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Home > Category Index for Science Quotations > Category Index E > Category: Equal

Equal Quotes (77 quotes)

...for the animals, which we resemble and which would be our equals if we did not have reason, do not reflect upon the actions or the passions of their external or internal senses, and do not know what is color, odor or sound, or if there is any differences between these objects, to which they are moved rather than moving themselves there. This comes about by the force of the impression that the different objects make on their organs and on their senses, for they cannot discern if it is more appropriate to go and drink or eat or do something else, and they do not eat or drink or do anything else except when the presence of objects or the animal imagination [l'imagination brutalle], necessitates them and transports them to their objects, without their knowing what they do, whether good or bad; which would happen to us just as to them if we were destitute of reason, for they have no enlightenment except what they must have to take their nourishment and to serve us for the uses to which God has destined them.
[Arguing the uniqueness of man by regarding animals to be merely automatons.].
Les Préludes de l'Harmonie Universelle (1634), 135-139. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 318.
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Douter de tout ou tout croire, ce sont deux solutions également commodes, qui l’une et l’autre nous dispensent de défléchir.
To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.
From 'Introduction', La Science et l’Hypothèse (1902), 2. Translation by George Bruce Halsted, 'Introduction', Science and Hypothesis (New York, 1905), 1. In 'Author’s Preface', Science and Hypothesis (London 1905), xxii, it is translated more closely as “To doubt everything and to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.”
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Question: Why do the inhabitants of cold climates eat fat? How would you find experimentally the relative quantities of heat given off when equal weights of sulphur, phosphorus, and carbon are thoroughly burned?
Answer: An inhabitant of cold climates (called Frigid Zoans) eats fat principally because he can't get no lean, also because he wants to rise is temperature. But if equal weights of sulphur phosphorus and carbon are burned in his neighbourhood he will give off eating quite so much. The relative quantities of eat given off will depend upon how much sulphur etc. is burnt and how near it is burned to him. If I knew these facts it would be an easy sum to find the answer.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 183, Question 32. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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[About the demand of the Board of Regents of the University of California that professors sign non-Communist loyalty oaths or lose their jobs within 65 days.] No conceivable damage to the university at the hands of hypothetical Communists among us could possibly have equaled the damage resulting from the unrest, ill-will and suspicion engendered by this series of events.
As quoted in 'Professors in West Call Oath “Indignity”', New York Times (26 Feb 1950), 38.
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A few days afterwards, I went to him [the same actuary referred to in another quote] and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly. I told him that the law was involved in this circumstance. Take the table of the expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come. “You don’t mean that this always happens?”—“Try it.” He did try, again and again; and found it as I said. “This is, indeed, a curious thing; this is a discovery!” I might have sent him about trumpeting the law of life: but I contented myself with informing him that the same thing would happen with any table whatsoever in which the first column goes up and the second goes down.
In Budget of Paradoxes (1872), 172.
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A work of morality, politics, criticism will be more elegant, other things being equal, if it is shaped by the hand of geometry.
From Préface sur l'Utilité des Mathématiques et de la Physique (1729), as translated in Florian Cajori, Mathematics in Liberal Education (1928), 61.
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All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible.
In article by Jean Itard, 'Legendre, Adrien-Marie', in Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1973), Vol. 8, 142.
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Already at the origin of the species man was equal to what he was destined to become.
Can Man Be Modified? (1959), 76.
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Archimedes said Eureka,
Cos in English he weren't too aversed in,
when he discovered that the volume of a body in the bath,
is equal to the stuff it is immersed in,
That is the law of displacement,
Thats why ships don't sink,
Its a shame he weren't around in 1912,
The Titanic would have made him think.
From lyrics of song Sod’s Law.
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Bodies, projected in our air, suffer no resistance but from the air. Withdraw the air, as is done in Mr. Boyle's vacuum, and the resistance ceases. For in this void a bit of fine down and a piece of solid gold descend with equal velocity.
In 'General Scholium' from The Mathematical Principles of Natural Philosophy (1729), Vol. 2, Book 3, 388.
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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 nothing is more estimable than a physician who, having studied nature from his youth, knows the properties of the human body, the diseases which assail it, the remedies which will benefit it, exercises his art with caution, and pays equal attention to the rich and the poor.
A Philosophical Dictionary: from the French? (2nd Ed.,1824), Vol. 5, 239-240.
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Certain elements have the property of producing the same crystal form when in combination with an equal number of atoms of one or more common elements, and the elements, from his point of view, can be arranged in certain groups. For convenience I have called the elements belonging to the same group … isomorphous.
Originally published in 'Om Förhållandet emellan chemiska sammansättningen och krystallformen hos Arseniksyrade och Phosphorsyrade Salter', (On the Relation between the Chemical Composition and Crystal Form of Salts of Arsenic and Phosphoric Acids), Kungliga Svenska vetenskapsakademiens handlingar (1821), 4. In F. Szabadváry article on 'Eilhard Mitscherlich' in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 424; perhaps from J.R. Partington, A History of Chemistry, Vol. 4 (1964), 210.
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Computers are fantastic. In a few moments they can make a mistake so great that it would take many men many months to equal it.
As quoted, without citation, in Laurence J. Peter, The Peter Prescription: How to be Creative, Confident & Competent (1972).
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Creation science has not entered the curriculum for a reason so simple and so basic that we often forget to mention it: because it is false, and because good teachers understand why it is false. What could be more destructive of that most fragile yet most precious commodity in our entire intellectual heritage—good teaching—than a bill forcing our honorable teachers to sully their sacred trust by granting equal treatment to a doctrine not only known to be false, but calculated to undermine any general understanding of science as an enterprise?.
In 'The Verdict on Creationism' The Sketical Inquirer (Winter 1987/88), 12, 186.
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Democracy: everyone should have an equal opportunity to obstruct everybody else.
In The Decline and Fall of Science (1976), 4.
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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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Every arsenate has its corresponding phosphate, composed according to the same proportions, combined with the same amount of water of crystallization, and endowed with the same physical properties: in fact, the two series of salts differ in no respect, except that the radical of the acid in one series in phosphorus, while in the other it is arsenic.
The experimental clue he used forming his law of isomerism. Originally published in 'Om Förhållandet emellan chemiska sammansättningen och krystallformen hos Arseniksyrade och Phosphorsyrade Salter', (On the Relation between the Chemical Composition and Crystal Form of Salts of Arsenic and Phosphoric Acids), Kungliga Svenska vetenskapsakademiens handlingar (1821), 4. Translation as shown in Joseph William Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry (1922), Vol. 1, 652. A very similar translation (“the same physical properties” is replaced with “nearly equal solubilities in water and acids”) is in F. Szabadváry article on 'Eilhard Mitscherlich' in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 424; perhaps from J.R. Partington, A History of Chemistry, Vol. 4 (1964), 210.
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Genes make enzymes, and enzymes control the rates of chemical processes. Genes do not make ‘novelty seeking’ or any other complex and overt behavior. Predisposition via a long chain of complex chemical reactions, mediated through a more complex series of life’s circumstances, does not equal identification or even causation.
…...
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Gradually, … the aspect of science as knowledge is being thrust into the background by the aspect of science as the power of manipulating nature. It is because science gives us the power of manipulating nature that it has more social importance than art. Science as the pursuit of truth is the equal, but not the superior, of art. Science as a technique, though it may have little intrinsic value, has a practical importance to which art cannot aspire.
In The Scientific Outlook (1931, 2009), xxiv.
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Great works are performed, not by strength, but by perserverance. He that shall walk, with vigour, three hours a day, will pass, in seven years, a space equal to the circumference of the globe.
As quoted, without citation, in John Walker, A Fork in the Road: Answers to Daily Dilemmas from the Teachings of Jesus Christ (2005), 179.
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He that borrows the aid of an equal understanding, doubles his own; he that uses that of a superior elevates his own to the stature of that he contemplates.
Collected, without citation, in Edge-tools of Speech (1886), 406. Also quoted, without citation, Ralph Waldo Emerson, 'Quotation and Originality', in Letters and Social Aims (1875, 1917), 178. Webmaster has not yet identified a primary source.
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He who has heard the same thing told by twelve thousand ocular [eye]witnesses, has only twelve thousand probabilities, equal to one strong one, which is not equal to certainty.
In 'Truth', Philosophical Dictionary (1824), Vol. 6, 297.
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I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
In 'Ueber das Lehrziel im mathemalischen Unterricht der höheren Realanstalten', Jahresbericht der Deutschen Mathematiker Vereinigung, 2, 192. (The Annual Report of the German Mathematical Association. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 73.
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I grew up in Japan and Hong Kong and then came to the States. Japan was a huge influence on me because, as a child, I would hear the oxcarts come and collect our sewage at night out of our house from the latrine and then take it off to the farms as fertilizer. And then the food would come back in oxcarts during the day. I always had this sort of “our poop became food” mental model. The idea of “waste equals food” was pretty inculcated, that everything was precious and the systems were coherent and cyclical.
In interview with Kerry A. Dolan, 'William McDonough On Cradle-to-Cradle Design', Forbes (4 Aug 2010)
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I have long recognized the theory and aesthetic of such comprehensive display: show everything and incite wonder by sheer variety. But I had never realized how power fully the decor of a cabinet museum can promote this goal until I saw the Dublin [Natural History Museum] fixtures redone right ... The exuberance is all of one piece–organic and architectural. I write this essay to offer my warmest congratulations to the Dublin Museum for choosing preservation–a decision not only scientifically right, but also ethically sound and decidedly courageous. The avant-garde is not an exclusive locus of courage; a principled stand within a reconstituted rear unit may call down just as much ridicule and demand equal fortitude. Crowds do not always rush off in admirable or defendable directions.
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I will sette as I doe often in woorke use, a paire of paralleles, or gemowe times of one lengthe, thus: =, bicause noe 2 thynges, can be moare equalle.
Explaining the sign he initiated to mean equality.
The Whetstone of Witte (1557). The word gemowe (related to the name Gemini) means twins.)
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If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
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In a few minutes a computer can make a mistake so great that it would have taken many men many months to equal.
Anonymous
In Civilization's Quotations: Life's Ideal (2002), 315.
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In any of the learned professions a vigorous constitution is equal to at least fifty per cent more brain.
In Getting on in the World; Or, Hints on Success in Life (1873), 55.
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It is a misfortune to pass at once from observation to conclusion, and to regard both as of equal value; but it befalls many a student.
In The Maxims and Reflections of Goethe (1906), 183.
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It is not equal time the creationists want. ... Don't kid yourself. They want all the time there is.
In The Roving Mind (1983), 18.
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Life is inseparable from water. For all terrestrial animals, including birds, the inescapable need for maintaining an adequate state of hydration in a hostile, desiccating environment is a central persistent constraint which exerts a sustained selective pressure on every aspect of the life cycle. It has been said, with some justification, that the struggle for existence is a struggle for free energy for doing physiological work. It can be said with equal justification for terrestrial organisms that the struggle for existence is a struggle to maintain an aqueous internal environment in which energy transformations for doing work can take place.
In 'The water economy of seed-eating birds that survive without drinking', Proceedings of the International Ornithological Congress (1972), 15, 237-238.
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Man, by reason of his greater intellect, can more reasonably hope to equal birds in knowledge than to equal nature in the perfection of her machinery.
In The Papers of Wilbur and Orville Wright: 1899-1905 (1953), 15.
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Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.
In 'Prop. 47: The human mind possesses an adequate knowledge of the eternal and infinite essence of God', Ethic, translated by William Hale White (1883), 93-94. Collected in The English and Foreign Philosophical Library, Vol. 21.
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Mathematics is a logical method … Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
In Tractatus Logico Philosophicus (1922), 169 (statements 6.2-6.211).
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Mathematics is the science of the connection of magnitudes. Magnitude is anything that can be put equal or unequal to another thing. Two things are equal when in every assertion each may be replaced by the other.
In Stücke aus dem Lehrbuche der Arithmetik, Werke (1904), Bd. 2, 298.
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My experiments with single traits all lead to the same result: that from the seeds of hybrids, plants are obtained half of which in turn carry the hybrid trait (Aa), the other half, however, receive the parental traits A and a in equal amounts. Thus, on the average, among four plants two have the hybrid trait Aa, one the parental trait A, and the other the parental trait a. Therefore, 2Aa+ A +a or A + 2Aa + a is the empirical simple series for two differing traits.
Letter to Carl Nägeli, 31 Dec 1866. In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 63.
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My visceral perception of brotherhood harmonizes with our best modern biological knowledge ... Many people think (or fear) that equality of human races represents a hope of liberal sentimentality probably squashed by the hard realities of history. They are wrong. This essay can be summarized in a single phrase, a motto if you will: Human equality is a contingent fact of history. Equality is not true by definition; it is neither an ethical principle (though equal treatment may be) nor a statement about norms of social action. It just worked out that way. A hundred different and plausible scenarios for human history would have yielded other results (and moral dilemmas of enormous magnitude). They didn’t happen.
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Naturally, some intriguing thoughts arise from the discovery that the three chief particles making up matter—the proton, the neutron, and the electron—all have antiparticles. Were particles and antiparticles created in equal numbers at the beginning of the universe? If so, does the universe contain worlds, remote from ours, which are made up of antiparticles?
In The Intelligent Man's Guide to the Physical Sciences (1960, 1968), 222. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 138.
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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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Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution.
'The Atomic Theory of Matter', third lecture at Columbia University (1909), in Max Planck and A. P. Wills (trans.), Eight Lectures on Theoretical Physics (1915), 44.
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Nature, with equal mind,
Sees all her sons at play,
Sees man control the wind,
The wind sweep man away.
From dramatic poem, 'Empedocles on Etna', first published anonymously, collected in Empedocles on Etna, and Other Poems (1852). As quoted in The Contemporary Review (1867), Vol. 6, 344. Also in The Poems of Matthew Arnold, 1840-1867 (1909), 94.
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Once when lecturing to a class he [Lord Kelvin] used the word “mathematician,” and then interrupting himself asked his class: “Do you know what a mathematician is?” Stepping to the blackboard he wrote upon it:— [an integral expression equal to the square root of pi]
Then putting his finger on what he had written, he turned to his class and said: “A mathematician is one to whom that is as obvious as that twice two makes four is to you. Liouville was a mathematician.”
In Life of Lord Kelvin (1910), 1139.
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One dictionary that I consulted remarks that “natural history” now commonly means the study of animals and plants “in a popular and superficial way,” meaning popular and superficial to be equally damning adjectives. This is related to the current tendency in the biological sciences to label every subdivision of science with a name derived from the Greek. “Ecology” is erudite and profound; while “natural history” is popular and superficial. Though, as far as I can see, both labels apply to just about the same package of goods.
In The Nature of Natural History (1961, 2014), 7.
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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Sign language is the equal of speech, lending itself equally to the rigorous and the poetic, to philosophical analysis or to making love.
In The Times (16 Jun 1994).
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Sir how pitiable is it to reflect, that altho you were so fully convinced of the benevolence of the Father of mankind, and of his equal and impartial distribution of those rights and privileges which he had conferred upon them, that you should at the Same time counteract his mercies, in detaining by fraud and violence so numerous a part of my brethren under groaning captivity and cruel oppression, that you should at the Same time be found guilty of that most criminal act, which you professedly detested in others, with respect to yourselves.
In Letter to Thomas Jefferson (19 Aug 1791). In John Hazlehurst Boneval Latrobe, Memoir of Benjamin Banneker: Read Before the Maryland Historical Society, at the Monthly Meeting, May 1, 1845 (1845), 15-16.
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Sooner or later in every talk, [David] Brower describes the creation of the world. He invites his listeners to consider the six days of Genesis as a figure of speech for what has in fact been 4 billion years. On this scale, one day equals something like six hundred and sixty-six million years, and thus, all day Monday and until Tuesday noon, creation was busy getting the world going. Life began Tuesday noon, and the beautiful organic wholeness of it developed over the next four days. At 4 p.m. Saturday, the big reptiles came on. At three minutes before midnight on the last day, man appeared. At one-fourth of a second before midnight Christ arrived. At one-fortieth of a second before midnight, the Industrial Revolution began. We are surrounded with people who think that what we have been doing for that one-fortieth of a second can go on indefinitely. They are considered normal, but they are stark. raving mad.
In Encounters with the Archdruid (1971), 79-80.
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Strictly speaking, it is really scandalous that science has not yet clarified the nature of number. It might be excusable that there is still no generally accepted definition of number, if at least there were general agreement on the matter itself. However, science has not even decided on whether number is an assemblage of things, or a figure drawn on the blackboard by the hand of man; whether it is something psychical, about whose generation psychology must give information, or whether it is a logical structure; whether it is created and can vanish, or whether it is eternal. It is not known whether the propositions of arithmetic deal with those structures composed of calcium carbonate [chalk] or with non-physical entities. There is as little agreement in this matter as there is regarding the meaning of the word “equal” and the equality sign. Therefore, science does not know the thought content which is attached to its propositions; it does not know what it deals with; it is completely in the dark regarding their proper nature. Isn’t this scandalous?
From opening paragraph of 'Vorwort', Über die Zahlen des Herrn H. Schubert (1899), iii. ('Foreword', On the Numbers of Mr. H. Schubert). Translated by Theodore J. Benac in Friedrich Waismann, Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (1959, 2003), 107. Webmaster added “[chalk]”.
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Technology is an inherent democratizer. Because of the evolution of hardware and software, you’re able to scale up almost anything you can think up. … We’ll have to see if in our lifetime that means that everybody has more or less tools that are of equal power.
Guest Lecture, UC Berkeley, 'Search Engines, Technology, and Business' (3 Oct 2005). At 10:37 in the YouTube video.
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The enemy is not fundamentalism; it is intolerance. In this case, the intolerance is perverse since it masquerades under the ‘liberal’ rhetoric of ‘equal time.’ But mistake it not.
…...
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The excitement that a gambler feels when making a bet is equal to the amount he might win times the probability of winning it.
Anonymous
As quoted, without citation, in Nicholas J. Rose Mathematical Maxims and Minims (1988). Rose attributes the quote to Blaise Pascal, but Webmaster has, so far, found nothing like it by Pascal. Can you help? [Present opinion: This quote does not ring true for Pascal —Webmaster.]
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The great Sir Isaac Newton,
He once made a valid proclamation,
That the forces equal to a nominated mass,
when multiplied by acceleration
That was the law of motion.
From lyrics of song Sod’s Law.
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The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.
In Elementarmathematik von höheren Standpunkte aus (1909), Bd. 2, 392.
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The Hypotenuse has a square on,
which is equal Pythagoras instructed,
to the sum of the squares on the other two sides
If a triangle is cleverly constructed.
From lyrics of song Sod’s Law.
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The landlady of a boarding-house is a parallelogram—that is, an oblong figure, which cannot be described, but which is equal to anything.
In 'Boarding-House Geometry', Literary Lapses (1928), 26.
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The most important effect of the suffrage is psychological. The permanent consciousness of power for effective action, the knowledge that their own thoughts have an equal chance with those of any other person … this is what has always rendered the men of a free state so energetic, so acutely intelligent, so powerful.
In “Common Sense” Applied to Woman Suffrage (1894), 180.
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The school of Plato has advanced the interests of the race as much through geometry as through philosophy. The modern engineer, the navigator, the astronomer, built on the truths which those early Greeks discovered in their purely speculative investigations. And if the poetry, statesmanship, oratory, and philosophy of our day owe much to Plato’s divine Dialogues, our commerce, our manufactures, and our science are equally indebted to his Conic Sections. Later instances may be abundantly quoted, to show that the labors of the mathematician have outlasted those of the statesman, and wrought mightier changes in the condition of the world. Not that we would rank the geometer above the patriot, but we claim that he is worthy of equal honor.
In 'Imagination in Mathematics', North American Review, 85, 228.
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The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.
The original script by Noel Langley was revised by Florence Ryerson and Edgar Allan Woolf to produce the final screenplay of movie The Wizard of Oz. Whoever originated this particular line, it was said by the Scarecrow character on receiving his Doctor of Thinkology Degree from the Wizard. Screenplay as in The Wizard of Oz: The Screenplay (1989), 123.
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The theory is confirmed that pea hybrids form egg and pollen cells, which, in their constitution, represent in equal numbers all constant forms which result for the combination of the characters united in fertilization.
As collected in Forest Ray Moulton (ed.), The Autobiography of Science (1945), 586.
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There is no one who equals him [Edward Teller] for sheer, speed of thought. There may be better scientists, but none more brilliant. You always find him a thousand feet ahead of you.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 61.
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Those who consider James Watt only as a great practical mechanic form a very erroneous idea of his character: he was equally distinguished as a natural philosopher and a chemist, and his inventions demonstrate his profound knowledge of those sciences, and that peculiar characteristic of genius, the union of them for practical application.
As reported in Proceedings of the Public Meeting held at Preemasons' Hall, on the 18th June, 1824, for Erecting a Monument to the Late James Watt (1824), 8.
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Thus died Negro Tom [Thomas Fuller], this untaught arithmetician, this untutored scholar. Had his opportunities of improvement been equal to those of thousands of his fellow-men, neither the Royal Society of London, the Academy of Science at Paris, nor even a Newton himself need have been ashamed to acknowledge him a brother in science.
[Thomas Fuller (1710-1790), although enslaved from Africa at age 14, was an arithmetical prodigy. He was known as the Virginia Calculator because of his exceptional ability with arithmetic calculations. His intellectual accomplishments were related by Dr. Benjamin Rush in a letter read to the Pennsylvania Society for the Abolition of Slavery.]
Obituary
From obituary in the Boston Columbian Centinal (29 Dec 1790), 14, No. 31. In George Washington Williams, History of the Negro Race in America from 1619 to 1880 (1882), Vol. 1, 400
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To know him [Sylvester] was to know one of the historic figures of all time, one of the immortals; and when he was really moved to speak, his eloquence equalled his genius.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 265. [Halsted was J.J. Sylvester’s first student at Johns Hopkins University.]
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Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.
In History of European Thought in the Nineteenth Century (1903), 630.
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We may lay it down as an incontestible axiom, that, in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment; the quality and quantity of the elements remain precisely the same; and nothing takes place beyond changes and modifications in the combination of these elements. Upon this principle the whole art of performing chemical experiments depends: We must always suppose an exact equality between the elements of the body examined and those of the products of its analysis.
Elements of Chemistry trans. Robert. Kerr, (1790, 5th Ed. 1802), Vol. 1, 226.
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We … came up with the notion that not all web pages are created equal. People are, but not web pages.
Guest Lecture, UC Berkeley, 'Search Engines, Technology, and Business' (3 Oct 2005). At 7:43 in the YouTube video.
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When the disease is stronger than the patient, the physician will not be able to help him at all, and if the strength of the patient is greater than the strength of the disease, he does not need a physician at all. But when both are equal, he needs a physician who will support the patient’s strength and help him against the disease.
Rhazes
…...
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While playing the part of the detective the investigator follows clues, but having captured his alleged fact, he turns judge and examines the case by means of logically arranged evidence. Both functions are equally essential but they are different.
In The Art of Scientific Investigation (1950, 1957), 92.
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Whoever looks at the insect world, at flies, aphides, gnats and innumerable parasites, and even at the infant mammals, must have remarked the extreme content they take in suction, which constitutes the main business of their life. If we go into a library or newsroom, we see the same function on a higher plane, performed with like ardor, with equal impatience of interruption, indicating the sweetness of the act. In the highest civilization the book is still the highest delight.
In Lecture, second in a series given at Freeman Place Chapel, Boston (Mar 1859), 'Quotation and Originality', in Letters and Social Aims (1875, 1917), 177.
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Why is it so very important to know that the lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal!
In Letter (29 May 1898), at age almost 18, to Mrs. Lawrence Hutton, excerpted in The Story of My Life: With her Letters (1887-1901) (1903, 1921), 242.
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You know the formula m over naught equals infinity, m being any positive number? [m/0 = ∞]. Well, why not reduce the equation to a simpler form by multiplying both sides by naught? In which case you have m equals infinity times naught [m = ∞ × 0]. That is to say, a positive number is the product of zero and infinity. Doesn't that demonstrate the creation of the Universe by an infinite power out of nothing? Doesn't it?
In Point Counter Point (1928), 162.
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Your goals, minus your doubts, equal your reality.
…...
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[Before college] I was almost more interested in literature and history than in the exact sciences; I was equally good in all subjects including the classical languages.
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 526. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
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…the simplicity, the indispensableness of each word, each letter, each little dash, that among all artists raises the mathematician nearest to the World-creator; it establishes a sublimity which is equalled in no other art,—Something like it exists at most in symphonic music.
As quoted in Robert E. Moritz, 'Meaning, Methods and Mission of Modern Mathematics', The Scientific Monthly (May 1928), 26, No. 5, 424.
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…what is man in the midst of nature? A nothing in comparison with the infinite, an all in comparison with nothingness: a mean between nothing and all. Infinitely far from comprehending the extremes, the end of things and their principle are for him inevitably concealed in an impenetrable secret; equally incapable of seeing the nothingness whence he is derived, and the infinity in which he is swallowed up.
Pensées. Collected in Blaise Pascal and O.W. Wright (trans.), The Thoughts, Letters and Opuscules of Blaise Pascal (1859), 160. There are versions by other translators. For example, an alternate translation for the last sentence is: [Man is] “equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed.”
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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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