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Home > Category Index for Science Quotations > Category Index R > Category: Reckon

Reckon 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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A game is on, at the other end of this infinite distance, and heads or tails will turn up. What will you wager? According to reason you cannot leave either; according to reason you cannot leave either undone... Yes, but wager you must; there is no option, you have embarked on it. So which will you have. Come. Since you must choose, let us see what concerns you least. You have two things to lose: truth and good, and two things to stake: your reason and your will, your knowledge and your happiness. And your nature has two things to shun: error and misery. Your reason does not suffer by your choosing one more than the other, for you must choose. That is one point cleared. But your happiness? Let us weigh gain and loss in calling heads that God is. Reckon these two chances: if you win, you win all; if you lose, you lose naught. Then do not hesitate, wager that He is.
Pensées (1670), Section I, aphorism 223. In H. F. Stewart (ed.), Pascal's Pensées (1950), 117-119.
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And above all things, never think that you’re not good enough yourself. A man should never think that. My belief is that in life people will take you at your own reckoning.
…...
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Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.
In Introduction to Mathematics (1911), 59.
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Belief cannot be reckoned with in terms of science, for science and faith are mutually exclusive.
In Fielding Hudson Garrison, An Introduction to the History of Medicine (1966), 576.
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But if the heavens are moved by a daily movement, it is necessary to assume in the principal bodies of the universe and in the heavens two ways of movement which are contrary to each other: one from east to west and the other from west to east, as has often been said. And with this, it is proper to assume an excessively great speed, for anyone who reckons and considers well the height of distance of the heavens and the magnitude of these and of their circuit, if such a circuit were made in a day, could not imagine or conceive how marvelously and excessively swift would be the movement of the heavens, and how unbelievable and unthinkable.
In Isaac Asimov and Jason A. Shulman (eds.), Isaac Asimov’s Book of Science and Nature Quotations (1988), 329. Webmaster so far has been unable to locate the primary source (can you help?)
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But the nature of our civilized minds is so detached from the senses, even in the vulgar, by abstractions corresponding to all the abstract terms our languages abound in, and so refined by the art of writing, and as it were spiritualized by the use of numbers, because even the vulgar know how to count and reckon, that it is naturally beyond our power to form the vast image of this mistress called ‘Sympathetic Nature.’
The New Science, bk. 2, para. 378 (1744, trans. 1984).
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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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For between true Science, and erroneous Doctrines, Ignorance is in the middle. Naturall sense and imagination, are not subject to absurdity. Nature it selfe cannot erre: and as men abound in copiousnesses of language; so they become more wise, or more mad than ordinary. Nor is it possible without Letters for any man to become either excellently wise, or (unless his memory be hurt by disease, or ill constitution of organs) excellently foolish. For words are wise men's counters, they do but reckon by them; but they are the money of fools that value them by the authority of an Aristotle, a Cicero, or a Thomas, or any other Doctor whatsoever, if but a man.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 4, 106.
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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 don't really care how time is reckoned so long as there is some agreement about it, but I object to being told that I am saving daylight when my reason tells me that I am doing nothing of the kind. I even object to the implication that I am wasting something valuable if I stay in bed after the sun has risen. As an admirer of moonlight I resent the bossy insistence of those who want to reduce my time for enjoying it. At the back of the Daylight Saving scheme I detect the bony, blue-fingered hand of Puritanism, eager to push people into bed earlier, and get them up earlier, to make them healthy, wealthy and wise in spite of themselves.
In The Diary of Samuel Marchbanks (1947), 75.
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I will not now discuss the Controversie betwixt some of the Modern Atomists, and the Cartesians; the former of whom think, that betwixt the Earth and the Stars, and betwixt these themselves there are vast Tracts of Space that are empty, save where the beams of Light do pass through them; and the later of whom tell us, that the Intervals betwixt the Stars and Planets (among which the Earth may perhaps be reckon'd) are perfectly fill'd, but by a Matter far subtiler than our Air, which some call Celestial, and others Æther. I shall not, I say, engage in this controversie, but thus much seems evident, That If there be such a Celestial Matter, it must ' make up far the Greatest part of the Universe known to us. For the Interstellar part of the world (If I may so stile it) bears so very great a proportion to the Globes, and their Atmospheres too, (If other Stars have any as well as the Earth,) that It Is almost incomparably Greater in respect of them, than all our Atmosphere is in respect of the Clouds, not to make the comparison between the Sea and the Fishes that swim in it.
A Continuation of New Experiments Physico-Mechanical, Touching the Spring and Weight of the Air, and their Effects (1669), 127.
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If I have succeeded in discovering any truths in the sciences…, I can declare that they are but the consequences and results of five or six principal difficulties which I have surmounted, and my encounters with which I reckoned as battles in which victory declared for me.
In Discours de la Méthode (1637), as translated by J. Veitch, A Discourse on Method (1912), 53. Also seen translated as, “If I found any new truths in the sciences…, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.”
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In modern thought, (if not in fact)
Nothing is that doesn’t act, So that is reckoned wisdom which
Describes the scratch but not the itch.
Anonymous
Understanding Media: the Extensions of Man? (2nd Ed.,1964), 25.
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It is a wrong business when the younger cultivators of science put out of sight and deprecate what their predecessors have done; but obviously that is the tendency of Huxley and his friends … It is very true that Huxley was bitter against the Bishop of Oxford, but I was not present at the debate. Perhaps the Bishop was not prudent to venture into a field where no eloquence can supersede the need for precise knowledge. The young naturalists declared themselves in favour of Darwin’s views which tendency I saw already at Leeds two years ago. I am sorry for it, for I reckon Darwin’s book to be an utterly unphilosophical one.
Letter to James D, Forbes (24 Jul 1860). Trinity College Cambridge, Whewell Manuscripts.
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It is curious to observe how differently these great men [Plato and Bacon] estimated the value of every kind of knowledge. Take Arithmetic for example. Plato, after speaking slightly of the convenience of being able to reckon and compute in the ordinary transactions of life, passes to what he considers as a far more important advantage. The study of the properties of numbers, he tells us, habituates the mind to the contemplation of pure truth, and raises us above the material universe. He would have his disciples apply themselves to this study, not that they may be able to buy or sell, not that they may qualify themselves to be shop-keepers or travelling merchants, but that they may learn to withdraw their minds from the ever-shifting spectacle of this visible and tangible world, and to fix them on the immutable essences of things.
Bacon, on the other hand, valued this branch of knowledge only on account of its uses with reference to that visible and tangible world which Plato so much despised. He speaks with scorn of the mystical arithmetic of the later Platonists, and laments the propensity of mankind to employ, on mere matters of curiosity, powers the whole exertion of which is required for purposes of solid advantage. He advises arithmeticians to leave these trifles, and employ themselves in framing convenient expressions which may be of use in physical researches.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 394.
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Man has been here 32,000 years. That it took a hundred million years to prepare the world for him is proof that that is what it was done for. I suppose it is, I dunno. If The Eiffel Tower were now to represent the world's age, the skin of paint on the pinnacle knob at its summit would represent man’s share of that age; and anybody would perceive that the skin was what the tower was built for. I reckon they would, I dunno.
Declaiming Alfred Russel Wallace's 'anthropocentric' theory, that the universe was created specifically for the evolution of mankind. From 'Was the World Made for Man?' (1903) collected in What is Man?: and Other Philosophical Writings (1973), 106. Twain used the age of the earth accepted in his time; it is now estimated as 4,500 million years. Man’s origin is now estimated as 250,000 years.
For the complete essay, see Was The World Made For Man?.
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Mathematics is no more the art of reckoning and computation than architecture is the art of making bricks or hewing wood, no more than painting is the art of mixing colors on a palette, no more than the science of geology is the art of breaking rocks, or the science of anatomy the art of butchering.
In Lectures on Science, Philosophy and Art (1908), 29.
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Men in general are very slow to enter into what is reckoned a new thing; and there seems to be a very universal as well as great reluctance to undergo the drudgery of acquiring information that seems not to be absolutely necessary.
In The Commercial and Political Atlas: Representing, by Means of Stained Copper Charts, the Progress of the Commerce, Revenues, Expenditure and Debts of England During the Whole of the Eighteenth Century (1786, 1801), 29.
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Of … habitable worlds, such as the Earth, all which we may suppose to be of a terrestrial or terraqueous nature, and filled with beings of the human species, subject to mortality, it may not be amiss in this place to compute how many may he conceived within our finite view every clear Star-light night. … In all together then we may safely reckon 170,000,000, and yet be much within compass, exclusive Of the Comets which I judge to be by far the most numerous part of the creation.
In The Universe and the Stars: Being an Original Theory on the Visible Creation, Founded on the Laws of Nature (1750, 1837), 131-132.
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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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Suppose that you are in love with a lady on Neptune and that she returns the sentiment. It will be some consolation for the melancholy separation if you can say to yourself at some possibly pre-arranged moment, “She is thinking of me now.” Unfortunately a difficulty has arisen because we have had to abolish Now. There is no absolute Now, but only the various relative Nows, differing according to their reckoning of different observers and covering the whole neutral wedge which at the distance of Neptune is about eight hours thick. She will have to think of you continuously for eight hours on end in order to circumvent the ambiguity “Now.”
In The Nature of the Physical World (1929), 49.
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The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning.
In Thomas Hobbes and William Molesworth (ed.) Leviathan: Or the Matter, Form and Power of a Commonwealth Ecclesiastical and Civil (1839), Vol. 3, 24.
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The next care to be taken, in respect of the Senses, is a supplying of their infirmities with Instruments, and, as it were, the adding of artificial Organs to the natural; this in one of them has been of late years accomplisht with prodigious benefit to all sorts of useful knowledge, by the invention of Optical Glasses. By the means of Telescopes, there is nothing so far distant but may be represented to our view; and by the help of Microscopes, there is nothing so small, as to escape our inquiry; hence there is a new visible World discovered to the understanding. By this means the Heavens are open'd, and a vast number of new Stars, and new Motions, and new Productions appear in them, to which all the ancient Astronomers were utterly Strangers. By this the Earth it self, which lyes so neer us, under our feet, shews quite a new thing to us, and in every little particle of its matter, we now behold almost as great a variety of creatures as we were able before to reckon up on the whole Universe it self.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), preface, sig. A2V.
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THE OATH. I swear by Apollo [the healing God], the physician and Aesclepius [son of Apollo], and Health [Hygeia], and All-heal [Panacea], and all the gods and goddesses, that, according to my ability and judgment, I will keep this Oath and this stipulation—to reckon him who taught me this Art equally dear to me as my parents, to share my substance with him, and relieve his necessities if required; to look upon his offspring in the same footing as my own brothers, and to teach them this art, if they shall wish to learn it, without fee or stipulation; and that by precept, lecture, and every other mode of instruction, I will impart a knowledge of the Art to my own sons, and those of my teachers, and to disciples bound by a stipulation and oath according to the law of medicine, but to none others. I will follow that system of regimen which, according to my ability and judgment, I consider for the benefit of my patients, and abstain from whatever is deleterious and mischievous. I will give no deadly medicine to any one if asked, nor suggest any such counsel; and in like manner I will not give to a woman a pessary to produce abortion. With purity and with holiness I will pass my life and practice my Art. I will not cut persons laboring under the stone, but will leave this to be done by men who are practitioners of this work. Into whatever houses I enter, I will go into them for the benefit of the sick, and will abstain from every voluntary act of mischief and corruption; and, further, from the seduction of females or males, of freemen and slaves. Whatever, in connection with my professional practice or not, in connection with it, I see or hear, in the life of men, which ought not to be spoken of abroad, I will not divulge, as reckoning that all such should be kept secret. While I continue to keep this Oath unviolated, may it be granted to me to enjoy life and the practice of the art, respected by all men, in all times! But should I trespass and violate this Oath, may the reverse be my lot!
The Genuine Works of Hippocrates, trans. Francis Adams (1886), Vol. 2, 344-5.
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The perfect reckoner needs no counting-slips.
In Lao Tsu and Arthur Waley (trans.), Tao Te Ching (1996), chap. 27, 28. Also seen translated as: “A good calculator does not need artificial aids,” Translated by James Legge as “The skilful reckoner uses no tallies.” Note: Before the abacus, slips of bamboo were thrown in small bowls for counting.
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The same algebraic sum of positive and negative charges in the nucleus, when the arithmetical sum is different, gives what I call “isotopes” or “isotopic elements,” because they occupy the same place in the periodic table. They are chemically identical, and save only as regards the relatively few physical properties which depend upon atomic mass directly, physically identical also. Unit changes of this nuclear charge, so reckoned algebraically, give the successive places in the periodic table. For any one “place” or any one nuclear charge, more than one number of electrons in the outer-ring system may exist, and in such a case the element exhibits variable valency. But such changes of number, or of valency, concern only the ring and its external environment. There is no in- and out-going of electrons between ring and nucleus.
Concluding paragraph of 'Intra-atomic Charge', Nature (1913), 92, 400. Collected in Alfred Romer, Radiochemistry and the Discovery of Isotopes (1970), 251-252.
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The study of mathematics—from ordinary reckoning up to the higher processes—must be connected with knowledge of nature, and at the same time with experience, that it may enter the pupil’s circle of thought.
In Johann Friedrich Herbart, Henry M. Felkin (trans.) and Emmie Felkin (trans.), Letters and Lectures on Education [Felkin] (1898), 117.
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There are about 3,000,000 people seriously ill in the United States…. More than half of this illness is preventable. If we count the value of each life lost at only $1700 and reckon the average earning lost by illness at $700 a year for grown men, we find that the economic gain from mitigation of preventable disease in the United States would exceed $1,500,000,000 a year. … This gain … can be secured through medical investigation and practice, school and factory hygiene, restriction of labor by women and children, the education of the people in both public and private hygiene, and through improving the efficiency of our health service, municipal, state, and national.
From 'National Efficiency', Report of the National Conservation Commission (Feb 1909), Vol. 1, 25. Collected in United States Congressional Serial Set (1909), Issue 5397, 60th Congress, 2nd Session, Senate, Document 676. In transmitting the report to Congress on 22 Jan 1909, President Theodore Roosevelt introduced this report as the “first inventory of natural resources,” which “presents a statement of our available capital in material resources, which are the means of progress.” [It is noteworthy that the above quoted commentary on “National Efficiency” was included with the inventory of mineral, lands, forest and lands of the United States. —Webmaster]
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To discover a Conception of the mind which will justly represent a train of observed facts is, in some measure, a process of conjecture, ... and the business of conjecture is commonly conducted by calling up before our minds several suppositions, selecting that one which most agrees with what we know of the observed facts. Hence he who has to discover the laws of nature may have to invent many suppositions before he hits upon the right one; and among the endowments which lead to his success, we must reckon that fertility of invention which ministers to him such imaginary schemes, till at last he finds the one which conforms to the true order of nature.
Philosophy of the Inductive Sciences (1847), Vol. 2, 54.
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While the method of the natural sciences is... analytic, the method of the social sciences is better described as compositive or synthetic. It is the so-called wholes, the groups of elements which are structurally connected, which we learn to single out from the totality of observed phenomena... Insofar as we analyze individual thought in the social sciences the purpose is not to explain that thought, but merely to distinguish the possible types of elements with which we shall have to reckon in the construction of different patterns of social relationships. It is a mistake... to believe that their aim is to explain conscious action ... The problems which they try to answer arise only insofar as the conscious action of many men produce undesigned results... If social phenomena showed no order except insofar as they were consciously designed, there would indeed be no room for theoretical sciences of society and there would be, as is often argued, only problems of psychology. It is only insofar as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised which demands a theoretical explanation... people dominated by the scientistic prejudice are often inclined to deny the existence of any such order... it can be shown briefly and without any technical apparatus how the independent actions of individuals will produce an order which is no part of their intentions... The way in which footpaths are formed in a wild broken country is such an instance. At first everyone will seek for himself what seems to him the best path. But the fact that such a path has been used once is likely to make it easier to traverse and therefore more likely to be used again; and thus gradually more and more clearly defined tracks arise and come to be used to the exclusion of other possible ways. Human movements through the region come to conform to a definite pattern which, although the result of deliberate decision of many people, has yet not be consciously designed by anyone.
…...
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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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Carl Gauss
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- 90 -
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Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
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Andre Ampere
Winston Churchill
- 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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- 10 -
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