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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Home > Category Index for Science Quotations > Category Index R > Category: Reckoning

Reckoning Quotes (19 quotes)

A first step in the study of civilization is to dissect it into details, and to classify these in their proper groups. Thus, in examining weapons, they are to be classed under spear, club, sling, bow and arrow, and so forth; among textile arts are to be ranged matting, netting, and several grades of making and weaving threads; myths are divided under such headings as myths of sunrise and sunset, eclipse-myths, earthquake-myths, local myths which account for the names of places by some fanciful tale, eponymic myths which account for the parentage of a tribe by turning its name into the name of an imaginary ancestor; under rites and ceremonies occur such practices as the various kinds of sacrifice to the ghosts of the dead and to other spiritual beings, the turning to the east in worship, the purification of ceremonial or moral uncleanness by means of water or fire. Such are a few miscellaneous examples from a list of hundreds … To the ethnographer, the bow and arrow is the species, the habit of flattening children’s skulls is a species, the practice of reckoning numbers by tens is a species. The geographical distribution of these things, and their transmission from region to region, have to be studied as the naturalist studies the geography of his botanical and zoological species.
In Primitive Culture (1871), Vol. 1, 7.
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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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All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the “expanding universe” might also be called the theory of the “shrinking atom”. …
:Let us then take the whole universe as our standard of constancy, and adopt the view of a cosmic being whose body is composed of intergalactic spaces and swells as they swell. Or rather we must now say it keeps the same size, for he will not admit that it is he who has changed. Watching us for a few thousand million years, he sees us shrinking; atoms, animals, planets, even the galaxies, all shrink alike; only the intergalactic spaces remain the same. The earth spirals round the sun in an ever-decreasing orbit. It would be absurd to treat its changing revolution as a constant unit of time. The cosmic being will naturally relate his units of length and time so that the velocity of light remains constant. Our years will then decrease in geometrical progression in the cosmic scale of time. On that scale man’s life is becoming briefer; his threescore years and ten are an ever-decreasing allowance. Owing to the property of geometrical progressions an infinite number of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being.
We walk the stage of life, performers of a drama for the benefit of the cosmic spectator. As the scenes proceed he notices that the actors are growing smaller and the action quicker. When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing.
In The Expanding Universe (1933) , 90-92.
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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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For the Members of the Assembly having before their eyes so many fatal Instances of the errors and falshoods, in which the greatest part of mankind has so long wandred, because they rely'd upon the strength of humane Reason alone, have begun anew to correct all Hypotheses by sense, as Seamen do their dead Reckonings by Cœlestial Observations; and to this purpose it has been their principal indeavour to enlarge and strengthen the Senses by Medicine, and by such outward Instruments as are proper for their particular works.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), preface sig.
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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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In Geometry, (which is the only Science that it hath pleased God hitherto to bestow on mankind,) men begin at settling the significations of their words; which settling of significations, they call Definitions; and place them in the beginning of their reckoning.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 4, 105.
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In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science, whatever the matter may be.
Often seen quoted in a condensed form: If you cannot measure it, then it is not science.
From lecture to the Institution of Civil Engineers, London (3 May 1883), 'Electrical Units of Measurement', Popular Lectures and Addresses (1889), Vol. 1, 80-81.
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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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Nature bears long with those who wrong her. She is patient under abuse. But when abuse has gone too far, when the time of reckoning finally comes, she is equally slow to be appeased and to turn away her wrath.
'What We Owe to the Trees', Harper's New Monthly Magazine (Apr 1882), 46, No. 383, 686.
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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 following story (here a little softened from the vernacular) was narrated by Lord Kelvin himself when dining at Trinity Hall:
A certain rough Highland lad at the university had done exceedingly well, and at the close of the session gained prizes both in mathematics and in metaphysics. His old father came up from the farm to see his son receive the prizes, and visited the College. Thomson was deputed to show him round the place. “Weel, Mr. Thomson,” asked the old man, “and what may these mathematics be, for which my son has getten a prize?” “I told him,” replied Thomson, “that mathematics meant reckoning with figures, and calculating.” “Oo ay,” said the old man, “he’ll ha’ getten that fra’ me: I were ever a braw hand at the countin’.” After a pause he resumed: “And what, Mr. Thomson, might these metapheesics be?” “I endeavoured,” replied Thomson, “to explain how metaphysics was the attempt to express in language the indefinite.” The old Highlander stood still and scratched his head. “Oo ay: may be he’ll ha’ getten that fra’ his mither. She were aye a bletherin’ body."
As given in Life of Lord Kelvin (1910), Vol. 2, 1124, footnote. [Note: William Thomson, later became Lord Kelvin. —Webmaster]
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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 only census of the senses, so far as I am aware, that ever before made them more than five, was the Irishman's reckoning of seven senses. I presume the Irishman's seventh sense was common sense; and I believe that the possession of that virtue by my countrymen—I speak as an Irishman.
In 'The Six Gateways of Knowledge', Presidential Address to the Birmingham and Midland Institute, Birmingham (3 Oct 1883), collected in Popular Lectures and Addresses (1891), Vol. 1, 260. Although biographies are found referring to Kelvin as being a Scottish scientist, because of his lifetime career spent in Glasgow, note that here Kelvin self-identifies as being Irish.
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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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[Boswell]: Sir Alexander Dick tells me, that he remembers having a thousand people in a year to dine at his house: that is, reckoning each person as one, each time that he dined there.
[Johnson]: That, Sir, is about three a day.
[Boswell]: How your statement lessens the idea.
[Johnson]: That, Sir, is the good of counting. It brings every thing to a certainty, which before floated in the mind indefinitely.
Entry for Fri 18 Apr 1783. In George Birkbeck-Hill (ed.), Boswell's Life of Johnson (1934-50), Vol. 4, 204.
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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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