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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 M > Category: Majority

Majority Quotes (66 quotes)

Je me rends parfaitement compte du desagreable effet que produit sur la majorite de l'humanité, tout ce qui se rapporte, même au plus faible dègré, á des calculs ou raisonnements mathematiques.
I am well aware of the disagreeable effect produced on the majority of humanity, by whatever relates, even at the slightest degree to calculations or mathematical reasonings.
From 'French Reply to Baron Czyllak' concerning the game at Monte Carlo, Monte Carlo Facts and Fallacies (1904), 290, originally published in L'Écho de la Mediterranée as a response to an earlier open letter by the Baron in the same magazine. Maxim defended his prior mathematical calculations about gambling games. At the end of his paper giving a cautionary mathematical analysis of 'The Gambler's Ruin', < a href="http://todayinsci.com/C/Coolidge_Julian/CoolidgeJulian-Quotations.htm">Julian Coolidge referenced this quotation, saying “it gives the best explanation which I have seen for the fact that the people continue to gamble.”
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Wenige sind imstande, von den Vorurteilen der Umgebung abweichende Meinungen gelassen auszusprechen; die Meisten sind sogar unfähig, überhaupt zu solchen Meinungen zu gelangen.
Few people are able to express opinions that dissent from the prejudices of their social group. The majority are even incapable of forming such opinions at all.
Original German in Essays Presented to Leo Baeck on the Occasion of His Eightieth Birthday (1954), 26. English text by Webmaster assisted by online translation tools.
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A cosmic mystery of immense proportions, once seemingly on the verge of solution, has deepened and left astronomers and astrophysicists more baffled than ever. The crux ... is that the vast majority of the mass of the universe seems to be missing.
[Reporting a Nature article discrediting explanation of invisible mass being due to neutrinos]
In 'If Theory is Right, Most of Universe is Still “Missing”', New York Times (11 Sep 1984).
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A man who is convinced of the truth of his religion is indeed never tolerant. At the least, he is to feel pity for the adherent of another religion but usually it does not stop there. The faithful adherent of a religion will try first of all to convince those that believe in another religion and usually he goes on to hatred if he is not successful. However, hatred then leads to persecution when the might of the majority is behind it.
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A man with God is always in the majority.
John Knox
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 144
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A vast number, perhaps the numerical majority, of animal forms cannot be shown unequivocally to possess mind.
In 'The Brain Collaborates With Psyche', Man On His Nature: The Gifford Lectures, Edinburgh 1937-8 (1940), 284.
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According to my derivative hypothesis, a change takes place first in the structure of the animal, and this, when sufficiently advanced, may lead to modifications of habits… . “Derivation” holds that every species changes, in time, by virtue of inherent tendencies thereto. “Natural Selection” holds that no such change can take place without the influence of altered external circumstances educing or selecting such change… . The hypothesis of “natural selection” totters on the extension of a conjectural condition, explanatory of extinction to the majority of organisms, and not known or observed to apply to the origin of any species.
In On the Anatomy of Vertebrates (1868), Vol. 3, 808.
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Although with the majority of those who study and practice in these capacities [engineers, builders, surveyors, geographers, navigators, hydrographers, astronomers], secondhand acquirements, trite formulas, and appropriate tables are sufficient for ordinary purposes, yet these trite formulas and familiar rules were originally or gradually deduced from the profound investigations of the most gifted minds, from the dawn of science to the present day. … The further developments of the science, with its possible applications to larger purposes of human utility and grander theoretical generalizations, is an achievement reserved for a few of the choicest spirits, touched from time to time by Heaven to these highest issues. The intellectual world is filled with latent and undiscovered truth as the material world is filled with latent electricity.
In Orations and Speeches, Vol. 3 (1870), 513.
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And in acting thus he remains equally at ease whether the majority agree with him or he finds himself in a minority. For he has done what he could: he has expressed his convictions; and he is not master of the minds or hearts of others.
In The Maxims and Reflections of Goethe (1906), 190.
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Anton Chekhov wrote that ‘one must not put a loaded rifle on stage if no one is thinking of firing it.’ Good drama requires spare and purposive action, sensible linking of potential causes with realized effects. Life is much messier; nothing happens most of the time. Millions of Americans (many hotheaded) own rifles (many loaded), but the great majority, thank God, do not go off most of the time. We spend most of real life waiting for Godot, not charging once more unto the breach.
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Any artist or novelist would understand—some of us do not produce their best when directed. We expect the artist, the novelist and the composer to lead solitary lives, often working at home. While a few of these creative individuals exist in institutions or universities, the idea of a majority of established novelists or painters working at the “National Institute for Painting and Fine Art” or a university “Department of Creative Composition” seems mildly amusing. By contrast, alarm greets the idea of a creative scientist working at home. A lone scientist is as unusual as a solitary termite and regarded as irresponsible or worse.
Homage to Gala: The Life of an Independent Scholar (2000), 2.
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Aristotle, in spite of his reputation, is full of absurdities. He says that children should be conceived in the Winter, when the wind is in the North, and that if people marry too young the children will be female. He tells us that the blood of females is blacker then that of males; that the pig is the only animal liable to measles; that an elephant suffering from insomnia should have its shoulders rubbed with salt, olive-oil, and warm water; that women have fewer teeth than men, and so on. Nevertheless, he is considered by the great majority of philosophers a paragon of wisdom.
From An Outline of Intellectual Rubbish (1937, 1943), 19. Collected in The Basic Writings of Bertrand Russell (2009), 63.
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As a scientist and geneticist I started to feel that science would probably soon reach the point where its interference into the life processes would be counterproductive if a properly designed governing policy was not implemented. A heavily overcrowded planet, ninety-five percent urbanized with nuclear energy as the main source of energy and with all aspects of life highly computerized, is not too pleasant a place for human life. The life of any individual soon will be predictable from birth to death. Medicine, able to cure almost everything, will make the load of accumulated defects too heavy in the next two or three centuries. The artificial prolongation of life, which looked like a very bright idea when I started research in aging about twenty-five years ago, has now lost its attractiveness for me. This is because I now know that the aging process is so multiform and complex that the real technology and chemistry of its prevention by artificial interference must be too complex and expensive. It would be the privilege of a few, not the method for the majority. I also was deeply concerned about the fact that most research is now either directly or indirectly related to military projects and objectives for power.
Quoted in 'Zhores A(leksandrovich) Medvedev', Contemporary Authors Online, Gale, 2002.
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Dr Ian G. MacDonald, a Los Angeles surgeon who smokes (but doesn't inhale), contends that “For the majority of people, the use of tobacco has a beneficial effect, far better for you than taking tranquilizers.”
Quoted in Newsweek (18 Nov 1969), 62, Pt. 2, 66. A misguided comment, often seen as the shortened quote “For the majority ... beneficial effect” in a list of regrettable remarks, without the fuller context of the quote given here. MacDonald was quoted in the article to be an example that physicians were not unanimous in their attitudes against smoking. The quote is an opinion expressed to the reporter; it was not the result of scholarly research.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
Science and Method (1914, 2003), 117-118.
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I propose to raise a revolution against the lie that the majority has the monopoly of the truth.
An Enemy of the People (1882), Act IV. In Ghosts and two Other Plays (1911), 218.
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I was unable to devote myself to the learning of this al-jabr [algebra] and the continued concentration upon it, because of obstacles in the vagaries of Time which hindered me; for we have been deprived of all the people of knowledge save for a group, small in number, with many troubles, whose concern in life is to snatch the opportunity, when Time is asleep, to devote themselves meanwhile to the investigation and perfection of a science; for the majority of people who imitate philosophers confuse the true with the false, and they do nothing but deceive and pretend knowledge, and they do not use what they know of the sciences except for base and material purposes; and if they see a certain person seeking for the right and preferring the truth, doing his best to refute the false and untrue and leaving aside hypocrisy and deceit, they make a fool of him and mock him.
A. P. Youschkevitch and B. A. Rosenfeld, 'Al-Khayyami', in C. C. Gillispie (ed.), Dictionary of Scientific Biography (1973), Vol. 7, 324.
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I would proclaim that the vast majority of what [say, Scientific American] is true—yet my ability to defend such a claim is weaker than I would like. And most likely the readers, authors, and editors of that magazine would be equally hard pressed to come up with cogent, non-technical arguments convincing a skeptic of this point, especially if pitted against a clever lawyer arguing the contrary. How come Truth is such a slippery beast?
Metamagical Themas (1985), 93.
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If the arrangement of society is bad (as ours is), and a small number of people have power over the majority and oppress it, every victory over Nature will inevitably serve only to increase that power and that oppression.
In Science, Liberty and Peace by Aldous Huxley (1947).
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In less than eight years “The Origin of Species” has produced conviction in the minds of a majority of the most eminent living men of science. New facts, new problems, new difficulties as they arise are accepted, solved, or removed by this theory; and its principles are illustrated by the progress and conclusions of every well established branch of human knowledge.
From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author in the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.
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In matters of conscience, the law of majority has no place.
…...
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In systemic searches for embryonic lethal mutants of Drosophila melanogaster we have identified 15 loci which when mutated alter the segmental patterns of the larva. These loci probably represent the majority of such genes in Drosophila. The phenotypes of the mutant embryos indicate that the process of segmentation involves at least three levels of spatial organization: the entire egg as developmental unit, a repeat unit with the length of two segments, and the individual segment.
[Co-author with American physiologist Eric Wieshaus (1947-)]
'Mutations Affecting Segment Number and Polarity in Drosophila', Nature, 1980, 287, 795.
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In the animal world we have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life: understood, of course, in its wide Darwinian sense—not as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress. The mutual protection which is obtained in this case, the possibility of attaining old age and of accumulating experience, the higher intellectual development, and the further growth of sociable habits, secure the maintenance of the species, its extension, and its further progressive evolution. The unsociable species, on the contrary, are doomed to decay.
Mutual Aid: A Factor of Evolution (1902), 293.
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In the world of science, however, these sentiments have never been of much account. There everything depends on making opinion prevail and dominate; few men are really independent; the majority draws the individual after it.
In The Maxims and Reflections of Goethe (1906), 191.
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It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
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It is important to realize that life on this planet has spent about three-quarters of its existence in single-celled form, and even today the majority of organisms still exist as single cells. The evolutionary pressure to become complex is evidently not very great.
and Robert Shapiro
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It is not worth a first class man’s time to express a majority opinion. By definition, there are already enough people to do that.
Quoted in the foreward to A Mathematician's Apology (1941, reprint with Foreward by C.P. Snow 1992), 46.
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It is true that mathematics, owing to the fact that its whole content is built up by means of purely logical deduction from a small number of universally comprehended principles, has not unfittingly been designated as the science of the self-evident [Selbstverständlichen]. Experience however, shows that for the majority of the cultured, even of scientists, mathematics remains the science of the incomprehensible [Unverständlichen].
In Ueber Wert und angeblichen Unwert der Mathematik, Jahresbericht der Deutschen Maihemaliker Vereinigung (1904), 357.
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Judged superficially, a progressive saturation of the germ plasm of a species with mutant genes a majority of which are deleterious in their effects is a destructive process, a sort of deterioration of the genotype which threatens the very existence of the species and can finally lead only to its extinction. The eugenical Jeremiahs keep constantly before our eyes the nightmare of human populations accumulating recessive genes that produce pathological effects when homozygous. These prophets of doom seem to be unaware of the fact that wild species in the state of nature fare in this respect no better than man does with all the artificality of his surroundings, and yet life has not come to an end on this planet. The eschatological cries proclaiming the failure of natural selection to operate in human populations have more to do with political beliefs than with scientific findings.
Genetics and Origin of Species (1937), 126.
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Minorities are the stars of the firmament; majorities, the darkness in which they float.
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Never to have seen anything but the temperate zone is to have lived on the fringe of the world. Between the Tropic of Capricorn and the Tropic of Cancer live the majority of all the plant species, the vast majority of the insects, most of the strange ... quadrupeds, all of the great and most of the poisonous snakes and large lizards, most of the brilliantly colored sea fishes, and the strangest and most gorgeously plumaged of the birds.
Exploring For Plants (1930), 329.
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No part of the world can be truly understood without a knowledge of its garment of vegetation, for this determines not only the nature of the animal inhabitants but also the occupations of the majority of human beings.
The Red Man's Continent: A Chronicle of Aboriginal America (1919), 88.
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One day a math-deficient frog was sitting on a tiny lily pad in a big pond—a lily pad that doubled in size each night—and on this day the pad covered just one-eighth of the pond. The frog still saw the vast majority of his beloved water and so was unconcerned. Then, just three days later, he woke to find the pond had vanished while he slept.
Epigraph, without citation, 'A sad cautionary tale for frogs with their heads in the sand.' in In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions (2016), 11.
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Ours is a golden age of minorities. At no time in the past have dissident minorities felt so much at home and had so much room to throw their weight around. They speak and act as if they were “the people,” and what they abominate most is the dissent of the majority.
In 'The Trend Toward Anarchy', In Our Time (1976), 52.
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Perhaps the majority of paleontologists of the present time, who believe in orthogenesis, the irreversibility of evolution and the polyphyletic origin families, will assume that a short molar must keep on getting shorter, that it can never get longer and then again grow relatively shorter and therefore that Propliopithecus with its extremely short third molar and Dryopithecus its long m3 are alike excluded from ancestry of the Gorilla, in which the is a slight retrogression in length of m3. After many years reflection and constant study of the evolution of the vertebrates however, I conclude that 'orthogenesis' should mean solely that structures and races evolve in a certain direction, or toward a certain goal, only until the direction of evolution shifts toward some other goal. I believe that the 'irreversibility of evolution' means only that past changes irreversibly limit and condition future possibilities, and that, as a matter of experience, if an organ is once lost the same (homogenous) organ can be regained, although nature is fertile in substituting imitations. But this not mean, in my judgement, that if one tooth is smaller than its fellows it will in all cases continue to grow smaller.
'Studies on the Evolution of the Primates’, Bulletin of the American Museum of Natural History, 1916, 35, 307.
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Persons possessing great intellect and a capacity for excelling in the creative arts and also in the sciences are generally likely to have heavier brains than the ordinary individual. Arguing from this we might expect to find a corresponding lightness in the brain of the criminal, but this is not always the case ... Many criminals show not a single anomaly in their physical or mental make-up, while many persons with marked evidences of morphological aberration have never exhibited the criminal tendency.
Every attempt to prove crime to be due to a constitution peculiar only to criminals has failed signally. It is because most criminals are drawn from the ranks of the low, the degraded, the outcast, that investigators were ever deceived into attempting to set up a 'type' of criminal. The social conditions which foster the great majority of crimes are more needful of study and improvement.
From study of known normal brains we have learned that there is a certain range of variation. No two brains are exactly alike, and the greatest source of error in the assertions of Benedict and Lombroso has been the finding of this or that variation in a criminal’s brains, and maintaining such to be characteristic of the 'criminal constitution,' unmindful of the fact that like variations of structure may and do exist in the brains of normal, moral persons.
Address to the American Association for the Advancement of Science in Philadelphia (28 Dec 1904), as quoted in 'Americans of Future Will Have Best Brains', New York Times (29 Dec 1904), 6.
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Probably our atomic weights merely represent a mean value around which the actual atomic weights of the atoms vary within certain narrow limits... when we say, the atomic weight of, for instance, calcium is 40, we really express the fact that, while the majority of calcium atoms have an actual atomic weight of 40, there are not but a few which are represented by 39 or 41, a less number by 38 or 42, and so on.
Presidential Address, 2 September 1886, Section B, Chemical Science. Reports of the British Association for the Advancement of Science (1886), 569.
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Religion shows a pattern of heredity which I think is similar to genetic heredity. ... There are hundreds of different religious sects, and every religious person is loyal to just one of these. ... The overwhelming majority just happen to choose the one their parents belonged to. Not the sect that has the best evidence in its favour, the best miracles, the best moral code, the best cathedral, the best stained-glass, the best music when it comes to choosing from the smorgasbord of available religions, their potential virtues seem to count for nothing compared to the matter of heredity.
From edited version of a speech, at the Edinburgh International Science Festival (15 Apr 1992), as reprinted from the Independent newspaper in Alec Fisher, The Logic of Real Arguments (2004), 82-83.
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Run the tape again, and let the tiny twig of Homo sapiens expire in Africa. Other hominids may have stood on the threshold of what we know as human possibilities, but many sensible scenarios would never generate our level of mentality. Run the tape again, and this time Neanderthal perishes in Europe and Homo erectus in Asia (as they did in our world). The sole surviving human stock, Homo erectus in Africa, stumbles along for a while, even prospers, but does not speciate and therefore remains stable. A mutated virus then wipes Homo erectus out, or a change in climate reconverts Africa into inhospitable forest. One little twig on the mammalian branch, a lineage with interesting possibilities that were never realized, joins the vast majority of species in extinction. So what? Most possibilities are never realized, and who will ever know the difference? Arguments of this form lead me to the conclusion that biology's most profound insight into human nature, status, and potential lies in the simple phrase, the embodiment of contingency: Homo sapiens is an entity, not a tendency.
Wonderful Life (1989), 320.
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Sometimes I am a little unkind to all my many friends in education … by saying that from the time it learns to talk every child makes a dreadful nuisance of itself by asking “Why?.” To stop this nuisance society has invented a marvellous system called education which, for the majority of people, brings to an end their desire to ask that question. The few failures of this system are known as scientists.
'The Making of a Scientist', Journal of the Royal Society of Arts, June 1983, 403.
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Species do not grow more perfect: the weaker dominate the strong, again and again— the reason being that they are the great majority, and they are also cleverer. Darwin forgot the mind (—that is English!): the weak possess more mind. … To acquire mind, one must need mind—one loses it when one no longer needs it.
[Criticism of Darwin’s Origin of Species.]
The Twilight of the Idols (1888), translated by R. J. Hollingdale, Twilight of the Idols and the Anti Christ (1990), 67. Also see alternate translations.
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Species do not evolve towards perfection: the weak always prevail over the strong—simply because they are the majority, and because they are also the more crafty. Darwin forgot the intellect (that is English!), the weak have more intellect. In order to acquire intellect, one must be in need of it. One loses it when one no longer needs it.
[Criticism of Darwin's Origin of Species.]
The Twilight of the Idols (1888) collected in Twilight of the Idols, with The Antichrist and Ecce Homo, translated by Anthony M. Ludovici (2007), 56. Also see alternate translations.
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That the great majority of those who leave school should have some idea of the kind of evidence required to substantiate given types of belief does not seem unreasonable. Nor is it absurd to expect that they should go forth with a lively interest in the ways in which knowledge is improved and a marked distaste for all conclusions reached in disharmony with the methods of scientific inquiry.
Address to Section L, Education, of the American Association for the Advancement of Science, at Boston (1909), 'Science as Subject-Matter and as Method'. Published in Science (28 Jan 1910), N.S. Vol. 31, No. 787, 126.
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The amount of knowledge which we can justify from evidence directly available to us can never be large. The overwhelming proportion of our factual beliefs continue therefore to be held at second hand through trusting others, and in the great majority of cases our trust is placed in the authority of comparatively few people of widely acknowledged standing.
Personal Knowledge (1958), 208.
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The fear of mathematics is a tradition handed down from days when the majority of teachers knew little about human nature and nothing at all about the nature of mathematics itself. What they did teach was an imitation.
in Mathematician’s Delight (1946), 12.
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The majority of evolutive movements are degenerative. Progressive cases are exceptional. Characters appear suddenly that have no meaning in the atavistic series. Evolution in no way shows a general tendency toward progress… . The only thing that could be accomplished by slow changes would be the accumulation of neutral characteristics without value for survival. Only important and sudden mutations can furnish the material which can be utilized by selection.
As quoted in Isaac Asimov's Book of Science and Nature Quotations (1988), 91. Please contact Webmaster if you know the primary source.
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The majority of mathematical truths now possessed by us presuppose the intellectual toil of many centuries. A mathematician, therefore, who wishes today to acquire a thorough understanding of modern research in this department, must think over again in quickened tempo the mathematical labors of several centuries. This constant dependence of new truths on old ones stamps mathematics as a science of uncommon exclusiveness and renders it generally impossible to lay open to uninitiated readers a speedy path to the apprehension of the higher mathematical truths. For this reason, too, the theories and results of mathematics are rarely adapted for popular presentation … This same inaccessibility of mathematics, although it secures for it a lofty and aristocratic place among the sciences, also renders it odious to those who have never learned it, and who dread the great labor involved in acquiring an understanding of the questions of modern mathematics. Neither in the languages nor in the natural sciences are the investigations and results so closely interdependent as to make it impossible to acquaint the uninitiated student with single branches or with particular results of these sciences, without causing him to go through a long course of preliminary study.
In Mathematical Essays and Recreations (1898), 32.
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The men you see waiting in the lobbies of doctors’ offices are, in a vast majority of cases, suffering through poisoning caused by an excess of food.
In Love, Life and Work (), 129.
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The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Physical astronomy, the branch of knowledge that does the greatest honor to the human mind, gives us an idea, albeit imperfect, of what such an intelligence would be. The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. Man owes that advantage to the power of the instrument he employs, and to the small number of relations that it embraces in its calculations. But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability.
'Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards' (1773, published 1776). In Oeuvres complètes de Laplace, 14 Vols. (1843-1912), Vol. 8, 144-5, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 26.
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The scientific theorist is not to be envied. For Nature, or more precisely experiment, is an inexorable and not very friendly judge of his work. It never says “Yes” to a theory. In the most favorable cases it says “Maybe,” and in the great majority of cases simply “No.” If an experiment agrees with a theory it means for the latter “Maybe,” and if it does not agree it means “No.” Probably every theory will someday experience its “No”—most theories, soon after conception.
In Albert Einstein: The Human Side by Helen Dukas and Banesh Hoffmann (1979).
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The species does not grow in perfection: the weak again and again get the upper hand of the strong,—and their large number and their greater cunning are the cause of it. Darwin forgot the intellect (that was English!); the weak have more intellect. ... One must need intellect in order to acquire it; one loses it when it is no longer necessary.
[Criticism of Darwin’s Origin of Species.]
In The Twilight of the Idols (1886) collected in Thomas Common (trans.), The Works of Nietzsche (1896), Vol. 11, 177. Also see alternate translations.
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The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.
In Popular Scientific Lectures (1910), 196.
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The tropical rain forests of the world harbor the majority of the planet’s species, yet this wealth of species is being quickly spent. While the exact numbers of species involved and the rate of forest clearing are still under debate, the trend is unmistakable—the richest terrestrial biome is being altered at a scale unparalleled in geologic history.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984),
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The trouble with human progress is that it tends to go too fast—that is, too fast for the great majority of comfortable and incurious men.
From Baltimore Evening Sun (6 Apr 1931). Collected in A Mencken Chrestomathy (1949, 1956), 329-330.
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The unavoidable conclusion is that the unprecedented meekness of the majority is responsible for the increase in violence. Social stability is the product of an equilibrium between a vigorous majority and violent minorities. Disorder does not come from an increased inner pressure or from the interaction of explosive ingredients. There is no reason to believe that the nature of the violent minorities is now greatly different from what it was in the past. What has changed is the will and ability of the majority to react.
In 'Thoughts on the Present', First Things, Last Things (1971), 110.
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There is nothing more odious than the majority; it consists of a few powerful men to lead the way; of accommodating rascals and submissive weaklings; and of a mass of men who trot after them, without in the least knowing their own mind.
In The Maxims and Reflections of Goethe (1906), 197.
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True majorities, in a TV-dominated and anti-intellectual age, may need sound bites and flashing lights–and I am not against supplying such lures if they draw children into even a transient concern with science. But every classroom has one [Oliver] Sacks, one [Eric] Korn, or one [Jonathan] Miller, usually a lonely child with a passionate curiosity about nature, and a zeal that overcomes pressures for conformity. Do not the one in fifty deserve their institutions as well–magic places, like cabinet museums, that can spark the rare flames of genius?
…...
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Walking home at night, I shine my flashlight up at the sky. I send billions of ... photons toward space. What is their destination? A tiny fraction will be absorbed by the air. An even smaller fraction will be intercepted by the surface of planets and stars. The vast majority ... will plod on forever. After some thousands of years they will leave our galaxy; after some millions of years they will leave our supercluster. They will wander through an even emptier, even colder realm. The universe is transparent in the direction of the future.
Atoms of Silence
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We all pay an involuntary homage to antiquity – a “blind homage,” as Bacon calls it in his “Novum Organum,” which tends greatly to the obstruction of truth. To the great majority of mortal eyes, Time sanctifies everything that he does not destroy. The mere fact of anything being spared by the great foe makes it a favourite with us, who are sure to fall his victims.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 314.
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We have not done the things that are necessary to lower emissions because these things fundamentally conflict with deregulated capitalism… We are stuck because the actions that would give us the best chance of averting catastrophe–and would benefit the vast majority–are extremely threatening to an elite minority that has a stranglehold over our economy, our political process, and most of our major media outlets.
From This Changes Everything: Capitalism vs. the Climate (2014), 18.
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What we do may be small, but it has a certain character of permanence and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.
From Inaugural Lecture, Oxford (1920). Recalled in A Mathematician’s Apology (1940, 1967), 76.
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When I think of vision, I have in mind the ability to see above and beyond the majority.
…...
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When understanding of the universe has become widespread, when the majority of men know that the stars are not sources of light but worlds, perhaps inhabited worlds like ours, then the Christian doctrine will be convicted of absurdity.
In Adolf Hitler, Hugh Redwald Trevor-Roper, translated by Norman Cameron and R. H. Stevens, '14 October 1941', Secret Conversations (1941 - 1944) (1953), 50
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[A]s you know, scientific education is fabulously neglected … This is an evil that is inherited, passed on from generation to generation. The majority of educated persons are not interested in science, and are not aware that scientific knowledge forms part of the idealistic background of human life. Many believe—in their complete ignorance of what science really is—that it has mainly the ancillary task of inventing new machinery, or helping to invent it, for improving our conditions of life. They are prepared to leave this task to the specialists, as they leave the repairing of their pipes to the plumber. If persons with this outlook decide upon the curriculum of our children, the result is necessarily such as I have just described it.
Opening remarks of the second of four public lectures for the Dublin Institute for Advanced Studies at University College, Dublin (Feb 1950), The Practical Achievements of Science Tending to Obliterate its True Import', collected in Science and Humanism: Physics in Our Time (1951). Reprinted in 'Nature and the Greeks' and 'Science and Humanism' (1996), 113.
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[In] the evolution of ideas… New ideas are thrown up spontaneously like mutations; the vast majority of them are useless crank theories, the equivalent of biological freaks without survival-value.
In Epilogue, The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), 515.
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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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Sophie Germain
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- 90 -
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Winston Churchill
- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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- 10 -
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