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Who said: “Science without religion is lame; religion without science is blind.”
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General Quotes (92 quotes)

Air Force Chief of Staff: Doctor, what do you think of our new creation, the … Corporation?
von Kármán: Why, General, I think that corporation has already had an effect on the whole industry.
Air Force Chief of Staff: I’m delighted. What effect is that?
von Kármán: Why, they’ve upset the salary schedule of the whole industry.
As quoted by William R. Sears in 'Some Recollections of Theodore von Kármán', Address to the Symposium in Memory of Theodore von Kármán, Society for Industrial and Applied Mathematics, National Meeting (13-14 May 1964), Washington, D.C. Printed in Journal of the Society for Industrial and Applied Mathematics (Mar 1965), 13>, No. 1, 181. These are likely not verbatim words of Karman, but as recollected by Sears, giving an example of von Kármán’s willingness to speak truth to power.
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La chaleur pénètre, comme la gravité, toutes les substances de l’univers, ses rayons occupent toutes les parties de l’espace. Le but de notre ouvrage est d’exposer les lois mathématiques que suit cet élément. Cette théorie formera désormais une des branches les plus importantes de la physique générale.
Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.
From 'Discours Préliminaire' to Théorie Analytique de la Chaleur (1822), i, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 1.
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[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.
Quoted, without source, in The Grolier Library of Science Biographies (1996), Vol. 3, 191.
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A fool who, after plain warning, persists in dosing himself with dangerous drugs should be free to do so, for his death is a benefit to the race in general.
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A Law of Nature, (Lex Naturalis) is a Precept, or general Rule, found out by Reason, by which a man is forbidden to do, that, which is destructive of his life, or taketh away the means of preserving the same; and to omit, that, by which he thinketh it may be best preserved
Leviathan, ch. 14 (1651).
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As regards religion, on the other hand, one is generally agreed that it deals with goals and evaluations and, in general, with the emotional foundation of human thinking and acting, as far as these are not predetermined by the inalterable hereditary disposition of the human species. Religion is concerned with man’s attitude toward nature at large, with the establishing of ideals for the individual and communal life, and with mutual human relationship. These ideals religion attempts to attain by exerting an educational influence on tradition and through the development and promulgation of certain easily accessible thoughts and narratives (epics and myths) which are apt to influence evaluation and action along the lines of the accepted ideals.
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At the age of three I began to look around my grandfather’s library. My first knowledge of astronomy came from reading and looking at pictures at that time. By the time I was six I remember him buying books for me. … I think I was eight, he bought me a three-inch telescope on a brass mounting. … So, as far back as I can remember, I had an early interest in science in general, astronomy in particular.
Oral History Transcript of interview with Dr. Jesse Greenstein by Paul Wright (31 Jul 1974), on website of American Institute of Physics.
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Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals—the flotsam and jetsam of historical currents. The men who radically altered history, the great creative scientists and mathematicians, are seldom mentioned if at all.
Opening paragraph of book review, 'Adventures Of a Mathematician: The Man Who Invented the H-Bomb', New York Times (9 May 1976), 201.
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Both social and biosocial factors are necessary to interpret crosscultural studies, with the general proviso that one’s research interest determines which elements, in what combinations, are significant for the provision of understanding.
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But nature is remarkably obstinate against purely logical operations; she likes not schoolmasters nor scholastic procedures. As though she took a particular satisfaction in mocking at our intelligence, she very often shows us the phantom of an apparently general law, represented by scattered fragments, which are entirely inconsistent. Logic asks for the union of these fragments; the resolute dogmatist, therefore, does not hesitate to go straight on to supply, by logical conclusions, the fragments he wants, and to flatter himself that he has mastered nature by his victorious intelligence.
'On the Principles of Animal Morphology', Proceedings of the Royal Society of Edinburgh (2 Apr 1888), 15, 289. Original as Letter to Mr John Murray, communicated to the Society by Professor Sir William Turner. Page given as in collected volume published 1889.
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But with regard to the material world, we can at least go so far as this;—we can perceive that events are brought about, not by insulated interpositions of Divine power, exerted in each particular ease, but by the establishment of general laws.
In Astronomy and General Physics Considered with Reference to Natural Theology (1833), 356. Charles Darwin placed this quote on the title page of his On the Origin of Species, identified as from Whewell's 'Bridgewater Treatise'.
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Chemistry is the study of the effects of heat and mixture, with a view of discovering their general and subordinate laws, and of improving the useful arts.
This is an editor’s shorter restatement of the definition given by Black in the first of a series of lectures on chemistry, collected in John Robison (ed.), Lectures on the Elements of Chemistry: Delivered in the University of Edinburgh (1807), Vol. 1, 11, footnote. For the definitions as given by Black, see elsewhere on this web page.
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Common to all these types is the anthropomorphic character of their conception of God. In general, only individuals of exceptional endowments, and exceptionally high-minded communities, rise to any considerable extent above this level. But there is a third stage of religious experience which belongs to all of them, even though it is rarely found in a pure form: I shall call it cosmic religious feeling. It is very difficult to elucidate this feeling to anyone who is entirely without it, especially as there is no anthropomorphic conception of God corresponding to it.
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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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ENGINEER, in the military art, an able expert man, who, by a perfect knowledge in mathematics, delineates upon paper, or marks upon the ground, all sorts of forts, and other works proper for offence and defence. He should understand the art of fortification, so as to be able, not only to discover the defects of a place, but to find a remedy proper for them; as also how to make an attack upon, as well as to defend, the place. Engineers are extremely necessary for these purposes: wherefore it is requisite that, besides being ingenious, they should be brave in proportion. When at a siege the engineers have narrowly surveyed the place, they are to make their report to the general, by acquainting him which part they judge the weakest, and where approaches may be made with most success. Their business is also to delineate the lines of circumvallation and contravallation, taking all the advantages of the ground; to mark out the trenches, places of arms, batteries, and lodgments, taking care that none of their works be flanked or discovered from the place. After making a faithful report to the general of what is a-doing, the engineers are to demand a sufficient number of workmen and utensils, and whatever else is necessary.
In Encyclopaedia Britannica or a Dictionary of Arts and Sciences (1771), Vol. 2, 497.
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Engineering is the practice of safe and economic application of the scientific laws governing the forces and materials of nature by means of organization, design and construction, for the general benefit of mankind.
1920
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For they are, in truth, textbooks of life: they gather outer and inner experiences into a general and connected whole.
In The Maxims and Reflections of Goethe (1906), 189.
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From a pragmatic point of view, the difference between living against a background of foreigness (an indifferent Universe) and one of intimacy (a benevolent Universe) means the difference between a general habit of wariness and one of trust.
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General Theory of Relativity = Gravity too; referentially, eh?
Anagram
Anagram by V. Rabin (2003) on anagramgenius.com website.
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Having discovered … by observation and comparison that certain objects agree in certain respects, we generalise the qualities in which they coincide,—that is, from a certain number of individual instances we infer a general law; we perform an act of Induction. This induction is erroneously viewed as analytic; it is purely a synthetic process.
In Lecture VI of his Biennial Course, by William Hamilton and Henry L. Mansel (ed.) and John Veitch (ed.), Metaphysics (1860), Vol. 1, 101.
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He that would learn by experiments, ought to proceed from particulars to generals; but the method of instructing academically, proceeds from generals to particulars
As quoted in Thomas Steele Hall, A Source Book in Animal Biology (1951), 486.
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I am convinced that this is the only means of advancing science, of clearing the mind from a confused heap of contradictory observations, that do but perplex and puzzle the Student, when he compares them, or misguide him if he gives himself up to their authority; but bringing them under one general head, can alone give rest and satisfaction to an inquisitive mind.
From 'A Discourse Delivered to the Students of the Royal Academy, on the Distribution of Prizes' (11 Dec 1770), in Seven Discourses Delivered in the Royal Academy (1778), 98.
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I believe television is going to be the test of the modern world, and that in this new opportunity to see beyond the range of our vision we shall discover either a new and unbearable disturbance of the general peace or a saving radiance in the sky. We shall stand or fall by television—of that I am quite sure
In 'Removal' (Jul 1938), collected in One Man's Meat (1942), 3.
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I contend that the continued racial classification of Homo sapiens represents an outmoded approach to the general problem of differentiation within a species. In other words, I reject a racial classification of humans for the same reasons that I prefer not to divide into subspecies the prodigiously variable West Indian land snails that form the subject of my own research.
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I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified. The comparative smallness of what we know today as gravitational effects is not a conclusive reason for ignoring the principle of general relativity in theoretical investigations of a fundamental character. In other words, I do not believe that it is justifiable to ask: What would physics look like without gravitation?
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I have always consistently opposed high-tension and alternating systems of electric lighting, not only on account of danger, but because of their general unreliability and unsuitability for any general system of distribution.
In 'The Dangers of Electric Lighting', North American Review (Nov 1889), 149, No. 396, 633.
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If the question were, “What ought to be the next objective in science?” my answer would be the teaching of science to the young, so that when the whole population grew up there would be a far more general background of common sense, based on a knowledge of the real meaning of the scientific method of discovering truth.
Marion Savin Selections from the Scientific Correspondence of Elihu Thomson (1971), v.
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In 1847 I gave an address at Newton, Mass., before a Teachers’ Institute conducted by Horace Mann. My subject was grasshoppers. I passed around a large jar of these insects, and made every teacher take one and hold it while I was speaking. If any one dropped the insect, I stopped till he picked it up. This was at that time a great innovation, and excited much laughter and derision. There can be no true progress in the teaching of natural science until such methods become general.
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In all matters of opinion and science ... the difference between men is ... oftener found to lie in generals than in particulars; and to be less in reality than in appearance. An explication of the terms commonly ends the controversy, and the disputants are surprised to find that they had been quarrelling, while at bottom they agreed in their judgement.
Dissertation IV, 'Of the Standard of Taste', Four Dissertations (1757), 204.
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In general, mankind, since the improvement of cookery, eat about twice as much as nature requires.
Louis Klopsch, Many Thoughts of Many Minds (1896), 67.
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In the republic of scholarship everybody wants to rule, there are no aldermen there, and that is a bad thing: every general must, so to speak, draw up the plan, stand sentry, sweep out the guardroom and fetch the water; no one wants to work for the good of another.
Aphorism 80 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 56.
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In the social production of their life, men enter into definite relations that are indispensable and independent of their will; these relations of production correspond to a definite stage of development of their material forces of production. The sum total of these relations of production constitutes the economic structure of society - the real foundation, on which rises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life determines the social, political and intellectual life process in general. It is not the consciousness of men that determines their being, but, on the contrary, their social being that determines their consciousness. At a certain stage of their development, the material productive forces in society come in conflict with the existing relations of production, or - what is but a legal expression for the same thing - with the property relations within which they have been at work before. From forms of development of the productive forces these relations turn into fetters. Then begins an epoch of social revolution. With the change of the economic foundation the entire immense superstructure is more or less rapidly transformed. In considering such transformations a distinction should always be made between the material transformation of the economic conditions of production, which can be determined with the precision of natural science, and the legal, political, religious, aesthetic or philosophic - in short, ideological forms in which men become conscious of this conflict and fight it out. Just as our opinion of an individual is not based on what he thinks of himself, so we can not judge of such a period of transformation by its own consciousness; on the contrary, this consciousness must be explained rather from the contradictions of material life, from the existing conflict between the social productive forces and the relations of production. No social order ever disappears before all the productive forces for which there is room in it have been developed; and new, higher relations of production never appear before the material conditions of their existence have matured in the womb of the old society itself. Therefore, mankind always sets itself only such tasks as it can solve; since, looking at the matter more closely, we will always find that the task itself arises only when the material conditions necessary for its solution already exist or are at least in the process of formation. In broad outlines we can designate the Asiatic, the ancient, the feudal, and the modern bourgeois modes of production as so many progressive epochs in the economic formation of society. The bourgeois relations of production are the last antagonistic form of the social process of production - antagonistic not in the sense of individual antagonism, but of one arising from the social conditions of life of the individuals; at the same time the productive forces developing in the womb of bourgeois society create the material conditions for the solution of that antagonism. This social formation constitutes, therefore, the closing chapter of the prehistoric stage of human society.
Karl Marx
…...
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Induction may be defined, the operation of discovering and proving general propositions.
In A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation (1843), Vol. 1, 347.
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Induction. The mental operation by which from a number of individual instances, we arrive at a general law. The process, according to Hamilton, is only logically valid when all the instances included in the law are enumerated. This being seldom, if ever, possible, the conclusion of an Induction is usually liable to more or less uncertainty, and Induction is therefore incapable of giving us necessary (general) truths.
Stated as narrative, not a direct quote, by his biographer W.H.S. Monck in 'Glossary of Philosophical Terms', appended in Sir William Hamilton (1881), 181.
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Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforth if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow. ... The consciousness of each of us is evolution looking at itself and reflecting upon itself....Man is not the center of the universe as once we thought in our simplicity, but something much more wonderful—the arrow pointing the way to the final unification of the world in terms of life. Man alone constitutes the last-born, the freshest, the most complicated, the most subtle of all the successive layers of life. ... The universe has always been in motion and at this moment continues to be in motion. But will it still be in motion tomorrow? ... What makes the world in which we live specifically modern is our discovery in it and around it of evolution. ... Thus in all probability, between our modern earth and the ultimate earth, there stretches an immense period, characterized not by a slowing-down but a speeding up and by the definitive florescence of the forces of evolution along the line of the human shoot.
In The Phenomenon of Man (1975), pp 218, 220, 223, 227, 228, 277.
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It has been said by a distinguished philosopher that England is “usually the last to enter into the general movement of the European mind.” The author of the remark probably meant to assert that a man or a system may have become famous on the continent, while we are almost ignorant of the name of the man and the claims of his system. Perhaps, however, a wider range might be given to the assertion. An exploded theory or a disadvantageous practice, like a rebel or a patriot in distress, seeks refuge on our shores to spend its last days in comfort if not in splendour.
Opening from essay, 'Elementary Geometry', included in The Conflict of Studies and Other Essays (1873), 136.
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It has been stated that the research should be discontinued because it involved “meddling with evolution.” Homo sapiens has been meddling with evolution in many ways and for a long time. We started in a big way when we domesticated plants and animals. We continue every time we alter the environment. In general, recombinant DNA research docs not seem to represent a significant increase in the risks associated with such meddling—although it may significantly increase the rate at which we meddle.
In letter to the Board of Directors of Friends of the Earth, published in The Coevolutionary Quarterly (Spring 1978), as abstracted and cited in New Scientist (6 Jul 1978), 35.
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It is astonishing how much the word infinitely is misused: everything is infinitely more beautiful, infinitely better, etc. The concept must have something pleasing about it, or its misuse could not have become so general.
Aphorism 133 in Notebook J (1789-1793), as translated by R. J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 155.
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It is not of the essence of mathematics to be conversant with the ideas of number and quantity. Whether as a general habit of mind it would be desirable to apply symbolic processes to moral argument, is another question.
An Investigation of the Laws of Thought (1854), 12.
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It is the function of notions in science to be useful, to be interesting, to be verifiable and to acquire value from anyone of these qualities. Scientific notions have little to gain as science from being forced into relation with that formidable abstraction, “general truth.”
In paper delivered before the Royal College of Surgeons of England (15 Feb 1932), in 'The Commemoration of Great Men', British Medical Journal (1932), 1, 32. Collected in The Collected Papers of Wilfred Trotter, FRS (1941), 29.
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Life through many long periods has been manifested in a countless host of varying structures, all circumscribed by one general plan, each appointed to a definite place, and limited to an appointed duration. On the whole the earth has been thus more and more covered by the associated life of plants and animals, filling all habitable space with beings capable of enjoying their own existence or ministering to the enjoyment of others; till finally, after long preparation, a being was created capable of the wonderful power of measuring and weighing all the world of matter and space which surrounds him, of treasuring up the past history of all the forms of life, and considering his own relation to the whole. When he surveys this vast and co-ordinated system, and inquires into its history and origin, can he be at a loss to decide whether it be a work of Divine thought and wisdom, or the fortunate offspring of a few atoms of matter, warmed by the anima mundi, a spark of electricity, or an accidental ray of sunshine?
Life on the Earth: Its Origin and Succession (1860), 216-7.
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Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
Essay,'Private Games', in Lewis Wolpert, Alison Richards (eds.), A Passion for Science (1988), 53.
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Men have called me mad; but the question is not yet settled, whether madness is or is not the loftiest intelligence—whether much that is glorious—whether all that is profound—does not spring from disease of thought—from moods of mind exalted at the expense of the general intellect.
In Eleonora (1850). Collected on The Works of the Late Edgar Allan Poe (1859), Vol. 1, 446.
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Modern cytological work involves an intricacy of detail, the significance of which can be appreciated by the specialist alone; but Miss Stevens had a share in a discovery of importance, and her work will be remembered for this, when the minutiae of detailed investigations that she carried out have become incorporated in the general body of the subject.
In obituary, 'The Scientific Work of Miss N.M. Steves', Science (11 Oct 1912), 36, No. 928, 468.
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Next to ignorance of the grammar of one’s native language, nothing betrays want of information so soon as ignorance in matters of geography, without which it is almost impossible to carry on conversation long on any general subject.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 5.
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Nobody supposes that doctors are less virtuous than judges; but a judge whose salary and reputation depended on whether the verdict was for plaintiff or defendant, prosecutor or prisoner, would be as little trusted as a general in the pay of the enemy.
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None of us knows anything, not even whether we know or do not know, nor do we know whether not knowing and knowing exist, nor in general whether there is anything or not.
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Not all living creatures die. An amoeba, for example, need never die; it need not even, like certain generals, fade away. It just divides and becomes two new amoebas.
In talk, 'Origin of Death' (1970).
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Now it came to me: … the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation. … This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.
In Paul Arthur Schilpp, 'Autobiographical Notes', Albert Einstein: Philosopher-Scientist (1949), 65-67.
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One general law, leading to the advancement of all organic beings, namely, multiply, vary, let the strongest live and the weakest die.
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Philosophers no longer write for the intelligent, only for their fellow professionals. The few thousand academic philosophers in the world do not stint themselves: they maintain more than seventy learned journals. But in the handful that cover more than one subdivision of philosophy, any given philosopher can hardly follow more than one or two articles in each issue. This hermetic condition is attributed to “technical problems” in the subject. Since William James, Russell, and Whitehead, philosophy, like history, has been confiscated by scholarship and locked away from the contamination of general use.
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Philosophy is not a science of things in general, but a science that investigates the presuppositions of experience and discovers the nature of the first principle.
Epigram to 'Philosophy in Outline', The Journal of Speculative Philosophy (Jul 1883), 17, No. 3, 296.
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Rulers and generals muster their troops. Magnates muster the sums of money which give them power. The fascist dictators muster the irrational human reactions which make it possible for them to attain and maintain their power over the masses. The scientists muster knowledge and means of research. But, thus far, no organization fighting for freedom has ever mustered the biological arsenal where the weapons are to be found for the establishment and the maintenance of human freedom. All precision of our social existence notwithstanding, there is as yet no definition of the word freedom which would be in keeping with natural science. No word is more misused and misunderstood. To define freedom is the same as to define sexual health. But nobody will openly admit this. The advocacy of personal and social freedom is connected with anxiety and guilt feelings. As if to be free were a sin or at least not quite as it should be. Sex-economy makes this guilt feeling comprehensible: freedom without sexual self-determination is in itself a contradiction. But to be sexual means—according to the prevailing human structure—to be sinful or guilty. There are very few people who experience sexual love without guilt feeling. “Free love” has acquired a degrading meaning: it lost the meaning given it by the old fighters for freedom. In films and in books, to be genital and to be criminal are presented as the same thing.
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Science is knowledge arranged and classified according to truth, facts, and the general laws of nature.
Interview in San Francisco Bulletin (22 Jan 1926). As cited in Michael C. and Linda Rose Thomsett, A Speaker's Treasury of Quotations: Maxims, Witticisms and Quips for Speeches and Presentations (2009), 102-103. Also in 'Science and Civilization', Prescott Evening Courier (3 Nov 1925), 6.
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Science, in its ultimate ideal, consists of a set of propositions arranged in a hierarchy, the lowest level of the hierarchy being concerned with particular facts, and the highest with some general law, governing everything in the universe. The various levels in the hierarchy have a two-fold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.
In The Scientific Outlook (1931, 2009), 38.
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Scientific discovery, or the formulation of scientific theory, starts in with the unvarnished and unembroidered evidence of the senses. It starts with simple observation—simple, unbiased, unprejudiced, naive, or innocent observation—and out of this sensory evidence, embodied in the form of simple propositions or declarations of fact, generalizations will grow up and take shape, almost as if some process of crystallization or condensation were taking place. Out of a disorderly array of facts, an orderly theory, an orderly general statement, will somehow emerge.
In 'Is the Scientific Paper Fraudulent?', The Saturday Review (1 Aug 1964), 42.
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Study and, in general, the pursuit of truth and beauty is a sphere of activity in which we are permitted to remain children all of our lives.
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The alternative to the Big Bang is not, in my opinion, the steady state; it is instead the more general theory of continuous creation. Continuous creation can occur in bursts and episodes. These mini-bangs can produce all the wonderful element-building that Fred Hoyle discovered and contributed to cosmology. This kind of element and galaxy formation can take place within an unbounded, non-expanding universe. It will also satisfy precisely the Friedmann solutions of general relativity. It can account very well for all the facts the Big Bang explains—and also for those devastating, contradictory observations which the Big Bang must, at all costs, pretend are not there
In 'Letters: Wrangling Over the Bang', Science News (27 Jul 1991), 140, No. 4, 51. Also quoted in Roy C. Martin, Astronomy on Trial: A Devastating and Complete Repudiation of the Big Bang Fiasco (1999), Appendix I, 217.
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The axioms of geometry are—according to my way of thinking—not arbitrary, but sensible. statements, which are, in general, induced by space perception and are determined as to their precise content by expediency.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 142.
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The contingency of history (both for life in general and for the cultures of Homo sapiens) and human free will (in the factual rather than theological sense) are conjoined concepts, and no better evidence can be produced than the ‘experimental’ production of markedly different solutions in identical environments.
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The development of civilization and industry in general has always shown itself so active in the destruction of forests that everything that has been done for their conservation and production is completely insignificant in comparison.
Karl Marx
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The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
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The effects of general change in literature are most tellingly recorded not in alteration of the best products, but in the transformation of the most ordinary workaday books; for when potboilers adopt the new style, then the revolution is complete.
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The essayist is … sustained by the childish belief that everything he thinks about, everything that happens to him, is of general interest.
First line of Foreword in Essays of E.B. White (1977, 2014), vii.
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The general mental qualification necessary for scientific advancement is that which is usually denominated “common sense,” though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts.
From presidential address (24 Nov 1877) to the Philosophical Society of Washington. As cited by L.A. Bauer in his retiring president address (5 Dec 1908), 'The Instruments and Methods of Research', published in Philosophical Society of Washington Bulletin, 15, 103. Reprinted in William Crookes (ed.) The Chemical News and Journal of Industrial Science (30 Jul 1909), 59.
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The history of acceptance of new theories frequently shows the following steps: At first the new idea is treated as pure nonsense, not worth looking at. Then comes a time when a multitude of contradictory objections are raised, such as: the new theory is too fancy, or merely a new terminology; it is not fruitful, or simply wrong. Finally a state is reached when everyone seems to claim that he had always followed this theory. This usually marks the last state before general acceptance.
In 'Field Theory and the Phase Space', collected in Melvin Herman Marx, Psychological Theory: Contemporary Readings (1951), 299.
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The laws expressing the relations between energy and matter are, however, not solely of importance in pure science. They necessarily come first in order ... in the whole record of human experience, and they control, in the last resort, the rise or fall of political systems, the freedom or bondage of nations, the movements of commerce and industry, the origin of wealth and poverty, and the general physical welfare of the race.
In Matter and Energy (1912), 10-11.
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The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.
Opening of Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree. The paper was originally published (1824) in French, as a pamphlet, in Oslo. Collected in Œuvres Complètes (1881), Vol. 1, 28. Translation by W.H. Langdon collected in David Eugene Smith, A Source Book in Mathematics (2012), 261. In this work, he showed why—despite two centuries of efforts by mathematicians—solving equations of the fifth degree would remain futile. The insights from this paper led to the modern theory of equations.
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The position in which we are now is a very strange one which in general political life never happened. Namely, the thing that I refer to is this: To have security against atomic bombs and against the other biological weapons, we have to prevent war, for if we cannot prevent war every nation will use every means that is at their disposal; and in spite of all promises they make, they will do it.
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The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren't the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown.
Interview for website of the Mathematical Association of America.
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The progress of Science consists in observing interconnections and in showing with a patient ingenuity that the events of this ever-shifting world are but examples of a few general relations, called laws. To see what is general in what is particular, and what is permanent in what is transitory, is the aim of scientific thought.
In An Introduction to Mathematics (1911), 11.
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The psychiatric interviewer is supposed to be doing three things: considering what the patient could mean by what he says; considering how he himself can best phrase what he wishes to communicate to the patient; and, at the same time, observing the general pattern of the events being communicated. In addition to that, to make notes which will be of more than evocative value, or come anywhere near being a verbatim record of what is said, in my opinion is beyond the capacity of most human beings.
From The Psychiatric Interview (1954, 1970), 48.
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The purpose of the history of science is to establish the genesis and the development of scientific facts and ideas, taking into account all intellectual exchanges and all influences brought into play by the very progress of civilization. It is indeed a history of civilization considered from its highest point of view. The center of interest is the evolution of science, but general history remains always in the background.
In The Monist (1916), 26, 333; as cited in 'The Teaching of the History of Science', The Scientific Monthly (Sep 1918), 194.
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The question of the origin of the hypothesis belongs to a domain in which no very general rules can be given; experiment, analogy and constructive intuition play their part here. But once the correct hypothesis is formulated, the principle of mathematical induction is often sufficient to provide the proof.
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), 15.
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The significance of a fact is relative to [the general body of scientific] knowledge. To say that a fact is significant in science, is to say that it helps to establish or refute some general law; for science, though it starts from observation of the particular, is not concerned essentially with the particular, but with the general. A fact, in science, is not a mere fact, but an instance. In this the scientist differs from the artist, who, if he deigns to notice facts at all, is likely to notice them in all their particularity.
In The Scientific Outlook (1931, 2009), 38.
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There are two processes which we adopt consciously or unconsciously when we try to prophesy. We can seek a period in the past whose conditions resemble as closely as possible those of our day, and presume that the sequel to that period will, save for some minor alterations, be similar. Secondly, we can survey the general course of development in our immediate past, and endeavor to prolong it into the near future. The first is the method the historian; the second that of the scientist. Only the second is open to us now, and this only in a partial sphere.
From 'Fifty Years Hence', Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57, No. 3, 393.
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There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes.
From letter to his professor Christoffer Hansteen (1826) in Oeuvres, 2, 263-65. In Morris Kline, Mathematical Thought from Ancient to Modern Times (1990), Vol. 3, 947.
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There is a finite number of species of plants and animals—even of insects—upon the earth. … Moreover, the universality of the genetic code, the common character of proteins in different species, the generality of cellular structure and cellular reproduction, the basic similarity of energy metabolism in all species and of photosynthesis in green plants and bacteria, and the universal evolution of living forms through mutation and natural selection all lead inescapably to a conclusion that, although diversity may be great, the laws of life, based on similarities, are finite in number and comprehensible to us in the main even now.
Presidential Address (28 Dec 1970) to the American Association for the Advancement of Science. 'Science: Endless Horizons or Golden Age?', Science (8 Jan 1971), 171, No. 3866, 24.
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There is no royal road to learning. But it is equally an error to confine attention to technical processes, excluding consideration of general ideas. Here lies the road to pedantry.
In An Introduction to Mathematics (1911), 8.
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They are a fairly aggressive conservation organization that was started to protect the great whales particularly, but in general all marine life around the world. So those are the people I’m trying to attach my name to.
…...
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This is really the cornerstone of our situation. Now, I believe what we should try to bring about is the general conviction that the first thing you have to abolish is war at all costs, and every other point of view must be of secondary importance.
…...
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This theme of mutually invisible life at widely differing scales bears an important implication for the ‘culture wars’ that supposedly now envelop our universities and our intellectual discourse in general ... One side of this false dichotomy features the postmodern relativists who argue that all culturally bound modes of perception must be equally valid, and that no factual truth therefore exists. The other side includes the benighted, old-fashioned realists who insist that flies truly have two wings, and that Shakespeare really did mean what he thought he was saying. The principle of scaling provides a resolution for the false parts of this silly dichotomy. Facts are facts and cannot be denied by any rational being. (Often, facts are also not at all easy to determine or specify–but this question raises different issues for another time.) Facts, however, may also be highly scale dependent–and the perceptions of one world may have no validity or expression in the domain of another. The one-page map of Maine cannot recognize the separate boulders of Acadia, but both provide equally valid representations of a factual coastline.
The World as I See It (1999)
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To derive two or three general Principles of Motion from Phænomena, and afterwards to tell us how the Properties and Actions of all corporeal Things follow from those manifest Principles, would be a very great step in Philosophy.
From 'Query 31', Opticks (1704, 2nd ed., 1718), 377.
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We are apt to consider that invention is the result of spontaneous action of some heavenborn genius, whose advent we must patiently wait for, but cannot artificially produce. It is unquestionable, however, that education, legal enactments, and general social conditions have a stupendous influence on the development of the originative faculty present in a nation and determine whether it shall be a fountain of new ideas or become simply a purchaser from others of ready-made inventions.
Epigraph, without citation, in Roger Cullisin, Patents, Inventions and the Dynamics of Innovation: A Multidisciplinary Study (2007), ix.
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We have no knowledge, that is, no general principles drawn from the contemplation of particular facts, but what has been built up by pleasure, and exists in us by pleasure alone. The Man of Science, the Chemist and Mathematician, whatever difficulties and disgusts they may have had to struggle with, know and feel this. However painful may be the objects with which the Anatomist's knowledge is connected, he feels that his knowledge is pleasure; and where he has no pleasure he has no knowledge.
In Lyrical Ballads: With Pastoral and Other Poems (3rd Ed., 1802), Vol. 1, Preface, xxxiv.
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When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home. [Coauthor with James R. Newman]
In Edward Kasner and James Newman, Mathematics and the Imagination (1940, 1949), 219.
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When we have amassed a great store of such general facts, they become the objects of another and higher species of classification, and are themselves included in laws which, as they dispose of groups, not individuals have a far superior degree of generality, till at length, by continuing the process, we arrive at axioms of the highest degree of generality of which science is capable. This process is what we mean by induction.
In A Preliminary Discourse on the Study of Natural Philosophy (1830), 102.
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When we meet a fact which contradicts a prevailing theory, we must accept the fact and abandon the theory, even when the theory is supported by great names and generally accepted.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (reprint 1999), 164.
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While the Mathematician is busy with deductions from general propositions, the Biologist is more especially occupied with observation, comparison, and those processes which lead to general propositions.
In 'On the Educational Value of the Natural History Sciences', Science and Education: Essays (1894), 57.
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Why then be concerned about the conservation of wildlife when for all practical purposes we would be much better off if humans and their domestic animals and pets were the only living creatures on the face of the earth? There is no obvious and demolishing answer to this rather doubtful logic although in practice the destruction of all wild animals would certainly bring devastating changes to our existence on this planet as we know it today...The trouble is that everything in nature is completely interdependent. Tinker with one part of it and the repercussions ripple out in all directions...Wildlife - and that includes everything from microbes to blue whales and from a fungus to a redwood tree - has been so much part of life on the earth that we are inclined to take its continued existence for granted...Yet the wildlife of the world is disappearing, not because of a malicious and deliberate policy of slaughter and extermination, but simply because of a general and widespread ignorance and neglect.
…...
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You can prepare yourself for work. The paintings of the great masters, the compositions of great musicians, the sermons of great preachers, the policies of great statesmen, and the campaigns of great generals, do not spring full bloom from barren rock. … If you are a true student you will be more dissatisfied with yourself when you graduate than you are now.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted in J.B. Collip 'Frederick Grant Banting, Discoverer of Insulin', The Scientific Monthly (May 1941), 52, No. 5, 473-474.
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You cannot do without one specialty. You must have some base-line to measure the work and attainments of others. For a general view of the subject, study the history of the sciences. Broad knowledge of all Nature has been the possession of no naturalist except Humboldt, and general relations constituted his specialty.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 146.
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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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- 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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