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Theory Quotes (682 quotes)


'Unless,' said I [Socrates], either philosophers become kings in our states or those whom we now call our kings:. and rulers take to the pursuit of' philosophy seriously and adequately, and there is a conjunction of these two things, political power and philosophic intelligence, while the motley horde of the natures who at present pursue either apart from the other are compulsorily excluded, there can be no cessation of troubles, dear Glaucon, for our states, nor, I fancy for the human race either. Nor, until this happens, will this constitution which we have been expounding in theory ever be put into practice within the limits of possibility and see the light of the sun.
Plato
The Republic 5 474ce, trans. P. Shorey (1930), Vol. 1, Book 5, 509.
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... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself … A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.
'Operational Definition and Analogy in Physical Theories', British Journal for the Philosophy of Science (Feb 1952), 2, No. 8, 291.
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... there is an external world which can in principle be exhaustively described in scientific language. The scientist, as both observer and language-user, can capture the external facts of the world in prepositions that are true if they correspond to the facts and false if they do not. Science is ideally a linguistic system in which true propositions are in one-to-one relation to facts, including facts that are not directly observed because they involve hidden entities or properties, or past events or far distant events. These hidden events are described in theories, and theories can be inferred from observation, that is the hidden explanatory mechnism of the world can be discovered from what is open to observation. Man as scientist is regarded as standing apart from the world and able to experiment and theorize about it objectively and dispassionately.
'Introduction', Revolutions and Reconstructions in the Philosophy of Science (1981), xii. In John Templeton and Robert L. Herrmann, Is God the Only Reality (1994), 11-12.
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...scientific theory is a contrived foothold in the chaos of living phenomena.
Function of the Orgasm
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Dilbert: It took weeks but I’ve calculated a new theory about the origin of the universe. According to my calculations it didn’t start with a “Big Bang” at all—it was more of “Phhbwt” sound. You may be wondering about the practical applications of the “Little Phhbwt” theory.
Dogbert: I was wondering when you’ll go away.
Dilbert comic strip (1 Jan 1993)
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Dilbert: You joined the “Flat Earth Society?”
Dogbert: I believe the earth must be flat. There is no good evidence to support the so-called “round earth theory.”
Dilbert: I think Christopher Columbus would disagree.
Dogbert: How convenient that your best witness is dead.
Dilbert comic strip (9 Oct 1989).
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Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. Kepler is said to have discovered the laws of planetary motion named after him, but no the many other 'laws' which he formulated. ... Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge.
Discovery in the Physical Sciences (1969). In Rodney P. Carlisle, Scientific American Inventions and Discoveries (2004), 179.
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Dogbert: So, Since Columbus is dead, you have no evidence that the earth is round.
Dilbert: Look. You can Ask Senator John Glenn. He orbited the earth when he was an astronaut.
Dogbert: So, your theory depends on the honesty of politicians.
Dilbert: Yes... no, wait...
Dilbert comic strip (10 Oct 1989).
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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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La théorie des séries infinies en général est justqu’à présent très mal fondée. On applique aux séries infinies toutes les opérations, come si elles aient finies; mais cela est-il bien permis? Je crois que non. Où est-il démonstré qu/on ontient la différentielle dune série infinie en prenant la différentiaella de chaque terme. Rien n’est plus facile que de donner des exemples où cela n’est pas juste.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
Quoted in Reinhold Remmert and Robert B. Burckel, Theory of Complex Functions: Readings in Mathematics (1991), 125.
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La théorie est l’hypothèse vérifiée, après qu’elle a été soumise au contrôle du raisonnement et de la critique expérimentale. La meilleure théorie est celle qui a été vérifiée par le plus grand nombre de faits. Mais une théorie, pour rester bonne, doit toujours se modifier avec les progrès de la science et demeurer constamment soumise à la vérification et à la critique des faits nouveaux qui apparaissent.
A theory is a verified hypothesis, after it has been submitted to the control of reason and experimental criticism. The soundest theory is one that has been verified by the greatest number of facts. But to remain valid, a theory must be continually altered to keep pace with the progress of science and must be constantly resubmitted to verification and criticism as new facts appear.
Original work in French, Introduction à l'Étude de la Médecine Expérimentale (1865), 385. English translation by Henry Copley Green in An Introduction to the Study of Experimental Medicine (1927, 1957), 220.
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La théorie n’est que l’idée scientifique contrôlée par l’expérience.
A theory is merely a scientific idea controlled by experiment.
Original work in French, Introduction à l'Étude de la Médecine Expérimentale (1865), 40. English translation by Henry Copley Green in An Introduction to the Study of Experimental Medicine (1927, 1957), 26.
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Les médecins les plus savans en théorie sont rarement les plus habile practiciens.
The doctors most learned in theory are seldom the most skilled practitioners.
Maxim No. 281 in Maximes, Réflexions et Pensées Diverses (1819), 236.
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Nous avons l’obligation aux Anciens de nous avoir épuisé la plus grande partie des idées fausses qu’on le pouvait faire
We are under obligation to the ancients for having exhausted all the false theories that could be formed.
In Digression sur les Anciens et les Modernes (1688), 165. Collected in Oeuvres Diverses (1727), Vol. 3, 139. English version as quoted in John Bagnell Bury, The Idea of Progress: An Inquiry Into Its Origin and Growth (1920), 104.
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Ron Hutcheson, a Knight-Ridder reporter: [Mr. President, what are your] personal views [about the theory of] intelligent design?
President George W. Bush: [Laughing. You're] doing a fine job of dragging me back to the past [days as governor of Texas]. ... Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught...”
Hutcheson: Both sides ought to be properly taught?
President: Yes ... so people can understand what the debate is about.
Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?
President: I think that part of education is to expose people to different schools of thought, and I'm not suggesting—you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.
Hutcheson: So we've got to give these groups—...
President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]
From conversation with reporters at the White House (1 Aug 2005), as quoted by Matthew Cooper in 'Fanning the Controversy Over “Intelligent Design”', Time (3 Aug 2005). The Time writer stated, “The president has gone farther in questioning the widely-taught theories of evolution and natural selection than any president since Ronald Reagan, who advocated teaching creationism in public schools alongside evolution.” Just a few months later, in the nation's first case on that point, on 20 Dec 2005, “a federal judge [John E. Jones] ruled it was unconstitutional for a Pennsylvania school district to present intelligent design as an alternative in high school biology courses, because it is a religious viewpoint,” as reported by Laurie Goodstein in 'Judge Rejects Teaching Intelligent Design', New York Times (21 Dec 2005). Goodstein also wrote “Judge Jones, a Republican appointed by President Bush, concluded that intelligent design was not science,” and that “the evidence in the trial proved that intelligent design was 'creationism relabeled.' The Supreme Court has already ruled that creationism ... cannot be taught as science in a public school.”
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Une même expression, dont les géomètres avaient considéré les propriétés abstraites, … représente'aussi le mouvement de la lumière dans l’atmosphère, quelle détermine les lois de la diffusion de la chaleur dans la matière solide, et quelle entre dans toutes les questions principales de la théorie des probabilités.
The same expression whose abstract properties geometers had considered … represents as well the motion of light in the atmosphere, as it determines the laws of diffusion of heat in solid matter, and enters into all the chief problems of the theory of probability.
From Théorie Analytique de la Chaleur (1822), translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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Von Theorie wild man nicht heller.
Gott geb' täglich unsern Teller.

When theory's light is less than stellar.
Give us, O Lord, our daily Teller.
This rhyme from an alphabet ditty describing various physicists was written for a party at Göttingen.
Quoted in Edward Teller with Judith L. Shoolery, Memoirs: A Twentieth-Century Journey in Science and Politics (2001), 75. The first clause, translated more literally than poetically, is given as, 'When theory does not enlighten us,' in Nina Byers and Gary Williams, Out of the Shadows (2006),130.
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Wenn uns alle einzelnen Thatsachen, alle einzelnen Erscheinungen unmittelbar zugänglich wären, so wie wir nach der Kenntniss derselben verlangen; so wäre nie eine Wissenschaft entstanden.
If all the individual facts, all the individual phenomena, were directly accessible to us, as we ask for the knowledge of them; no science would ever have arisen.
From original German in Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit (1872), 30-31. English translation by Webmaster using Google translate until it made sense. Also found translated as “If all single facts, all separate phenomena, were as directly accessible to us as we demand that knowledge of them to be; science would never have arisen,” in Ernst Cassirer, The Problem of Knowledge: Philosophy, Science, and History since Hegel (1950), 108. Citing from
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[In refutation of evolution] There is not enough evidence, consistent evidence to make it as fact, and I say that because for theory to become a fact, it needs to consistently have the same results after it goes through a series of tests. The tests that they put—that they use to support evolution do not have consistent results. Now too many people are blindly accepting evolution as fact. But when you get down to the hard evidence, it’s merely a theory.
[In favor of the teaching of creationism alongside evolution in schools.]
From interview by Miles O'Brien on CNN (30 Mar 1996). Reported from transcript, via Nexis, in New York Magazine (15 Sep 2010).
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A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.
'On the Development of the Methods of Theoretical Physics in Recent Times', Populäre Schriften, Essay 14. Address to the Meeting of Natural Scientists at Munich, 22 September 1899. In Brian McGuinness (ed.), Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, Selected Writings (1974), 79.
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A complete theory of evolution must acknowledge a balance between ‘external’ forces of environment imposing selection for local adaptation and ‘internal’ forces representing constraints of inheritance and development. Vavilov placed too much emphasis on internal constraints and downgraded the power of selection. But Western Darwinians have erred equally in practically ignoring (while acknowledging in theory) the limits placed on selection by structure and development–what Vavilov and the older biologists would have called ‘laws of form.’
…...
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A conceptual scheme is never discarded merely because of a few stubborn facts with which it cannot be reconciled; a conceptual scheme is either modified or replaced by a better one, never abandoned with nothing left to take its place.
Science and Common Sense (1951), 173.

A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.
Science and the Common Understanding (1954), 53-4.
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A discovery is generally an unforeseen relation not included in theory.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 38.
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A formative influence on my undergraduate self was the response of a respected elder statesmen of the Oxford Zoology Department when an American visitor had just publicly disproved his favourite theory. The old man strode to the front of the lecture hall, shook the American warmly by the hand and declared in ringing, emotional tones: ‘My dear fellow, I wish to thank you. I have been wrong these fifteen years.’ And we clapped our hands red. Can you imagine a Government Minister being cheered in the House of Commons for a similar admission? “Resign, Resign” is a much more likely response!
…...
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A good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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A man who is all theory is like “a rudderless ship on a shoreless sea.” ... Theories and speculations may be indulged in with safety only as long as they are based on facts that we can go back to at all times and know that we are on solid ground.
In Nature's Miracles: Familiar Talks on Science (1899), Vol. 1, Introduction, vii.
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A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.
…...
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A metaphysical conclusion is either a false conclusion or a concealed experimental conclusion.
'On Thought in Medicine' (1877). Trans. E. Atkinson, Popular Lectures on Scientific Subjects (1881), 234.
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A new theory is guilty until proven innocent, and the pre-existing theory innocent until proven guilty ... Continental drift was guilty until proven innocent.
The Nemesis Affair: A Story of the Death of the Dinosaurs and the Ways of Science (1986), 195-205.
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A physical theory remains an empty shell until we have found a reasonable physical interpretation.
At the 4th Soviet Gravitational Conference, Minsk, USSR (Jul 1976). Quoted in Anton Z. Capri, From Quanta to Quarks: More Anecdotal History of Physics (2007), 120.
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A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: “... this principle”, says Reichenbach, “determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.” Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds.
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A scientifically unimportant discovery is one which, however true and however interesting for other reasons, has no consequences for a system of theory with which scientists in that field are concerned.
The Structure of Social Action (1937), Vol. 1, 7.
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A taxonomy of abilities, like a taxonomy anywhere else in science, is apt to strike a certain type of impatient student as a gratuitous orgy of pedantry. Doubtless, compulsions to intellectual tidiness express themselves prematurely at times, and excessively at others, but a good descriptive taxonomy, as Darwin found in developing his theory, and as Newton found in the work of Kepler, is the mother of laws and theories.
From Intelligence: Its Structure, Growth and Action: Its Structure, Growth and Action (1987), 61.
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A theory can be proved by experiment; but no path leads from experiment to the birth of a theory.
As quoted in Antonina Vallentin, Einstein: A Biography (1954), 105. The author, a close friend of Einstein’s family, cites the quote only as “which he has recently made public.”
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A theory has only the alternative of being right or wrong. A model has a third possibility: it may be right, but irrelevant.
Manfred Eigen, 'The Origin of Biological Information', in Jagdish Mehra (ed.), The Physicists's Conception of Nature (1973), 618.
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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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A theory is scientific only if it can be disproved. But the moment you try to cover absolutely everything the chances are that you cover nothing.
From Assumption and Myth in Physical Theory (1967), 12.
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A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown.
Autobiographical Notes (1946), 33. Quoted in Gerald Holton and Yehuda Elkana, Albert Einstein: Historical and Cultural Perspectives (1997), 227.
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A theory that you can’t explain to a bartender is probably no damn good.
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A theory which cannot be mortally endangered cannot be alive.
Personal communication quoted by John R. Platt in 'Science, Strong Inference', Science (16 Oct 1964), 146, No. 3642, 349.
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A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.
In Scientific American (May 1963). As quoted and cited in The Hutchinson Encyclopedia of Science (1998), 468.
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A … difference between most system-building in the social sciences and systems of thought and classification of the natural sciences is to be seen in their evolution. In the natural sciences both theories and descriptive systems grow by adaptation to the increasing knowledge and experience of the scientists. In the social sciences, systems often issue fully formed from the mind of one man. Then they may be much discussed if they attract attention, but progressive adaptive modification as a result of the concerted efforts of great numbers of men is rare.
The Study of Man (1941), 19-20.
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About thirty years ago there was much talk that geologists ought only to observe and not theorise; and I well remember some one saying that at this rate a man might as well go into a gravel-pit and count the pebbles and describe the colours. How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!
Letter to Henry Fawcett (18 Sep 1861). In Charles Darwin, Francis Darwin, Albert Charles Seward, More Letters of Charles Darwin (1903), Vol. 1, 195.
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According to the theory of aerodynamics, as may be readily demonstrated through wind tunnel experiments, the bumblebee is unable to fly. This is because the size, weight and shape of his body in relation to the total wingspread make flying impossible. But the bumblebee, being ignorant of these scientific truths, goes ahead and flies anyway—and makes a little honey every day.
Anonymous
Sign in a General Motors Corporation factory. As quoted in Ralph L. Woods, The Businessman's Book of Quotations (1951), 249-50. Cited in Suzy Platt (ed)., Respectfully Quoted: A Dictionary of Quotations (1989), 118.
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After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Atombau und Spektrallinien (1919), viii, Atomic Structure and Spectral Lines, trans. Henry L. Brose (1923), viii.
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After … the general experimental knowledge has been acquired, accompanied with just a sufficient amount of theory to connect it together…, it becomes possible to consider the theory by itself, as theory. The experimental facts then go out of sight, in a great measure, not because they are unimportant, but because … they are fundamental, and the foundations are always hidden from view in well-constructed buildings.
In Electromagnetic Theory (1892), Vol. 2, 1.
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All good intellects have repeated, since Bacon’s time, that there can be no real knowledge but that which is based on observed facts. This is incontestable, in our present advanced stage; but, if we look back to the primitive stage of human knowledge, we shall see that it must have been otherwise then. If it is true that every theory must be based upon observed facts, it is equally true that facts cannot be observed without the guidance of some theory. Without such guidance, our facts would be desultory and fruitless; we could not retain them: for the most part we could not even perceive them.
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 3-4.
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All interesting issues in natural history are questions of relative frequency, not single examples. Everything happens once amidst the richness of nature. But when an unanticipated phenomenon occurs again and again–finally turning into an expectation–then theories are overturned.
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All science has one aim, namely, to find a theory of nature.
In Nature (1849), 2.
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All scientific theories are provisional and may be changed, but ... on the whole, they are accepted from Washington to Moscow because of their practical success. Where religion has opposed the findings of science, it has almost always had to retreat.
Essay 'Science Will Never Give Us the Answers to All Our Questions', collected in Henry Margenau, and Roy Abraham Varghese (eds.), Cosmos, Bios, Theos (1992), 65.
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All that stuff I was taught about evolution, embryology, Big Bang theory, all that is lies straight from the pit of hell. It’s lies to try to keep me and all the folks who are taught that from understanding that they need a savior.
[Revealing his anti-science views, contrary to the qualifications needed to make important public policy on matters of science.]
From speech (27 Sep 2012) to a sportman's banquet at Liberty Baptist Church, Hartwell, Georgia, as quoted in Matt Pearce, 'U.S. Rep. Paul Broun: Evolution a lie ‘from the pit of hell’', Los angeles Times (7 Oct 2012).
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Almost everyone... seems to be quite sure that the differences between the methodologies of history and of the natural sciences are vast. For, we are assured, it is well known that in the natural sciences we start from observation and proceed by induction to theory. And is it not obvious that in history we proceed very differently? Yes, I agree that we proceed very differently. But we do so in the natural sciences as well.
In both we start from myths—from traditional prejudices, beset with error—and from these we proceed by criticism: by the critical elimination of errors. In both the role of evidence is, in the main, to correct our mistakes, our prejudices, our tentative theories—that is, to play a part in the critical discussion, in the elimination of error. By correcting our mistakes, we raise new problems. And in order to solve these problems, we invent conjectures, that is, tentative theories, which we submit to critical discussion, directed towards the elimination of error.
The Myth of the Framework: In Defence of Science and Rationality (1993), 140.
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An enthusiastic philosopher, of whose name we are not informed, had constructed a very satisfactory theory on some subject or other, and was not a little proud of it. “But the facts, my dear fellow,” said his friend, “the facts do not agree with your theory.”—“Don't they?” replied the philosopher, shrugging his shoulders, “then, tant pis pour les faits;”—so much the worse for the facts!
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 313, footnote.
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An old French geometer used to say that a mathematical theory was never to be considered complete till you had made it so clear that you could explain it to the first man you met in the street.
In Nature (1873), 8, 458.
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And yet I think that the Full House model does teach us to treasure variety for its own sake–for tough reasons of evolutionary theory and nature’s ontology, and not from a lamentable failure of thought that accepts all beliefs on the absurd rationale that disagreement must imply disrespect. Excellence is a range of differences, not a spot. Each location on the range can be occupied by an excellent or an inadequate representative– and we must struggle for excellence at each of these varied locations. In a society driven, of ten unconsciously, to impose a uniform mediocrity upon a former richness of excellence–where McDonald’s drives out the local diner, and the mega-Stop & Shop eliminates the corner Mom and Pop–an understanding and defense of full ranges as natural reality might help to stem the tide and preserve the rich raw material of any evolving system: variation itself.
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Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of facts will certainly reject my theory.
The Origin of Species (1859), 482.
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Any theory is better than no theory.
In Barry G. Firkin, Judith A. Whitworth, Dictionary of Medical Eponyms (1996), 5.

Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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Anyone who has examined into the history of the theories of earth evolution must have been astounded to observe the manner in which the unique and the difficultly explainable has been made to take the place of the common and the natural in deriving the framework of these theories.
Earth Evolution and Facial Expression (1921), 174.
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Anything at all that can be the object of scientific thought becomes dependent on the axiomatic method, and thereby indirectly on mathematics, as soon as it is ripe for the formation of a theory. By pushing ahead to ever deeper layers of axioms … we become ever more conscious of the unity of our knowledge. In the sign of the axiomatic method, mathematics is summoned to a leading role in science.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zürich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1115.
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Architects who have aimed at acquiring manual skill without scholarship have never been able to reach a position of authority to correspond to their pains, while those who relied only upon theories and scholarship were obviously hunting the shadow, not the substance. But those who have a thorough knowledge of both, like men armed at all points, have the sooner attained their object and carried authority with them.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 3.
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As every circumstance relating to so capital a discovery as this (the greatest, perhaps, that has been made in the whole compass of philosophy, since the time of Sir Isaac Newton) cannot but give pleasure to all my readers, I shall endeavour to gratify them with the communication of a few particulars which I have from the best authority. The Doctor [Benjamin Franklin], after having published his method of verifying his hypothesis concerning the sameness of electricity with the matter lightning, was waiting for the erection of a spire in Philadelphia to carry his views into execution; not imagining that a pointed rod, of a moderate height, could answer the purpose; when it occurred to him, that, by means of a common kite, he could have a readier and better access to the regions of thunder than by any spire whatever. Preparing, therefore, a large silk handkerchief, and two cross sticks, of a proper length, on which to extend it, he took the opportunity of the first approaching thunder storm to take a walk into a field, in which there was a shed convenient for his purpose. But dreading the ridicule which too commonly attends unsuccessful attempts in science, he communicated his intended experiment to no body but his son, who assisted him in raising the kite.
The kite being raised, a considerable time elapsed before there was any appearance of its being electrified. One very promising cloud passed over it without any effect; when, at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he inmmediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute, and when the rain had wetted the string, he collected electric fire very copiously. This happened in June 1752, a month after the electricians in France had verified the same theory, but before he had heard of any thing that they had done.
The History and Present State of Electricity, with Original Experiments (1767, 3rd ed. 1775), Vol. 1, 216-7.
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As far as I see, such a theory [of the primeval atom] remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being. He may keep, for the bottom of space-time, the same attitude of mind he has been able to adopt for events occurring in non-singular places in space-time. For the believer, it removes any attempt to familiarity with God, as were Laplace's chiquenaude or Jeans' finger. It is consonant with the wording of Isaiah speaking of the 'Hidden God' hidden even in the beginning of the universe ... Science has not to surrender in face of the Universe and when Pascal tries to infer the existence of God from the supposed infinitude of Nature, we may think that he is looking in the wrong direction.
'The Primeval atom Hypothesis and the Problem of Clusters of Galaxies', in R. Stoops (ed.), La Structure et l'Evolution de l'Univers (1958), 1-32. Trans. Helge Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (1996), 60.
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As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
President’s address (1883) to the British Association for the Advancement of Science, in The Collected Mathematical Papers (1895), Vol. 8, xxii.
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As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.
Collected Works (1877), Vol. 5, 25-26. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 412.
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As soon … as it was observed that the stars retained their relative places, that the times of their rising and setting varied with the seasons, that sun, moon, and planets moved among them in a plane, … then a new order of things began.… Science had begun, and the first triumph of it was the power of foretelling the future; eclipses were perceived to recur in cycles of nineteen years, and philosophers were able to say when an eclipse was to be looked for. The periods of the planets were determined. Theories were invented to account for their eccentricities; and, false as those theories might be, the position of the planets could be calculated with moderate certainty by them.
Lecture delivered to the Royal Institution (5 Feb 1864), 'On the Science of History'. Collected in Notices of the Proceedings at the Meetings of the Members of the Royal Institution of Great Britain with Abstracts of the Discourses (1866), Vol. 4, 187.
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As usual, nature’s imagination far surpasses our own, as we have seen from the other theories which are subtle and deep.
In The Character of Physical Law (1965, 2001), 162.
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Astronomy was thus the cradle of the natural sciences and the starting point of geometrical theories. The stars themselves gave rise to the concept of a ‘point’; triangles, quadrangles and other geometrical figures appeared in the constellations; the circle was realized by the disc of the sun and the moon. Thus in an essentially intuitive fashion the elements of geometrical thinking came into existence.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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Astrophysicists closing in on the grand structure of matter and emptiness in the universe are ruling out the meatball theory, challenging the soap bubble theory, and putting forward what may be the strongest theory of all: that the cosmos is organized like a sponge.
'Rethinking Clumps and Voids in the Universe', New York Times (9 Nov 1986), A1.
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Be suspicious of a theory if more and more hypotheses are needed to support it as new facts become available, or as new considerations are brought to bear.
Given as the authors’ preferred interpretation of Ockham’s Razor. With co-author Nalin Chandra Wickramasinghe, Evolution from Space (1981), 135.
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Bertrand, Darboux, and Glaisher have compared Cayley to Euler, alike for his range, his analytical power, and, not least, for his prolific production of new views and fertile theories. There is hardly a subject in the whole of pure mathematics at which he has not worked.
In Proceedings of London Royal Society (1895), 58, 21.
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Besides electrical engineering theory of the transmission of messages, there is a larger field [cybernetics] which includes not only the study of language but the study of messages as a means of controlling machinery and society, the development of computing machines and other such automata, certain reflections upon psychology and the nervous system, and a tentative new theory of scientific method.
In Cybernetics (1948).
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Biological determinism is, in its essence, a theory of limits. It takes the current status of groups as a measure of where they should and must be ... We inhabit a world of human differences and predilections, but the extrapolation of these facts to theories of rigid limits is ideology.
The Mismeasure of Man (1981), 28-9.
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Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime.
In Radio Lecture (30 Jun 1973) broadcast by the Open University, collected in Imre Lakatos, John Worrall (ed.) and Gregory Currie (ed.), 'Introduction: Science and Pseudoscience', The Methodology of Scientific Research Programmes (1978, 1980), Vol. 1, 1.
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Buffon, who, with all his theoretical ingenuity and extraordinary eloquence, I suspect had little actual information in the science on which he wrote so admirably For instance, he tells us that the cow sheds her horns every two years; a most palpable error. ... It is wonderful that Buffon who lived so much in the country at his noble seat should have fallen into such a blunder I suppose he has confounded the cow with the deer.
In The Life of Samuel Johnson, LL.D. (1826), Vol. 3, 70, footnote.
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But although in theory physicists realize that their conclusions are ... not certainly true, this ... does not really sink into their consciousness. Nearly all the time ... they ... act as if Science were indisputably True, and what's more, as if only science were true.... Any information obtained otherwise than by the scientific method, although it may be true, the scientists will call “unscientific,” using this word as a smear word, by bringing in the connotation from its original [Greek] meaning, to imply that the information is false, or at any rate slightly phony.
In Science is a Sacred Cow (1950), 176-77.
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But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
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But no other theory can explain so much. Continental drift is without a cause or a physical theory. It has never been applied to any but the last part of geological time.
In 'Geophysics and Continental Growth', American Scientist (1959), 47, 23.
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But, contrary to the lady’s prejudices about the engineering profession, the fact is that quite some time ago the tables were turned between theory and applications in the physical sciences. Since World War II the discoveries that have changed the world are not made so much in lofty halls of theoretical physics as in the less-noticed labs of engineering and experimental physics. The roles of pure and applied science have been reversed; they are no longer what they were in the golden age of physics, in the age of Einstein, Schrödinger, Fermi and Dirac.
'The Age of Computing: a Personal Memoir', Daedalus (1992), 121, 120.
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By an application of the theory of relativity to the taste of readers, today in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!
Times (28 Nov 1919). In Robert Andrews Famous Lines: a Columbia Dictionary of Familiar Quotations (1997), 414. Variations of this quote were made by Einstein on other occasions.
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Chaos theory is a new theory invented by scientists panicked by the thought that the public were beginning to understand the old ones.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 273.
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Chemistry and physics are experimental sciences; and those who are engaged in attempting to enlarge the boundaries of science by experiment are generally unwilling to publish speculations; for they have learned, by long experience, that it is unsafe to anticipate events. It is true, they must make certain theories and hypotheses. They must form some kind of mental picture of the relations between the phenomena which they are trying to investigate, else their experiments would be made at random, and without connection.
From 'Radium and Its Products', Harper’s Magazine (Dec 1904), 52.
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Chemistry is like a majestic skyscraper. The concrete secure foundation of chemistry consists of countless experimentally observed facts. The theories, principles and laws developed from these observations are like an elevator which runs from the bottom to the top of the edifice.
Ernest R. Toon and George L. Ellis (eds.), Foundations of Chemistry (1968), 1.
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Children are told that an apple fell on Isaac Newton’s head and he was led to state the law of gravity. This, of course, is pure foolishness. What Newton discovered was that any two particles in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is not learned from a falling apple, but by observing quantities of data and developing a mathematical theory that can be verified by additional data. Data gathered by Galileo on falling bodies and by Johannes Kepler on motions of the planets were invaluable aids to Newton. Unfortunately, such false impressions about science are not universally outgrown like the Santa Claus myth, and some people who don’t study much science go to their graves thinking that the human race took until the mid-seventeenth century to notice that objects fall.
In How to Tell the Liars from the Statisticians (1983), 127.
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Classical thermodynamics ... is the only physical theory of universal content which I am convinced ... will never be overthrown.
Quoted in Albert Einstein and Stephen Hawking (ed.), A Stubbornly Persistent Illusion (2007), 353.
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Considered in its entirety, psychoanalysis won’t do. It is an end product, moreover, like a dinosaur or a zeppelin, no better theory can ever be erected on its ruins, which will remain for ever one of the saddest and strangest of all landmarks in the history of twentieth century thought.
From 'Further Comments on Psychoanalysis', The Hope of Progress: A Scientist Looks at Problems in Philosophy, Literature and Science (1973), 69.
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Cosmology, for centuries consisting of speculation based on a minimum of observational evidence and a maximum of philosophical predilection, became in the twentieth century an observational science, its theories now subject to verification or refutation to a degree previously unimaginable.
Opening sentence in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41.
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Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.
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Dalton transformed the atomic concept from a philosophical speculation into a scientific theory—framed to explain quantitative observations, suggesting new tests and experiments, and capable of being given quantitative form through the establishment of relative masses of atomic particles.
Development of Concepts of Physics. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 175.
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Darwin's theory was received in Russia with profound sympathy. While in Western Europe it met firmly established old traditions which it had first to overcome, in Russia its appearance coincided with the awakening of our society after the Crimean War and here it immediately received the status of full citizenship and ever since has enjoyed widespread popularity.
Quoted in Thomas F. Glick (ed.), The Comparative Reception of Darwinism (1988), 229-30.
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Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”
In article 'Mathematics', Encyclopedia Britannica (1911, 11th ed.), Vol. 17, 880. In the 2006 DVD edition of the encyclopedia, the definition of mathematics is given as “The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects.” [Premiss is a variant form of “premise”. —Webmaster]
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Do not say hypothesis, and even less theory: say way of thinking.
Aphorism 263 in Notebook J (1789-1793), as translated by R. J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 181.
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Do you see this egg? With this you can topple every theological theory, every church or temple in the world.
'Conversation Between d'Alembert and Diderot,' D'Alembert's Dream (written 1769, published 1830). Reprinted in Selected Writings, ed. Lester G. Crocker (1966).
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Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944), 7.
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During my stay in London I resided for a considerable time in Clapham Road in the neighbourhood of Clapham Common... One fine summer evening I was returning by the last bus 'outside' as usual, through the deserted streets of the city, which are at other times so full of life. I fell into a reverie (Träumerei), and 10, the atoms were gambolling before my eyes! Whenever, hitherto, these diminutive beings had appeared to me, they had always been in motion: but up to that time I had never been able to discern the nature of their motion. Now, however, I saw how, frequently, two smaller atoms united to form a pair: how the larger one embraced the two smaller ones: how still larger ones kept hold of three or even four of the smaller: whilst the whole kept whirling in a giddy dance. I saw how the larger ones formed a chain, dragging the smaller ones after them but only at the ends of the chain. I saw what our past master, Kopp, my highly honoured teacher and friend has depicted with such charm in his Molekular-Welt: but I saw it long before him. The cry of the conductor 'Clapham Road', awakened me from my dreaming: but I spent part of the night in putting on paper at least sketches of these dream forms. This was the origin of the 'Structural Theory'.
Kekule at Benzolfest in Berichte (1890), 23, 1302.
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Each worldview was a cultural product, but evolution is true and separate creation is not ... Worldviews are social constructions, and they channel the search for facts. But facts are found and knowledge progresses, however fitfully. Fact and theory are intertwined, and all great scientists understand the interaction.
…...
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Earlier theories … were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past. [Coining the “big bang” expression.]
From microfilmed Speaker's Copy of a radio script held at the BBC Written Archive Centre, for Hoyle's radio talk on the BBC Third Programme (28 Mar 1949). The date and time of the broadcast, 6:30pm, are given in that week’s Radio Times. The quote, with these references given in footnotes, in Simon Mitton, Fred Hoyle: A Life in Science (2011), 127-128 and 332. The text of the talk, the first printed use of the “big bang” expression, in the BBC’s The Listener magazine (7 Apr 1949), Vol.41, 568.
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Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in spite of the abstract nature of its theory, involving quantities whose nature is entirely unknown at the present, is really and truly founded on the observations of real Newtonian forces, electric and magnetic respectively.
From 'Electromagnetic Theory, CXII', The Electrician (23 Feb 1900), Vol. 44, 615.
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Engineering is the art of directing the great sources of power in nature for the use and the convenience of people. In its modern form engineering involves people, money, materials, machines, and energy. It is differentiated from science because it is primarily concerned with how to direct to useful and economical ends the natural phenomena which scientists discover and formulate into acceptable theories. Engineering therefore requires above all the creative imagination to innovate useful applications of natural phenomena. It seeks newer, cheaper, better means of using natural sources of energy and materials.
In McGraw Hill, Science and Technology Encyclopedia
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Engineers apply the theories and principles of science and mathematics to research and develop economical solutions to practical technical problems. Their work is the link between scientific discoveries and commercial applications. Engineers design products, the machinery to build those products, the factories in which those products are made, and the systems that ensure the quality of the product and efficiency of the workforce and manufacturing process. They design, plan, and supervise the construction of buildings, highways, and transit systems. They develop and implement improved ways to extract, process, and use raw materials, such as petroleum and natural gas. They develop new materials that both improve the performance of products, and make implementing advances in technology possible. They harness the power of the sun, the earth, atoms, and electricity for use in supplying the Nation’s power needs, and create millions of products using power. Their knowledge is applied to improving many things, including the quality of health care, the safety of food products, and the efficient operation of financial systems.
Bureau of Labor Statistics, Occupational Outlook Handbook (2000) as quoted in Charles R. Lord. Guide to Information Sources in Engineering (2000), 5. This definition has been revised and expanded over time in different issues of the Handbook.
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Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them.
In Entropy and Art: An Essay on Disorder and Order (1974), 21.
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Entropy theory, on the other hand, is not concerned with the probability of succession in a series of items but with the overall distribution of kinds of items in a given arrangement.
In Entropy and Art: An Essay on Disorder and Order (1974), 19.
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Even in the dark times between experimental breakthroughs, there always continues a steady evolution of theoretical ideas, leading almost imperceptibly to changes in previous beliefs.
In Nobel Lecture (8 Dec 1989), 'Conceptual Foundations of the Unified Theory of Weak and Electromagnetic Interactions.'
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Even mistaken hypotheses and theories are of use in leading to discoveries. This remark is true in all the sciences. The alchemists founded chemistry by pursuing chimerical problems and theories which are false. In physical science, which is more advanced than biology, we might still cite men of science who make great discoveries by relying on false theories. It seems, indeed, a necessary weakness of our mind to be able to reach truth only across a multitude of errors and obstacles.
An Introduction to the Study of Experimental Medicine (1865, translation 1927, 1957), 170.
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Every discovery opens a new field for investigation of facts, shows us the imperfection of our theories. It has justly been said, that the greater the circle of light, the greater the boundary of darkness by which it is surrounded.
Humphry Davy and John Davy, 'Consolations in Travel--Dialogue V--The Chemical Philosopher', The Collected Works of Sir Humphry Davy (1840), Vol. 9, 362.
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Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer. This was true of electron theory—perhaps some readers will remember a book called The Electrical Theory of the Universe by de Tunzelman. It is true of general relativity theory with its belief that we can formulate a mathematical scheme that will extrapolate to all past and future time and the unfathomed depths of space. It has been true of wave mechanics, with its first enthusiastic claim a brief ten years ago that no problem had successfully resisted its attack provided the attack was properly made, and now the disillusionment of age when confronted by the problems of the proton and the neutron. When will we learn that logic, mathematics, physical theory, are all only inventions for formulating in compact and manageable form what we already know, like all inventions do not achieve complete success in accomplishing what they were designed to do, much less complete success in fields beyond the scope of the original design, and that our only justification for hoping to penetrate at all into the unknown with these inventions is our past experience that sometimes we have been fortunate enough to be able to push on a short distance by acquired momentum.
The Nature of Physical Theory (1936), 136.
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Every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics. He knows that they are all equivalent, and that nobody is ever going to be able to decide which one is right at that level, but he keeps them in his head, hoping that they will give him different ideas for guessing.
In The Character of Physical Law (1965, 2001), 168.
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Everybody firmly believes in it [Nomal Law of Errors] because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.
…...
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Everything should be made as simple as possible, but not simpler.
Attributed.

Evolution ... is really two theories, the vague theory and the precise theory. The vague theory has been abundantly proved.... The precise theory has never been proved at all. However, like relativity, it is accepted on faith.... On getting down to actual details, difficulties begin.
In Science is a Sacred Cow (1950), 101 & 103.
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Evolution is a theory of organic change, but it does not imply, as many people assume, that ceaseless flux is the irreducible state of nature and that structure is but a temporary incarnation of the moment. Change is more often a rapid transition between stable states than a continuous transformation at slow and steady rates. We live in a world of structure and legitimate distinction. Species are the units of nature’s morphology.
…...
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Experience teaches nothing without theory.
In On the Management of Statistical Techniques for Quality and Productivity (1981), 86.
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Facts alone, no matter how numerous or verifiable, do not automatically arrange themselves into an intelligible, or truthful, picture of the world. It is the task of the human mind to invent a theoretical framework to account for them.
In Francis Bello, Lawrence Lessing and George A.W. Boehm, Great American Scientists (1960, 1961), 116.
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Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein's theory of gravitation replaced Newton's, but apples did not suspend themselves in mid-air pending the outcome.
'Evolution as Fact and Theory', in Hen's Teeth and Horse's Toes (1983, 1994), Chap. 19.
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Facts are a heap of bricks and timber. It is only a successful theory that can convert the heap into a stately mansion
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 324.
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Facts are not pure unsullied bits of information; culture also influences what we see and how we see it. Theories, moreover, are not inexorable inductions from facts. The most creative theories are often imaginative visions imposed upon facts; the source of imagination is also strongly cultural.
In The Mismeasure of Man (1981, 1996), 54.
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Facts are of not much use, considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory, however, and brought into mutual harmony, and it is another matter.
From article 'Electro-magnetic Theory II', in The Electrician (16 Jan 1891), 26, No. 661, 331.
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Factual assertions and fundamental principles are... merely parts of theories: they are given within the framework of a theory; they are chosen and valid within this framework; and subsequently they are dependent upon it. This holds for all empirical sciences—for the natural sciences as well as those pertaining to history.
Critique of Scientific Reason (1983), 106.
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Finding the world would not accommodate to his theory, he wisely determined to accommodate the theory to the world.
Under the pseudonym of Diedrich Knickerbocker, in A History of New York (1809). Collected in The Works of Washington Irving (1840), Vol. 1, 24.
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First... a new theory is attacked as absurd; then it is admitted to be true, but obvious and insignificant; finally it is seen to be so important that its adversaries claim that they themselves discovered it.
'Pragmatism's Conception of Truth', in Pragmatism: A New Name for some Old Ways of Thinking, Popular Lectures on Philosophy (1907), 198.
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For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created.
In 'Mathematics in the Physical Sciences', Scientific American (Sep 1964), 211, No. 3, 129.
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For if as scientists we seek simplicity, then obviously we try the simplest surviving theory first, and retreat from it only when it proves false. Not this course, but any other, requires explanation. If you want to go somewhere quickly, and several alternate routes are equally likely to be open, no one asks why you take the shortest. The simplest theory is to be chosen not because it is the most likely to be true but because it is scientifically the most rewarding among equally likely alternatives. We aim at simplicity and hope for truth.
Problems and Projects (1972), 352.
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For if there is any truth in the dynamical theory of gases the different molecules in a gas at uniform temperature are moving with very different velocities. Put such a gas into a vessel with two compartments [A and B] and make a small hole in the wall about the right size to let one molecule through. Provide a lid or stopper for this hole and appoint a doorkeeper, very intelligent and exceedingly quick, with microscopic eyes but still an essentially finite being.
Whenever he sees a molecule of great velocity coming against the door from A into B he is to let it through, but if the molecule happens to be going slow he is to keep the door shut. He is also to let slow molecules pass from B to A but not fast ones ... In this way the temperature of B may be raised and that of A lowered without any expenditure of work, but only by the intelligent action of a mere guiding agent (like a pointsman on a railway with perfectly acting switches who should send the express along one line and the goods along another).
I do not see why even intelligence might not be dispensed with and the thing be made self-acting.
Moral The 2nd law of Thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea you cannot get the same tumblerful of water out again.
Letter to John William Strutt (6 Dec 1870). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 582-3.
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For strictly scientific or technological purposes all this is irrelevant. On a pragmatic view, as on a religious view, theory and concepts are held in faith. On the pragmatic view the only thing that matters is that the theory is efficacious, that it 'works' and that the necessary preliminaries and side issues do not cost too much in time and effort. Beyond that, theory and concepts go to constitute a language in which the scientistic matters at issue can be formulated and discussed.
'Slow Neutron Spectroscopy and the Grand Atlas of the Physical World', Nobel Lecture, 8 December 1994. In Nobel Lectures: Physics 1991-1995 (1997), 111.
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Fortunately I experienced Max Wertheimer's teaching in Berlin and collaborated for over a decade with Wolfgang Köhler. I need not emphasize my debts to these outstanding personalities. The fundamental ideas of Gestalt theory are the foundation of all our investigations in the field of the will, of affection, and of the personality.
From A Dynamic Theory of Personality. Selected papers (1935), 240.
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Freudian psychoanalytical theory is a mythology that answers pretty well to Levi-Strauss's descriptions. It brings some kind of order into incoherence; it, too, hangs together, makes sense, leaves no loose ends, and is never (but never) at a loss for explanation. In a state of bewilderment it may therefore bring comfort and relief … give its subject a new and deeper understanding of his own condition and of the nature of his relationship to his fellow men. A mythical structure will be built up around him which makes sense and is believable-in, regardless of whether or not it is true.
From 'Science and Literature', The Hope of Progress: A Scientist Looks at Problems in Philosophy, Literature and Science (1973), 29.
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From a certain temperature on, the molecules 'condense' without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there some truth in it.
Letter to Ehrenfest (Dec 1924). Quoted in Abraham Pais, Roger Penrose, Subtle Is the Lord: The Science and the Life of Albert Einstein (2005), 432.
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From astronomy we find the east, west, south, and north, as well as the theory of the heavens, the equinox, solstice, and courses of the stars. If one has no knowledge of these matters, he will not be able to have any comprehension of the theory of sundials.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 10. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 10.
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From the medical theoretical standpoint, it suffices to deliberate and speculate regarding most illnesses. However, therapeutically, speculation is not adequate, and true and correct knowledge is imperative.
As quoted in Fred Rosner, The Medical Legacy of Moses Maimonides (1998), 54.
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From the point of view of the pure morphologist the recapitulation theory is an instrument of research enabling him to reconstruct probable lines of descent; from the standpoint of the student of development and heredity the fact of recapitulation is a difficult problem whose solution would perhaps give the key to a true understanding of the real nature of heredity.
Form and Function: A Contribution to the History of Animal Morphology (1916), 312-3.
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Generally speaking, geologists seem to have been much more intent on making little worlds of their own, than in examining the crust of that which they inhabit. It would be much more desirable that facts should be placed in the foreground and theories in the distance, than that theories should be brought forward at the expense of facts. So that, in after times, when the speculations of the present day shall have passed away, from a greater accumulation of information, the facts may be readily seized and converted to account.
Sections and Views Illustrative of Geological Phenomena (1830), iv.
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Genetics was, I would say, the first part of biology to become a pretty good theoretical subject, based on the theory of the gene and patterns of inheritance of characteristics.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 738.
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Germs of a theory, though in their present condition they are vague and formless … may be said to resemble stones in the quarry, rough and unhewn, but which may some time become corner-stones, columns, and entablatures in the future edifice.
In Report on the Geology of the High Plateaus of Utah (1880), 114.
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Given a large mass of data, we can by judicious selection construct perfectly plausible unassailable theories—all of which, some of which, or none of which may be right.
I-Ching and the citric acid cycle. Unpublished manuscript/seminar notes quoted in Frederick Grinnell, Everyday Practice of Science (2008), 86.
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Good lawyers know that in many cases where the decisions are correct, the reasons that are given to sustain them may be entirely wrong. This is a thousand times more likely to be true in the practice of medicine than in that of the law, and hence the impropriety, not to say the folly, in spending your time in the discussion of medical belief and theories of cure that are more ingenious and seductive than they are profitable.
Introductory lecture (22 Sep 1885), Hahnemann Medical College, Chicago, printed in United States Medical Investigator (1885), 21, 526.
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Great scientific discoveries have been made by men seeking to verify quite erroneous theories about the nature of things.
From 'Wordsworth in the Tropics', in Life and Letters and the London Mercury (1928), Vol. 1, 349.
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Great theories are expansive; failures mire us in dogmatism and tunnel vision.
…...
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He who has mastered the Darwinian theory, he who recognizes the slow and subtle process of evolution as the way in which God makes things come to pass, … sees that in the deadly struggle for existence that has raged throughout countless aeons of time, the whole creation has been groaning and travailing together in order to bring forth that last consummate specimen of God’s handiwork, the Human Soul
In The Destiny of Man Viewed in the Light of his Origin (1884), 32. Collected in Studies in Religion (1902), 19–20.
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He who loves practice without theory is like a seafarer who boards ship without wheel or compass and knows not wither he travels.
From the original Italian: “Quelli che s’inamorā di pratica sāza sciētia, sō come ’l nochiere che ēstra navilio sanza timone o bussola che mai à certezza dove si uada.” Italian and English in Jean Paul Richter (trans), G. 8a, 'General Introduction to the Book on Painting', The Literary Works of Leonardo da Vinci (1883), Vol. 1, 18. Also seen translated as “He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast,” in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972), 224.
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He [Samuel Johnson] bid me always remember this, that after a system is well settled upon positive evidence, a few objections ought not to shake it. “The human mind is so limited that it cannot take in all parts of a subject; so that there may be objections raised against anything. There are objections against a plenum, and objections against a vacuum. Yet one of them must certainly be true.”
Note: Whereas vacuum means devoid of matter, plenum regards a space with matter throughout.
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Here I shall present, without using Analysis [mathematics], the principles and general results of the Théorie, applying them to the most important questions of life, which are indeed, for the most part, only problems in probability. One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth—induction and analogy—are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.
Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 1.
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His [Thomas Edison] method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calculation would have saved him 90 per cent of the labor. But he had a veritable contempt for book learning and mathematical knowledge, trusting himself entirely to his inventor's instinct and practical American sense. In view of this, the truly prodigious amount of his actual accomplishments is little short of a miracle.
As quoted in 'Tesla Says Edison Was an Empiricist', The New York Times (19 Oct 1931), 25. In 1884, Tesla had moved to America to assist Edison in the designing of motors and generators.
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Historical theories are, after all, intellectual apple carts. They are quite likely to be upset. Nor should it be forgotten that they tend to attract, when they gain ascendancy, a fair number of apple-polishers
'Books of the Times'. New York Times (9 Dec 1965), 45.
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How strange it would be if the final theory were to be discovered in our lifetimes! The discovery of the final laws of nature will mark a discontinuity in human intellectual history, the sharpest that has occurred since the beginning of modern science in the seventeenth century. Can we now imagine what that would be like?
In Dreams of a Final Theory (1992), 235.
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How then did we come to the “standard model”? And how has it supplanted other theories, like the steady state model? It is a tribute to the essential objectivity of modern astrophysics that this consensus has been brought about, not by shifts in philosophical preference or by the influence of astrophysical mandarins, but by the pressure of empirical data.
In The First Three Minutes: A Modern View of the Origin of the Universe (1977), 9.
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Human language is in some ways similar to, but in other ways vastly different from, other kinds of animal communication. We simply have no idea about its evolutionary history, though many people have speculated about its possible origins. There is, for instance, the “bow-bow” theory, that language started from attempts to imitate animal sounds. Or the “ding-dong” theory, that it arose from natural sound-producing responses. Or the “pooh-pooh” theory, that it began with violent outcries and exclamations.
We have no way of knowing whether the kinds of men represented by the earliest fossils could talk or not…
Language does not leave fossils, at least not until it has become written.
Man in Nature (1961), 10.
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Hygiene is the corruption of medicine by morality. It is impossible to find a hygienist who does not debase his theory of the healthful with a theory of the virtuous. 3. The aim of medicine is surely not to make men virtuous; it is to safeguard them from the consequences of their vices.
In 'The Physician', Prejudices: third series (1922), 269.
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I always love geology. In winter, particularly, it is pleasant to listen to theories about the great mountains one visited in the summer; or about the Flood or volcanoes; about great catastrophes or about blisters; above all about fossils … Everywhere there are hypotheses, but nowhere truths; many workmen, but no experts; priests, but no God. In these circumstances each man can bring his hypothesis like a candle to a burning altar, and on seeing his candle lit declare ‘Smoke for smoke, sir, mine is better than yours’. It is precisely for this reason that I love geology.
In Nouvelles Genevoises (1910), 306. First edition, 1841.
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I am a firm believer in the theory that you can do or be anything that you wish in this world, within reason, if you are prepared to make the sacrifices, think and work hard enough and long enough.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted and cited in Editorial Section, 'Sir Frederick Banting', Canadian Public Health Journal (May 1941), 32, No. 5, 266-267.
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I am afraid all we can do is to accept the paradox and try to accommodate ourselves to it, as we have done to so many paradoxes lately in modern physical theories. We shall have to get accustomed to the idea that the change of the quantity R, commonly called the 'radius of the universe', and the evolutionary changes of stars and stellar systems are two different processes, going on side by side without any apparent connection between them. After all the 'universe' is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure.
Kosmos (1932), 133.
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I am more fond of achieving than striving. My theories must prove to be facts or be discarded as worthless. My efforts must soon be crowned with success, or discontinued.
The Rest of My Life, ch. 4 (1937).Wells wrote, in addition to other works, the popular 'Fleming Stone' detective series.
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I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years. The isolation and counting of gaseous ions, on the one hand, which have crowned with success the long and brilliant researches of J.J. Thomson, and, on the other, agreement of the Brownian movement with the requirements of the kinetic hypothesis, established by many investigators and most conclusively by J. Perrin, justify the most cautious scientist in now speaking of the experimental proof of the atomic nature of matter, The atomic hypothesis is thus raised to the position of a scientifically well-founded theory, and can claim a place in a text-book intended for use as an introduction to the present state of our knowledge of General Chemistry.
In Grundriss der allgemeinen Chemie (4th ed., 1909), Preface, as cited by Erwin N. Hiebert and Hans-Gunther Korber in article on Ostwald in Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography Supplement 1, Vol 15-16, 464.
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I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
In 'Ueber das Lehrziel im mathemalischen Unterricht der höheren Realanstalten', Jahresbericht der Deutschen Mathematiker Vereinigung, 2, 192. (The Annual Report of the German Mathematical Association. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 73.
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I argued that it was important not to place too much reliance on any single piece of experimental evidence. It might turn out to be misleading, as the 5.1 Å reflection undoubtedly was. Jim was a little more brash, stating that no good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong. A theory that did fit all the data would have been “carpentered” to do so and would thus be open to suspicion.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 59-60.
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I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?" I thought for a moment about our cut-off procedures and said, “Four." He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over.
As given in 'A Meeting with Enrico Fermi', Nature (22 Jan 2004), 427, 297. As quoted in Steven A. Frank, Dynamics of Cancer: Incidence, Inheritance, and Evolution (2007), 87. Von Neumann meant nobody need be impressed when a complex model fits a data set well, because if manipulated with enough flexible parameters, any data set can be fitted to an incorrect model, even one that plots a curve on a graph shaped like an elephant!
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I believe that certain erroneous developments in particle theory ... are caused by a misconception by some physicists that it is possible to avoid philosophical arguments altogether. Starting with poor philosophy, they pose the wrong questions. It is only a slight exaggeration to say that good physics has at times been spoiled by poor philosophy.
…...
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I bet it would have been a lot of fun to work with Einstein. What I really respect about Einstein is his desire to throw aside all conventional modes and just concentrate on what seems to be the closest we can get to an accurate theory of nature.
Alan Guth
As quoted by Christina Couch, '10 Questions for Alan Guth, Pioneer of the Inflationary Model of the Universe' (7 Jan 2016) on the website for NPR radio program Science Friday.
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I can assure you, reader, that in a very few hours, even during the first day, you will learn more natural philosophy about things contained in this book, than you could learn in fifty years by reading the theories and opinions of the ancient philosophers. Enemies of science will scoff at the astrologers: saying, where is the ladder on which they have climbed to heaven, to know the foundation of the stars? But in this respect I am exempt from such scoffing; for in proving my written reason, I satisfy sight, hearing, and touch: for this reason, defamers will have no power over me: as you will see when you come to see me in my little Academy.
The Admirable Discourses (1580), trans. Aurele La Rocque (1957), 27.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I can well appreciate, Holy Father, that as soon as certain people realise that in these books which I have written about the Revolutions of the spheres of the universe I attribute certain motions to the globe of the Earth, they will at once clamour for me to be hooted off the stage with such an opinion.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A.M. Duncan (1976), 23.
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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
The Fractal Geometry of Nature (1977, 1983), Introduction, xiii.
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I first met J. Robert Oppenheimer on October 8, 1942, at Berkeley, Calif. There we discussed the theoretical research studies he was engaged in with respect to the physics of the bomb. Our discussions confirmed my previous belief that we should bring all of the widely scattered theoretical work together. … He expressed complete agreement, and it was then that the idea of the prompt establishment of a Los Alamos was conceived.”
In 'Some Recollections of July 16, 1945', Bulletin of the Atomic Scientists (Jun 1970), 26, No. 6, 21.
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I forget whether you take in the Times; for the chance of your not doing so, I send the enclosed rich letter. It is, I am sure, by Fitz-Roy. … It is a pity he did not add his theory of the extinction of Mastodon, etc., from the door of the Ark being made too small.
Letter (5 Dec 1859) to Charles Lyell. In Francis Darwin and Albert Charles Seward (eds.), More Letters of Charles Darwin: A Record of his Work in a Series of Hitherto Unpublished Letters (103), Vol. 1, 129. The referenced letters in the Times were on 1 Dec and 5 Dec 1859, signed under the pseudonym “Senex”, on the topic of “Works of Art in the Drift.”
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I grow daily to honor facts more and more, and theory less and less.
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I had made considerable advance ... in calculations on my favourite numerical lunar theory, when I discovered that, under the heavy pressure of unusual matters (two transits of Venus and some eclipses) I had committed a grievous error in the first stage of giving numerical value to my theory. My spirit in the work was broken, and I have never heartily proceeded with it since.
[Concerning his calculations on the orbital motion of the Moon.]
Private note (29 Sep 1890). In George Biddell Airy and Wilfrid Airy (ed.), Autobiography of Sir George Biddell Airy (1896), 350.
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I have a peculiar theory about radium, and I believe it is the correct one. I believe that there is some mysterious ray pervading the universe that is fluorescing to it. In other words, that all its energy is not self-constructed but that there is a mysterious something in the atmosphere that scientists have not found that is drawing out those infinitesimal atoms and distributing them forcefully and indestructibly.
Quoted in 'Edison Fears Hidden Perils of the X-Rays', New York World (3 Aug 1903), 1.
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I have been scientifically studying the traits and dispositions of the “lower animals” (so-called,) and contrasting them with the traits and dispositions of man. I find the result profoundly humiliating to me. For it obliges me to renounce my allegiance to the Darwinian theory of the Ascent of Man from the Lower Animals; since it now seems plain to me that that theory ought to be vacated in favor of a new and truer one, this new and truer one to be named the Descent of Man from the Higher Animals.
From 'Man's Place in the Animal World' (1896) in What is Man?: and Other Philosophical Writings (1973), 81.
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I have just got a new theory of eternity.
Alleged comment to the secretary of the Netherlands embassy, seated beside him at a National Academy of Sciences annual awards ceremony (1921), after listening to lengthy formal speeches. As quoted in Ronald W. Clark, Einstein: The Life and Times (1971), 389.
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I have learnt that all our theories are not Truth itself, but resting places or stages on the way to the conquest of Truth, and that we must be contented to have obtained for the strivers after Truth such a resting place which, if it is on a mountain, permits us to view the provinces already won and those still to be conquered.
Liebig to Gilbert (25 Dec 1870). Rothamsted Archives. Quotation supplied by W. H. Brock.
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I have long recognized the theory and aesthetic of such comprehensive display: show everything and incite wonder by sheer variety. But I had never realized how power fully the decor of a cabinet museum can promote this goal until I saw the Dublin [Natural History Museum] fixtures redone right ... The exuberance is all of one piece–organic and architectural. I write this essay to offer my warmest congratulations to the Dublin Museum for choosing preservation–a decision not only scientifically right, but also ethically sound and decidedly courageous. The avant-garde is not an exclusive locus of courage; a principled stand within a reconstituted rear unit may call down just as much ridicule and demand equal fortitude. Crowds do not always rush off in admirable or defendable directions.
…...
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I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations. … For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it.
Although this preface would have been assumed by contemporary readers to be written by Copernicus, it was unsigned. It is now believed to have been written and added at press time by Andreas Osiander (who was then overseeing the printing of the book). It suggests the earth’s motion as described was merely a mathematical device, and not to be taken as absolute reality. Text as given in 'To the Reader on the Hypotheses in this Work', Copernicus: On the Revolutions of the Heavenly Spheres (1543), translated by ‎Alistair Matheson Duncan (1976), 22-3. By adding this preface, Osiander wished to stave off criticism by theologians. See also the Andreas Osiander Quotes page of this website.
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I have no trouble publishing in Soviet astrophysical journals, but my work is unacceptable to the American astrophysical journals.
[Referring to the trouble he had with the peer reviewers of Anglo-American astrophysical journals because his ideas often conflicted with the generally accepted or “standard"” theories.]
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),197.
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I know very well the people you mean: they are all mind and theory and haven't the wit to sew on a button. Plenty of head but not hand enough to sew on a button.
Aphorism 75 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 55.
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I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.
From a 1977 lecture. Quoted in Pesi Rustom Masani, Norbert Wiener, 1894-1964 (1990), 6.
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I noticed affixed to a laboratory door the following words: “Les théories passent. Le Grenouille reste. [The theories pass. The frog remains.] &mdashJean Rostand, Carnets d’un biologiste.” There is a risk that in the less severe discipline of criticism the result may turn out to be different; the theories will remain but the frog may disappear.
In An Appetite for Poetry (1989), 5.
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I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.
In Ernst Mach and Thomas Joseph McCormack, Space and Geometry (1906), 93.
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I pass with relief from the tossing sea of Cause and Theory to the firm ground of Result and Fact.
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I remember one occasion when I tried to add a little seasoning to a review, but I wasn’t allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: “The author discusses valueless measures in pointless spaces.”
In I Want to be a Mathematician: An Automathography (1985), 120.
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I respect Kirkpatrick both for his sponges and for his numinous nummulosphere. It is easy to dismiss a crazy theory with laughter that debars any attempt to understand a man’s motivation–and the nummulosphere is a crazy theory. I find that few men of imagination are not worth my attention. Their ideas may be wrong, even foolish, but their methods often repay a close study ... The different drummer often beats a fruitful tempo.
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I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first compleat and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.
An Attempt to Prove the Motion of the Earth from Observations (1674), 27-8. Based on a Cutlerian Lecture delivered by Hooke at the Royal Society four years earlier.
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I should like to call the number of atom groups, with which an elementary atom coordinates … to form a complex radical, the coordination number of the atom in question … We must differentiate between valence number and coordination number. The valence number indicates the maximum number of monovalent atoms which can be bound directly to the atom in question without the participation of other elementary atoms … Perhaps this concept [of coordination number] is destined to serve as a basis for the theory of the constitution of inorganic compounds, just as valence theory formed the basis for the constitutional theory of carbon compounds.
In 'Beitrag zur Konstitution anorganischer Verbindungen', Zeitschrift fur anorganische Chemie, (1893), 3, 267-330. Translated in George G. Kauffman (ed.), Classics in Coordination Chemistry: Part I: The Selected Papers of Alfred Werner (1968), 84-87.
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I therefore took this opportunity and also began to consider the possibility that the Earth moved. Although it seemed an absurd opinion, nevertheless, because I knew that others before me had been granted the liberty of imagining whatever circles they wished to represent the phenomena of the stars, I thought that I likewise would readily be allowed to test whether, by assuming some motion of the Earth's, more dependable representations than theirs could be found for the revolutions of the heavenly spheres.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 26.
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I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.
Responding to the toast, 'Science!' at the Royal Academy of the Arts in 1932.)
Quoted in Lawrence Badash, 'Ernest Rutherford and Theoretical Physics,' in Robert Kargon and Peter Achinstein (eds.) Kelvin's Baltimore Lectures and Modern Theoretical Physics: Historical and Philosophical Perspectives (1987), 352.
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I want to argue that the ‘sudden’ appearance of species in the fossil record and our failure to note subsequent evolutionary change within them is the proper prediction of evolutionary theory as we understand it ... Evolutionary ‘sequences’ are not rungs on a ladder, but our retrospective reconstruction of a circuitous path running like a labyrinth, branch to branch, from the base of the bush to a lineage now surviving at its top.
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I was pretty good in science. But again, because of the small budget, in science class we couldn’t do experiments in order to prove theories. We just believed everything. Actually I think that class was call Religion. Religion was always an easy class. All you had to do was suspend the logic and reasoning you were taught in all the other classes.
In autobiography, Brain Droppings (1998), 227.
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I was there when Abbe Georges Lemaître first proposed this [Big Bang] theory. ... There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. .... It is only myth that attempts to say how the universe came to be, either four thousand or twenty billion years ago.
[Expressing his belief that the Big Bang is a myth devised to explain creation. He said he heard Lemaître (who was, at the time both a member of the Catholic hierarchy and an accomplished scientist) say in private that this theory was a way to reconcile science with St. Thomas Aquinas' theological dictum of creatio ex nihilo—creation out of nothing.]
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),196.
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I was very impressed that one simple theory could incorporate so much physics
Alan Guth
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I will simply express my strong belief, that that point of self-education which consists in teaching the mind to resist its desires and inclinations, until they are proved to be right, is the most important of all, not only in things of natural philosophy, but in every department of dally life.
'Observations On Mental Education', a lecture before the Prince Consort and the Royal Institution, 6 May 1854. Experimental researches in chemistry and physics (1859), 477.
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If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
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If all this damned quantum jumping were really here to stay, I should be sorry, I should be sorry I ever got involved with quantum theory.
As reported by Heisenberg describing Schrödinger’s time spent debating with Bohr in Copenhagen (Sep 1926). In Werner Heisenberg, Physics and Beyond: Encounters and Conversations (1971), 75. As cited in John Gribbin, Erwin Schrodinger and the Quantum Revolution.
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If an idea presents itself to us, we must not reject it simply because it does not agree with the logical deductions of a reigning theory.
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If Darwin were alive today the insect world would delight and astound him with its impressive verification of his theories of the survival of the fittest. Under the stress of intensive chemical spraying the weaker members of the insect populations are being weeded out… . Only the strong and fit remain to defy our efforts to control them.
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If even in science there is no a way of judging a theory but by assessing the number, faith and vocal energy of its supporters, then this must be even more so in the social sciences: truth lies in power.
In Radio Lecture (30 Jun 1973) broadcast by the Open University, collected in Imre Lakatos, John Worrall (ed.) and Gregory Currie (ed.), 'Introduction: Science and Pseudoscience', The Methodology of Scientific Research Programmes (1978, 1980), Vol. 1, 9.
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If faith cannot be reconciled with rational thinking, it has to be eliminated as an anachronistic remnant of earlier stages of culture and replaced by science dealing with facts and theories which are intelligible and can be validated.
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If he [Thomas Edison] had a needle to find in a haystack, he would not stop to reason where it was most likely to be, but would proceed at once with the feverish diligence of a bee, to examine straw after straw until he found the object of his search. … [J]ust a little theory and calculation would have saved him ninety percent of his labor.
As quoted in 'Tesla Says Edison Was an Empiricist', The New York Times (19 Oct 1931), 25. In 1884, Tesla had moved to America to assist Edison in the designing of motors and generators.
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If history is any guide at all, it seems to me to suggest that there is a final theory. In this century we have seen a convergence of the arrows of explanation, like the convergence of meridians toward the North Pole.
In Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature (1992), 232.
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If in a discussion of many matters … we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability.
Plato
Timaeus. Quoted in Robert J. Scully, The Demon and the Quantum (2007), 20.

If it could be demonstrated that any complex organ existed which could not possibly have been formed by numerous, successive slight modifications, my theory would absolutely break down.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1861), 171.
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If the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics.
The Aim and Structure of Physical Theory (1906), 2nd edition (1914), trans. Philip P. Wiener (1954), 10.
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If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.
Feynman Lectures on Gravitation, edited by Brian Hatfield (2002), 21.
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If this plane were to crash, we could get a new start on this quasar problem.
Said to colleagues, dramatically cupping his hand over his brow, shortly after the take-off of a propeller plane leaving Austin, Texas, after the Second Texas Symposium for Relativistic Astrophysics in Dec 1964. Various different theories had been presented at the conference. The flight passengers included many of the major scientists in quasar research, including Margaret and Geoffrey Burbridge, Subrahmanyan Chandrasekhar, John Wheeler and Maarten Schmidt.
As quoted by Arthur I. Miller, Empire of the Stars (2005), 226.
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If we do discover a complete theory, it should be in time understandable in broad principle by everyone ... Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.
A Brief History of Time (1988), 191.
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If we look at the problems raised by Aristotle, we are astonished at his gift of observation. What wonderful eyes the Greeks had for many things! Only they committed the mistake of being overhasty, of passing straightway from the phenomenon to the explanation of it, and thereby produced certain theories that are quite inadequate. But this is the mistake of all times, and still made in our own day.
In The Maxims and Reflections of Goethe (1906), 195.
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If you are out to describe the truth, leave elegance to the tailor.
On being reproached that his formula of gravitation was longer and more cumbersome than Newton’s.
Quoted in J. H. Mitchell, Writing for Professional and Technical Journals (1968), Introduction.
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In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”
In 'Einstein's Impact on Theoretical Physics', collected in Jong-Ping Hsu, Leonard Hsu (eds.), JingShin Theoretical Physics Symposium in Honor of Professor Ta-You Wu (1998), 70. Reprinted from Physics Today (Jun 1980), 49. The article was adapted from a talk given at the Second Marcel Grossman meeting, held in Trieste, Italy (Jul 1979), in honor of the 100th anniversary of the birth of Albert Einstein.
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In theory there is no difference between theory and practice; but in practice, there is.
Attributed. Although widely seen, a reliable source is never cited. If you know a primary print source, please contact Webmaster. Occasionally also seen attributed to Yogi Berra, Chuck Reid, Grant Gainey or Jerry Percell. The earliest example found by Webmaster is in Walter J. Savitch, An Introduction to the Art and Science of Programming (1986), where it is merely attributed as "Remark overheard at a computer science conference."
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In a sense, of course, probability theory in the form of the simple laws of chance is the key to the analysis of warfare;… My own experience of actual operational research work, has however, shown that its is generally possible to avoid using anything more sophisticated. … In fact the wise operational research worker attempts to concentrate his efforts in finding results which are so obvious as not to need elaborate statistical methods to demonstrate their truth. In this sense advanced probability theory is something one has to know about in order to avoid having to use it.
In 'Operations Research', Physics Today (Nov 1951), 19. As cited by Maurice W. Kirby and Jonathan Rosenhead, 'Patrick Blackett (1897)' in Arjang A. Assad (ed.) and Saul I. Gass (ed.),Profiles in Operations Research: Pioneers and Innovators (2011), 25.
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In addition to this it [mathematics] provides its disciples with pleasures similar to painting and music. They admire the delicate harmony of the numbers and the forms; they marvel when a new discovery opens up to them an unexpected vista; and does the joy that they feel not have an aesthetic character even if the senses are not involved at all? … For this reason I do not hesitate to say that mathematics deserves to be cultivated for its own sake, and I mean the theories which cannot be applied to physics just as much as the others.
(1897) From the original French, “Et surtout, leurs adeptes y trouvent des jouissances analogues á celles que donnent la peinture et la musique. Ils admirent la délicate harmonie des nombres et des formes; ils s’émerveillent quand une découverte nouvelle leur ouvre une perspective inattendue; et la joie qu’ils éprouvent ainsi n’a-t-elle pas le caractère esthétique, bien que les sens n’y prennent aucune part?...C’est pourquoi je n’hésite pas à dire que les mathématiques méritent d’être cultivées pour elles-mêmes et que les théories qui ne peuvent être appliquées á la physique doivent l’être comme les autres.” Address read for him at the First International Congress of Mathematicians in Zurich: '‘Sur les rapports de l’analyse pure et de la physique', in Proceedings of that Congress 81-90, (1898). Also published as 'L’Analyse et la Physique', in La Valeur de la Science (1905), 137-151. As translated in Armand Borel, 'On the Place of Mathematics in Culture', in Armand Borel: Œvres: Collected Papers (1983), Vol. 4, 420-421.
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In an enterprise such as the building of the atomic bomb the difference between ideas, hopes, suggestions and theoretical calculations, and solid numbers based on measurement, is paramount. All the committees, the politicking and the plans would have come to naught if a few unpredictable nuclear cross sections had been different from what they are by a factor of two.
Epigraph in Richard Rhodes, The Making of the Atomic Bomb (1986), 8.
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In chemistry, our theories are crutches; to show that they are valid, they must be used to walk... A theory established with the help of twenty facts must explain thirty, and lead to the discovery of ten more.
Leçons sur la Philosophie Chimique (1837), 60. Trans. S. Kapoor, 'Dumas and Organic Classification', Ambix, 1969, 16, 4.
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In Darwin’s theory, you just have to substitute ‘mutations’ for his ‘slight accidental variations’ (just as quantum theory substitutes ‘quantum jump’ for ‘continuous transfer of energy’). In all other respects little change was necessary in Darwin’s theory.
…...
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In degenerating programmes, however, theories are fabricated only in order to accommodate known facts.
In Radio Lecture (30 Jun 1973) broadcast by the Open University, collected in Imre Lakatos, John Worrall (ed.) and Gregory Currie (ed.), 'Introduction: Science and Pseudoscience', The Methodology of Scientific Research Programmes (1978, 1980), Vol. 1, 5.
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In due time the evolution theory will have to abate its vehemence, cannot be allow’d to dominate everything else, and will have to take its place as a segment of the circle, the cluster—as but one of many theories, many thoughts, of profoundest value—and readjusting the differentiating much, yet leaving the divine secrets just as inexplicable and unreachable as before—maybe more so.
In Specimen days & Collect (1883), 326.
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In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
... a l'ouverture du cours de mechanique industrielle á Metz (1827), 2-3, trans. Ivor Grattan-Guinness.
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In general, a fact is worth more than theories in the long run. The theory stimulates, but the fact builds. The former in due time is replaced by one better but the fact remains and becomes fertile.
Letter to Dr. E. B. Krumhaar (11 Oct 1933), in Journal of Bacteriology (Jan 1934), 27, No. 1, 20.
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In general, art has preceded science. Men have executed great, and curious, and beautiful works before they had a scientific insight into the principles on which the success of their labours was founded. There were good artificers in brass and iron before the principles of the chemistry of metals were known; there was wine among men before there was a philosophy of vinous fermentation; there were mighty masses raised into the air, cyclopean walls and cromlechs, obelisks and pyramids—probably gigantic Doric pillars and entablatures—before there was a theory of the mechanical powers. … Art was the mother of Science.
Lecture (26 Nov 1851), to the London Society of Arts, 'The General Bearing of the Great Exhibition on the Progress of Art and Science', collected in Lectures on the Results of the Great Exhibition of 1851' (1852), 7-8.
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In geometry, as in most sciences, it is very rare that an isolated proposition is of immediate utility. But the theories most powerful in practice are formed of propositions which curiosity alone brought to light, and which long remained useless without its being able to divine in what way they should one day cease to be so. In this sense it may be said, that in real science, no theory, no research, is in effect useless.
In 'Geometry', A Philosophical Dictionary, (1881), Vol. l, 374.
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In less than eight years “The Origin of Species” has produced conviction in the minds of a majority of the most eminent living men of science. New facts, new problems, new difficulties as they arise are accepted, solved, or removed by this theory; and its principles are illustrated by the progress and conclusions of every well established branch of human knowledge.
From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author in the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.
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In my intercourse with mankind, I have always found those who would thrust theory into practical matters to be, at bottom, men of no judgement and pure quacks.
Quoted in James Kip Finch, Engineering Classics of James Kip Finch.
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In my opinion the English excel in the art of writing text-books for mathematical teaching; as regards the clear exposition of theories and the abundance of excellent examples, carefully selected, very few books exist in other countries which can compete with those of Salmon and many other distinguished English authors that could be named.
In Projective Geometry (1886), Preface.
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In my own view, some advice about what should be known, about what technical education should be acquired, about the intense motivation needed to succeed, and about the carelessness and inclination toward bias that must be avoided is far more useful than all the rules and warnings of theoretical logic.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 6.
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In our day grand generalizations have been reached. The theory of the origin of species is but one of them. Another, of still wider grasp and more radical significance, is the doctrine of the Conservation of Energy, the ultimate philosophical issues of which are as yet but dimly seem-that doctrine which “binds nature fast in fate” to an extent not hitherto recognized, exacting from every antecedent its equivalent consequent, and bringing vital as well as physical phenomena under the dominion of that law of causal connexion which, so far as the human understanding has yet pierced, asserts itself everywhere in nature.
'Address Delivered Before The British Association Assembled at Belfast', (19 Aug 1874). Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 1801.
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In point of fact, no conclusive disproof of a theory can ever be produced; for it is always possible to say that the experimental results are not reliable or that the discrepancies which are asserted to exist between the experimental results and the theory are only apparent and that they will disappear with the advance of our understanding. If you insist on strict proof (or strict disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are.
The Logic of Scientific Discovery: Logik Der Forschung (2002), 28.
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In science “fact” can only mean “confirmed to such a degree that it would be perverse to withhold provisional assent.” I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms.
'Evolution as Fact and Theory', in Hen’s Teeth and Horse’s Toes: Further Reflections in Natural History (1983), 255.
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In scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.
The Ethical Functions of Scientific Study: An Address Delivered at the Annual Commencement of the University of Michigan, 28 June 1888, 7-8.
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In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world “simplest.” It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = κ(d²x/dy²) much less simple than “it oozes,” of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plain man, namely the rate of change of a rate of change.
In 'Science and Theology as Art-Forms', Possible Worlds (1927), 227.
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In the 1860s, Pasteur not only applied his germ theory to create “Pasteurization,” rescuing France’s wine and vinegar industries, but also found both the cause and cure of silkworm disease, saving growers millions of dollars. When Napoleon asked the scientist why he had not legitimately profited by his findings, Pasteur replied: “In France scientists would consider they lowered themselves by doing so.”
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 190.
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In the days when geology was young, now some two hundred years ago, it found a careful foster-mother in theology, who watched over its early growth with anxious solicitude, and stored its receptive mind with the most beautiful stories, which the young science never tired of transforming into curious fancies of its own, which it usually styled “theories of the earth.”
In British Association Address to Workingmen, 'Geology and Deluges', published in Nature (1984), 50, 505-510. Also printed in Popular Science Monthly (Dec 1894), 46 245.
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In the expressions we adopt to prescribe physical phenomena we necessarily hover between two extremes. We either have to choose a word which implies more than we can prove, or we have to use vague and general terms which hide the essential point, instead of bringing it out. The history of electrical theories furnishes a good example.
Opening Address to the Annual Meeting of the British Association by Prof. Arthur Schuster, in Nature (4 Aug 1892), 46, 325.
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In the field of thinking, the whole history of science from geocentrism to the Copernican revolution, from the false absolutes of Aristotle’s physics to the relativity of Galileo’s principle of inertia and to Einstein’s theory of relativity, shows that it has taken centuries to liberate us from the systematic errors, from the illusions caused by the immediate point of view as opposed to “decentered” systematic thinking.
As quoted in D. E. Berlyne, Structure and Direction in Thinking (1965), 232.
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In the world of science different levels of esteem are accorded to different kinds of specialist. Mathematicians have always been eminently respectable, and so are those who deal with hard lifeless theories about what constitutes the physical world: the astronomers, the physicists, the theoretical chemists. But the more closely the scientist interests himself in matters which are of direct human relevance, the lower his social status. The real scum of the scientific world are the engineers and the sociologists and the psychologists. Indeed, if a psychologist wants to rate as a scientist he must study rats, not human beings. In zoology the same rules apply. It is much more respectable to dissect muscle tissues in a laboratory than to observe the behaviour of a living animal in its natural habitat.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
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In the year 1666 he retired again from Cambridge... to his mother in Lincolnshire & whilst he was musing in a garden it came into his thought that the power of gravity (wch brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought. Why not as high as the moon said he to himself & if so that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition but being absent from books & taking the common estimate in use among Geographers & our seamen before Norwood had measured the earth, that 60 English miles were contained in one degree of latitude on the surface of the Earth his computation did not agree with his theory & inclined him then to entertain a notion that together with the force of gravity there might be a mixture of that force wch the moon would have if it was carried along in a vortex.
[The earliest account of Newton, gravity and an apple.]
Memorandum of a conversation with Newton in August 1726. Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 154.
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In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those which are implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as representing essentially the arrangement of electrons in the atom ... In accordance with the idea of Mendeleef, that hydrogen is the first member of a full period, I erroneously assumed helium to have a shell of eight electrons. Regarding the disposition in the positive charge which balanced the electrons in the neutral atom, my ideas were very vague; I believed I inclined at that time toward the idea that the positive charge was also made up of discrete particles, the localization of which determined the localization of the electrons.
Valence and the Structure of Atoms and Molecules (1923), 29-30.
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In theory one is aware that the earth revolves but in practice one does not perceive it, the ground on which one treads seems not to move, and one can live undisturbed. So it is with Time in one's life. (1918)
'À l’ombre des jeunes filles en fleurs', À la recherche du temps perdu (1913-27).
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In these researches I followed the principles of the experimental method that we have established, i.e., that, in presence of a well-noted, new fact which contradicts a theory, instead of keeping the theory and abandoning the fact, I should keep and study the fact, and I hastened to give up the theory.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 164.
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Louis Agassiz quote: In-depth studies have an influence on general ideas, whereas theories, in turn, in order to maintain themse
In-depth studies have an influence on general ideas, whereas theories, in turn, in order to maintain themselves, push their spectators to search for new evidence. The mind’s activity that is maintained by the debates about these works, is probably the source of the greatest joys given to man to experience on Earth.
La théorie des glaciers et ses progrès les plus récents. Bibl. universelle de Geneve, (3), Vol. 41, p. 139. Trans. Karin Verrecchia.
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Indeed, the most important part of engineering work—and also of other scientific work—is the determination of the method of attacking the problem, whatever it may be, whether an experimental investigation, or a theoretical calculation. … It is by the choice of a suitable method of attack, that intricate problems are reduced to simple phenomena, and then easily solved.
In Engineering Mathematics: A Series of Lectures Delivered at Union College (1911, 1917), Vol. 2, 275.
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Indeed, this epistemological theory of the relation between theory and experiment differs sharply from the epistemological theory of naive falsificationism.
In Radio Lecture (30 Jun 1973) broadcast by the Open University, collected in Imre Lakatos, John Worrall (ed.) and Gregory Currie (ed.), 'Introduction: Science and Pseudoscience', The Methodology of Scientific Research Programmes (1978, 1980), Vol. 1, 35.
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Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain. “Omne exit in infinitum” is their favorite motto and accepted axiom.
In 'A Plea for the Mathematician', Nature, Vol. 1, 861. [The Latin phrase “Omne exit in infinitum” means “Everything goes to infinity”.
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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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Is it not true that the doctrine of attraction and gravity has done nothing but astonish our imagination? Is it not true that all chemical discoveries have done only the same?
Letter to Jean le Rond D'Alembert (7 Jan 1768). Collected in Correspondence: Letters Between Frederick II and M. D’Alembert (1789), 79, as translated by Thomas Holcroft.
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It appears that anything you say about the way that theory and experiment may interact is likely to be correct, and anything you say about the way that theory and experiment must interact is likely to be wrong.
In Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature (1992), 128.
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It does appear that on the whole a physicist… tries to reduce his theory at all times to as few parameters as possible and is inclined to feel that a theory is a “respectable” one, though by no means necessarily correct, if in principle it does offer reasonably specific means for its possible refutation. Moreover the physicist will generally arouse the irritation amongst fellow physicists if he is not prepared to abandon his theory when it clashes with subsequent experiments. On the other hand it would appear that the chemist regards theories—or perhaps better his theories (!) —as far less sacrosanct, and perhaps in extreme cases is prepared to modify them continually as each bit of new experimental evidence comes in.
'Discussion: Physics and Chemistry: Comments on Caldin's View of Chemistry', British Journal of the Philosophy of Science, 1960, 11, 222.
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It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.
…...
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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 the final aim of Lie from the beginning to make progress in the theory of differential equations; as subsidiary to this may be regarded both his geometrical developments and the theory of continuous groups.
In Lectures on Mathematics (1911), 24.
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It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 37.
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It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.
A Scandal in Bohemia (1891) in Adventures of Sherlock Holmes (1892), 5.
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It is a capital mistake to theorize before you have all the evidence. It biases the judgment.
A Study in Scarlet (1887), in Works of Arthur Conan Doyle (1902), Vol. 11, 39.
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It is a constant struggle not to let the theory lead the science in the way that is most beneficial to one’s assumptions.
In U.S. News & World Report (1997), 123, 262.
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It is a good thing Heaven has not given us the power to change as much of our body as we would like to or as our theory would assert is necessary.
Aphorism 34 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 48.
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It is a serious question whether America, following England’s lead, has not gone into problem-solving too extensively. Certain it is that we are producing no text-books in which the theory is presented in the delightful style which characterizes many of the French works … , or those of the recent Italian school, or, indeed, those of the continental writers in general.
In The Teaching of Elementary Mathematics (1902), 219.
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It is a test of true theories not only to account for but to predict phenomena.
Aphorism 12, 'Aphorisms Concerning Science', The Philosophy of the Inductive Sciences (1840), Vol. 1, xxxvi.
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It is a vulgar belief that our astronomical knowledge dates only from the recent century when it was rescued from the monks who imprisoned Galileo; but Hipparchus … who among other achievements discovered the precession of the eqinoxes, ranks with the Newtons and the Keplers; and Copernicus, the modern father of our celestial science, avows himself, in his famous work, as only the champion of Pythagoras, whose system he enforces and illustrates. Even the most modish schemes of the day on the origin of things, which captivate as much by their novelty as their truth, may find their precursors in ancient sages, and after a careful analysis of the blended elements of imagination and induction which charaterise the new theories, they will be found mainly to rest on the atom of Epicurus and the monad of Thales. Scientific, like spiritual truth, has ever from the beginning been descending from heaven to man.
Lothair (1879), preface, xvii.
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It is always better to have no ideas than false ones; to believe nothing than to believe what is wrong.
In Letter (19 Jul 1788) to James Madison. Collected in Thomas Jefferson Randolph, Memoirs, Correspondence, and Private Papers of Thomas Jefferson (1829), Vol. 2, 223.
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It is an old saying, abundantly justified, that where sciences meet there growth occurs. It is true moreover to say that in scientific borderlands not only are facts gathered that [are] often new in kind, but it is in these regions that wholly new concepts arise. It is my own faith that just as the older biology from its faithful studies of external forms provided a new concept in the doctrine of evolution, so the new biology is yet fated to furnish entirely new fundamental concepts of science, at which physics and chemistry when concerned with the non-living alone could never arrive.
'Biological Thought and Chemical Thought: A Plea for Unification', Linacre Lecture, Cambridge (6 May 1938), published in Lancet (1938),2, 1204.
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It is curious how often erroneous theories have had a beneficial effect for particular branches of science.
The Growth of Biological Thought: Diversity, Evolution and Inheritance (1982), 847.
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It is customary to connect Medicine with Botany, yet scientific treatment demands that we should consider each separately. For the fact is that in every art, theory must be disconnected and separated from practice, and the two must be dealt with singly and individually in their proper order before they are united. And for that reason, in order that Botany, which is, as it were, a special branch of Natural Philosophy [Physica], may form a unit by itself before it can be brought into connection with other sciences, it must be divided and unyoked from Medicine.
Methodi herbariae libri tres (1592), translated in Agnes Arber, Herbals: Their Origin and Evolution, 2nd edition (1938), 144.
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It is difficult even to attach a precise meaning to the term “scientific truth.” So different is the meaning of the word “truth” according to whether we are dealing with a fact of experience, a mathematical proposition or a scientific theory. “Religious truth” conveys nothing clear to me at all.
From 'Scientific Truth' in Essays in Science (1934, 2004), 11.
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It is easy to make out three areas where scientists will be concentrating their efforts in the coming decades. One is in physics, where leading theorists are striving, with the help of experimentalists, to devise a single mathematical theory that embraces all the basic phenomena of matter and energy. The other two are in biology. Biologists—and the rest of us too—would like to know how the brain works and how a single cell, the fertilized egg cell, develops into an entire organism
Article 'The View From Mars', in Annals of the New York Academy of Sciences: Research Facilities of the Future (1994), 735, 37.
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It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations. Confirmations should count only if they are the result of risky predictions... A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. Every genuine test of a theory is an attempt to falsify it, or refute it.
Conjectures and Refutations: The Growth of Scientific Knowledge (1963), 36.
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It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.
International Journal of Theoretical Physics (1982), 21 Nos. 6-7, 468. Quoted in Brian Rotman, Mathematics as Sign (2000), 82.
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It is in scientific honesty that I endorse the presentation of alternative theories for the origin of the universe, life and man in the science classroom. It would be an error to overlook the possibility that the universe was planned rather than happening by chance.
In letter to California State board of Education (14 Sep 1972).
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It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 37-38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112.
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It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.
In 'The Evolution of the Physicist’s Picture of Nature', Scientific American, May 1963, 208, 47.

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is not that we propose a theory and Nature may shout NO; rather, we propose a maze of theories, and Nature may shout INCONSISTENT.
In 'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London 1965 (1970), Vol. 4, 130.
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It is often held that scientific hypotheses are constructed, and are to be constructed, only after a detailed weighing of all possible evidence bearing on the matter, and that then and only then may one consider, and still only tentatively, any hypotheses. This traditional view however, is largely incorrect, for not only is it absurdly impossible of application, but it is contradicted by the history of the development of any scientific theory. What happens in practice is that by intuitive insight, or other inexplicable inspiration, the theorist decides that certain features seem to him more important than others and capable of explanation by certain hypotheses. Then basing his study on these hypotheses the attempt is made to deduce their consequences. The successful pioneer of theoretical science is he whose intuitions yield hypotheses on which satisfactory theories can be built, and conversely for the unsuccessful (as judged from a purely scientific standpoint).
Co-author with Raymond Arthur Lyttleton, in 'The Internal Constitution of the Stars', Occasional Notes of the Royal Astronomical Society 1948, 12, 90.
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It is scientists, not sceptics, who are most willing to consider explanations that conflict with their own. And far from quashing dissent, it is the scientists, not the sceptics, who do most to acknowledge gaps in their studies and point out the limitations of their data—which is where sceptics get much of the mud they fling at the scientists. By contrast, the [sceptics] are not trying to build a theory of anything. They have set the bar much lower, and are happy muddying the waters.
Editorial, Nature (28 Jul 2011), 475, 423-424.
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It is the theory that decides what can be observed.
…...
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It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.
Proclus
In scholium to Book X of Euclid t. V, 417 as quoted and cited in Ettore Carruccio and Isabel Quigly (trans.), Mathematics And Logic in History And in Contemporary Thought (1964), 27.
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It is with theories as with wells: you may see to the bottom of the deepest if there be any water there, while another shall pass for wondrous profound when ‘tis merely shallow, dark, and empty.
As quoted, citing only the author, in 'New Publications: Dr. Wigan', The Edinburgh Review: Or Critical Journal (Oct 1844), 80, 67.
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It is … a sign of the times—though our brothers of physics and chemistry may smile to hear me say so—that biology is now a science in which theories can be devised: theories which lead to predictions and predictions which sometimes turn out to be correct. These facts confirm me in a belief I hold most passionately—that biology is the heir of all the sciences.
From Nobel Banquet speech (10 Dec 1960).
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It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory...
'On the Generalized Theory of Gravitation', Scientific American (Apr 1950), 13. In David H. Levy (Ed.), The Scientific American Book of the Cosmos (2000), 19.
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It seems sensible to discard all hope of observing hitherto unobservable quantities, such as the position and period of the electron... Instead it seems more reasonable to try to establish a theoretical quantum mechanics, analogous to classical mechanics, but in which only relations between observable quantities occur.
In Helge Kragh, Quantum Generations: A History of Physics in the Twentieth Century (1999), 161.
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It seems that the rivers know the theory. It only remains to convince the engineers of the validity of this analysis.
Epigraph, without citation, in Péter Érdi, Complexity Explained (2007), 339. In French, “Il semble que les rivières connaissent déjà la théorie Il ne reste qu'à convaincre les ingénieurs de la validité de cette analyse.”
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It seems to me, he says, that the test of “Do we or not understand a particular subject in physics?” is, “Can we make a mechanical model of it?” I have an immense admiration for Maxwell’s model of electromagnetic induction. He makes a model that does all the wonderful things that electricity docs in inducing currents, etc., and there can be no doubt that a mechanical model of that kind is immensely instructive and is a step towards a definite mechanical theory of electromagnetism.
From stenographic report by A.S. Hathaway of the Lecture 20 Kelvin presented at Johns Hopkins University, Baltimore, on 'Molecular Dynamics and the Wave Theory of Light' (1884), 132. (Hathaway was a Mathematics fellow there.) This remark is not included in the first typeset publication—a revised version, printed twenty years later, in 1904, as Lord Kelvin’s Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. The original notes were reproduced by the “papyrograph” process. They are excerpted in Pierre Maurice Marie Duhem, Essays in the History and Philosophy of Science (1996), 54-55.
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It surely can be no offence to state, that the progress of science has led to new views, and that the consequences that can be deduced from the knowledge of a hundred facts may be very different from those deducible from five. It is also possible that the facts first known may be the exceptions to a rule and not the rule itself, and generalisations from these first-known facts, though useful at the time, may be highly mischievous, and impede the progress of the science if retained when it has made some advance.
Sections and Views Illustrative of Geological Phenomena (1830), viii.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule.* This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
[* This sentence has been reworded for the purpose of this quotation.]
In Leibnitz (1884), 44-45.
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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Just now nuclear physicists are writing a great deal about hypothetical particles called neutrinos supposed to account for certain peculiar facts observed in β-ray disintegration. We can perhaps best describe the neutrinos as little bits of spin-energy that have got detached. I am not much impressed by the neutrino theory. In an ordinary way I might say that I do not believe in neutrinos… But I have to reflect that a physicist may be an artist, and you never know where you are with artists. My old-fashioned kind of disbelief in neutrinos is scarcely enough. Dare I say that experimental physicists will not have sufficient ingenuity to make neutrinos? Whatever I may think, I am not going to be lured into a wager against the skill of experimenters under the impression that it is a wager against the truth of a theory. If they succeed in making neutrinos, perhaps even in developing industrial applications of them, I suppose I shall have to believe—though I may feel that they have not been playing quite fair.
From Tarner Lecture, 'Discovery or Manufacture?' (1938), in The Philosophy of Physical Science (1939, 2012), 112.
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Langmuir is a regular thinking machine. Put in facts, and you get out a theory.
Quoted in C. Guy Suits (ed.), The Collected Works of Irving Langmuir (1962), Vol. 12, 6.
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Later scientific theories are better than earlier ones for solving puzzles in the often quite different environments to which they are applied. That is not a relativist's position, and it displays the sense in which I am a convinced believer in scientific progress.
The Structure of Scientific Revolutions, 2nd edition (1970), 206.
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Let him [the author] be permitted also in all humility to add … that in consequence of the large arrears of algebraical and arithmetical speculations waiting in his mind their turn to be called into outward existence, he is driven to the alternative of leaving the fruits of his meditations to perish (as has been the fate of too many foregone theories, the still-born progeny of his brain, now forever resolved back again into the primordial matter of thought), or venturing to produce from time to time such imperfect sketches as the present, calculated to evoke the mental co-operation of his readers, in whom the algebraical instinct has been to some extent developed, rather than to satisfy the strict demands of rigorously systematic exposition.
In Philosophic Magazine (1863), 460.
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Let us award a just, a brilliant homage to those rare men whom nature has endowed with the precious privilege of arranging a thousand isolated facts, of making seductive theories spring from them; but let us not forget to state, that the scythe of the reaper had cut the stalks before one had thought of uniting them into sheaves!
In François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, 'Fourier', Biographies of Distinguished Scientific Men (1859), Vol. 1, 409.
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Let us now discuss the extent of the mathematical quality in Nature. According to the mechanistic scheme of physics or to its relativistic modification, one needs for the complete description of the universe not merely a complete system of equations of motion, but also a complete set of initial conditions, and it is only to the former of these that mathematical theories apply. The latter are considered to be not amenable to theoretical treatment and to be determinable only from observation.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 125.
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Let us now recapitulate all that has been said, and let us conclude that by hermetically sealing the vials, one is not always sure to prevent the birth of the animals in the infusions, boiled or done at room temperature, if the air inside has not felt the ravages of fire. If, on the contrary, this air has been powerfully heated, it will never allow the animals to be born, unless new air penetrates from outside into the vials. This means that it is indispensable for the production of the animals that they be provided with air which has not felt the action of fire. And as it would not be easy to prove that there were no tiny eggs disseminated and floating in the volume of air that the vials contain, it seems to me that suspicion regarding these eggs continues, and that trial by fire has not entirely done away with fears of their existence in the infusions. The partisans of the theory of ovaries will always have these fears and will not easily suffer anyone's undertaking to demolish them.
Nouvelles Recherches sur les Découvertes Microscopiques, et la Génération des Corps Organisés (1769), 134-5. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 510-1.
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Man has never been a particularly modest or self-deprecatory animal, and physical theory bears witness to this no less than many other important activities. The idea that thought is the measure of all things, that there is such a thing as utter logical rigor, that conclusions can be drawn endowed with an inescapable necessity, that mathematics has an absolute validity and controls experience—these are not the ideas of a modest animal. Not only do our theories betray these somewhat bumptious traits of self-appreciation, but especially obvious through them all is the thread of incorrigible optimism so characteristic of human beings.
In The Nature of Physical Theory (1936), 135-136.
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Marxism: The theory that all the important things in history are rooted in an economic motive, that history is a science, a science of the search for food.
From Daily News (31 Jul 1909). In Dale Ahlquist (ed.) The Universe According to G.K. Chesterton: A Dictionary of the Mad, Mundane and Metaphysical (2013), 71.
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Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe.
Lecture to Sigma Xi, 'The Problem of the Expanding Universe' (1941), printed in Sigma Xi Quarterly (1942), 30, 104-105. Reprinted in Smithsonian Institution Report of the Board of Regents (1943), 97, 123. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 63.
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Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics.
In 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97.
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Maxwell's theory is Maxwell's system of equations.
Electric Waves (1893), 21.

Men who believe too firmly in their theories, do not believe enough in the theories of others. So … these despisers of their fellows … make experiments only to destroy a theory, instead of to seek the truth.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 38.
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Men who have excessive faith in their theories or ideas are not only ill prepared for making discoveries; they also make very poor observations. Of necessity, they observe with a preconceived idea, and when they devise an experiment, they can see, in its results,only a confirmation of their theory. In this way they distort observation and often neglect very important facts because they do not further their aim.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 38.
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Men who have excessive faith in their theories … make poor observations, because they choose among the results of their experiments only what suits their object, neglecting whatever is unrelated to it and carefully setting aside everything which might tend toward the idea they wish to combat
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 38.
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Modern theories did not arise from revolutionary ideas which have been, so to speak, introduced into the exact sciences from without. On the contrary they have forced their way into research which was attempting consistently to carry out the programme of classical physics—they arise out of its very nature. It is for this reason that the beginnings of modern physics cannot be compared with the great upheavals of previous periods like the achievements of Copernicus. Copernicus’s idea was much more an import from outside into the concepts of the science of his time, and therefore caused far more telling changes in science than the ideas of modern physics are creating to-day.
In Philosophical Problems of Nuclear Science: Eight Lectures (1952), 13.
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MOLECULE, n. The ultimate, indivisible unit of matter. It is distinguished from the corpuscle, also the ultimate, indivisible unit of matter, by a closer resemblance to the atom, also the ultimate, indivisible unit of matter. Three great scientific theories of the structure of the universe are the molecular, the corpuscular and the atomic. A fourth affirms, with Haeckel, the condensation or precipitation of matter from ether—whose existence is proved by the condensation or precipitation. The present trend of scientific thought is toward the theory of ions. The ion differs from the molecule, the corpuscle and the atom in that it is an ion. A fifth theory is held by idiots, but it is doubtful if they know any more about the matter than the others.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  220-221.
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Morphological information has provided the greatest single source of data in the formulation and development of the theory of evolution and that even now, when the preponderance of work is experimental, the basis for interpretation in many areas of study remains the form and relationships of structures.
'Morphology, Paleontology, and Evolution', in Sol Tax (ed.), Evolution After Darwin, Vol. 1, The Evolution of Life (1960), 524.
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Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
Co-authored with Leopold Infeld.
The Evolution of Physics: The Growth of Ideas from the Early Concepts to Relativity and Quanta (1938), 29. Infeld was a Polish physicist (1898-1968).

Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you’ll never notice the flaws; if you doubt too much you won’t get started. It requires a lovely balance.
'You and Your Research', Bell Communications Research Colloquium Seminar, 7 Mar 1986.
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Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.
In 'A Plea for the Mathematician', Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.
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Mr Hooke sent, in his next letter [to Sir Isaac Newton] the whole of his Hypothesis, scil that the gravitation was reciprocall to the square of the distance: ... This is the greatest Discovery in Nature that ever was since the World's Creation. It was never so much as hinted by any man before. I wish he had writt plainer, and afforded a little more paper.
Brief Lives (1680), edited by Oliver Lawson Dick (1949), 166-7.
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Mr Justus Liebig is no doubt a very clever gentleman and a most profound chemist, but in our opinion he knows as much of agriculture as the horse that ploughs the ground, and there is not an old man that stands between the stilts of a plough in Virginia, that cannot tell him of facts totally at variance with his finest spun theories.
Magazine
The Southern Planter (1845), 3, 23.
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Much as I admired the elegance of physical theories, which at that time geology wholly lacked, I preferred a life in the woods to one in the laboratory.
From J. Tuzo Wilson, 'Early Days in University Geophysics', Ann. Rev. Earth Planet Sci. (1982), 10, 4.
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Much of the geographical work of the past hundred years... has either explicitly or implicitly taken its inspiration from biology, and in particular Darwin. Many of the original Darwinians, such as Hooker, Wallace, Huxley, Bates, and Darwin himself, were actively concerned with geographical exploration, and it was largely facts of geographical distribution in a spatial setting which provided Darwin with the germ of his theory.
'Darwin's Impact on Geography', Annals of the Association of American Geographers (1966), 56, 683.
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My Lord said that he who knew men only in this way [from history] was like one who had got the theory of anatomy perfectly, but who in practice would find himself very awkward and liable to mistakes. That he again who knew men by observation was like one who picked up anatomy by practice, but who like all empirics would for a long time be liable to gross errors.
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My theory of electrical forces is that they are called into play in insulating media by slight electric displacements, which put certain small portions of the medium into a state of distortion which, being resisted by the elasticity of the medium, produces an electromotive force ... I suppose the elasticity of the sphere to react on the electrical matter surrounding it, and press it downwards.
From the determination by Kohlrausch and Weber of the numerical relation between the statical and magnetic effects of electricity, I have determined the elasticity of the medium in air, and assuming that it is the same with the luminiferous ether I have determined the velocity of propagation of transverse vibrations.
The result is
193088 miles per second
(deduced from electrical & magnetic experiments).
Fizeau has determined the velocity of light
= 193118 miles per second
by direct experiment.
This coincidence is not merely numerical. I worked out the formulae in the country, before seeing Webers [sic] number, which is in millimetres, and I think we have now strong reason to believe, whether my theory is a fact or not, that the luminiferous and the electromagnetic medium are one.
Letter to Michael Faraday (19 Oct 1861). In P. M. Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1990), Vol. 1, 1846-1862, 684-6.
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My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology
In Scientific American (Sep 1958). As cited in '50, 100 & 150 years ago', Scientific American (Sep 2008), 299, No. 3, 14.
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Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does.
In Day the Universe Changed (1985), 11.
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Nazis started the Science of Eugenics. It’s the theory that to them, justified the holocaust. The problem is the Science has been broadly accepted around the world, including the United States. We even went as far as to hire the Scientists that were working on it and brought them over here rather then charging them with war crimes. [Project Paperclip] I think it is a very dangerous Science that contains ideologies that are a grave danger to the entire world.
James Dye
…...
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Newton’s theory is the circle of generalization which includes all the others [as Kepler’s laws, Ptolemy’s theory, etc.];—the highest point of the inductive ascent;—the catastrophe of the philosophic drama to which Plato had prologized;— the point to which men’s minds had been journeying for two thousand years.
In History of the Inductive Sciences, Bk. 7, chap. 2, sect. 5.
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No amount of experimentation can ever prove me right; a single experiment can prove me wrong.
Attributed to Einstein. Quoted in Alice Calaprice, The Quotable Einstein (1996), 224.
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No experimental result can ever kill a theory: any theory can be saved from counterinstances either by some auxiliary hypothesis or by a suitable reinterpretation of its terms.
In 'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London 1965 (1970), Vol. 4, 116.
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No generalizing beyond the data, no theory. No theory, no insight. And if no insight, why do research.
'Developing Theory About the Development of Theory,' in Ken G. Smith and Michael A. Hitt, Great Minds in Management: the Theory of Process Development (2005), 361.
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No matter how we twist and turn we shall always come back to the cell. The eternal merit of Schwann does not lie in his cell theory that has occupied the foreground for so long, and perhaps will soon be given up, but in his description of the development of the various tissues, and in his demonstration that this development (hence all physiological activity) is in the end traceable back to the cell. Now if pathology is nothing but physiology with obstacles, and diseased life nothing but healthy life interfered with by all manner of external and internal influences then pathology too must be referred back to the cell.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 13-14, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 81.
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No one has yet been found so firm of mind and purpose as resolutely to compel himself to sweep away all theories and common notions, and to apply the understanding, thus made fair and even, to a fresh examination of particulars. Thus it happens that human knowledge, as we have it, is a mere medley and ill-digested mass, made up of much credulity and much accident, and also of the childish notions which we at first imbibed.
In Novum Organum (1620), Book 2, Aphorism 20.
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No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. …because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory… The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity.
In 'Conclusion', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 326.
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No part of Mathematics suffers more from the triviality of its initial presentation to beginners than the great subject of series. Two minor examples of series, namely arithmetic and geometric series, are considered; these examples are important because they are the simplest examples of an important general theory. But the general ideas are never disclosed; and thus the examples, which exemplify nothing, are reduced to silly trivialities.
In An Introduction to Mathematics (1911), 194.
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No theory ever agrees with all the facts in its domain, yet it is not always the theory that is to blame. Facts are constituted by older ideologies, and a clash between facts and theories may be proof of progress. It is also a first step in our attempt to find the principles implicit in familiar observational notions.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 39. This is his summary at the head of Chapter 5.
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No theory of physics that deals only with physics will ever explain physics. I believe that as we go on trying to understand the universe, we are at the same time trying to understand man.
In The Intellectual Digest (June 1973), as quoted and cited in Mark Chandos, 'Philosophical Essay: Story Theory", Kosmoautikon: Exodus From Sapiens (2015).
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Nothing in our experience suggests the introduction of [complex numbers]. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 537.
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Nothing in physics seems so hopeful to as the idea that it is possible for a theory to have a high degree of symmetry was hidden from us in everyday life. The physicist's task is to find this deeper symmetry.
In American Scientist (1977) (as cited in The Atlantic (1984), 254, 81.) As an epigraph in Crystal and Dragon: The Cosmic Dance of Symmetry and Chaos in Nature, Art and Consciousness (1993), 139.
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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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Now that we locate them [genes] in the chromosomes are we justified in regarding them as material units; as chemical bodies of a higher order than molecules? Frankly, these are questions with which the working geneticist has not much concern himself, except now and then to speculate as to the nature of the postulated elements. There is no consensus of opinion amongst geneticists as to what the genes are—whether they are real or purely fictitious—because at the level at which the genetic experiments lie, it does not make the slightest difference whether the gene is a hypothetical unit, or whether the gene is a material particle. In either case the unit is associated with a specific chromosome, and can be localized there by purely genetic analysis. Hence, if the gene is a material unit, it is a piece of chromosome; if it is a fictitious unit, it must be referred to a definite location in a chromosome—the same place as on the other hypothesis. Therefore, it makes no difference in the actual work in genetics which point of view is taken. Between the characters that are used by the geneticist and the genes that his theory postulates lies the whole field of embryonic development.
'The Relation of Genetics to Physiology and Medicine', Nobel Lecture (4 Jun 1934). In Nobel Lectures, Physiology or Medicine 1922-1941 (1965), 315.
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Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.
From article 'Electro-magnetic Theory II', in The Electrician (16 Jan 1891), 26, No. 661, 331.
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Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
In Men of Mathematics (1937), 431-432.
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Observation is so wide awake, and facts are being so rapidly added to the sum of human experience, that it appears as if the theorizer would always be in arrears, and were doomed forever to arrive at imperfect conclusion; but the power to perceive a law is equally rare in all ages of the world, and depends but little on the number of facts observed.
In A Week on the Concord and Merrimack Rivers (1862), 383.
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Observations always involve theory.
In The Realm of the Nebulae (1936), 35.
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Of all regions of the earth none invites speculation more than that which lies beneath our feet, and in none is speculation more dangerous; yet, apart from speculation, it is little that we can say regarding the constitution of the interior of the earth. We know, with sufficient accuracy for most purposes, its size and shape: we know that its mean density is about 5½ times that of water, that the density must increase towards the centre, and that the temperature must be high, but beyond these facts little can be said to be known. Many theories of the earth have been propounded at different times: the central substance of the earth has been supposed to be fiery, fluid, solid, and gaseous in turn, till geologists have turned in despair from the subject, and become inclined to confine their attention to the outermost crust of the earth, leaving its centre as a playground for mathematicians.
'The Constitution of the Interior of the Earth, as Revealed by Earthquakes', Quarterly Journal of the Geological Society (1906), 62, 456.
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On one occasion when [William] Smart found him engrossed with his fundamental theory, he asked Eddington how many people he thought would understand what he was writing—after a pause came the reply, 'Perhaps seven.'
A. V. Douglas, The Life of Arthur Stanley Eddington (1956), 110.
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On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
Considerations on the Doctrine of Phlogiston (1796), 57-8.
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Once the data are in, the theory has to follow along meekly.
Hardfought (1983). Quoted in Gary Westfahl, Science Fiction Quotations (2005), 322.
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One day when the whole family had gone to a circus to see some extraordinary performing apes, I remained alone with my microscope, observing the life in the mobile cells of a transparent star-fish larva, when a new thought suddenly flashed across my brain. It struck me that similar cells might serve in the defence of the organism against intruders. Feeling that there was in this something of surpassing interest, I felt so excited that I began striding up and down the room and even went to the seashore in order to collect my thoughts.
I said to myself that, if my supposition was true, a splinter introduced into the body of a star-fish larva, devoid of blood-vessels or of a nervous system, should soon be surrounded by mobile cells as is to be observed in a man who runs a splinter into his finger. This was no sooner said than done.
There was a small garden to our dwelling, in which we had a few days previously organised a 'Christmas tree' for the children on a little tangerine tree; I fetched from it a few rose thorns and introduced them at once under the skin of some beautiful star-fish larvae as transparent as water.
I was too excited to sleep that night in the expectation of the result of my experiment, and very early the next morning I ascertained that it had fully succeeded.
That experiment formed the basis of the phagocyte theory, to the development of which I devoted the next twenty-five years of my life.
In Olga Metchnikoff, Life of Elie Metchnikoff 1845-1916 (1921), 116-7.
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One of Euler’s main recreations was music, and by cultivating it he brought with it all his geometrical spirit; … he rested his serious researches and composed his Essay of a New Theory of Music, published in 1739; a book full of new ideas presented in a new point of view, but that did not have a great success, apparently for the sole reason that it contains too much of geometry for the musician and too much music for the geometer.
From his Eulogy of Leonhard Euler, read at the Imperial Academy of Sciences of Saint Petersburg (23 Oct 1783). Published in 'Éloge de Léonard Euler, Prononcé en Français par Nicolas Fuss'. Collected in Leonard Euler, Oeuvres Complètes en Français de L. Euler (1839), Vol. 1, xii. From the original French, “Un des principaux délassements d'Euler était la musique, et en la cultivant il y apporta tout son esprit géométrique; … il accordait à ses recherches profondes, il composa son Essai d'une nouvelle théorie de la musique, publié en 1739; ouvrage rempli d'idées neuves ou présentées sous un nouveau point de vue, mais qui n’eut pas un grand succès, apparemment par la seule raison qu’il renferme trop de géométrie pour le musicien et trop de musique pour le géomètre.” English version by Webmaster using Google translate.
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One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.
In 'Number', Scientific American (Sep 1964), 211, No. 3, 55.
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Our most successful theories in physics are those that explicitly leave room for the unknown, while confining this room sufficiently to make the theory empirically disprovable. It does not matter whether this room is created by allowing for arbitrary forces as Newtonian dynamics does, or by allowing for arbitrary equations of state for matter, as General Relativity does, or for arbitrary motions of charges and dipoles, as Maxwell's electrodynamics does. To exclude the unknown wholly as a “unified field theory” or a “world equation” purports to do is pointless and of no scientific significance.
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Our natural way of thinking about these coarser emotions is that the mental perception of some fact excites the mental affection called the emotion, and that this latter state of mind gives rise to the bodily expression. My theory, on the contrary, is that the bodily changes follow directly the perception of the exciting fact, and that our feeling of the same changes as they occur IS the emotion. Common-sense says, we lose our fortune, are sorry and weep; we meet a bear, are frightened and run; we are insulted by a rival, are angry and strike. The hypothesis here to be defended says that this order of sequence is incorrect, that the one mental state is not immediately induced by the other, that the bodily manifestations must first be interposed between, and that the more rational statement is that we feel sorry because we cry, angry because we strike, afraid because we tremble, and not that we cry, strike, or tremble, because we are sorry, angry, or fearful, as the case may be. Without the bodily states following on the perception, the latter would be purely cognitive in form, pale, colorless, destitute of emotional warmth. We might then see the bear, and judge it best to run, receive the insult and deem it right to strike, but we should not actually feel afraid or angry.
The Principles or Psychology (1890), Vol. 2, 449-50.
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Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things, differing medical philosophies, different diagnoses and treatments—all of these are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge.
'Strategies of Resort to Curers in South India', contributed in Charles M. Leslie (ed.), Asian Medical Systems: A Comparative Study (1976), 185.
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Parkinson's Law is a purely scientific discovery, inapplicable except in theory to the politics of the day. It is not the business of the botanist to eradicate the weeds. Enough for him if he can tell us just how fast they grow.
Parkinson's Law or the Pursuit of Progress (1958), 15.
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People declare as much, without, apparently, looking into the matter very closely. They seem able to dispense with the conscientious observer’s scruples, when inflating their bladder of theory.
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Perfect as the wing of a bird may be, it will never enable the bird to fly if unsupported by the air. Facts are the air of science. Without them a man of science can never rise. Without them your theories are vain surmises. But while you are studying, observing, experimenting, do not remain content with the surface of things. Do not become a mere recorder of facts, but try to penetrate the mystery of their origin. Seek obstinately for the laws that govern them.
Translation of a note, 'Bequest of Pavlov to the Academic Youth of his Country', written a few days before his death for a student magazine, The Generation of the Victors. As published in 'Pavlov and the Spirit of Science', Nature (4 Apr 1936), 137, 572.
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Philosophers of science constantly discuss theories and representation of reality, but say almost nothing about experiment, technology, or the use of knowledge to alter the world. This is odd, because ‘experimental method’ used to be just another name for scientific method.... I hope [to] initiate a Back-to-Bacon movement, in which we attend more seriously to experimental science. Experimentation has a life of its own.
Representing and Intervening, p. 149f (1983). Announcing the author's intention to stress 'intervening' as an essential component of science.
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Positivism is a theory of knowledge according to which the only kind of sound knowledge available to human kind is that if science grounded in observation.
(1891). As given as an epigraph in M.J. Vinod and Meena Deshpande, Contemporary Political Theory (2013), 3.
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Precise facts alone are worthy of science. They cast premature theories into oblivion.
From the French original, “Les faits précis sont seuls dignes de la science. Ils rejettent dans l’oubli les théories prématurées”, by F. Marguet, 'Les “Souvenirs entomologiques” de J.-H. Fabre', Revue des Deux Mondes (1910), 60, 870. As translated in Augustin Fabre, The Life of Jean Henri Fabre: The Entomologist, 1823-1910 (1921), 315. Marguet gives no source citation for quote. It might be synthesized by Marguet from the writings of Fabre, to represent Fabre’s work ethic. (Webmaster so far has not found a primary source for the French sentences as verbatim. Can you help?)
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Professor Bethe … is a man who has this characteristic: If there’s a good experimental number you’ve got to figure it out from theory. So, he forced the quantum electrodynamics of the day to give him an answer [for the experimentally measured Lamb-shift of hydrogen], … and thus, made the most important discovery in the history of the theory of quantum electrodynamics. He worked this out on the train from Ithaca, New York to Schenectady.
Bethe calculated, what Lamb had experimentally just measured, for the separation of the 2S½ and 2P½ of hydrogen. Both theory and measurement yielded about one thousand megacycles for the Lamb-shift. Feynman was at the time associated with Bethe at Cornell. In Feynman’s Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 170.
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Professor, how can you bring yourself to enter this chemical building that has Ionic columns?
[Kahlenberg, a physical chemist, was an opponent of ionic theory.]
Quoted in Ralph Oesper, The Human Side of Scientists (1975), 106.
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Professors in every branch of the sciences, prefer their own theories to truth: the reason is that their theories are private property, but truth is common stock.
Reflection 378, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 169.
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Progress is achieved by exchanging our theories for new ones which go further than the old, until we find one based on a larger number of facts. … Theories are only hypotheses, verified by more or less numerous facts. Those verified by the most facts are the best, but even then they are never final, never to be absolutely believed.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 165.
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Propose theories which can be criticized. Think about possible decisive falsifying experiments—crucial experiments. But do not give up your theories too easily—not, at any rate, before you have critically examined your criticism.
'The Problem of Demarcation' (1974). Collected in David Miller (ed.) Popper Selections (1985), 126-127.
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Psychoanalytic theory is the most stupendous intellectual confidence trick of the twentieth century and a terminal product as well—something akin to a dinosaur or zeppelin in the history of ideas, a vast structure of radically unsound design and with no posterity.
'Victims of Psychiatry', The New York Review of Books (23 Jan 1975), 21. Cited in David E. Stannard, Shrinking History: On Freud and the Failure of Psychohistory (1980), 150.
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Psychology appeared to be a jungle of confusing, conflicting, and arbitrary concepts. These pre-scientific theories doubtless contained insights which still surpass in refinement those depended upon by psychiatrists or psychologists today. But who knows, among the many brilliant ideas offered, which are the true ones? Some will claim that the statements of one theorist are correct, but others will favour the views of another. Then there is no objective way of sorting out the truth except through scientific research.
From The Scientific Analysis of Personality (1965), 14.
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Psychotherapy–the theory that the patient will probably get well anyhow, and is certainly a damn fool.
In A Mencken Chrestomathy (1949, 1956), 626.
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Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.
In 'Non-Euclidian Geometry of the Fourth Dimension', collected in Henry Parker Manning (ed.), The Fourth Dimension Simply Explained (1910), 58.
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Pure mathematics is much more than an armoury of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations.
In 100 Years of Mathematics: a Personal Viewpoint (1981), 3.
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Quantum mechanics and relativity, taken together, are extraordinarily restrictive, and they therefore provide us with a great logical machine. We can explore with our minds any number of possible universes consisting of all kinds of mythical particles and interactions, but all except a very few can be rejected on a priori grounds because they are not simultaneously consistent with special relativity and quantum mechanics. Hopefully in the end we will find that only one theory is consistent with both and that theory will determine the nature of our particular universe.
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Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
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Quite recently the human descent theory has been stigmatized as the “gorilla theory of human ancestry.” All this despite the fact that Darwin himself, in the days when not a single bit of evidence regarding the fossil ancestors of man was recognized, distinctly stated that none of the known anthropoid apes, much less any of the known monkeys, should be considered in any way as ancestral to the human stock.
In Henry Fairfield Osborn, 'Osborn States the Case For Evolution', New York Times (12 Jul 1925), XX1. Written at the time of the Scopes Monkey Trial, in rebuttal of the anti-evolution position publicized by William Jennings Bryan.
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Reality is what kicks back when you kick it. This is just what physicists do with their particle accelerators. We kick reality and feel it kick back. From the intensity and duration of thousands of those kicks over many years, we have formed a coherent theory of matter and forces, called the standard model, that currently agrees with all observations.
In Has Science Foun