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Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Realm Quotes (85 quotes)

A peculiar beauty reigns in the realm of mathematics, a beauty which resembles not so much the beauty of art as the beauty of nature and which affects the reflective mind, which has acquired an appreciation of it, very much like the latter.
From Berliner Monatsberichte (1867), 395. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 185.
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A theory is a supposition which we hope to be true, a hypothesis is a supposition which we expect to be useful; fictions belong to the realm of art; if made to intrude elsewhere, they become either make-believes or mistakes.
As quoted by William Ramsay, in 'Radium and Its Products', Harper’s Magazine (Dec 1904), 52. The first part, about suppositions, appears in a paper read by G. Johnson Stoney to the American Philosophical Society, Philadelphia (3 Apr 1903), printed in 'On the Dependence of What Apparently Takes Place in Nature Upon What Actually Occurs in the Universe of Real Existences', Proceedings of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge (Apr-May 1903) 42, No. 173, 107. If you know a primary source for the part on fictions and mistakes, please contact Webmaster.
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All men and women are born, live suffer and die; what distinguishes us one from another is our dreams, whether they be dreams about worldly or unworldly things, and what we do to make them come about... We do not choose to be born. We do not choose our parents. We do not choose our historical epoch, the country of our birth, or the immediate circumstances of our upbringing. We do not, most of us, choose to die; nor do we choose the time and conditions of our death. But within this realm of choicelessness, we do choose how we live.
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All that comes above that surface [of the globe] lies within the province of Geography. All that comes below that surface lies inside the realm of Geology. The surface of the earth is that which, so to speak, divides them and at the same time “binds them together in indissoluble union.” We may, perhaps, put the case metaphorically. The relationships of the two are rather like that of man and wife. Geography, like a prudent woman, has followed the sage advice of Shakespeare and taken unto her “an elder than herself;” but she does not trespass on the domain of her consort, nor could she possibly maintain the respect of her children were she to flaunt before the world the assertion that she is “a woman with a past.”
From Anniversary Address to Geological Society of London (20 Feb 1903), 'The Relations of Geology', published in Quarterly Journal of the Geological Society of London (22 May 1903), 59, Part 2, lxxviii. As reprinted in Annual Report of the Board of Regents of the Smithsonian Institution (1904), 373.
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As an eminent pioneer in the realm of high frequency currents … I congratulate you [Nikola Tesla] on the great successes of your life’s work.
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As I look back over my efforts, I would characterize my contributions as being largely in the realm of model building. ... I perceive myself as rather uninhibited, with a certain mathematical facility and more interest in the broad aspect of a problem than the delicate nuances. I am more interested in discovering what is over the next rise than in assiduously cultivating the beautiful garden close at hand.
'Men, Mines and Molecules', Annual Review of Physical Chemistry, 1977, 28, 13.
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As modern physics started with the Newtonian revolution, so modern philosophy starts with what one might call the Cartesian Catastrophe. The catastrophe consisted in the splitting up of the world into the realms of matter and mind, and the identification of “mind” with conscious thinking. The result of this identification was the shallow rationalism of l’esprit Cartesien, and an impoverishment of psychology which it took three centuries to remedy even in part.
The Act of Creation (1964), 148.
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Beyond lonely Pluto, dark and shadowless, lies the glittering realm of interstellar space, the silent ocean that rolls on and on, past stars and galaxies alike, to the ends of the Universe. What do men know of this vast infinity, this shoreless ocean? Is it hostile or friendly–or merely indifferent?
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Even though the realms of religion and science in themselves are clearly marked off from each other, nevertheless there exist between the two strong reciprocal relationships and dependencies. Though religion may be that which determines the goal, it has, nevertheless, learned from science, in the broadest sense, what means will contribute to the attainment of the goals it has set up. But science can only be created by those who are thoroughly imbued with the aspiration toward truth and understanding. This source of feeling, however, springs from the sphere of religion. To this there also belongs the faith in the possibility that the regulations valid for the world of existence are rational, that is, comprehensible to reason. I cannot conceive of a genuine scientist without that profound faith. The situation may be expressed by an image: science without religion is lame, religion without science is blind.
From paper 'Science, Philosophy and Religion', prepared for initial meeting of the Conference on Science, Philosophy and Religion in Their Relation to the Democratic Way of Life, at the Jewish Theological Seminary of America, New York City (9-11 Sep 1940). Collected in Albert Einstein: In His Own Words (2000), 212.
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Every discoverer of a new truth, or inventor of the method which evolves it, makes a dozen, perhaps fifty, useless combinations, experiments, or trials for one successful one. In the realm of electricity or of mechanics there is no objection to this. But when such rejected failures involve a torture of animals, sometimes fearful in its character, there is a distinct objection to it.
From 'Vivisection', an original paper in Surgical Anaesthesia: Addresses, and Other Papers (1894, 1900), 369-370.
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First causes are outside the realm of science.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 66.
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However, all scientific statements and laws have one characteristic in common: they are “true or false” (adequate or inadequate). Roughly speaking, our reaction to them is “yes” or “no.” The scientific way of thinking has a further characteristic. The concepts which it uses to build up its coherent systems are not expressing emotions. For the scientist, there is only “being,” but no wishing, no valuing, no good, no evil; no goal. As long as we remain within the realm of science proper, we can never meet with a sentence of the type: “Thou shalt not lie.” There is something like a Puritan's restraint in the scientist who seeks truth: he keeps away from everything voluntaristic or emotional.
Essays in Physics (1950), 68.
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I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
Religion and Science (1935), 243.
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I picture the vast realm of the sciences as an immense landscape scattered with patches of dark and light. The goal towards which we must work is either to extend the boundaries of the patches of light, or to increase their number. One of these tasks falls to the creative genius; the other requires a sort of sagacity combined with perfectionism.
Thoughts on the Interpretation of Nature and Other Philosophical Works (1753/4), ed. D. Adams (1999), Section XIV, 42.
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I shall consider this paper an essay in geopoetry. In order not to travel any further into the realm of fantasy than is absolutely necessary I shall hold as closely as possibly to a uniformitarian approach; even so, at least one great catastrophe will be required early in the Earth's history.
'History of Ocean Basins', in A. E. J. Engel, H. L. James and B. F. Leonard (eds.), Petrologic Studies: A Volume to Honour F. Buddington (1962), 599-600.
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I think science has enjoyed an extraordinary success because it has such a limited and narrow realm in which to focus its efforts. Namely, the physical universe.
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If all history is only an amplification of biography, the history of science may be most instructively read in the life and work of the men by whom the realms of Nature have been successively won.
The Founders of Geology (1905), 4.
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If we turn our backs on things as yet untried within our own small realm of reference, we’re guilty of a sin against ourselves: An unwillingness to experiment.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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In design, people like Buckminster Fuller amazed me at the levels at which he could think. He could think molecularly. And he could think at the almost galactic scale. And the idea that somebody could actually talk about molecules and talk about buildings and structures and talk about space just amazed me. As I get older–I’ll be 60 next year–what I’ve discovered is that I find myself in those three realms too.
In interview with Kerry A. Dolan, 'William McDonough On Cradle-to-Cradle Design', Forbes (4 Aug 2010)
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In fields of air he writes his name,
And treads the chambers of the sky;
He reads the stars, and grasps the flame
That quivers in the realms on high.
In poem 'Art', collected in Samuel Kettell (ed.), Specimens of American Poetry, with Critical and Biographical Notices (1829), Vol. 3, 198.
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In mathematics it is notorious that we start from absurdities to reach a realm of law, and our whole (mathematical) conception of the world is based on a foundation which we believe to have no existence.
In The Dance of Life (1923), 86.
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In the benzene nucleus we have been given a soil out of which we can see with surprise the already-known realm of organic chemistry multiply, not once or twice but three, four, five or six times just like an equivalent number of trees. What an amount of work had suddenly become necessary, and how quickly were busy hands found to carry it out! First the eye moves up the six stems opening out from the tremendous benzene trunk. But already the branches of the neighbouring stems have become intertwined, and a canopy of leaves has developed which becomes more spacious as the giant soars upwards into the air. The top of the tree rises into the clouds where the eye cannot yet follow it. And to what an extent is this wonderful benzene tree thronged with blossoms! Everywhere in the sea of leaves one can spy the slender hydroxyl bud: hardly rarer is the forked blossom [Gabelblüte] which we call the amine group, the most frequent is the beautiful cross-shaped blossom we call the methyl group. And inside this embellishment of blossoms, what a richness of fruit, some of them shining in a wonderful blaze of color, others giving off an overwhelming fragrance.
A. W. Hofmann, after-dinner speech at Kekulé Benzolfest (Mar 1890). Trans. in W. H. Brock, O. Theodor Benfrey and Susanne Stark, 'Hofmann's Benzene Tree at the Kekulé Festivities', Journal of Chemical Education (1991), 68, 887-8.
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In the realm of science all attempts to find any evidence of supernatural beings, of metaphysical conceptions, as God, immortality, infinity, etc., thus far have failed, and if we are honest we must confess that in science there exists no God, no immortality, no soul or mind as distinct from the body.
In 'Religion and Modern Science', The Christian Register (16 Nov 1922), 101, 1089. The article is introduced as “the substance of an address to the Laymen’s League in All Soul’s Church (5 Nov 1922).
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Infidels are intellectual discoverers. They sail the unknown seas and find new isles and continents in the infinite realms of thought. An Infidel is one who has found a new fact, who has an idea of his own, and who in the mental sky has seen another star. He is an intellectual capitalist, and for that reason excites the envy and hatred of the theological pauper.
In 'The Great Infidels', The Works of Robert G. Ingersoll (1902), Vol. 3, 309.
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Inspiration in the field of science by no means plays any greater role, as academic conceit fancies, than it does in the field of mastering problems of practical life by a modern entrepreneur. On the other hand, and this also is often misconstrued, inspiration plays no less a role in science than it does in the realm of art.
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
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Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
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It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.
In J.R. Newman (ed.), 'Commentary on The Foundations of Mathematics', The World of Mathematics (1956), Vol. 3, 1614.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It is the constant attempt in this country [Canada] to make fundamental science responsive to the marketplace. Because technology needs science, it is tempting to require that scientific projects be justified in terms of the worth of the technology they can be expected to generate. The effect of applying this criterion is, however, to restrict science to developed fields where the links to technology are most evident. By continually looking for a short-term payoff we disqualify the sort of science that … attempts to answer fundamental questions, and, having answered them, suggests fundamentally new approaches in the realm of applications.
'A Scientist and the World He Lives In', Speech to the Empire Club of Canada (27 Nov 1986) in C. Frank Turner and Tim Dickson (eds.), The Empire Club of Canada Speeches 1986-1987 (1987), 149-161.
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It is, so to speak, a scientific tact, which must guide mathematicians in their investigations, and guard them from spending their forces on scientifically worthless problems and abstruse realms, a tact which is closely related to esthetic tact and which is the only thing in our science which cannot be taught or acquired, and is yet the indispensable endowment of every mathematician.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 28. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 92. From the original German, “Es ist, so zu sagen, ein wissenschaftlicher Tact, welcher die Mathematiker bei ihren Untersuchungen leiten, und sie davor bewahren muss, ihre Kräfte auf wissenschaftlich werthlose Probleme und abstruse Gebiete zu wenden, ein Tact, der dem ästhetischen nahe verwandt, das einzige ist, was in unserer Wissenschaft nicht gelehrt und gelernt werden kann, aber eine unentbehrliche Mitgift eines Mathematikers sein sollte.”
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Knowing how contented, free and joyful is life in the realms of science, one fervently wishes that many would enter their portals.
In The Principles of Chemistry (1891), Vol. 1, preface, footnote, ix, as translated from the Russian 5th edition by George Kamensky, edited by A. J. Greenaway.
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Life, forever dying to be born afresh, forever young and eager, will presently stand upon this Earth as upon a footstool, and stretch out its realm amidst the stars.
…...
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Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skilful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures.
In Werke [Kehrbach] (1890), Bd. 5, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
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Mathematics in its pure form, as arithmetic, algebra, geometry, and the applications of the analytic method, as well as mathematics applied to matter and force, or statics and dynamics, furnishes the peculiar study that gives to us, whether as children or as men, the command of nature in this its quantitative aspect; mathematics furnishes the instrument, the tool of thought, which we wield in this realm.
In Psychologic Foundations of Education (1898), 325.
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Mathematics is an infinity of flexibles forcing pure thought into a cosmos. It is an arc of austerity cutting realms of reason with geodesic grandeur.
In The American Mathematical Monthly (1949), 56, 19. Excerpted in John Ewing (ed,), A Century of Mathematics: Through the Eyes of the Monthly (1996), 186.
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Never regard study as a duty, but as the enviable opportunity to learn to know the liberating influence of beauty in the realm of the spirit for your own personal joy and to the profit of the community to which your later work belongs.
…...
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Not only did he teach by accomplishment, but he taught by the inspiration of a marvelous imagination that refused to accept the permanence of what appeared to others to be insuperable difficulties: an imagination of the goals of which, in a number of instances, are still in the realms of speculation.
Testimonial on Tesla’s 75th birthday, Tesla Museum, Belgrade, Serbia. In Margaret Cheney, Tesla: Man Out of Time (2001), 86.
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One of the great problems of philosophy, is the relationship between the realm of knowledge and the realm of values. Knowledge is what is; values are what ought to be. I would say that all traditional philosophies up to and including Marxism have tried to derive the “ought” from the “is.” My point of view is that this is impossible, this is a farce.
Quoted in John C. Hess, 'French Nobel Biologist Says World Based On Chance', New York Times (15 Mar 1971), 6. Cited in Barbara Bennett, Linda Amster, Who Said what (and When, and Where, and How) in 1971 (1972, 168.
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ORGANIC LIFE beneath the shoreless waves
Was born and nurs'd in Ocean's pearly caves;
First, forms minute, unseen by spheric glass,
Move on the mud, or pierce the watery mass;
These, as successive generations bloom,
New powers acquire, and larger limbs assume;
Whence countless groups of vegetation spring,
And breathing realms of fin, and feet, and wing.
Thus the tall Oak, the giant of the wood,
Which bears Britannia's thunders on the flood;
The Whale, unmeasured monster of the main,
The lordly Lion, monarch of the plain,
The Eagle soaring in the realms of air,
Whose eye undazzled drinks the solar glare,
Imperious man, who rules the bestial crowd,
Of language, reason, and reflection proud,
With brow erect, who scorns this earthy sod,
And styles himself the image of his God;
Arose from rudiments of form and sense,
An embryon point, or microscopic ens!
The Temple of Nature (1803), canto 1, lines 295-314, pages 26-8.
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Papyra, throned upon the banks of Nile,
Spread her smooth leaf, and waved her silver style.
The storied pyramid, the laurel’d bust,
The trophy’d arch had crumbled into dust;
The sacred symbol, and the epic song (Unknown the character, forgot the tongue,)
With each unconquer’d chief, or sainted maid,
Sunk undistinguish’d in Oblivion’s shade.
Sad o’er the scatter’d ruins Genius sigh’d,
And infant Arts but learn’d to lisp, and died.
Till to astonish’d realms Papyra taught To paint in mystic colours Sound and Thought,
With Wisdom’s voice to print the page sublime,
And mark in adamant the steps of Time.
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Poets need be in no degree jealous of the geologists. The stony science, with buried creations for its domains, and half an eternity charged with its annals, possesses its realms of dim and shadowy fields, in which troops of fancies already walk like disembodied ghosts in the old fields of Elysium, and which bid fair to be quite dark and uncertain enough for all the purposes of poesy for centuries to come.
Lecture Third, collected in Popular Geology: A Series of Lectures Read Before the Philosophical Institution of Edinburgh, with Descriptive Sketches from a Geologist's Portfolio (1859), 127.
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Religion belongs to the realm that is inviolable before the law of causation and therefore closed to science.
In Max Planck and James Vincent Murphy (trans.), Where is Science Going?, (1932), 168.
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Science would have us believe that such accuracy, leading to certainty, is the only criterion of knowledge, would make the trial of Galileo the paradigm of the two points of view which aspire to truth, would suggest, that is, that the cardinals represent only superstition and repression, while Galileo represents freedom. But there is another criterion which is systematically neglected in this elevation of science. Man does not now—and will not ever—live by the bread of scientific method alone. He must deal with life and death, with love and cruelty and despair, and so must make conjectures of great importance which may or may not be true and which do not lend themselves to experimentation: It is better to give than to receive; Love thy neighbor as thyself; Better to risk slavery through non-violence than to defend freedom with murder. We must deal with such propositions, must decide whether they are true, whether to believe them, whether to act on them—and scientific method is no help for by their nature these matters lie forever beyond the realm of science.
In The End of the Modern Age (1973), 89.
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Scientific training gives its votaries freedom from the impositions of modern quackery. Those who know nothing of the laws and processes of Nature fall an easy prey to quacks and impostors. Perfectionism in the realm of religion; a score of frauds in the realm of medicine, as electric shoe soles, hair brushes and belts, electropises, oxydonors, insulating bed casters, and the like; Christian science. In the presence of whose unspeakable stillness and self-stultifying idealism a wise man knows not whether to laugh or cry; Prof. Weltmer's magnetic treatment of disease; divine healing and miracle working by long-haired peripatetics—these and a score of other contagious fads and rank impostures find their followers among those who have no scientific training. Among their deluded victims are thousands of men and women of high character, undoubted piety, good intentions, charitable impulses and literary culture, but none trained to scientific research. Vaccinate the general public with scientific training and these epidemics will become a thing of the past.
As quoted by S.D. Van Meter, Chairman, closing remarks for 'Report of Committee on Public Policy and Legislation', to the Colorado State Medical Society in Denver, printed in Colorado Medicine (Oct 1904), 1, No. 12, 363. Van Meter used the quote following his statement, “In conclusion, allow me to urge once more the necessity of education of the public as well as the profession if we ever expect to correct the evils we are striving to reach by State and Society legislation. Much can be accomplished toward this end by the publication of well edited articles in the secular press upon medical subjects the public is eager to know about.” Prof. Weitmer is presumably Sidney A. Weltmer, founder of The Weltmer Institute of Suggestive Therapeutics, who offered a Course in Magnetic Healing by mail order correspondance (1899).
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So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us.
To the German Society of Scientists and Physicists, Braunschweig, Germany (Sep 1896). As quoted in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 20. Wiechert was reporting his measurement of the mass of the moving particles in a cathode ray beam (electrons).
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So why fret and care that the actual version of the destined deed was done by an upper class English gentleman who had circumnavigated the globe as a vigorous youth, lost his dearest daughter and his waning faith at the same time, wrote the greatest treatise ever composed on the taxonomy of barnacles, and eventually grew a white beard, lived as a country squire just south of London, and never again traveled far enough even to cross the English Channel? We care for the same reason that we love okapis, delight in the fossil evidence of trilobites, and mourn the passage of the dodo. We care because the broad events that had to happen, happened to happen in a certain particular way. And something unspeakably holy –I don’t know how else to say this–underlies our discovery and confirmation of the actual details that made our world and also, in realms of contingency, assured the minutiae of its construction in the manner we know, and not in any one of a trillion other ways, nearly all of which would not have included the evolution of a scribe to record the beauty, the cruelty, the fascination, and the mystery.
…...
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So-called “common sense” is definitely detrimental to an understanding of the quantum realm!
Anonymous
As given in an epigraph, without citation, in David M. Harland (ed.), The Big Bang: A View from the 21st Century (2003), ix.
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That atomic energy though harnessed by American scientists and army men for destructive purposes may be utilised by other scientists for humanitarian purposes is undoubtedly within the realm of possibility. … An incendiary uses fire for his destructive and nefarious purpose, a housewife makes daily use of it in preparing nourishing food for mankind.
In The Words of Gandhi (2001), 87.
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The domain of mathematics is the sole domain of certainty. There and there alone prevail the standards by which every hypothesis respecting the external universe and all observation and all experiment must be finally judged. It is the realm to which all speculation and thought must repair for chastening and sanitation, the court of last resort, I say it reverently, for all intellection whatsoever, whether of demon, or man, or deity. It is there that mind as mind attains its highest estate.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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The Earth Speaks, clearly, distinctly, and, in many of the realms of Nature, loudly, to William Jennings Bryan, but he fails to hear a single sound. The earth speaks from the remotest periods in its wonderful life history in the Archaeozoic Age, when it reveals only a few tissues of its primitive plants. Fifty million years ago it begins to speak as “the waters bring forth abundantly the moving creatures that hath life.” In successive eons of time the various kinds of animals leave their remains in the rocks which compose the deeper layers of the earth, and when the rocks are laid bare by wind, frost, and storm we find wondrous lines of ascent invariably following the principles of creative evolution, whereby the simpler and more lowly forms always precede the higher and more specialized forms.
The earth speaks not of a succession of distinct creations but of a continuous ascent, in which, as the millions of years roll by, increasing perfection of structure and beauty of form are found; out of the water-breathing fish arises the air-breathing amphibian; out of the land-living amphibian arises the land-living, air-breathing reptile, these two kinds of creeping things resembling each other closely. The earth speaks loudly and clearly of the ascent of the bird from one kind of reptile and of the mammal from another kind of reptile.
This is not perhaps the way Bryan would have made the animals, but this is the way God made them!
The Earth Speaks to Bryan (1925), 5-6. Osborn wrote this book in response to the Scopes Monkey Trial, where William Jennings Bryan spoke against the theory of evolution. They had previously been engaged in the controversy about the theory for several years. The title refers to a Biblical verse from the Book of Job (12:8), “Speak to the earth and it shall teach thee.”
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The entire cosmos is made out of one and the same world-stuff, operated by the same energy as we ourselves. “Mind” and “matter” appears as two aspects of our unitary mind-bodies. There is no separate supernatural realm: all phenomena are part of one natural process of evolution. There is no basic cleavage between science and religion; they are both organs of evolving humanity.
In essay, 'The New Divinity', originally published in The Twentieth Century (1962), 170, 9. Collected in Essays of a Humanist (1964), 218.
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The essential difference, which we meet in entering the realm of spirit and mind, seems to hang round the word “Ought.”
Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 54.
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The explorations of space end on a note of uncertainty. And necessarily so. … We know our immediate neighborhood rather intimately. With increasing distance our knowledge fades, and fades rapidly. Eventually, we reach the dim boundary—the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial. The search will continue. Not until the empirical resources are exhausted, need we pass on to the dreamy realms of speculation.
From conclusion of The Silliman Memorial Lectures Series delivered at Yale University (Fall 1935). Collected in The Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202.
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The fact that astronomies change while the stars abide is a true analogy of every realm of human life and thought, religion not least of all.
In The Living of These Days: An Autobiography (1956), 230.
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The idea of an atom has been so constantly associated with incredible assumptions of infinite strength, absolute rigidity, mystical actions at a distance, and individuality, that chemists and many other reasonable naturalists of modern times, losing all patience with it, have dismissed it to the realms of metaphysics, and made it smaller than ‘anything we can conceive.’ But if atoms are inconceivably small, why are not all chemical actions infinitely swift? Chemistry is powerless to deal with this question, and many others of paramount importance, if barred by the hardness of its fundamental assumptions, from contemplating the atom as a real portion of matter occupying a finite space, and forming not an immeasurably small constituent of any palpable body.
Sir William Thomson and Peter Guthrie Tait, A Treatise on Natural Philosophy (1883), Vol. I, Part 2, 495.
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The influence of modern physics goes beyond technology. It extends to the realm of thought and culture where it has led to a deep revision in man’s conception of the universe and his relation to it
In The Tao of Physics (1975), 17.
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The known is finite, the unknown infinite; intellectually we stand on an islet in the midst of an illimitable ocean of inexplicability. Our business in every generation is to reclaim a little more land, to add something to the extent and the solidity of our possessions. And even a cursory glance at the history of the biological sciences during the last quarter of a century is sufficient to justify the assertion, that the most potent instrument for the extension of the realm of natural knowledge which has come into men's hands, since the publication of Newton's ‘Principia’, is Darwin's ‘Origin of Species.’
From concluding remarks to a chapter by Thomas Huxley, 'On the Reception of the ‘Origin of Species’', the last chapter in Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin (1887), Vol. 1, 557.
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The major gift of science to the world is a mighty increase of power. Did science then create that power? Not a bit of it! Science discovered that power in the universe and set it free. Science found out the conditions, fulfilling which, the endless dynamic forces of the cosmos are liberated. Electricity is none of man’s making, but man has learned how to fulfill the conditions that release it. Atomic energy is a force that man did not create, but that some day man may liberate. Man by himself is still a puny animal; a gorilla is much the stronger. Man's significance lies in another realm—he knows how to fulfill conditions so that universal power not his own is set free. The whole universe as man now sees it is essentially a vast system of power waiting to be released.
In 'When Prayer Means Power', collected in Living Under Tension: Sermons On Christianity Today (1941), 78-79.
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The marriage of reason and nightmare which has dominated the 20th century has given birth to an ever more ambiguous world. Across the communications landscape move the specters of sinister technologies and the dreams that money can buy. Thermonuclear weapons systems and soft drink commercials coexist in an overlit realm ruled by advertising and pseudoevents, science and pornography. Over our lives preside the great twin leitmotifs of the 20th century—sex and paranoia.
Crash (1973, 1995), catalogue notes. In J. G. Ballard, The Kindness of Women (2007), 221.
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The mathematical take-over of physics has its dangers, as it could tempt us into realms of thought which embody mathematical perfection but might be far removed, or even alien to, physical reality. Even at these dizzying heights we must ponder the same deep questions that troubled both Plato and Immanuel Kant. What is reality? Does it lie in our mind, expressed by mathematical formulae, or is it “out there”.
In Book Review 'Pulling the Strings,' of Lawrence Krauss's Hiding in the Mirror: The Mysterious Lure of Extra Dimensions, from Plato to String Theory and Beyond in Nature (22 Dec 2005), 438, 1081.
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The more I study the things of the mind the more mathematical I find them. In them as in mathematics it is a question of quantities; they must be treated with precision. I have never had more satisfaction than in proving this in the realms of art, politics and history.
Notes made after the completion of the third chapter of Vol. 3 of La Rivolution, 22 April 1883. In E. Sparvel-Bayly (trans.), Life and Letters of H. Taine (1902-1908), Vol. 3, 239.
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The morphological characteristics of plant and animal species form the chief subject of the descriptive natural sciences and are the criteria for their classification. But not until recently has it been recognized that in living organisms, as in the realm of crystals, chemical differences parallel the variation in structure.
The Specificity of Serological Reactions (1936), 3.
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The mystic and the physicist arrive at the same conclusion; one starting from the inner realm, the other from the outer world. The harmony between their views confirms the ancient Indian wisdom that Brahman, the ultimate reality without, is identical to Atman, the reality within.
In The Tao of Physics (1975), 305.
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The Pacific coral reef, as a kind of oasis in a desert, can stand as an object lesson for man who must now learn that mutualism between autotrophic and heterotrophic components, and between producers and consumers in the societal realm, coupled with efficient recycling of materials and use of energy, are the keys to maintaining prosperity in a world of limited resources.
'The Emergence of Ecology as a New Integrative Discipline', Science (1977), 195, 1290.
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The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. … Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
In Science and the Modern World: Lowell Lectures, 1925 (1925), 31.
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The stream of human knowledge is heading towards a non-mechanical reality. The universe begins to look more like a great thought than a great machine. Mind no longer appears to be an accidental intruder into the realm of matter. We are beginning to suspect that we ought rather to hail it as the creator and governor of this realm.
The Mysterious Universe (1930), 137.
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The universality of parasitism as an offshoot of the predatory habit negatives the position taken by man that it is a pathological phenomenon or a deviation from the normal processes of nature. The pathological manifestations are only incidents in a developing parasitism. As human beings intent on maintaining man's domination over nature we may regard parasitism as pathological insofar as it becomes a drain upon human resources. In our efforts to protect ourselves we may make every kind of sacrifice to limit, reduce, and even eliminate parasitism as a factor in human life. Science attempts to define the terms on which this policy of elimination may or may not succeed. We must first of all thoroughly understand the problem, put ourselves in possession of all the facts in order to estimate the cost. Too often it has been assumed that parasitism was abnormal and that it needed only a slight force to reestablish what was believed to be a normal equilibrium without parasitism. On the contrary, biology teaches us that parasitism is a normal phenomenon and if we accept this view we shall be more ready to pay the price of freedom as a permanent and ever recurring levy of nature for immunity from a condition to which all life is subject. The greatest victory of man over nature in the physical realm would undoubtedly be his own delivery from the heavy encumbrance of parasitism with which all life is burdened.
Parasitism and Disease (1934), 4.
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There is a strange disparity between the sciences of inert matter and those of life. Astronomy, mechanics, and physics are based on concepts which can be expressed, tersely and elegantly, in mathematical language. They have built up a universe as harmonious as the monuments of ancient Greece. They weave about it a magnificent texture of calculations and hypotheses. They search for reality beyond the realm of common thought up to unutterable abstractions consisting only of equations of symbols. Such is not the position of biological sciences. Those who investigate the phenomena of life are as if lost in an inextricable jungle, in the midst of a magic forest, whose countless trees unceasingly change their place and their shape. They are crushed under a mass of facts, which they can describe but are incapable of defining in algebraic equations.
Man the Unknown (1935), 1.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
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There is no field of biological inquiry in which the influence of the Origin of Species is not traceable; the foremost men of science in every country are either avowed champions of its leading doctrines, or at any rate abstain from opposing them; a host of young and ardent investigators seek for and find inspiration and guidance in Mr. Darwin’s great work; and the general doctrine of Evolution, to one side of which it gives expression, finds in the phenomena of biology a firm base of operations whence it may conduct its conquest of the whole realm of nature.
From Lecture (19 Mar 1880) delivered at the Royal Institute 'The Coming of Age of The Origin of Species', printed in John Michels (ed.), Science (3 Jul 1880), 1, 15.
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This sceptred isle,…
This fortress built by Nature for herself…
This precious stone set in the silver sea,
Which serves it in the office of a wall
Or as a moat defensive to a house,
Against the envy of less happier lands,
This blessed plot, this earth, this realm, this England.
In Richard II, Act 2, Scene 1.
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To cosmologists that [the universe is expanding] is the most amazing scientific discovery ever made. … It’s an audacious quest that is unparalleled in human inquiry. … We have entered what once was the ethereal realm only of speculative philosophers.
As quoted in John Noble Wilford, 'Sizing up the Cosmos: An Astronomers Quest', New York Times (12 Mar 1991), C10.
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To-day, science has withdrawn into realms that are hardly understanded of the people. Biology means very largely histology, the study of the cell by difficult and elaborate microscopical processes. Chemistry has passed from the mixing of simple substances with ascertained reactions, to an experimentation of these processes under varying conditions of temperature, pressure, and electrification—all requiring complicated apparatus and the most delicate measurement and manipulation. Similarly, physics has outgrown the old formulas of gravity, magnetism, and pressure; has discarded the molecule and atom for the ion, and may in its recent generalizations be followed only by an expert in the higher, not to say the transcendental mathematics.
Anonymous
‘Exit the Amateur Scientist.’ Editorial, The Nation, 23 August 1906, 83, 160.
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Today there is a wide measure of agreement, which on the physical side of science approaches almost to unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a great machine. Mind no longer appears as an accidental intruder into the realm of matter; we are beginning to suspect that we ought rather to hail it as a creator and governor of the realm of matter. …
In The Mysterious Universe (1930, 1932), 181.
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Truth and falsity, indeed understanding, is not necessarily something purely intellectual, remote from feelings and attitudes. ... It is in the total conduct of men rather than in their statements that truth or falsehood lives, more in what a man does, in his real reaction to other men and to things, in his will to do them justice, to live at one with them. Here lies the inner connection between truth and justice. In the realm of behavior and action, the problem recurs as to the difference between piece and part.
From 'On Truth', collected in Mary Henle (ed.), Documents of Gestalt Psychology (1961), 28.
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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 do whatever we can to deny intuition of the invisible realms. We clog up our senses with smog, jam our minds with media overload. We drown ourselves in alcohol or medicate ourselves into rigidly artificial states... we take pride in our cynicism and detachment. Perhaps we are terrified to discover that our “rationality” is itself a kind of faith, an artifice, that beneath it lies the vast territory of the unknown.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 29
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We must take the abiding spiritual values which inhere in the deep experiences of religion in all ages and give them new expression in terms of the framework which our new knowledge gives us. Science forces religion to deal with new ideas in the theoretical realm and new forces in the practical realm.
Address to Seventh Annual Midsummer Conferences of Ministers and Other Christian Workers, held by Union Theological Seminary, at Columbia University gymnasium (19 Jul 1927), as quoted in 'Fosdick Sees Bible Outrun by Science', New York Times (20 Jul 1927), 23.
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What we see in history is not a transformation, a passing of one race into another, but entirely new and perfect creations, which the ever-youthful productivity of nature sends forth from the invisible realm of Hades.
Translated from Das Besdändige in den Menschenrassen und die Spielweite ihrer Veränderlichkeit (1868), 26. As cited, with quotation marks, in Houston Stewart Chamberlain, The Foundations of the Nineteenth Century (1911), Vol. 1, 272. Note: Webmaster cannot find and recognize the original quote in German in the Bastian source book, and especially cannot find it on page 26.
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When I worked on the polio vaccine, I had a theory. Experiments were done to determine what might or might not occur. I guided each one by imagining myself in the phenomenon in which I was interested. The intuitive realm is constantly active—the realm of imagination guides my thinking.
From interview with James Reston, Jr., in Pamela Weintraub (ed.), The Omni Interviews (1984), 98. Previously published in magazine, Omni (May 1982).
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When the solution is simple, God is answering. Where the world ceases to be the scene of our personal hopes and wishes, where we face it as free beings admiring, asking and observing, there we enter the realm of Art and Science.
…...
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Where the world ceases to be the scene of our personal hopes and wishes, where we face it as free beings admiring, asking and observing, there we enter the realm of Art and Science. If what is seen is seen and experienced is portrayed in the language of logic, we are engaged in science. If it is communicated through forms whose connections are not accessible to the conscious mind but are recognized intuitively as meaningful, then we are engaged in art.
'What Artistic and Scientific Experience Have in Common', Menschen (27 Jan 1921). In Albert Einstein, Helen Dukas, Banesh Hoffmann, Albert Einstein, The Human Side (1981), 37-38. The article was published in a German magazine on modern art, upon a request from the editor, Walter Hasenclever, for a few paragraphs on the idea that there was a close connection between the artistic developments and the scientific results belonging to a given epoch. (The magazine name, and editor's name are given by Ze'ev Rosenkranz, The Einstein Scrapbook (2002), 27.
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[In] the realm of science, … what we have achieved will be obsolete in ten, twenty or fifty years. That is the fate, indeed, that is the very meaning of scientific work. … Every scientific “fulfillment” raises new “questions” and cries out to be surpassed and rendered obsolete. Everyone who wishes to serve science has to resign himself to this.
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As translated by Rodney Livingstone in David Owen (ed.), The Vocation Lectures: Science as a Vocation: Politics as a Vocation (2004), 11. A different translation of a longer excerpt for this quote, beginning “In science, each of us knows …”, is also on the Max Weber Quotes web page on this site.
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[L]et us not overlook the further great fact, that not only does science underlie sculpture, painting, music, poetry, but that science is itself poetic. The current opinion that science and poetry are opposed is a delusion. ... On the contrary science opens up realms of poetry where to the unscientific all is a blank. Those engaged in scientific researches constantly show us that they realize not less vividly, but more vividly, than others, the poetry of their subjects. Whoever will dip into Hugh Miller's works on geology, or read Mr. Lewes's “Seaside Studies,” will perceive that science excites poetry rather than extinguishes it. And whoever will contemplate the life of Goethe will see that the poet and the man of science can co-exist in equal activity. Is it not, indeed, an absurd and almost a sacrilegious belief that the more a man studies Nature the less he reveres it? Think you that a drop of water, which to the vulgar eye is but a drop of water, loses anything in the eye of the physicist who knows that its elements are held together by a force which, if suddenly liberated, would produce a flash of lightning? Think you that what is carelessly looked upon by the uninitiated as a mere snow-flake, does not suggest higher associations to one who has seen through a microscope the wondrously varied and elegant forms of snow-crystals? Think you that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of a geologist, who knows that over this rock a glacier slid a million years ago? The truth is, that those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedge-rows can assume. Whoever has not sought for fossils, has little idea of the poetical associations that surround the places where imbedded treasures were found. Whoever at the seaside has not had a microscope and aquarium, has yet to learn what the highest pleasures of the seaside are. Sad, indeed, is it to see how men occupy themselves with trivialities, and are indifferent to the grandest phenomena—care not to understand the architecture of the Heavens, but are deeply interested in some contemptible controversy about the intrigues of Mary Queen of Scots!—are learnedly critical over a Greek ode, and pass by without a glance that grand epic written by the finger of God upon the strata of the Earth!
Education: Intellectual, Moral, and Physical (1889), 82-83.
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[The surplus of basic knowledge of the atomic nucleus was] largely used up [during the war with the atomic bomb as the dividend.] We must, without further delay restore this surplus in preparation for the important peacetime job for the nucleus - power production. ... Many of the proposed applications of atomic power - even for interplanetary rockets - seem to be within the realm of possibility provided the economic factor is ruled out completely, and the doubtful physical and chemical factors are weighted heavily on the optimistic side. ... The development of economic atomic power is not a simple extrapolation of knowledge gained during the bomb work. It is a new and difficult project to reach a satisfactory answer. Needless to say, it is vital that the atomic policy legislation now being considered by the congress recognizes the essential nature of this peacetime job, and that it not only permits but encourages the cooperative research-engineering effort of industrial, government and university laboratories for the task. ... We must learn how to generate the still higher energy particles of the cosmic rays - up to 1,000,000,000 volts, for they will unlock new domains in the nucleus.
Addressing the American Institute of Electrical Engineering, in New York (24 Jan 1946). In Schenectady Gazette (25 Jan 1946),
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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 -
Pierre Fermat
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- 30 -
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- 20 -
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- 10 -
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