative that it shook, and continues to shake, man’s perception of causality.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230.
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We live in a cultural milieu ... The idea that culture is our ecological niche is still applicable. The impact and force of natural selection on the human physique are conditioned by the dimensions of culture.
Interview with Pat Shipman, 21 January 1991. Quoted in Erik Trinkaus and Pat Shipman, The Neanderthals: Changing the Image of Mankind (1993), 334.
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[Mathematics is] the study of ideal constructions (often applicable to real problems), and the discovery thereby of relations between the parts of these constructions, before unknown.
In 'Mathematics', Century Dictionary.
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[Science] is not perfect. It can be misused. It is only a tool. But it is by far the best tool we have, self-correcting, ongoing, applicable to everything. It has two rules. First: there are no sacred truths; all assumptions must be critically examined; arguments from authority are worthless. Second: whatever is inconsistent with the facts must be discarded or revised. ... The obvious is sometimes false; the unexpected is sometimes true.
Cosmos (1985), 277.
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… on these expanded membranes [butterfly wings] Nature writes, as on a tablet, the story of the modifications of species, so truly do all changes of the organisation register themselves thereon. Moreover, the same colour-patterns of the wings generally show, with great regularity, the degrees of blood-relationship of the species. As the laws of nature must be the same for all beings, the conclusions furnished by this group of insects must be applicable to the whole world.
From The Naturalist on the River Amazons: A record of Adventures, Habits of Animals, Sketches of Brazilian and Indian life, and Aspects of Nature under the Equator, During Eleven Years of Travel (1864), 413.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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