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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Convenience Quotes (50 quotes)
Convenient Quotes, Conveniently Quotes, Conveniences Quotes


... I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
Quoted in Sir Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), 541. Science and Method (1908) 51-52, 392.
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Dilbert: You joined the “Flat Earth Society?”
Dogbert: I believe the earth must be flat. There is no good evidence to support the so-called “round earth theory.”
Dilbert: I think Christopher Columbus would disagree.
Dogbert: How convenient that your best witness is dead.
Dilbert comic strip (9 Oct 1989).
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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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A vast technology has been developed to prevent, reduce, or terminate exhausting labor and physical damage. It is now dedicated to the production of the most trivial conveniences and comfort.
Reflections on Behaviorism and Society (1978), 6.
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Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence…. The two propositions: “The earth turns round” and “it is more convenient to suppose the earth turns round” have the same meaning; there is nothing more in the one than in the other.
From La Science et l’Hypothèse (1908), 141, as translated by George Bruce Halsted in Science and Hypothesis (1905), 85-86. From the original French, “L’espace absolu, c’est-à-dire le repère auquel il faudrait rapporter la terre pour savoir si réellement elle tourne, n’a aucune existence objective. … Ces deux propositions: ‘la terre tourne’, et: ‘il est plus commode de supposer que la terre tourne’, ont un seul et même sens; il n’y a rien de plus dans l’une que dans l’autre.”
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Boundaries which mark off one field of science from another are purely artificial, are set up only for temporary convenience. Let chemists and physicists dig deep enough, and they reach common ground.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 183.
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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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Thomas Tredgold quote
Engineering … the great sources of power in nature (source)
Engineering is the art of directing the great sources of power in nature for the use and convenience of man.
(1828) At a meeting of the Council of the Institution of Civil Engineers of Great Britain (29 Dec 1827), by resolution, Honorary Member Thomas Tredgold was asked for a description of what a Civil Engineer is, in order that it could be put in the petition for a charter. (As cited by F.R. Hutton, in 'The Field of the Mechanical Engineer', The Engineering Digest (1908), Vol. 3 , 10.) The wording was repeated in the Charter of the Institution. (Reported in 'Society of Civil Engineers', The Gentleman's Magazine (1828), 143, 628.) The quote is excerpted from the longer definition therein.
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Engineering is the art of directing the great sources of power in nature for the use and the convenience of people. In its modern form engineering involves people, money, materials, machines, and energy. It is differentiated from science because it is primarily concerned with how to direct to useful and economical ends the natural phenomena which scientists discover and formulate into acceptable theories. Engineering therefore requires above all the creative imagination to innovate useful applications of natural phenomena. It seeks newer, cheaper, better means of using natural sources of energy and materials.
In McGraw Hill, Science and Technology Encyclopedia
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Exper. I. I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation I placed a small looking-glass without the window-shutter, in such a position as to reflect the sun's light, in a direction nearly horizontal, upon the opposite wall, and to cause the cone of diverging light to pass over a table on which were several little screens of card-paper. I brought into the sunbeam a slip of card, about one-thirtieth of an inch in breadth, and observed its shadow, either on the wall or on other cards held at different distances. Besides the fringes of colour on each side of the shadow, the shadow itself was divided by similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the shadow was observed, but leaving the middle of the shadow always white. Now these fringes were the joint effects of the portions of light passing on each side of the slip of card and inflected, or rather diffracted, into the shadow. For, a little screen being placed a few inches from the card, so as to receive either edge of the shadow on its margin, all the fringes which had before been observed in the shadow on the wall, immediately disappeared, although the light inflected on the other side was allowed to retain its course, and although this light must have undergone any modification that the proximity of the other edge of the slip of card might have been capable of occasioning... Nor was it for want of a sufficient intensity of light that one of the two portions was incapable of producing the fringes alone; for when they were both uninterrupted, the lines appeared, even if the intensity was reduced to one-tenth or one-twentieth.
'Experiments and Calculations Relative to Physical Optics' (read in 1803), Philosophical Transactions (1804), 94, 2-3.
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For books [Charles Darwin] had no respect, but merely considered them as tools to be worked with. ... he would cut a heavy book in half, to make it more convenient to hold. He used to boast that he had made Lyell publish the second edition of one of his books in two volumes, instead of in one, by telling him how ho had been obliged to cut it in half. ... his library was not ornamental, but was striking from being so evidently a working collection of books.
In Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of his Published Letters (1908), 96.
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Geometry enlightens the intellect and sets one’s mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
In Ibn Khaldûn, Franz Rosenthal (trans.) and N.J. Dawood (ed.), The Muqaddimah: An Introduction to History (1967, 1969), Vol. 1, 378.
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He who appropriates land to himself by his labor, does not lessen but increases the common stock of mankind. For the provisions serving to the support of human life, produced by one acre of inclosed and cultivated land, are … ten times more than those which are yielded by an acre of land, of an equal richness lying waste in common. And therefore he that incloses land and has a greater plenty of the conveniences of life from ten acres than he could have from a hundred left to nature, may truly be said to give ninety acres to mankind.
In John Locke and Thomas Preston Peardon (ed.), The Second Treatise of Civil Government: An Essay Concerning the True Original, Extent and End of Civil Government (Dec 1689, 1952), 22.
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I strongly oppose cloning, as do most Americans. We recoil at the idea of growing human beings for spare body parts or creating life for our convenience. And while we must devote enormous energy to conquering disease, it is equally important that we pay attention to the moral concerns raised by the new frontier of human embryo stem cell research. Even the most noble ends do not justify any means.
'Address to the Nation on Stem Cell Research', (9 Aug 2001) in Public Papers Of The Presidents Of The United States, George W. Bush, 2001 (2004), Book 2, 955.
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In early times, when the knowledge of nature was small, little attempt was made to divide science into parts, and men of science did not specialize. Aristotle was a master of all science known in his day, and wrote indifferently treatises on physics or animals. As increasing knowledge made it impossible for any one man to grasp all scientific subjects, lines of division were drawn for convenience of study and of teaching. Besides the broad distinction into physical and biological science, minute subdivisions arose, and, at a certain stage of development, much attention was, given to methods of classification, and much emphasis laid on the results, which were thought to have a significance beyond that of the mere convenience of mankind.
But we have reached the stage when the different streams of knowledge, followed by the different sciences, are coalescing, and the artificial barriers raised by calling those sciences by different names are breaking down. Geology uses the methods and data of physics, chemistry and biology; no one can say whether the science of radioactivity is to be classed as chemistry or physics, or whether sociology is properly grouped with biology or economics. Indeed, it is often just where this coalescence of two subjects occurs, when some connecting channel between them is opened suddenly, that the most striking advances in knowledge take place. The accumulated experience of one department of science, and the special methods which have been developed to deal with its problems, become suddenly available in the domain of another department, and many questions insoluble before may find answers in the new light cast upon them. Such considerations show us that science is in reality one, though we may agree to look on it now from one side and now from another as we approach it from the standpoint of physics, physiology or psychology.
In article 'Science', Encyclopedia Britannica (1911), 402.
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In this physical world there is no real chaos; all is in fact orderly; all is ordered by the physical principles. Chaos is but unperceived order- it is a word indicating the limitations of the human mind and the paucity of observational facts. The words “chaos,” “accidental,” “chance,” “unpredictable," are conveniences behind which we hide our ignorance.
From Of Stars and Men: The Human Response to an Expanding Universe (1958 Rev. Ed. 1964), Foreword.
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It is arguable whether the human race have been gainers by the march of science beyond the steam engine. Electricity opens a field of infinite conveniences to ever greater numbers, but they may well have to pay dearly for them. But anyhow in my thought I stop short of the internal combustion engine which has made the world so much smaller. Still more must we fear the consequences of entrusting a human race so little different from their predecessors of the so-called barbarous ages such awful agencies as the atomic bomb. Give me the horse.
Address to the Royal College of Surgeons (10 Jul 1951). Collected in Stemming the Tide: Speeches 1951 and 1952 (1953), 91.
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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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It is not nature which imposes time and space upon us, it is we who impose them upon nature because we find them convenient.
…...
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It is often more convenient to possess the ashes of great men than to possess the men themselves during their lifetime.
Commenting on the return of Descartes’ remains to France. Quoted, without citation, in Eric Temple Bell Men of Mathematics (1937), 52.
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It seems to me that God is a convenient invention of the human mind.
…...
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Just as the introduction of the irrational numbers … is a convenient myth [which] simplifies the laws of arithmetic … so physical objects are postulated entities which round out and simplify our account of the flux of existence… The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.
In J. Koenderink Solid Shape (1990.), 16.
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On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
'The Work of Nicholas Bourbaki'American Mathematical Monthly (1970), 77, 134. In Carl C. Gaither, Alma E. Cavazos-Gaither, Mathematically Speaking: a Dictionary of Quotations (), 194.
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One geometry cannot be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.
…...
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Psychologists pay lip service to the scientific method, and use it whenever it is convenient; but when it isn’t they make wild leaps of their uncontrolled fancy.…
In Science is a Sacred Cow (1950), 127.
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Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all.
The Human Use of Human Beings: Cybernetics and Society (1950), 137.
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Scientists often invent words to fill the holes in their understanding.These words are meant as conveniences until real understanding can be found. … Words such as dimension and field and infinity … are not descriptions of reality, yet we accept them as such because everyone is sure someone else knows what the words mean.
In God’s Debris: A Thought Experiment (2004), 20-21.
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So far, the clumsily long name 'quasi-stellar radio sources' is used to describe these objects. Because the nature of these objects is entirely unknown, it is hard to prepare a short, appropriate nomenclature for them so that their essential properties are obvious from their name. For convenience, the abbreviated form 'quasar' will be used throughout this paper.
'Gravitational Collapse', Physics Today, 1964, 17, 21.
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So long as the fur of the beaver was extensively employed as a material for fine hats, it bore a very high price, and the chase of this quadruped was so keen that naturalists feared its speedy consideration. When a Parisian manufacturer invented the silk hat, which soon came into almost universal use, the demand for beavers' fur fell off, and this animal–whose habits, as we have seen, are an important agency in the formation of bogs and other modifications of forest nature–immediately began to increase, reappeared in haunts which we had long abandoned, and can no longer be regarded as rare enough to be in immediate danger of extirpation. Thus the convenience or the caprice of Parisian fashion has unconsciously exercised an influence which may sensibly affect the physical geography of a distant continent.
In Man and Nature, (1864), 84.
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The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.
Remarking on the paper, ‘Statistics in Agricultural Research’ by J. Wishart, Journal of the Royal Statistical Society, Supplement (1934), 1, 52. As cited in Michael Cowle, Statistics in Psychology: An Historical Perspective (2005), 210.
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The attitude which the man in the street unconsciously adopts towards science is capricious and varied. At one moment he scorns the scientist for a highbrow, at another anathematizes him for blasphemously undermining his religion; but at the mention of a name like Edison he falls into a coma of veneration. When he stops to think, he does recognize, however, that the whole atmosphere of the world in which he lives is tinged by science, as is shown most immediately and strikingly by our modern conveniences and material resources. A little deeper thinking shows him that the influence of science goes much farther and colors the entire mental outlook of modern civilised man on the world about him.
Reflections of a Physicist (1950), 81.
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The figure of 2.2 children per adult female was felt to be in some respects absurd, and a Royal Commission suggested that the middle classes be paid money to increase the average to a rounder and more convenient number.
Magazine
Quoted from Punch in epigraph, M.J. Moroney, 'On the Average', Facts From Figures (1951), Chap. 4, 34.
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The Frog—that arch-martyr to science—affords the most convenient subject.
Carl Wedl
In Rudiments of Pathological Histology (1855), trans. and ed. by George Busk, 15.
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The God whom science recognizes must be a God of universal laws exclusively, a God who does a wholesale, not a retail business. He cannot accommodate his processes to the convenience of individuals.
The Varieties of Religious Experience: A Study in Human Nature (1902), 493-5.
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The great truths with which it [mathematics] deals, are clothed with austere grandeur, far above all purposes of immediate convenience or profit. It is in them that our limited understandings approach nearest to the conception of that absolute and infinite, towards which in most other things they aspire in vain. In the pure mathematics we contemplate absolute truths, which existed in the divine mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven. They existed not merely in metaphysical possibility, but in the actual contemplation of the supreme reason. The pen of inspiration, ranging all nature and life for imagery to set forth the Creator’s power and wisdom, finds them best symbolized in the skill of the surveyor. "He meted out heaven as with a span;" and an ancient sage, neither falsely nor irreverently, ventured to say, that “God is a geometer”.
In Orations and Speeches (1870), Vol. 3, 614.
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The most important object of Civil Engineering is to improve the means of production and of traffic in states, both for external and internal trade. It is applied in the construction and management of roads, bridges, railroads, aqueducts, canals, river navigation, docks and storehouses, for the convenience of internal intercourse and exchange; and in the construction of ports, harbours, moles, breakwaters and lighthouses; and in the navigation by artificial power for the purposes of commerce. It is applied to the protection of property where natural powers are the sources of injury, as by embankments forthe defence of tracts of country from the encroachments of the sea, or the overflowing of rivers; it also directs the means of applying streams and rivers to use, either as powers to work machines, or as supplies for the use of cities and towns, or for irrigation; as well as the means of removing noxious accumulations, as by the drainage of towns and districts to ... secure the public health.
1828
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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The original Marxist notion of ideology was conveniently forgotten because it inconveniently did not exempt common sense and empiricism from the charge of ideology.
In Social Amnesia (1975), 6-7.
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The wise man, however, will avoid partial views of things. He will not, with the miser, look to gold and silver as the only blessings of life; nor will he, with the cynic, snarl at mankind for preferring them to copper and iron. … That which is convenient is that which is useful, and that which is useful is that which is valuable.
From 13th Lecture in 1818, in Bence Jones, The Life and Letters of Faraday (1870), Vol. 1, 255.
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The world is a construct of our sensations, perceptions, memories. It is convenient to regard it as existing objectively on its own. But it certainly does not become manifest by its mere existence.
Opening remark in first Tarner Lecture, at Trinity College, Cambridge (Oct 1956), 'The Physical Basis of Consciousness', printed in Mind and Matter (1958), 1. Also collected in What is Life?: With Mind and Matter and Autobiographical Sketches (1992, 2012).
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The “control of nature” is a phrase conceived in arrogance, born of the Neanderthal age of biology and the convenience of man.
In Silent Spring (1962), 297.
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There is a single general space, a single vast immensity which we may freely call void: in it are unnumerable globes like this on which we live and grow, this space we declare to be infinite, since neither reason, convenience, sense-perception nor nature assign to it a limit.
Quoted in Joseph Silk, The Big Bang (1997), 89.
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There is no reason that the universe should be designed for our convenience.
In The Origin Of The Universe: Science Masters Series (1997), 82.
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Time... is an essential requirement for effective research. An investigator may be given a palace to live in, a perfect laboratory to work in, he may be surrounded by all the conveniences money can provide; but if his time is taken from him he will remain sterile.
Quoted in S. Benison, A. C. Barger and E. L. Wolfe, Walter B Cannon: The Life and Times of a Young Scientist (1987), 253.
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Visualize yourself confronted with the task of killing, one after the other, a cabbage, a fly, a fish, a lizard, a guinea pig, a cat, a dog, a monkey and a baby chimpanzee. In the unlikely case that you should experience no greater inhibitions in killing the chimpanzee than in destroying the cabbage or the fly, my advice to you is to commit suicide at your earliest possible convenience, because you are a weird monstrosity and a public danger.
'The Enmity Between Generations and Its Probable Ethological Causes'. In Richard I. Evans, Konrad Lorenz: The Man and his Ideas (1975), 227.
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Water at command, by turning a tap and paying a tax, is more convenient than carrying it from a free spring.
In Sinner Sermons: A Selection of the Best Paragraphs of E. W. Howe (1926), 49.
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We must remember that all our [models of flying machine] inventions are but developments of crude ideas; that a commercially successful result in a practically unexplored field cannot possibly be got without an enormous amount of unremunerative work. It is the piled-up and recorded experience of many busy brains that has produced the luxurious travelling conveniences of to-day, which in no way astonish us, and there is no good reason for supposing that we shall always be content to keep on the agitated surface of the sea and air, when it is possible to travel in a superior plane, unimpeded by frictional disturbances.
Paper to the Royal Society of New South Wales (4 Jun 1890), as quoted in Octave Chanute, Progress in Flying Machines (1894), 2226.
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Why there is one Body in or System qualified to give Light and Heat to all ye rest, I know no reason, but because ye author of the Systeme thought it convenient.
Letter to Bentley (10 Dec 1692). In The Works of Richard Bentley (1838), Vol. 3, 204.
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Without natural resources life itself is impossible. From birth to death, natural resources, transformed for human use, feed, clothe, shelter, and transport us. Upon them we depend for every material necessity, comfort, convenience, and protection in our lives. Without abundant resources prosperity is out of reach.
Breaking New Ground (1998), 505.
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[From uranium] there are present at least two distinct types of radiation one that is very readily absorbed, which will be termed for convenience the α radiation, and the other of a more penetrative character, which will be termed the β radiation.
Originating the names for these two types of radiation. In 'Uranium Radiation and the Electrical Conduction Produced by It', Philosophical Magazine (1899), 47, 116.
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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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- 50 -
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- 40 -
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