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Home > Category Index for Science Quotations > Category Index M > Category: Method

Method Quotes (505 quotes)

...Outer space, once a region of spirited international competition, is also a region of international cooperation. I realized this as early as 1959, when I attended an international conference on cosmic radiation in Moscow. At this conference, there were many differing views and differing methods of attack, but the problems were common ones to all of us and a unity of basic purpose was everywhere evident. Many of the papers presented there depended in an essential way upon others which had appeared originally in as many as three or four different languages. Surely science is one of the universal human activities.
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An diesen Apparate ist nichts neu als seine Einfachkeit und die vollkommene zu Verlaessigkeit, welche er gewaehst.
In this apparatus is nothing new but its simplicity and thorough trustworthiness.
On his revolutionary method of organic analysis.
Poggendorf's Annalen, (1831), 21, 4. Trans. W. H. Brock.
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Dilbert: Evolution must be true because it is a logical conclusion of the scientific method.
Dogbert: But science is based on the irrational belief that because we cannot perceive reality all at once, things called “time” and “cause and effect” exist.
Dilbert: That’s what I was taught and that’s what I believe.
Dogbert: Sounds cultish.
Dilbert comic strip (8 Feb 1992).
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Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics.
Physicist: I'm afraid I don’t understand the method of characteristics.
Neumann: In mathematics you don't understand things. You just get used to them.
Attributed, as related by Dr. Felix Smith (Head of Molecular Physics, Stanford Research Institute) to author Gary Zukav, who quoted it in The Dancing Wu Li Masters: An Overview of the New Physics (1979, 2001), 208, footnote. The physicist (a friend of Dr. Smith) worked at Los Alamos after WW II. It should be noted that although the author uses quotation marks around the spoken remarks, that they represent the author's memory of Dr. Smith's recollection, who heard it from the physicist. Therefore the fourth-hand wording is very likely not verbatim. Webmaster finds Zukav's book seems to be the only source for this quote.
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Phenomenology is not a philosophy; it is a philosophical method, a tool. It is like an adjustable spanner that can be used for dismantling a refrigerator or a car, or used for hammering in nails, or even for knocking somebody out.
In Introduction to the New Existentialism (1966), 92.
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Question: Explain why, in order to cook food by boiling, at the top of a high mountain, you must employ a different method from that used at the sea level.
Answer: It is easy to cook food at the sea level by boiling it, but once you get above the sea level the only plan is to fry it in its own fat. It is, in fact, impossible to boil water above the sea level by any amount of heat. A different method, therefore, would have to be employed to boil food at the top of a high mountain, but what that method is has not yet been discovered. The future may reveal it to a daring experimentalist.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 178-9, Question 11. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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Question: State what are the conditions favourable for the formation of dew. Describe an instrument for determining the dew point, and the method of using it.
Answer: This is easily proved from question 1. A body of gas as it ascends expands, cools, and deposits moisture; so if you walk up a hill the body of gas inside you expands, gives its heat to you, and deposits its moisture in the form of dew or common sweat. Hence these are the favourable conditions; and moreover it explains why you get warm by ascending a hill, in opposition to the well-known law of the Conservation of Energy.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 179, Question 12. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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Standardization does not produce although admirable as an efficiency method.
Aphorism listed Frederick Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932) (1999), 55, being Transactions of the American Philosophical Society, Held at Philadelphia For Promoting Useful Knowledge, Vol. 86, Pt. 6.
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The Charms of Statistics.—It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence. Some people hate the very name of statistics, but I find them full of beauty and interest. Whenever they are not brutalised, but delicately handled by the higher methods, and are warily interpreted, their power of dealing with complicated phenomena is extraordinary. They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man.
Natural Inheritance (1889), 62-3.
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A cell has a history; its structure is inherited, it grows, divides, and, as in the embryo of higher animals, the products of division differentiate on complex lines. Living cells, moreover, transmit all that is involved in their complex heredity. I am far from maintaining that these fundamental properties may not depend upon organisation at levels above any chemical level; to understand them may even call for different methods of thought; I do not pretend to know. But if there be a hierarchy of levels we must recognise each one, and the physical and chemical level which, I would again say, may be the level of self-maintenance, must always have a place in any ultimate complete description.
'Some Aspects of Biochemistry', The Irish Journal of Medical Science (1932), 79, 346.
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A cell of a higher organism contains a thousand different substances, arranged in a complex system. This great organized system was not discovered by chemical or physical methods; they are inadequate to its refinement and delicacy and complexity.
'The Cell in Relation to its Environment', Journal of the Maryland Academy of Sciences (1931), 2, 25.
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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.
In 'On the Development of the Methods of Theoretical Physics in Recent Times', Populäre Schriften, Essay 14. Address (22 Sep 1899) to the Meeting of Natural Scientists at Munich. Collected in Brian McGuinness (ed.), Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, Selected Writings (1974), 79.
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A comparison between the triplets tentatively deduced by these methods with the changes in amino acid sequence produced by mutation shows a fair measure of agreement.
In Nobel Lecture (11 Dec 1962). Collected in Nobel Lectures, Physiology or Medicine 1942-1962 (1964).
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A conflict arises when a religious community insists on the absolute truthfulness of all statements recorded in the Bible. This means an intervention on the part of religion into the sphere of science; this is where the struggle of the Church against the doctrines of Galileo and Darwin belongs. On the other hand, representatives of science have often made an attempt to arrive at fundamental judgments with respect to values and ends on the basis of scientific method, and in this way have set themselves in opposition to religion. These conflicts have all sprung from fatal errors.
…...
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A DNA sequence for the genome of bacteriophage ΦX174 of approximately 5,375 nucleotides has been determined using the rapid and simple “plus and minus” method. The sequence identifies many of the features responsible for the production of the proteins of the nine known genes of the organism, including initiation and termination sites for the proteins and RNAs. Two pairs of genes are coded by the same region of DNA using different reading frames.
[Paper co-author]
Frederick Sanger, et al., 'Nucleotide Sequence of Bacteriophage ΦX174 DNA', Nature (1977), 265, 687.
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A good method of discovery is to imagine certain members of a system removed and then see how what is left would behave: for example, where would we be if iron were absent from the world: this is an old example.
Aphorism 258 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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A great advantage of X-ray analysis as a method of chemical structure analysis is its power to show some totally unexpected and surprising structure with, at the same time, complete certainty.
In 'X-ray Analysis of Complicated Molecules', Nobel Lecture (11 Dec 1964). In Nobel Lectures: Chemistry 1942-1962 (1964), 83.
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A great part of its [higher arithmetic] theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.
Quoted in H. Eves, Mathematical Circles (1977) .
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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 137-138. (Note that Bernard overlooks how the statistical method can be useful: a surgeon announcing a mortality rate of 40% invites comparison. A surgeon with worse outcomes should adopt this method. If a surgeon has a better results, that method should be adopted.)
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A noteworthy and often-remarked similarity exists between the facts and methods of geology and those of linguistic study. The science of language is, as it were, the geology of the most modern period, the Age of the Man, having for its task to construct the history of development of the earth and its inhabitants from the time when the proper geological record remains silent … The remains of ancient speech are like strata deposited in bygone ages, telling of the forms of life then existing, and of the circumstances which determined or affected them; while words are as rolled pebbles, relics of yet more ancient formations, or as fossils, whose grade indicates the progress of organic life, and whose resemblances and relations show the correspondence or sequence of the different strata; while, everywhere, extensive denudation has marred the completeness of the record, and rendered impossible a detailed exhibition of the whole course of development.
In Language and the Study of Language (1867), 47.
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A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 140-141.
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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 scientific or technical study always consists of the following three steps:
1. One decides the objective.
2. One considers the method.
3. One evaluates the method in relation to the objective.
System of Experimental Design (1987), xxix.
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According to the older view, for every single effect of a serum, there was a separate substance, or at least a particular chemical group... A normal serum contained as many different haemagglutinins as it agglutinated different cells. The situation was undoubtedly made much simpler if, to use the Ehrlich terminology... the separate haptophore groups can combine with an extremely large number of receptors in stepwise differing quantities as a stain does with different animal tissues, though not always with the same intensity. A normal serum would therefore visibly affect such a large number of different blood cells... not because it contained countless special substances, but because of the colloids of the serum, and therefore of the agglutinins by reason of their chemical constitution and the electrochemical properties resulting from it. That this manner of representation is a considerable simplification is clear; it also opens the way to direct experimental testing by the methods of structural chemistry.
'Die Theorien der Antikorperbildung ... ', Wiener klinische Wöchenschrift (1909), 22, 1623-1631. Trans. Pauline M. H. Mazumdar.
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Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable.
In Science and Philosophy (1948), 116.
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All children are curious and I wonder by what process this trait becomes developed in some and suppressed in others. I suspect again that schools and colleges help in the suppression insofar as they meet curiosity by giving the answers, rather than by some method that leads from narrower questions to broader questions. It is hard to satisfy the curiosity of a child, and even harder to satisfy the curiosity of a scientist, and methods that meet curiosity with satisfaction are thus not apt to foster the development of the child into the scientist. I don't advocate turning all children into professional scientists, although I think there would be advantages if all adults retained something of the questioning attitude, if their curiosity were less easily satisfied by dogma, of whatever variety.
The Nature of Natural History (1950, 1990), 256-257.
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Almost every major systematic error which has deluded men for thousands of years relied on practical experience. Horoscopes, incantations, oracles, magic, witchcraft, the cures of witch doctors and of medical practitioners before the advent of modern medicine, were all firmly established through the centuries in the eyes of the public by their supposed practical successes. The scientific method was devised precisely for the purpose of elucidating the nature of things under more carefully controlled conditions and by more rigorous criteria than are present in the situations created by practical problems.
Personal Knowledge (1958), 183.
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Among the current discussions, the impact of new and sophisticated methods in the study of the past occupies an important place. The new 'scientific' or 'cliometric' history—born of the marriage contracted between historical problems and advanced statistical analysis, with economic theory as bridesmaid and the computer as best man—has made tremendous advances in the last generation.
Co-author with Geoffrey Rudolph Elton (1921-94), British historian. Which Road to the Past? Two Views of History (1983), 2.
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And yet in a funny way our lack of success led to our breakthrough; because, since we could not get a cell line off the shelf doing what we wanted, we were forced to construct it. And the original experiment ... developed into a method for the production of hybridomas ... [which] was of more importance than our original purpose.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 256-257.
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Another diversity of Methods is according to the subject or matter which is handled; for there is a great difference in delivery of the Mathematics, which are the most abstracted of knowledges, and Policy, which is the most immersed ... , yet we see how that opinion, besides the weakness of it, hath been of ill desert towards learning, as that which taketh the way to reduce learning to certain empty and barren generalities; being but the very husks and shells of sciences, all the kernel being forced out and expulsed with the torture and press of the method.
Advancement of Learning, Book 2. In James Spedding, The Works of Francis Bacon (1863), Vol. 6, 292-293 . Peter Pešić, explains that 'By Mathematics, he had in mind a sterile and rigid scheme of logical classifications, called dichotomies in his time,' inLabyrinth: A Search for the Hidden Meaning of Science (2001), 73.
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Anthropology has reached that point of development where the careful investigation of facts shakes our firm belief in the far-reaching theories that have been built up. The complexity of each phenomenon dawns on our minds, and makes us desirous of proceeding more cautiously. Heretofore we have seen the features common to all human thought. Now we begin to see their differences. We recognize that these are no less important than their similarities, and the value of detailed studies becomes apparent. Our aim has not changed, but our method must change. We are still searching for the laws that govern the growth of human culture, of human thought; but we recognize the fact that before we seek for what is common to all culture, we must analyze each culture by careful and exact methods, as the geologist analyzes the succession and order of deposits, as the biologist examines the forms of living matter. We see that the growth of human culture manifests itself in the growth of each special culture. Thus we have come to understand that before we can build up the theory of the growth of all human culture, we must know the growth of cultures that we find here and there among the most primitive tribes of the Arctic, of the deserts of Australia, and of the impenetrable forests of South America; and the progress of the civilization of antiquity and of our own times. We must, so far as we can, reconstruct the actual history of mankind, before we can hope to discover the laws underlying that history.
The Jesup North Pacific Expedition: Memoir of the American Museum of Natural History (1898), Vol. 1, 4.
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Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance.
Letter to William Huggins (13 Oct 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 451-2.
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Anyone who considers arithmetical methods of producing random digits is, of course, in the state of sin. For, as has been pointed out several times, there is no such thing as a random number—there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
In paper delivered at a symposium on the Monte Carlo method. 'Various Techniques Used in Connection with Random Digits', Journal of Research of the National Bureau of Standards, Appl. Math. Series, Vol. 3 (1951), 3, 36. Reprinted in John von Neumann: Collected Works (1963), Vol. 5, 700. Also often seen misquoted (?) as “Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.”
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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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Archimedes possessed so high a spirit, so profound a soul, and such treasures of highly scientific knowledge, that though these inventions [used to defend Syracuse against the Romans] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Art and science have their meeting point in method.
Caxtoniana (1875), 303.
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As a progressive discipline [biochemistry] belongs to the present century. From the experimental physiologists of the last century it obtained a charter, and, from a few pioneers of its own, a promise of success; but for the furtherance of its essential aim that century left it but a small inheritance of facts and methods. By its essential or ultimate aim I myself mean an adequate and acceptable description of molecular dynamics in living cells and tissues.
'Some Chemical Aspects of Life', Address (Sep 1933) in Report on the 103rd Meeting of the British Association for the Advancement of Science (1933), 3.
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As a scientist and geneticist I started to feel that science would probably soon reach the point where its interference into the life processes would be counterproductive if a properly designed governing policy was not implemented. A heavily overcrowded planet, ninety-five percent urbanized with nuclear energy as the main source of energy and with all aspects of life highly computerized, is not too pleasant a place for human life. The life of any individual soon will be predictable from birth to death. Medicine, able to cure almost everything, will make the load of accumulated defects too heavy in the next two or three centuries. The artificial prolongation of life, which looked like a very bright idea when I started research in aging about twenty-five years ago, has now lost its attractiveness for me. This is because I now know that the aging process is so multiform and complex that the real technology and chemistry of its prevention by artificial interference must be too complex and expensive. It would be the privilege of a few, not the method for the majority. I also was deeply concerned about the fact that most research is now either directly or indirectly related to military projects and objectives for power.
Quoted in 'Zhores A(leksandrovich) Medvedev', Contemporary Authors Online, Gale, 2002.
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As arithmetic and algebra are sciences of great clearness, certainty, and extent, which are immediately conversant about signs, upon the skilful use whereof they entirely depend, so a little attention to them may possibly help us to judge of the progress of the mind in other sciences, which, though differing in nature, design, and object, may yet agree in the general methods of proof and inquiry.
In Alciphron: or the Minute Philosopher, Dialogue 7, collected in The Works of George Berkeley D.D. (1784), Vol. 1, 621.
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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 for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.
In Cours d’analyse (1821), Preface, trans. Ivor Grattan-Guinness.
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As geology is essentially a historical science, the working method of the geologist resembles that of the historian. This makes the personality of the geologist of essential importance in the way he analyzes the past.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 453.
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As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths. For Hypotheses are not to be regarded in experimental Philosophy.
From Opticks, (1704, 2nd ed. 1718), Book 3, Query 31, 380.
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As soon as we touch the complex processes that go on in a living thing, be it plant or animal, we are at once forced to use the methods of this science [chemistry]. No longer will the microscope, the kymograph, the scalpel avail for the complete solution of the problem. For the further analysis of these phenomena which are in flux and flow, the investigator must associate himself with those who have labored in fields where molecules and atoms, rather than multicellular tissues or even unicellular organisms, are the units of study.
'Experimental and Chemical Studies of the Blood with an Appeal for More Extended Chemical Training for the Biological and Medical Investigator', Science (6 Aug 1915), 42, 176.
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As systematic unity is what first raises ordinary knowledge to the rank of science, that is, makes a system out of a mere aggregate of knowledge, architectonic is the doctrine of the scientific in our knowledge, and therefore necessarily forms part of the doctrine of method.
In'The Transcendental Doctrine of Method', Critique of Pure Reason (2016), 653. Note: architectonic = the art of constructing systems.
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Ask a scientist what he conceives the scientific method to be, and he will adopt an expression that is at once solemn and shifty eyed: solemn because he feels he ought to declare an opinion; shifty eyed because he is wondering how to conceal the fact that he has no opinion to declare. If taunted he would probably mumble something about “Induction” and “Establishing the Laws of Nature”, but if anyone working in a laboratory professed to be trying to establish the Laws of Nature by induction, we should think he was overdue for leave.
From a Jayne Lecture (1968), 'Induction and Intuition in Scientific Thought', printed in Memoirs of the American Philosophical Society (1969), Vol. 75. Lecture republished as Induction and Intuition in Scientific Thought (2009), 11. Also included in Peter Medawar, Pluto’s Republic (1984), 80.
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At the beginning of its existence as a science, biology was forced to take cognizance of the seemingly boundless variety of living things, for no exact study of life phenomena was possible until the apparent chaos of the distinct kinds of organisms had been reduced to a rational system. Systematics and morphology, two predominantly descriptive and observational disciplines, took precedence among biological sciences during the eighteenth and nineteenth centuries. More recently physiology has come to the foreground, accompanied by the introduction of quantitative methods and by a shift from the observationalism of the past to a predominance of experimentation.
In Genetics and the Origin of Species (1937, 1982), 6.
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Attitudes are more important than abilities
Motives are more important than methods
Character is more important than cleverness,
And the Heart takes precedence over the head.
when asked to autograph his book
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Bacon first taught the world the true method of the study of nature, and rescued science from that barbarism in which the followers of Aristotle, by a too servile imitation of their master.
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1845), 5.
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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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Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.
'Mathematical Problems', Bulletin of the American Mathematical Society (Jul 1902), 8, 441.
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But ... the working scientist ... is not consciously following any prescribed course of action, but feels complete freedom to utilize any method or device whatever which in the particular situation before him seems likely to yield the correct answer. ... No one standing on the outside can predict what the individual scientist will do or what method he will follow.
…...
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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 twenty years previous to 1847 a force had been at work in a little county town of Germany destined to effect the education of Christendom, and at the same time to enlarge the boundaries of human knowledge, first in chemistry and the allied branches, then in every other one of the natural sciences. The place was Giessen; the inventor Liebig; the method, a laboratory for instruction and research.
A Semi-Centennial Discourse, 1847-97' (28 Oct 1897), The Sheffield Scientific School of Yale University. Quoted in Daniel Coit Gilman, University Problems in the United States (1898), 120.
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But in practical affairs, particularly in politics, men are needed who combine human experience and interest in human relations with a knowledge of science and technology. Moreover, they must be men of action and not contemplation. I have the impression that no method of education can produce people with all the qualities required. I am haunted by the idea that this break in human civilization, caused by the discovery of the scientific method, may be irreparable.
Max Born
My Life & My Views (1968), 57-8.
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But it seems to me equally obvious that the orderliness is not all-pervasive. There are streaks of order to be found among the chaos, and the nature of scientific method is to seek these out and to stick to them when found and to reject or neglect the chaos. It is obvious that we have succeeded in finding some order in nature, but this fact in itself does not prove anything farther.
Scientific Method: An Inquiry into the Character and Validy of Natural Law (1923), 200.
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But medicine has long had all its means to hand, and has discovered both a principle and a method, through which the discoveries made during a long period are many and excellent, while full discovery will be made, if the inquirer be competent, conduct his researches with knowledge of the discoveries already made, and make them his starting-point. But anyone who, casting aside and rejecting all these means, attempts to conduct research in any other way or after another fashion, and asserts that he has found out anything, is and has been victim of deception.
Ancient Medicine, in Hippocrates, trans. W. H. S. Jones (1923), Vol. I, 15.
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But neither thirty years, nor thirty centuries, affect the clearness, or the charm, of Geometrical truths. Such a theorem as “the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the sides” is as dazzlingly beautiful now as it was in the day when Pythagoras first discovered it, and celebrated its advent, it is said, by sacrificing a hecatomb of oxen—a method of doing honour to Science that has always seemed to me slightly exaggerated and uncalled-for. One can imagine oneself, even in these degenerate days, marking the epoch of some brilliant scientific discovery by inviting a convivial friend or two, to join one in a beefsteak and a bottle of wine. But a hecatomb of oxen! It would produce a quite inconvenient supply of beef.
Written without pseudonym as Charles L. Dodgson, in Introduction to A New Theory of Parallels (1888, 1890), xvi. Note: a hecatomb is a great public sacrifice, originally of a hundred oxen.
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By research in pure science I mean research made without any idea of application to industrial matters but solely with the view of extending our knowledge of the Laws of Nature. I will give just one example of the ‘utility’ of this kind of research, one that has been brought into great prominence by the War—I mean the use of X-rays in surgery. Now, not to speak of what is beyond money value, the saving of pain, or, it may be, the life of the wounded, and of bitter grief to those who loved them, the benefit which the state has derived from the restoration of so many to life and limb, able to render services which would otherwise have been lost, is almost incalculable. Now, how was this method discovered? It was not the result of a research in applied science starting to find an improved method of locating bullet wounds. This might have led to improved probes, but we cannot imagine it leading to the discovery of X-rays. No, this method is due to an investigation in pure science, made with the object of discovering what is the nature of Electricity. The experiments which led to this discovery seemed to be as remote from ‘humanistic interest’ —to use a much misappropriated word—as anything that could well be imagined. The apparatus consisted of glass vessels from which the last drops of air had been sucked, and which emitted a weird greenish light when stimulated by formidable looking instruments called induction coils. Near by, perhaps, were great coils of wire and iron built up into electro-magnets. I know well the impression it made on the average spectator, for I have been occupied in experiments of this kind nearly all my life, notwithstanding the advice, given in perfect good faith, by non-scientific visitors to the laboratory, to put that aside and spend my time on something useful.
In Speech made on behalf of a delegation from the Conjoint Board of Scientific Studies in 1916 to Lord Crewe, then Lord President of the Council. In George Paget Thomson, J. J. Thomson and the Cavendish Laboratory in His Day (1965), 167-8.
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By these pleasures it is permitted to relax the mind with play, in turmoils of the mind, or when our labors are light, or in great tension, or as a method of passing the time. A reliable witness is Cicero, when he says (De Oratore, 2): 'men who are accustomed to hard daily toil, when by reason of the weather they are kept from their work, betake themselves to playing with a ball, or with knucklebones or with dice, or they may also contrive for themselves some new game at their leisure.'
The Book of Games of Chance (1663), final sentences, trans. Sydney Henry Gould. In Oysten Ore, The Gambling Scholar (1953), 241.
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By three methods we may learn wisdom: first, by reflection, which is noblest; second, by imitation, which is easiest; and third, by experience, which is the most bitter.
Confucius
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 109
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Chemistry affords two general methods of determining the constituent principles of bodies, the method of analysis, and that of synthesis. When, for instance, by combining water with alkohol, we form the species of liquor called, in commercial language, brandy or spirit of wine, we certainly have a right to conclude, that brandy, or spirit of wine, is composed of alkohol combined with water. We can produce the same result by the analytical method; and in general it ought to be considered as a principle in chemical science, never to rest satisfied without both these species of proofs. We have this advantage in the analysis of atmospherical air, being able both to decompound it, and to form it a new in the most satisfactory manner.
Elements of Chemistry (1790), trans. R. Kerr, 33.
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Chemistry is one of those branches of human knowledge which has built itself upon methods and instruments by which truth can presumably be determined. It has survived and grown because all its precepts and principles can be re-tested at any time and anywhere. So long as it remained the mysterious alchemy by which a few devotees, by devious and dubious means, presumed to change baser metals into gold, it did not flourish, but when it dealt with the fact that 56 g. of fine iron, when heated with 32 g. of flowers of sulfur, generated extra heat and gave exactly 88 g. of an entirely new substance, then additional steps could be taken by anyone. Scientific research in chemistry, since the birth of the balance and the thermometer, has been a steady growth of test and observation. It has disclosed a finite number of elementary reagents composing an infinite universe, and it is devoted to their inter-reaction for the benefit of mankind.
Address upon receiving the Perkin Medal Award, 'The Big Things in Chemistry', The Journal of Industrial and Engineering Chemistry (Feb 1921), 13, No. 2, 163.
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Darwin’s book is very important and serves me as a basis in natural science for the class struggle in history. One has to put up with the crude English method of development, of course. Despite all deficiencies not only is the death-blow dealt here for the first time to “teleology” in the natural sciences, but their rational meaning is empirically explained.
Karl Marx
Marx to Lasalle, 16 Jan 1861. In Marx-Engels Selected Correspondence, 1846-95, trans. Donna Torr (1934), 125.
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Defenders of the short-sighted men who in their greed and selfishness will, if permitted, rob our country of half its charm by their reckless extermination of all useful and beautiful wild things sometimes seek to champion them by saying the “the game belongs to the people.” So it does; and not merely to the people now alive, but to the unborn people. The “greatest good for the greatest number” applies to the number within the womb of time, compared to which those now alive form but an insignificant fraction. Our duty to the whole, including the unborn generations, bids us restrain an unprincipled present-day minority from wasting the heritage of these unborn generations. The movement for the conservation of wild life and the larger movement for the conservation of all our natural resources are essentially democratic in spirit, purpose, and method.
'Bird Reserves at the Mouth of the Mississippi', A Book-Lover's Holidays in the Open (1920), 300-301.
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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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Deprived, therefore, as regards this period, of any assistance from history, but relieved at the same time from the embarrassing interference of tradition, the archaeologist is free to follow the methods which have been so successfully pursued in geology—the rude bone and stone implements of bygone ages being to the one what the remains of extinct animals are to the other. The analogy may be pursued even further than this. Many mammalia which are extinct in Europe have representatives still living in other countries. Our fossil pachyderms, for instance, would be almost unintelligible but for the species which still inhabit some parts of Asia and Africa; the secondary marsupials are illustrated by their existing representatives in Australia and South America; and in the same manner, if we wish clearly to understand the antiquities of Europe, we must compare them with the rude implements and weapons still, or until lately, used by the savage races in other parts of the world. In fact, the Van Diemaner and South American are to the antiquary what the opossum and the sloth are to the geologist.
Pre-historic Times, as Illustrated by Ancient Remains, and the Manners and Customs of Modern Savages, (2nd ed. 1869, 1890), 429-430.
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Descriptive geometry has two objects: the first is to establish methods to represent on drawing paper which has only two dimensions,—namely, length and width,—all solids of nature which have three dimensions,—length, width, and depth,—provided, however, that these solids are capable of rigorous definition.
The second object is to furnish means to recognize accordingly an exact description of the forms of solids and to derive thereby all truths which result from their forms and their respective positions.
From On the Purpose of Descriptive Geometry as translated by Arnold Emch in David Eugene Smith, A Source Book in Mathematics (1929), 426.
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DISCUSSION, n. A method of confirming others in their errors.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  72.
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Edison was by far the most successful and, probably, the last exponent of the purely empirical method of investigation. Everything he achieved was the result of persistent trials and experiments often performed at random but always attesting extraordinary vigor and resource. Starting from a few known elements, he would make their combinations and permutations, tabulate them and run through the whole list, completing test after test with incredible rapidity until he obtained a clue. His mind was dominated by one idea, to leave no stone unturned, to exhaust every possibility.
As quoted in 'Tesla Says Edison Was an Empiricist', The New York Times (19 Oct 1931), 25.
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Educators may bring upon themselves unnecessary travail by taking a tactless and unjustifiable position about the relation between scientific and religious narratives. … The point is that profound but contradictory ideas may exist side by side, if they are constructed from different materials and methods and have different purposes. Each tells us something important about where we stand in the universe, and it is foolish to insist that they must despise each other.
In The End of Education: Redefining the Value of School (1995), 107.
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Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.
Ampère gives this example drawn from geometry to illustrate his meaning for “direct synthesis” when deductions following from more simple, already-known theorems leads to a new discovery. In James R. Hofmann, André-Marie Ampère (1996), 159. Cites Académie des Sciences Ampère Archives, box 261.
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Engineering is quite different from science. Scientists try to understand nature. Engineers try to make things that do not exist in nature. Engineers stress invention. To embody an invention the engineer must put his idea in concrete terms, and design something that people can use. That something can be a device, a gadget, a material, a method, a computing program, an innovative experiment, a new solution to a problem, or an improvement on what is existing. Since a design has to be concrete, it must have its geometry, dimensions, and characteristic numbers. Almost all engineers working on new designs find that they do not have all the needed information. Most often, they are limited by insufficient scientific knowledge. Thus they study mathematics, physics, chemistry, biology and mechanics. Often they have to add to the sciences relevant to their profession. Thus engineering sciences are born.
Y.C. Fung and P. Tong, Classical and Computational Solid Mechanics (2001), 1.
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Engineering is the art or science of utilizing, directing or instructing others in the utilization of the principles, forces, properties and substance of nature in the production, manufacture, construction, operation and use of things ... or of means, methods, machines, devices and structures ...
(1920}
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Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.
Vitruvius
In De Architectura, Book 1, Chap 6, Sec. 9. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 27-28.
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Essentially only one thing in life interests us: our psychical constitution, the mechanism of which was and is wrapped in darkness. All human resources, art, religion, literature, philosophy and historical sciences, all of them join in bringing lights in this darkness. But man has still another powerful resource: natural science with its strictly objective methods. This science, as we all know, is making huge progress every day. The facts and considerations which I have placed before you at the end of my lecture are one out of numerous attempts to employ a consistent, purely scientific method of thinking in the study of the mechanism of the highest manifestations of life in the dog, the representative of the animal kingdom that is man's best friend.
'Physiology of Digestion', Nobel Lecture (12 Dec 1904). In Nobel Lectures: Physiology or Medicine 1901-1921 (1967), 134
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Events and developments, such as … the Copernican Revolution, … occurred only because some thinkers either decided not to be bound by certain “obvious” methodological rules, or because they unwittingly broke them.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14.
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Every discoverer of a new truth, or inventor of the method which evolves it, makes a dozen, perhaps fifty, useless combinations, experiments, or trials for one successful one. In the realm of electricity or of mechanics there is no objection to this. But when such rejected failures involve a torture of animals, sometimes fearful in its character, there is a distinct objection to it.
From 'Vivisection', an original paper in Surgical Anaesthesia: Addresses, and Other Papers (1894, 1900), 369-370.
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Everybody praises the incomparable power of the mathematical method, but so is everybody aware of its incomparable unpopularity.
In Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 13, 17.
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Everywhere science is enriched by unscientific methods and unscientific results, ... the separation of science and non-science is not only artificial but also detrimental to the advancement of knowledge. If we want to understand nature, if we want to master our physical surroundings, then we must use all ideas, all methods, and not just a small selection of them.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975), 305-6.
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Experimentation is the least arrogant method of gaining knowledge. The experimenter humbly asks a question of nature.
[Unverified. Please contact Webmaster if you can identify the primary source.]
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Facts may belong to the past history of mankind, to the social statistics of our great cities, to the atmosphere of the most distant stars, to the digestive organs of a worm, or to the life of a scarcely visible bacillus. It is not the facts themselves which form science, but the method in which they are dealt with.
From The Grammar of Science (1892), 15.
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Few will deny that even in the first scientific instruction in mathematics the most rigorous method is to be given preference over all others. Especially will every teacher prefer a consistent proof to one which is based on fallacies or proceeds in a vicious circle, indeed it will be morally impossible for the teacher to present a proof of the latter kind consciously and thus in a sense deceive his pupils. Notwithstanding these objectionable so-called proofs, so far as the foundation and the development of the system is concerned, predominate in our textbooks to the present time. Perhaps it will be answered, that rigorous proof is found too difficult for the pupil’s power of comprehension. Should this be anywhere the case,—which would only indicate some defect in the plan or treatment of the whole,—the only remedy would be to merely state the theorem in a historic way, and forego a proof with the frank confession that no proof has been found which could be comprehended by the pupil; a remedy which is ever doubtful and should only be applied in the case of extreme necessity. But this remedy is to be preferred to a proof which is no proof, and is therefore either wholly unintelligible to the pupil, or deceives him with an appearance of knowledge which opens the door to all superficiality and lack of scientific method.
In 'Stücke aus dem Lehrbuche der Arithmetik', Werke, Bd. 2 (1904), 296.
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For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.
Letter (4 Aug 1597) to Kepler, expressing thanks and interest in the book Kepler sent him. As quoted in translation in Jackson J. Spielvogel, Western Civilization: Alternate Volume: Since 1300 (2010), Vol. 2, 494.
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For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.
In Letter to Johannes Kepler. As quoted in The Portable Renaissance Reader (1968), 597.
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For just as musical instruments are brought to perfection of clearness in the sound of their strings by means of bronze plates or horn sounding boards, so the ancients devised methods of increasing the power of the voice in theaters through the application of the science of harmony.
Vitruvius
In Vitruvius Pollio and Morris Hicky Morgan (trans.), 'Book V: Chapter III', Vitruvius, the Ten Books on Architecture (1914), 139. From the original Latin, “Ergo veteres Architecti, naturae vestigia persecuti, indagationibus vocis scandentes theatrorum perfecerunt gradationes: & quaesiuerunt per canonicam mathematicorum,& musicam rationem, ut quaecunq; vox effet in scena, clarior & suauior ad spectatorum perueniret aures. Uti enim organa in aeneis laminis, aut corneis, diesi ad chordarum sonituum claritatem perficiuntur: sic theatrorum, per harmonicen ad augendam vocem, ratiocinationes ab antiquis sunt constitutae.” In De Architectura libri decem (1552), 175.
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For me, a rocket is only a means--only a method of reaching the depths of space—and not an end in itself… There’s no doubt that it’s very important to have rocket ships since they will help mankind to settle elsewhere in the universe. But what I’m working for is this resettling… The whole idea is to move away from the Earth to settlements in space.
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For the educated, the authority of science rested on the strictness of its method; for the mass, it rested on its powers of explanation.
In Science: The Glorious Entertainment (1964).
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For the holy Bible and the phenomena of nature proceed alike from the divine Word, the former as the dictate of the Holy Ghost and the latter as the observant executrix of God's commands. It is necessary for the Bible, in order to be accommodated to the understanding of every man, to speak many things which appear to differ from the absolute truth so far as the bare meaning of the words is concerned. But Nature, on the other hand, is inexorable and immutable; she never transgresses the laws imposed upon her, or cares a whit whether her abstruse reasons and methods of operation are understandable to men. For that reason it appears that nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called in question (much less condemned) upon the testimony of biblical passages which may have some different meaning beneath their words.
Letter to Madame Christina of Lorraine, Grand Duchess of Tuscany: Concerning the Use of Biblical Quotations in Matters of Science (1615), trans. Stillman Drake, Discoveries and Opinions of Galileo (1957), 182-3.
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For the most part, statistics is a method of investigation that is used when other methods are of no avail; it is often a last resort and a forlorn hope.
In Facts from Figures (1951), 3.
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For, every time a certain portion is destroyed, be it of the brain or of the spinal cord, a function is compelled to cease suddenly, and before the time known beforehand when it would stop naturally, it is certain that this function depends upon the area destroyed. It is in this way that I have recognized that the prime motive power of respiration has its seat in that part of the medulla oblongata that gives rise to the nerves of the eighth pair [vagi]; and it is by this method that up to a certain point it will be possible to discover the use of certain parts of the brain.
Expériences sur le Principe de la Vie, Notamment sur celui des Mouvements du Coeur, et sur le Siege de ce Principe (1812), 148-149. Translated in Edwin Clarke and L. S. Jacyna, Nineteenth Century Origins of Neuroscientific Concepts (1987), 247.
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Fragments of the natural method must be sought with the greatest care. This is the first and last desideratum among botanists.
Nature makes no jumps.
[Natura non facit saltus]
All taxa show relationships on all sides like the countries on a map of the world.
Philosophia Botanica (1751), aphorism 77. Trans. Frans A. Stafleu, Linnaeus and the Linnaeans: The Spreading of their Ideas in Systematic Botany, 1735-1789 (1971), 45.
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From the intensity of the spots near the centre, we can infer that the protein molecules are relatively dense globular bodies, perhaps joined together by valency bridges, but in any event separated by relatively large spaces which contain water. From the intensity of the more distant spots, it can be inferred that the arrangement of atoms inside the protein molecule is also of a perfectly definite kind, although without the periodicities characterising the fibrous proteins. The observations are compatible with oblate spheroidal molecules of diameters about 25 A. and 35 A., arranged in hexagonal screw-axis. ... At this stage, such ideas are merely speculative, but now that a crystalline protein has been made to give X-ray photographs, it is clear that we have the means of checking them and, by examining the structure of all crystalline proteins, arriving at a far more detailed conclusion about protein structure than previous physical or chemical methods have been able to give.
'X-Ray Photographs of Crystalline Pepsin', Nature (1934), 133, 795.
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Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
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Genuine religion has its root deep down in the heart of humanity and in the reality of things. It is not surprising that by our methods we fail to grasp it: the actions of the Deity make no appeal to any special sense, only a universal appeal; and our methods are, as we know, incompetent to detect complete uniformity. There is a principle of Relativity here, and unless we encounter flaw or jar or change, nothing in us responds; we are deaf and blind therefore to the Immanent Grandeur, unless we have insight enough to recognise in the woven fabric of existence, flowing steadily from the loom in an infinite progress towards perfection, the ever-growing garment of a transcendent God.
Continuity: The Presidential Address to the British Association (1913), 92-93.
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Geometric writings are not rare in which one would seek in vain for an idea at all novel, for a result which sooner or later might be of service, for anything in fact which might be destined to survive in the science; and one finds instead treatises on trivial problems or investigations on special forms which have absolutely no use, no importance, which have their origin not in the science itself but in the caprice of the author; or one finds applications of known methods which have already been made thousands of times; or generalizations from known results which are so easily made that the knowledge of the latter suffices to give at once the former. Now such work is not merely useless; it is actually harmful because it produces a real incumbrance in the science and an embarrassment for the more serious investigators; and because often it crowds out certain lines of thought which might well have deserved to be studied.
From 'On Some Recent Tendencies in Geometric Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
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God pity the man of science who believes in nothing but what he can prove by scientific methods; for if ever a human being needed divine pity, he does.
Every-Day Topics, a Book of Briefs (1882), 5.
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Gold is found in our own part of the world; not to mention the gold extracted from the earth in India by the ants, and in Scythia by the Griffins. Among us it is procured in three different ways; the first of which is in the shape of dust, found in running streams. … A second mode of obtaining gold is by sinking shafts or seeking among the debris of mountains …. The third method of obtaining gold surpasses the labors of the giants even: by the aid of galleries driven to a long distance, mountains are excavated by the light of torches, the duration of which forms the set times for work, the workmen never seeing the light of day for many months together.
In Pliny and John Bostock (trans.), The Natural History of Pliny (1857), Vol. 6, 99-101.
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Good methods can teach us to develop and use to better purpose the faculties with which nature has endowed us, while poor methods may prevent us from turning them to good account. Thus the genius of inventiveness, so precious in the sciences, may be diminished or even smothered by a poor method, while a good method may increase and develop it.
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GOOSE, n. A bird that supplies quills for writing. These, by some occult process of nature, are penetrated and suffused with various degrees of the bird's intellectual energies and emotional character, so that when inked and drawn mechanically across paper by a person called an "author," there results a very fair and accurate transcript of the fowl's thought and feeling. The difference in geese, as discovered by this ingenious method, is considerable: many are found to have only trivial and insignificant powers, but some are seen to be very great geese indeed.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  119-120.
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Hardly a year passes that fails to find a new, oft-times exotic, research method or technique added to the armamentarium of political inquiry. Anyone who cannot negotiate Chi squares, assess randomization, statistical significance, and standard deviations
…...
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He that would learn by experiments, ought to proceed from particulars to generals; but the method of instructing academically, proceeds from generals to particulars
As quoted in Thomas Steele Hall, A Source Book in Animal Biology (1951), 486.
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He who seeks for methods without having a definite problem in mind seeks for the most part in vain.
'Mathematical Problems', Bulletin of the American Mathematical Society (Jul 1902), 8, 444.
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He [Lord Bacon] appears to have been utterly ignorant of the discoveries which had just been made by Kepler’s calculations … he does not say a word about Napier’s Logarithms, which had been published only nine years before and reprinted more than once in the interval. He complained that no considerable advance had been made in Geometry beyond Euclid, without taking any notice of what had been done by Archimedes and Apollonius. He saw the importance of determining accurately the specific gravities of different substances, and himself attempted to form a table of them by a rude process of his own, without knowing of the more scientific though still imperfect methods previously employed by Archimedes, Ghetaldus and Porta. He speaks of the εὕρηκα of Archimedes in a manner which implies that he did not clearly appreciate either the problem to be solved or the principles upon which the solution depended. In reviewing the progress of Mechanics, he makes no mention either of Archimedes, or Stevinus, Galileo, Guldinus, or Ghetaldus. He makes no allusion to the theory of Equilibrium. He observes that a ball of one pound weight will fall nearly as fast through the air as a ball of two, without alluding to the theory of acceleration of falling bodies, which had been made known by Galileo more than thirty years before. He proposed an inquiry with regard to the lever,—namely, whether in a balance with arms of different length but equal weight the distance from the fulcrum has any effect upon the inclination—though the theory of the lever was as well understood in his own time as it is now. … He speaks of the poles of the earth as fixed, in a manner which seems to imply that he was not acquainted with the precession of the equinoxes; and in another place, of the north pole being above and the south pole below, as a reason why in our hemisphere the north winds predominate over the south.
From Spedding’s 'Preface' to De Interpretations Naturae Proœmium, in The Works of Francis Bacon (1857), Vol. 3, 511-512. [Note: the Greek word “εὕρηκα” is “Eureka” —Webmaster.]
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HEART, n. An automatic, muscular blood- pump. Figuratively, this useful organ is said to be the seat of emotions and sentiments—a very pretty fancy which, however, is nothing but a survival of a once universal belief. It is now known that the sentiments and emotions reside in the stomach, being evolved from food by chemical action of the gastric fluid. The exact process by which a beefsteak becomes a feeling—tender or not, according to the age of the animal from which it was cut; the successive stages of elaboration through which a caviar sandwich is transmuted to a quaint fancy and reappears as a pungent epigram; the marvelous functional methods of converting a hard-boiled egg into religious contrition, or a cream-puff into a sigh of sensibility—these things have been patiently ascertained by M. Pasteur, and by him expounded with convincing lucidity. 
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  133-134.
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Hence, even in the domain of natural science the aid of the experimental method becomes indispensable whenever the problem set is the analysis of transient and impermanent phenomena, and not merely the observation of persistent and relatively constant objects.
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His [J.J. Sylvester’s] lectures were generally the result of his thought for the preceding day or two, and often were suggested by ideas that came to him while talking. The one great advantage that this method had for his students was that everything was fresh, and we saw, as it were, the very genesis of his ideas. One could not help being inspired by such teaching.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 267-268.
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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 science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation (you don’t see electrons, gravity, or black holes either).
…...
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History shows that the human animal has always learned but progress used to be very slow. This was because learning often depended on the chance coming together of a potentially informative event on the one hand and a perceptive observer on the other. Scientific method accelerated that process.
In article Total Quality: Its Origins and its Future (1995), published at the Center for Quality and Productivity Improvement.
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I am a creationist and an evolutionist. Evolution is God's, or Nature's method of creation. Creation is not an event that happened in 4004 BC; it is a process that began some 10 billion years ago and is still under way.
In 'Nothing in Biology Makes Sense Except in the Light of Evolution', The American Biology Teacher (Mar 1973), 125-129.
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I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge—knowledge mingled with ignorance, producing doubt.
The Principles of Science: A Treatise on Logic and Scientific Method, 2nd edition (1877), 197.
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I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.
In Teaching of Mathematics (1902), 14.
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I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
Religion and Science (1935), 243.
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I consider [H. G. Wells], as a purely imaginative writer, to be deserving of very high praise, but our methods are entirely different. I have always made a point in my romances of basing my so-called inventions upon a groundwork of actual fact, and of using in their construction methods and materials which are not entirely without the pale of contemporary engineering skill and knowledge. ... The creations of Mr. Wells, on the other hand, belong unreservedly to an age and degree of scientific knowledge far removed from the present, though I will not say entirely beyond the limits of the possible.
Gordon Jones, 'Jules Verne at Home', Temple Bar (Jun 1904), 129, 670.
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I do not forget that Medicine and Veterinary practice are foreign to me. I desire judgment and criticism upon all my contributions. Little tolerant of frivolous or prejudiced contradiction, contemptuous of that ignorant criticism which doubts on principle, I welcome with open arms the militant attack which has a method of doubting and whose rule of conduct has the motto “More light.”
In Louis Pasteur and Harold Clarence Ernst (trans), The Germ Theory and Its Application to Medicine and Surgery, Chap. 12. Reprinted in Charles W. Eliot (ed.), The Harvard Classics: Scientific Papers: Physiology, Medicine, Surgery, Geology (1897, 1910), Vol. 38, 401-402. Cited as read before French Academy of Science (20 Apr 1878), published in Comptes Rendus de l’Académie des Sciences, 84, 1037-43.
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I do not think we can impose limits on research. Through hundreds of thousands of years, man’s intellectual curiosity has been essential to all the gains we have made. Although in recent times we have progressed from chance and hit-or-miss methods to consciously directed research, we still cannot know in advance what the results may be. It would be regressive and dangerous to trammel the free search for new forms of truth.
In Margaret Mead and Rhoda Bubendey Métraux (ed.), Margaret Mead, Some Personal Views (1979), 89.
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I do not … reject the use of statistics in medicine, but I condemn not trying to get beyond them and believing in statistics as the foundation of medical science. … Statistics … apply only to cases in which the cause of the facts observed is still [uncertain or] indeterminate. … There will always be some indeterminism … in all the sciences, and more in medicine than in any other. But man’s intellectual conquest consists in lessening and driving back indeterminism in proportion as he gains ground for determinism by the help of the experimental method..
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 138-140.
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I have been described on more than one occasion as belonging to something called the 'Functional School of Social Anthropology' and even as being its leader, or one of its leaders. This Functional School does not really exist; it is a myth invented by Professor Malinowski ... There is no place in natural science for 'schools' in this sense, and I regard social anthropology as a branch of natural science. ... I conceive of social anthropology as the theoretical natural science of human society, that is, the investigation of social phenomena by methods essentially similar to those used in the physical and biological sciences. I am quite willing to call the subject 'comparative sociology', if anyone so wishes.
In A. Kuper, Anthropologists and Anthropology: The Modern British School (1983), 36.
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I have come to the conclusion that the exertion, without which a knowledge of mathematics cannot be acquired, is not materially increased by logical rigor in the method of instruction.
In Jahresbericht der Deutschen Mathematiker Vereinigung (1898), 143.
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I have no fault to find with those who teach geometry. That science is the only one which has not produced sects; it is founded on analysis and on synthesis and on the calculus; it does not occupy itself with the probable truth; moreover it has the same method in every country.
In Oeuvres de Frederic Le Grand edited by J.D.E. Preuss (1849), Vol. 7, 100. In Robert Édouard Moritz, Memorabilia Mathematica (1917), 310.
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I have often thought that an interesting essay might be written on the influence of race on the selection of mathematical methods. methods. The Semitic races had a special genius for arithmetic and algebra, but as far as I know have never produced a single geometrician of any eminence. The Greeks on the other hand adopted a geometrical procedure wherever it was possible, and they even treated arithmetic as a branch of geometry by means of the device of representing numbers by lines.
In A History of the Study of Mathematics at Cambridge (1889), 123
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I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.
Max Born
My Life & My Views (1968), 48.
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I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.
Explaining his choice for the exposition in historical order of the topics in A Treatise on Differential Equations (1859), Preface, v-vi.
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I regarded as quite useless the reading of large treatises of pure analysis: too large a number of methods pass at once before the eyes. It is in the works of application that one must study them; one judges their utility there and appraises the manner of making use of them.
As reported by J. F. Maurice in Moniteur Universel (1814), 228.
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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 see with much pleasure that you are working on a large work on the integral Calculus [ ... ] The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.
Letter to S. F. Lacroix, 1792. Quoted in S. F. Lacroix, Traité du calcul differentiel et du calcul integral (1797), Vol. 1, xxiv, trans. Ivor Grattan-Guinness.
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I think equation guessing might be the best method to proceed to obtain the laws for the part of physics which is presently unknown.
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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I took a glass retort, capable of containing eight ounces of water, and distilled fuming spirit of nitre according to the usual method. In the beginning the acid passed over red, then it became colourless, and lastly again all red: no sooner did this happen, than I took away the receiver; and tied to the mouth of the retort a bladder emptied of air, which I had moistened in its inside with milk of lime lac calcis, (i.e. lime-water, containing more quicklime than water can dissolve) to prevent its being corroded by the acid. Then I continued the distillation, and the bladder gradually expanded. Here-upon I left every thing to cool, tied up the bladder, and took it off from the mouth of the retort.— I filled a ten-ounce glass with this air and put a small burning candle into it; when immediately the candle burnt with a large flame, of so vivid a light that it dazzled the eyes. I mixed one part of this air with three parts of air, wherein fire would not burn; and this mixture afforded air, in every respect familiar to the common sort. Since this air is absolutely necessary for the generation of fire, and makes about one-third of our common air, I shall henceforth, for shortness sake call it empyreal air, [literally fire-air] the air which is unserviceable for the fiery phenomenon, and which makes abut two-thirds of common air, I shall for the future call foul air [literally corrupted air].
Chemische Abhandlung von der Luft und dem Feuer (1777), Chemical Observations and Experiments on Air and Fire (1780), trans. J. R. Forster, 34-5.
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I was fascinated by fractional distillation as a method while still a school-boy, and built in the cellar of my home, which was my combined workshop and laboratory, distillation columns, packed with coke of graded size, some five feet in height. They were made from coffee tins (obtained from the kitchen), with the bottoms removed and soldered together! Experience with them served me in good stead and by the time I graduated I had a good understanding of the problems of fractional distillation.
Nobel Lectures in Chemistry (1999), Vol. 3, 359-360.
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I was in a Printing-house in Hell, and saw the method in which knowledge is transmitted from generation to generation.
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I wish that one would be persuaded that psychological experiments, especially those on the complex functions, are not improved [by large studies]; the statistical method gives only mediocre results; some recent examples demonstrate that. The American authors, who love to do things big, often publish experiments that have been conducted on hundreds and thousands of people; they instinctively obey the prejudice that the persuasiveness of a work is proportional to the number of observations. This is only an illusion.
L' Études expérimentale de l'intelligence (1903), 299.
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I … share an excitement and a certain pride in the wonders opened up by scientific investigation …, and also a recognition of the value in scientific method of keeping the hypotheses as simple as possible—my Oxford tutor gave me a great respect for Occam’s razor.
In Letter to periodical, Chemistry and Industry (17 Feb 1997).
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If a little less time was devoted to the translation of letters by Julius Caesar describing Britain 2000 years ago and a little more time was spent on teaching children how to describe (in simple modern English) the method whereby ethylene was converted into polythene in 1933 in the ICI laboratories at Northwich, and to discussing the enormous social changes which have resulted from this discovery, then I believe that we should be training future leaders in this country to face the world of tomorrow far more effectively than we are at the present time.
Quoted in an Obituary, D. P. Craig, Biographical Memoirs of Fellows of the Royal Society (1972), 18, 461.
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If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
From final remarks in 'The Semantic Conception of Truth and the Foundations of Semantics' (1944), collected in Leonard Linsky (ed.), Semantics and the Philosophy of Language: A Collection of Readings (1952), 41.
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If I had my life to live over again I would not devote it to develop new industrial processes: I would try to add my humble efforts to use Science to the betterment of the human race.
I despair of the helter-skelter methods of our vaulted homo sapiens, misguided by his ignorance and his politicians. If we continue our ways, there is every possibility that the human race may follow the road of former living races of animals whose fossils proclaim that they were not fit to continue. Religion, laws and morals is not enough. We need more. Science can help us.
Letter to a friend (14 Jan 1934). In Savage Grace (1985, 2007), 62.
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If I have put the case of science at all correctly, the reader will have recognised that modern science does much more than demand that it shall be left in undisturbed possession of what the theologian and metaphysician please to term its “legitimate field.” It claims that the whole range of phenomena, mental as well as physical—the entire universe—is its field. It asserts that the scientific method is the sole gateway to the whole region of knowledge.
From The Grammar of Science (1892), 29-30.
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If it were possible for a metaphysician to be a golfer, he might perhaps occasionally notice that his ball, instead of moving forward in a vertical plane (like the generality of projectiles, such as brickbats and cricket balls), skewed away gradually to the right. If he did notice it, his methods would naturally lead him to content himself with his caddies’s remark-“ye heeled that yin,” or “Ye jist sliced it.” … But a scientific man is not to be put off with such flimsy verbiage as that. He must know more. What is “Heeling”, what is “slicing”, and why would either operation (if it could be thoroughly carried out) send a ball as if to cover point, thence to long slip, and finally behind back-stop? These, as Falstaff said, are “questions to be asked.”
In 'The Unwritten Chapter on Golf, Nature (1887), 36, 502.
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If it were possible to transfer the methods of physical or of biological science directly to the study of man, the transfer would long ago have been made ... We have failed not for lack of hypotheses which equate man with the rest of the universe, but for lack of a hypothesis (short of animism) which provides for the peculiar divergence of man ... Let me now state my belief that the peculiar factor in man which forbids our explaining his actions upon the ordinary plane of biology is a highly specialized and unstable biological complex, and that this factor is none other than language.
Linguistics as a Science (1930), 555.
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If the question were, “What ought to be the next objective in science?” my answer would be the teaching of science to the young, so that when the whole population grew up there would be a far more general background of common sense, based on a knowledge of the real meaning of the scientific method of discovering truth.
Marion Savin Selections from the Scientific Correspondence of Elihu Thomson (1971), v.
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If we are to achieve results never before accomplished, we must employ methods never before attempted.
…...
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If we betake ourselves to the statistical method, we do so confessing that we are unable to follow the details of each individual case, and expecting that the effects of widespread causes, though very different in each individual, will produce an average result on the whole nation, from a study of which we may estimate the character and propensities of an imaginary being called the Mean Man.
'Does the Progress of Physical Science tend to give any advantage to the opinion of necessity (or determinism) over that of the continuency of Events and the Freedom of the Will?' In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 818.
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If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds. To him who is a discoverer in this field the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities.
From 'On the Method of Theoretical Physics', in Essays in Science (1934, 2004), 12.
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If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don’t listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.
In Herbert Spencer Lecture at Oxford (10 Jun 1933), 'On the Methods of Theoretical Physics'. Printed inPhilosophy of Science (Apr 1934), 1, No. 2, 163.
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In 1735 the solving of an astronomical problem, proposed by the Academy, for which several eminent mathematicians had demanded several months’ time, was achieved in three days by Euler with aid of improved methods of his own. … With still superior methods this same problem was solved by the illustrious Gauss in one hour.
In History of Mathematics (1897), 248.
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In 1847 I gave an address at Newton, Mass., before a Teachers’ Institute conducted by Horace Mann. My subject was grasshoppers. I passed around a large jar of these insects, and made every teacher take one and hold it while I was speaking. If any one dropped the insect, I stopped till he picked it up. This was at that time a great innovation, and excited much laughter and derision. There can be no true progress in the teaching of natural science until such methods become general.
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In 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 any conceivable method ever invented by man, an automaton which produces an object by copying a pattern, will go first from the pattern to a description to the object. It first abstracts what the thing is like, and then carries it out. It’s therefore simpler not to extract from a real object its definition, but to start from the definition.
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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In describing a protein it is now common to distinguish the primary, secondary and tertiary structures. The primary structure is simply the order, or sequence, of the amino-acid residues along the polypeptide chains. This was first determined by Sanger using chemical techniques for the protein insulin, and has since been elucidated for a number of peptides and, in part, for one or two other small proteins. The secondary structure is the type of folding, coiling or puckering adopted by the polypeptide chain: the a-helix structure and the pleated sheet are examples. Secondary structure has been assigned in broad outline to a number of librous proteins such as silk, keratin and collagen; but we are ignorant of the nature of the secondary structure of any globular protein. True, there is suggestive evidence, though as yet no proof, that a-helices occur in globular proteins, to an extent which is difficult to gauge quantitatively in any particular case. The tertiary structure is the way in which the folded or coiled polypeptide chains are disposed to form the protein molecule as a three-dimensional object, in space. The chemical and physical properties of a protein cannot be fully interpreted until all three levels of structure are understood, for these properties depend on the spatial relationships between the amino-acids, and these in turn depend on the tertiary and secondary structures as much as on the primary. Only X-ray diffraction methods seem capable, even in principle, of unravelling the tertiary and secondary structures.
Co-author with G. Bodo, H. M. Dintzis, R. G. Parrish, H. Wyckoff, and D. C. Phillips
'A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-ray Analysis', Nature (1958) 181, 662.
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In early times, when the knowledge of nature was small, little attempt was made to divide science into parts, and men of science did not specialize. Aristotle was a master of all science known in his day, and wrote indifferently treatises on physics or animals. As increasing knowledge made it impossible for any one man to grasp all scientific subjects, lines of division were drawn for convenience of study and of teaching. Besides the broad distinction into physical and biological science, minute subdivisions arose, and, at a certain stage of development, much attention was, given to methods of classification, and much emphasis laid on the results, which were thought to have a significance beyond that of the mere convenience of mankind.
But we have reached the stage when the different streams of knowledge, followed by the different sciences, are coalescing, and the artificial barriers raised by calling those sciences by different names are breaking down. Geology uses the methods and data of physics, chemistry and biology; no one can say whether the science of radioactivity is to be classed as chemistry or physics, or whether sociology is properly grouped with biology or economics. Indeed, it is often just where this coalescence of two subjects occurs, when some connecting channel between them is opened suddenly, that the most striking advances in knowledge take place. The accumulated experience of one department of science, and the special methods which have been developed to deal with its problems, become suddenly available in the domain of another department, and many questions insoluble before may find answers in the new light cast upon them. Such considerations show us that science is in reality one, though we may agree to look on it now from one side and now from another as we approach it from the standpoint of physics, physiology or psychology.
In article 'Science', Encyclopedia Britannica (1911), 402.
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In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.
In 'Geometry', Encyclopedia Britannica (9th edition).
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In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
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In light of new knowledge ... an eventual world state is not just desirable in the name of brotherhood, it is necessary for survival ... Today we must abandon competition and secure cooperation. This must be the central fact in all our considerations of international affairs; otherwise we face certain disaster. Past thinking and methods did not prevent world wars. Future thinking must prevent wars.
…...
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In my considered opinion the peer review system, in which proposals rather than proposers are reviewed, is the greatest disaster visited upon the scientific community in this century. No group of peers would have approved my building the 72-inch bubble chamber. Even Ernest Lawrence told me he thought I was making a big mistake. He supported me because he knew my track record was good. I believe that U.S. science could recover from the stultifying effects of decades of misguided peer reviewing if we returned to the tried-and-true method of evaluating experimenters rather than experimental proposals. Many people will say that my ideas are elitist, and I certainly agree. The alternative is the egalitarianism that we now practice and I’ve seen nearly kill basic science in the USSR and in the People's Republic of China.
Alvarez: Adventures of a Physicist (1987), 200-1.
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In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skilful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them.
'Cosmology', in Arthur Beer (ed.), Vistas in Astronomy (1956), Vol. 2, 1722.
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In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
In 'Die Theorie der algebraischen Zahlkorper', Vorwort, Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 4.
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In our search after the Knowledge of Substances, our want of Ideas, that are suitable to such a way of proceeding, obliges us to a quite different method. We advance not here, as in the other (where our abstract Ideas are real as well as nominal Essences) by contemplating our Ideas, and considering their Relations and Correspondencies; that helps us very little, for the Reasons, and in another place we have at large set down. By which, I think it is evident, that Substances afford Matter of very little general Knowledge; and the bare Contemplation of their abstract Ideas, will carry us but a very little way in the search of Truth and Certainty. What then are we to do for the improvement of our Knowledge in Substantial beings? Here we are to take a quite contrary Course, the want of Ideas of their real essences sends us from our own Thoughts, to the Things themselves, as they exist.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 9, 644.
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In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science, whatever the matter may be.
Often seen quoted in a condensed form: If you cannot measure it, then it is not science.
From lecture to the Institution of Civil Engineers, London (3 May 1883), 'Electrical Units of Measurement', Popular Lectures and Addresses (1889), Vol. 1, 80-81.
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In science men have discovered an activity of the very highest value in which they are no longer, as in art, dependent for progress upon the appearance of continually greater genius, for in science the successors stand upon the shoulders of their predecessors; where one man of supreme genius has invented a method, a thousand lesser men can apply it. … In art nothing worth doing can be done without genius; in science even a very moderate capacity can contribute to a supreme achievement.
Essay, 'The Place Of Science In A Liberal Education.' In Mysticism and Logic: and Other Essays (1919), 41.
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In short, the greatest contribution to real security that science can make is through the extension of the scientific method to the social sciences and a solution of the problem of complete avoidance of war.
In "Science and Security", Science (25 Jun 1948), 107, 665. Written while Director of the U.S. National Bureau of Standards.
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In the beginning (if there was such a thing), God created Newton’s laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematical methods by means of deduction.
Autobiographical Notes (1946), 19. In Albert Einstein, Alice Calaprice, Freeman Dyson , The Ultimate Quotable Einstein (2011), 397.
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In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Bionomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 143.
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In the discovery of lemmas the best aid is a mental aptitude for it. For we may see many who are quick at solutions and yet do not work by method ; thus Cratistus in our time was able to obtain the required result from first principles, and those the fewest possible, but it was his natural gift which helped him to the discovery.
Proclus
As given in Euclid, The Thirteen Books of Euclid's Elements, translated from the text of Johan Ludvig Heiberg by Sir Thomas Little Heath, Vol. 1, Introduction and Books 1,2 (1908), 133. The passage also states that Proclus gives the definition of the term lemma as a proposition not proved beforehand. Glenn Raymond Morrow in A Commentary on the First Book of Euclid's Elements (1992), 165, states nothing more seems to be known of Cratistus.
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In the fight which we have to wage incessantly against ignorance and quackery among the masses and follies of all sorts among the classes, diagnosis, not drugging, is our chief weapon of offence. Lack of systematic personal training in the methods of the recognition of disease leads to the misapplication of remedies, to long courses of treatment when treatment is useless, and so directly to that lack of confidence in our methods which is apt to place us in the eyes of the public on a level with empirics and quacks.
Address to the Canadian Medical Association, Montreal (17 Sep 1902), 'Chauvinism in Medicine', published in The Montreal Medical Journal (1902), 31, 267. Collected in Aequanimitas, with Other Addresses to Medical Students, Nurses and Practitioners of Medicine (1904), 299.
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In the great debates of early-nineteenth century geology, catastrophists followed the stereotypical method of objective science-empirical literalism. They believed what they saw, interpolated nothing, and read the record of the rocks directly.
'The Stinkstones of Oeningen', In Hen's Teeth and Horse's Toes (1983), 105.
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In the main, Bacon prophesied the direction of subsequent progress. But he “anticipated” the advance. He did not see that the new science was for a long time to be worked in the interest of old ends of human exploitation. He thought that it would rapidly give man new ends. Instead, it put at the disposal of a class the means to secure their old ends of aggrandizement at the expense of another class. The industrial revolution followed, as he foresaw, upon a revolution in scientific method. But it is taking the revolution many centuries to produce a new mind.
In Democracy and Education: An Introduction to the Philosophy of Education (1916), 330-331.
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In the mathematical investigations I have usually employed such methods as present themselves naturally to a physicist. The pure mathematician will complain, and (it must be confessed) sometimes with justice, of deficient rigour. But to this question there are two sides. For, however important it may be to maintain a uniformly high standard in pure mathematics, the physicist may occasionally do well to rest content with arguments which are fairly satisfactory and conclusive from his point of view. To his mind, exercised in a different order of ideas, the more severe procedure of the pure mathematician may appear not more but less demonstrative. And further, in many cases of difficulty to insist upon the highest standard would mean the exclusion of the subject altogether in view of the space that would be required.
In Preface to second edition, The Theory of Sound (1894), Vol. 1, vii.
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In the modern interpretation of Mendelism, facts are being transformed into factors at a rapid rate. If one factor will not explain the facts, then two are involved; if two prove insufficient, three will sometimes work out. The superior jugglery sometimes necessary to account for the results may blind us, if taken too naively, to the common-place that the results are often so excellently 'explained' because the explanation was invented to explain them. We work backwards from the facts to the factors, and then, presto! explain the facts by the very factors that we invented to account for them. I am not unappreciative of the distinct advantages that this method has in handling the facts. I realize how valuable it has been to us to be able to marshal our results under a few simple assumptions, yet I cannot but fear that we are rapidly developing a sort of Mendelian ritual by which to explain the extraordinary facts of alternative inheritance. So long as we do not lose sight of the purely arbitrary and formal nature of our formulae, little harm will be done; and it is only fair to state that those who are doing the actual work of progress along Mendelian lines are aware of the hypothetical nature of the factor-assumption.
'What are 'Factors' in Mendelian Explanations?', American Breeders Association (1909), 5, 365.
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In the twenties the late Dr. Glenn Frank, an eminent social scientist, developed a new statement of the scientific code, which has been referred to as the “Five Fingers of the Scientific Method.” It may be outlined as follows: find the facts; filter the facts; focus the facts; face the facts; follow the facts. The facts or truths are found by experimentation; the motivation is material. The facts are filtered by research into the literature; the motivation is material. The facts are focused by the publication of results; again the motivation is material. Thus the first three-fifths of the scientific method have a material motivation. It is about time scientists acknowledge that there is more to the scientific convention than the material aspect. Returning to the fourth and fifth fingers of Dr. Frank's conception of the scientific method, the facts should be faced by the proper interpretation of them for society. In other words, a scientist must assume social responsibility for his discoveries, which means that he must have a moral motivation. Finally, in the fifth definition of the scientific method, the facts are to be followed by their proper application to everyday life in society, which means moral motivation through responsibility to society.
From 'Scientists and Society', American Scientist (Jul 1954), 42, No. 3, 495.
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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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Inanimate objects are classified scientifically into three categories—those that don't work, those that break down, and those that get lost. The goal of all inanimate objects is to resist man and ultimately to defeat him, and the three major classifications are based on the method each object uses to achieve its purpose
'Observer: The Plot Against People', New York Times (18 Jun 1968), 46.
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Indeed, the aim of teaching [mathematics] should be rather to strengthen his [the pupil’s] faculties, and to supply a method of reasoning applicable to other subjects, than to furnish him with an instrument for solving practical problems.
In John Perry (ed.), Discussion on the Teaching of Mathematics (1901), 84. The discussion took place on 14 Sep 1901 at the British Association at Glasgow, during a joint meeting of the mathematics and physics sections with the education section. The proceedings began with an address by John Perry. Magnus spoke in the Discussion that followed.
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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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Inexact method of observation, as I believe, is one flaw in clinical pathology to-day. Prematurity of conclusion is another, and in part follows from the first; but in chief part an unusual craving and veneration for hypothesis, which besets the minds of most medical men, is responsible. Except in those sciences which deal with the intangible or with events of long past ages, no treatises are to be found in which hypothesis figures as it does in medical writings. The purity of a science is to be judged by the paucity of its recorded hypotheses. Hypothesis has its right place, it forms a working basis; but it is an acknowledged makeshift, and, at the best, of purpose unaccomplished. Hypothesis is the heart which no man with right purpose wears willingly upon his sleeve. He who vaunts his lady love, ere yet she is won, is apt to display himself as frivolous or his lady a wanton.
The Mechanism and Graphic Registration of the Heart Beat (1920), vii.
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Influenced by him, and probably even more so by my brother Theodore a year older than me, I soon became interested in biology and developed a respect for the importance of science and the scientific method.
From biographical sketch in Wilhelm Odelberg (ed.) Les Prix Nobel. The Nobel Prizes 1980, (1981).
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Intelligence is important in psychology for two reasons. First, it is one of the most scientifically developed corners of the subject, giving the student as complete a view as is possible anywhere of the way scientific method can be applied to psychological problems. Secondly, it is of immense practical importance, educationally, socially, and in regard to physiology and genetics.
From Intelligence: Its Structure, Growth and Action: Its Structure, Growth and Action (1987), 1.
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Investigating the conditions under which mutations occur … requires studies of mutation frequency under various methods of handling the organisms. As yet, extremely little has been done along this line. That is because, in the past, a mutation was considered a windfall, and the expression “mutation frequency” would have seemed a contradiction in terms. To attempt to study it would have seemed as absurd as to study the conditions affecting the distribution of dollar bills on the sidewalk. You were simply fortunate if you found one. … Of late, however, we may say that certain very exceptional banking houses have been found, in front of which the dollars fall more frequently—in other words, specially mutable genes have been discovered, that are beginning to yield abundant data at the hands of Nilsson-Ehle, Zeleny, Emerson, Anderson and others.
In 'Variation Due to Change in the Individual Gene', The American Naturalist (Jan-Feb 1922), 56, No. 642, 44.
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Is it possible that a promiscuous Jumble of Printing Letters should often fall into a Method and Order, which should stamp on Paper a coherent Discourse; or that a blind fortuitous Concourse of Atoms, not guided by an Understanding Agent, should frequently constitute the Bodies of any Species of Animals.
In 'Of Wrong Assent, or Error', An Essay Concerning Humane Understanding (1706), Book 4, 601.
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It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
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It has been recognized that hydrogen bonds restrain protein molecules to their native configurations, and I believe that as the methods of structural chemistry are further applied to physiological problems it will be found that the significance of the hydrogen bond for physiology is greater than that of any other single structural feature.
Nature of the Chemical Bond and the Structure of Molecules and Crystals (1939), 265.
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It is almost a miracle that modern teaching methods have not yet entirely strangled the holy curiousity of inquiry; for what this delicate little plant needs more than anything, besides stimulation, is freedom.
Quoted in H. Eves, Return to Mathematical Circles.
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It is characteristic of our age to endeavour to replace virtues by technology. That is to say, wherever possible we strive to use methods of physical or social engineering to achieve goals which our ancestors thought attainable only by the training of character. Thus, we try so far as possible to make contraception take the place of chastity, and anaesthetics to take the place of fortitude; we replace resignation by insurance policies and munificence by the Welfare State. It would be idle romanticism to deny that such techniques and institutions are often less painful and more efficient methods of achieving the goods and preventing the evils which unaided virtue once sought to achieve and avoid. But it would be an equal and opposite folly to hope that the take-over of virtue by technology may one day be complete, so that the necessity for the laborious acquisition of the capacity for rational choice by individuals can be replaced by the painless application of the fruits of scientific discovery over the whole field of human intercourse and enterprise.
'Mental Health in Plato's Republic', in The Anatomy of the Soul: Historical Essays in the Philosophy of Mind (1973), 26.
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It is clear, from these considerations, that the three methods of classifying mankind—that according to physical characters, according to language, and according to culture—all reflect the historical development of races from different standpoints; and that the results of the three classifications are not comparable, because the historical facts do not affect the three classes of phenomena equally. A consideration of all these classes of facts is needed when we endeavour to reconstruct the early history of the races of mankind.
'Summary of the Work of the Committee in British Columbia', Report of the Sixty-Eighth Meeting of the British Association for the Advancement of Science, 1899, 670.
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It is clear, then, that the idea of a fixed method, or of a fixed theory of rationality, rests on too naive a view of man and his social surroundings. To those who look at the rich material provided by history, and who are not intent on impoverishing it in order to please their lower instincts, their craving for intellectual security in the form of clarity, precision, “objectivity”, “truth”, it will become clear that there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 18-19.
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It is easy to create an interstellar radio message which can be recognized as emanating unambiguously from intelligent beings. A modulated signal (‘beep,’ ‘beep-beep,’…) comprising the numbers 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, for example, consists exclusively of the first 12 prime numbers…. A signal of this kind, based on a simple mathematical concept, could only have a biological origin. … But by far the most promising method is to send pictures.
From 'The Quest for Extraterrestrial Intelligence', in the magazine Smithsonian (May 1978), 43-44. Reprinted in Cosmic Search (Mar 1979), 1, No. 2, 5.
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It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery—Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.
Quoted in James Roy Newman, The World of Mathematics (2000), Vol. 1, 239.
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It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
Quoted in Return to Mathematical Circles H. Eves (Boston 1988).
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It is not only a decided preference for synthesis and a complete denial of general methods which characterizes the ancient mathematics as against our newer Science [modern mathematics]: besides this extemal formal difference there is another real, more deeply seated, contrast, which arises from the different attitudes which the two assumed relative to the use of the concept of variability. For while the ancients, on account of considerations which had been transmitted to them from the Philosophie school of the Eleatics, never employed the concept of motion, the spatial expression for variability, in their rigorous system, and made incidental use of it only in the treatment of phonoromically generated curves, modern geometry dates from the instant that Descartes left the purely algebraic treatment of equations and proceeded to investigate the variations which an algebraic expression undergoes when one of its variables assumes a continuous succession of values.
In 'Untersuchungen über die unendlich oft oszillierenden und unstetigen Functionen', Ostwald’s Klassiker der exacten Wissenschaften (1905), No. 153, 44-45. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 115. From the original German, “Nicht allein entschiedene Vorliebe für die Synthese und gänzliche Verleugnung allgemeiner Methoden charakterisiert die antike Mathematik gegenüber unserer neueren Wissenschaft; es gibt neben diesem mehr äußeren, formalen, noch einen tiefliegenden realen Gegensatz, welcher aus der verschiedenen Stellung entspringt, in welche sich beide zu der wissenschaftlichen Verwendung des Begriffes der Veränderlichkeit gesetzt haben. Denn während die Alten den Begriff der Bewegung, des räumlichen Ausdruckes der Veränderlichkeit, aus Bedenken, die aus der philosophischen Schule der Eleaten auf sie übergegangen waren, in ihrem strengen Systeme niemals und auch in der Behandlung phoronomisch erzeugter Kurven nur vorübergehend verwenden, so datiert die neuere Mathematik von dem Augenblicke, als Descartes von der rein algebraischen Behandlung der Gleichungen dazu fortschritt, die Größenveränderungen zu untersuchen, welche ein algebraischer Ausdruck erleidet, indem eine in ihm allgemein bezeichnete Größe eine stetige Folge von Werten durchläuft.”
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It is often assumed that because the young child is not competent to study geometry systematically he need be taught nothing geometrical; that because it would be foolish to present to him physics and mechanics as sciences it is useless to present to him any physical or mechanical principles.
An error of like origin, which has wrought incalculable mischief, denies to the scholar the use of the symbols and methods of algebra in connection with his early essays in numbers because, forsooth, he is not as yet capable of mastering quadratics! … The whole infant generation, wrestling with arithmetic, seek for a sign and groan and travail together in pain for the want of it; but no sign is given them save the sign of the prophet Jonah, the withered gourd, fruitless endeavor, wasted strength.
From presidential address (9 Sep 1884) to the General Meeting of the American Social Science Association, 'Industrial Education', printed in Journal of Social Science (1885), 19, 121. Collected in Francis Amasa Walker, Discussions in Education (1899), 132.
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It is the man not the method that solves the problem.
In 'Present Problems of Algebra and Analysis', Congress of Arts and Sciences: Universal Exposition, St. Louis, 1904 (1905), Vol. 1, 530.
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It is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstance can it be of the smallest possible utility.
Quoted as “It is reported that once in a lecture after explaining a new solution of an old problem he said…”, in Alexander Macfarlane, 'Henry John Stephen Smith', Lectures on Ten British Mathematicians of the Nineteenth Century (1916), 100.
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It must be gently but firmly pointed out that analogy is the very corner-stone of scientific method. A root-and-branch condemnation would invalidate any attempt to explain the unknown in terms of the known, and thus prune away every hypothesis.
In 'On Analogy', The Cambridge Magazine (2 Mar 1918), 476. As quoted in Robert Scott Root-Bernstein and Michèle Root-Bernstein, Sparks of Genius: The Thirteen Thinking Tools of the World’s Most Creative (2001), 144.
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It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method—I know not what.
The Theory of Political Economy (1871), 3.
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It seems to me that there is a good deal of ballyhoo about scientific method. I venture to think that the people who talk most about it are the people who do least about it. Scientific method is what working scientists do, not what other people or even they themselves may say about it. No working scientist, when he plans an experiment in the laboratory, asks himself whether he is being properly scientific, nor is he interested in whatever method he may be using as method.
…...
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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.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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