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Who said: “The conservation of natural resources is the fundamental problem. Unless we solve that problem it will avail us little to solve all others.”
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Home > Category Index for Science Quotations > Category Index M > Category: Method

Method Quotes (105 quotes)

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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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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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 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 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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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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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 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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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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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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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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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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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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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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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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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 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 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 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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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 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.'
'The Unwritten Chapter on Golf, Nature (1887), 36, 502.
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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 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 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 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 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 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.
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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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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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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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 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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Mathematics, including not merely Arithmetic, Algebra, Geometry, and the higher Calculus, but also the applied Mathematics of Natural Philosophy, has a marked and peculiar method or character; it is by preeminence deductive or demonstrative, and exhibits in a nearly perfect form all the machinery belonging to this mode of obtaining truth. Laying down a very small number of first principles, either self-evident or requiring very little effort to prove them, it evolves a vast number of deductive truths and applications, by a procedure in the highest degree mathematical and systematic.
In Education as a Science (1879), 148.
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Method means that arrangement of subject matter which makes it most effective in use. Never is method something outside of the material.
Democracy and Education: an Introduction to the Philosophy of Education (1916), 194.
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Moreover, the works already known are due to chance and experiment rather than to sciences; for the sciences we now possess are merely systems for the nice ordering and setting forth of things already invented; not methods of invention or directions for new works.
From Novum Oranum (1620), Book 1, Aphorism 8. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 48.
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My [algebraic] methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.
Letter to H. Hasse (1931). As quoted in Israel Kleiner, A History of Abstract Algebra (2007), 100. The author used the quote to remark on Noether’s widespread influence, either directly or indirectly, for the introduction of algebra (her specialty) or its terminology into a variety of mathematical fields in the twentieth century.
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Nominally a great age of scientific inquiry, ours has become an age of superstition about the infallibility of science; of almost mystical faith in its non-mystical methods; above all—which perhaps most explains the expert's sovereignty—of external verities; of traffic-cop morality and rabbit-test truth.
In Company Manners: A Cultural Inquiry into American Life (1954), 94.
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Ordinarily logic is divided into the examination of ideas, judgments, arguments, and methods. The two latter are generally reduced to judgments, that is, arguments are reduced to apodictic judgments that such and such conclusions follow from such and such premises, and method is reduced to judgments that prescribe the procedure that should be followed in the search for truth.
Ampére expresses how arguments have a logical structure which he expected should be applied to relate scientific theories to experimental evidence. In James R. Hofmann, André-Marie Ampère (1996), 158. Cites Académie des Sciences Ampère Archives, École Normale lecture 15 notes, box 261.
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Physio-philosophy has to show how, and in accordance indeed with what laws, the Material took its origin; and, therefore, how something derived its existence from nothing. It has to portray the first periods of the world's development from nothing; how the elements and heavenly bodies originated; in what method by self-evolution into higher and manifold forms, they separated into minerals, became finally organic, and in Man attained self-consciousness.
In Lorenz Oken, trans. by Alfred Tulk, Elements of Physiophilosophy (1847), 1.
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Psychologism is, I believe, correct only in so far as it insists upon what may be called 'methodological individualism' as opposed to 'methodological collectivism'; it rightly insists that the 'behaviour' and the 'actions' of collectives, such as states or social groups, must be reduced to the behaviour and to the actions of human individuals. But the belief that the choice of such an individualist method implies the choice of a psychological method is mistaken.
The Open Society and Its Enemies (1945), Vol. 22, 87.
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Science finds it methods.
Journal excerpt in 'Notes', collected in The Complete Works of Ralph Waldo Emerson (1903), 380.
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Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
Letter to G. F. Becker, 11 June 1893. Merrill Collection, Library of Congress. Quoted in Nathan Reingold, Science in Nineteenth-Century America: A Documentary History (1966), 231-2.
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Science has to be understood in its broadest sense, as a method for apprehending all observable reality, and not merely as an instrument for acquiring specialized knowledge.
In Alfred Armand Montapert, Words of Wisdom to Live By: An Encyclopedia of Wisdom in Condensed Form (1986), 217, without citation. If you know the primary source, please contact Webmaster.
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Science is a method of logical analysis of nature’s operations. It has lessened human anxiety about the cosmos by demonstrating the materiality of nature’s forces, and their frequent predictability.
In Sexual Personae: Art and Decadence from Nefertiti to Emily Dickinson (1990), 5.
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Science is not a system of certain, or -established, statements; nor is it a system which steadily advances towards a state of finality... And our guesses are guided by the unscientific, the metaphysical (though biologically explicable) faith in laws, in regularities which we can uncover—discover. Like Bacon, we might describe our own contemporary science—'the method of reasoning which men now ordinarily apply to nature'—as consisting of 'anticipations, rash and premature' and as 'prejudices'.
The Logic of Scientific Discovery (1959), 278.
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Science quickens and cultivates directly the faculty of observation, which in very many persons lies almost dormant through life, the power of accurate and rapid generalizations, and the mental habit of method and arrangement; it accustoms young persons to trace the sequence of cause and effect; it familiarizes then with a kind of reasoning which interests them, and which they can promptly comprehend; and it is perhaps the best corrective for that indolence which is the vice of half-awakened minds, and which shrinks from any exertion that is not, like an effort of memory, merely mechanical.
Report of the Royal Commission on Education (1861), Parliamentary Papers (1864), Vol 20, 32-33, as cited in Paul White, Thomas Huxley: Making the "Man of Science" (2003), 77, footnote. Also quoted in John Lubbock, The Pleasures of Life (1887, 2007), 63.
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Scientists and particularly the professional students of evolution are often accused of a bias toward mechanism or materialism, even though believers in vitalism and in finalism are not lacking among them. Such bias as may exist is inherent in the method of science. The most successful scientific investigation has generally involved treating phenomena as if they were purely materialistic, rejecting any metaphysical hypothesis as long as a physical hypothesis seems possible. The method works. The restriction is necessary because science is confined to physical means of investigation and so it would stultify its own efforts to postulate that its subject is not physical and so not susceptible to its methods.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 127.
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Since religion intrinsically rejects empirical methods, there should never be any attempt to reconcile scientific theories with religion. [An infinitely old universe, always evolving may not be compatible with the Book of Genesis. However, religions such as Buddhism get along without having any explicit creation mythology and are in no way contradicted by a universe without a beginning or end.] Creatio ex nihilo, even as religious doctrine, only dates to around AD 200. The key is not to confuse myth and empirical results, or religion and science.
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),196.
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Since the seventeenth century, physical intuition has served as a vital source for mathematical porblems and methods. Recent trends and fashions have, however, weakened the connection between mathematics and physics; mathematicians, turning away from their roots of mathematics in intuition, have concentrated on refinement and emphasized the postulated side of mathematics, and at other times have overlooked the unity of their science with physics and other fields. In many cases, physicists have ceased to appreciate the attitudes of mathematicians. This rift is unquestionably a serious threat to science as a whole; the broad stream of scientific development may split into smaller and smaller rivulets and dry out. It seems therefore important to direct our efforts towards reuniting divergent trends by classifying the common features and interconnections of many distinct and diverse scientific facts.
In R. Courant and David Hilbert, Methods of Mathematical Physics (1937, 1989), Preface, v.
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The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.
Remarking on the paper, ‘Statistics in Agricultural Research’ by J. Wishart, Journal of the Royal Statistical Society, Supplement (1934), 1, 52. As cited in Michael Cowle, Statistics in Psychology: An Historical Perspective (2005), 210.
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The chemists work with inaccurate and poor measuring services, but they employ very good materials. The physicists, on the other hand, use excellent methods and accurate instruments, but they apply these to very inferior materials. The physical chemists combine both these characteristics in that they apply imprecise methods to impure materials.
Quoted in R. Desper, The Human Side of Scientists (1975), 116.
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The classification of facts and the formation of absolute judgments upon the basis of this classification—judgments independent of the idiosyncrasies of the individual mind—essentially sum up the aim and method of modern science. The scientific man has above all things to strive at self-elimination in his judgments, to provide an argument which is as true for each individual mind as for his own.
From The Grammar of Science (1892), 7-8.
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The difference between the amoeba and Einstein is that, although both make use of the method of trial and error elimination, the amoeba dislikes erring while Einstein is intrigued by it.
In Objective Knowledge: An Evolutionary Approach (1972), 70. As cited in Alexander Naraniecki, Returning to Karl Popper: A Reassessment of his Politics and Philosophy (2014), 89, footnote.
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The full impact of the Lobatchewskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobatchewsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
From a page of quotations, without citations, in G.E. Martin The Foundations of Geometry and the Non-Euclidean Plane (1975), 225. If you know the primary source, please contact Webmaster.
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The great difference between science and technology is a difference of initial attitude. The scientific man follows his method whithersoever it may take him. He seeks acquaintance with his subject­matter, and he does not at all care about what he shall find, what shall be the content of his knowledge when acquaintance-with is transformed into knowledge-about. The technologist moves in another universe; he seeks the attainment of some determinate end, which is his sole and obsessing care; and he therefore takes no heed of anything that he cannot put to use as means toward that end.
Systematic Psychology: Prolegomena (1929), 66.
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The greatest invention of the nineteenth century was the invention of the method of invention.
In Science and the Modern World (1925, 1997), 96.
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The Historic Method may be described as the comparison of the forms of an idea, or a usage, or a belief, at any given time, with the earlier forms from which they were evolved, or the later forms into which they were developed and the establishment from such a comparison, of an ascending and descending order among the facts. It consists in the explanation of existing parts in the frame of society by connecting them with corresponding parts in some earlier frame; in the identification of present forms in the past, and past forms in the present. Its main process is the detection of corresponding customs, opinions, laws, beliefs, among different communities, and a grouping of them into general classes with reference to some one common feature. It is a certain way of seeking answers to various questions of origin, resting on the same general doctrine of evolution, applied to moral and social forms, as that which is being applied with so much ingenuity to the series of organic matter.
On Compromise (1874), 22-3.
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The history of science teaches only too plainly the lesson that no single method is absolutely to be relied upon, that sources of error lurk where they are least expected, and that they may escape the notice of the most experienced and conscientious worker.
Transactions of the Sections', Reports of the British Association for the Advancement of Science (1883), 438.
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The hybridoma technology was a by-product of basic research. Its success in practical applications is to a large extent the result of unexpected and unpredictable properties of the method. It thus represents another clear-cut example of the enormous practical impact of an investment in research which might not have been considered commercially worthwhile, or of immediate medical relevance. It resulted from esoteric speculations, for curiosity’s sake, only motivated by a desire to understand nature.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and ‎Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 267-268.
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The idea of a method that contains firm, unchanging, and absolutely binding principles for conducting the business of science meets considerable difficulty when confronted with the results of historical research. We find, then, that there is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time or another.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14.
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The idea of making a fault a subject of study and not an object to be merely determined has been the most important step in the course of my methods of observation. If I have obtained some new results it is to this that I owe it.
'Notice sur les Travaux Scientifiques de Marcel Bertrand' (1894). In Geological Society of London, The Quarterly Journal of the Geological Society of London (May 1908), 64, li.
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The institutional goal of science is the extension of certified knowledge. The technical methods employed toward this end provide the relevant definition of knowledge: empirically confirmed and logically consistent predictions. The institutional imperatives (mores) derive from the goal and the methods. The entire structure of technical and moral norms implements the final objective. The technical norm of empirical evidence, adequate, valid and reliable, is a prerequisite for sustained true prediction; the technical norm of logical consistency, a prerequisite for systematic and valid prediction. The mores of science possess a methodologic rationale but they are binding, not only because they are procedurally efficient, but because they are believed right and good. They are moral as well as technical prescriptions. Four sets of institutional imperatives–universalism, communism, disinterestedness, organized scepticism–comprise the ethos of modern science.
Social Theory and Social Structure (1957), 552-3.
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The method I take to do this is not yet very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course (as a Specimen of the Political Arithmetic I have long aimed at) to express myself in Terms of Number, Weight, or Measure; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature.
From Essays in Political Arithmetic (1679, 1755), 98.
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The method of arithmetical teaching is perhaps the best understood of any of the methods concerned with elementary studies.
In Education as a Science (1879), 288.
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The one who stays in my mind as the ideal man of science is, not Huxley or Tyndall, Hooker or Lubbock, still less my friend, philosopher and guide Herbert Spencer, but Francis Galton, whom I used to observe and listen to—I regret to add, without the least reciprocity—with rapt attention. Even to-day. I can conjure up, from memory’s misty deep, that tall figure with its attitude of perfect physical and mental poise; the clean-shaven face, the thin, compressed mouth with its enigmatical smile; the long upper lip and firm chin, and, as if presiding over the whole personality of the man, the prominent dark eyebrows from beneath which gleamed, with penetrating humour, contemplative grey eyes. Fascinating to me was Francis Galton’s all-embracing but apparently impersonal beneficence. But, to a recent and enthusiastic convert to the scientific method, the most relevant of Galton’s many gifts was the unique contribution of three separate and distinct processes of the intellect; a continuous curiosity about, and rapid apprehension of individual facts, whether common or uncommon; the faculty for ingenious trains of reasoning; and, more admirable than either of these, because the talent was wholly beyond my reach, the capacity for correcting and verifying his own hypotheses, by the statistical handling of masses of data, whether collected by himself or supplied by other students of the problem.
In My Apprenticeship (1926), 134-135.
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The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits—he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher—the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do—and if a man does his best, what else can you ask of him?
The Rise of Scientific Philosophy (1951, 1973), 248-9. Collected in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 376.
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The process of discovery is very simple. An unwearied and systematic application of known laws to nature, causes the unknown to reveal themselves. Almost any mode of observation will be successful at last, for what is most wanted is method.
A Week on the Concord and Merrimack Rivers (1873), 384.
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The second [argument about motion] is the so-called Achilles, and it amounts to this, that in a race the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
Statement of the Achilles and the Tortoise paradox in the relation of the discrete to the continuous.; perhaps the earliest example of the reductio ad absurdum method of proof.
Zeno
Aristotle, Physics, 239b, 14-6. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 1, 404.
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The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.
Opening to An Introduction to Mathematics (1911), 7.
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The theory of the method of knowing which is advanced in these pages may be termed pragmatic. ... Only that which has been organized into our disposition so as to enable us to adapt the environment to our needs and adapt our aims and desires to the situation in which we live is really knowledge.
Democracy and Education: an Introduction to the Philosophy of Education (1916), 400.
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The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d. Some of his sayings are handed down from generation to generation:
“In order to solve this differential equation you look at it till a solution occurs to you.”
“This principle is so perfectly general that no particular application of it is possible.”
“Geometry is the science of correct reasoning on incorrect figures.”
“My method to overcome a difficulty is to go round it.”
“What is the difference between method and device? A method is a device which you used twice.”
In How to Solve It: A New Aspect of Mathematical Method (2004), 208.
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The transition from a paradigm in crisis to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field's most elementary theoretical generalizations as well as many of its paradigm methods and applications. During the transition period there will be a large but never complete overlap between the problems that can be solved by the old and by the new paradigm. But there will also be a decisive difference in the modes of solution. When the transition is complete, the profession will have changed its view of the field, its methods, and its goals.
The Structure of Scientific Revolutions (1962), 84-5.
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The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute by rational interpretation.
Gifford lectures delivered in the University of Edinburgh during the session 1927-28. Process and Reality: An Essay in Cosmology (1929, 1979), 5.
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The truth may be puzzling. It may take some work to grapple with. It may be counterintuitive. It may contradict deeply held prejudices. It may not be consonant with what we desperately want to be true. But our preferences do not determine what's true. We have a method, and that method helps us to reach not absolute truth, only asymptotic approaches to the truth—never there, just closer and closer, always finding vast new oceans of undiscovered possibilities. Cleverly designed experiments are the key.
In 'Wonder and Skepticism', Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.
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The visible universe is subject to quantification, and is so by necessity. … Between you and me only reason will be the judge … since you proceed according to the rational method, so shall I. … I will also give reason and take it. … This generation has an innate vice. It can’t accept anything that has been discovered by a contemporary!
As quoted in James Burke, The Day the Universe Changed (1985), 41. Burke also quotes the first sentence in The Axemaker's Gift (1995), 112, but after the first ellipsis, is substituted “If you wish to hear more from me, give and take reason, because I am not the kind of man to satisfy his hunger on the picture of a steak!”
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The way of pure research is opposed to all the copy-book maxims concerning the virtues of industry and a fixed purpose, and the evils of guessing, but it is damned useful when it comes off. It is the diametrical opposite of Edison’s reputed method of trying every conceivable expedient until he hit the right one. It requires, not diligence, but experience, information, and a good nose for the essence of a problem.
Letter to Paul de Kruif (3 Aug 1933), as quoted in Nathan Reingold, Science in America: A Documentary History 1900-1939 (1981), 409.
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There are two processes which we adopt consciously or unconsciously when we try to prophesy. We can seek a period in the past whose conditions resemble as closely as possible those of our day, and presume that the sequel to that period will, save for some minor alterations, be similar. Secondly, we can survey the general course of development in our immediate past, and endeavor to prolong it into the near future. The first is the method the historian; the second that of the scientist. Only the second is open to us now, and this only in a partial sphere.
From 'Fifty Years Hence', Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57, No. 3, 393.
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There are two ways of extending life: firstly by moving the two points “born” and “died” farther away from one another… The other method is to go more slowly and leave the two points wherever God wills they should be, and this method is for the philosophers.
Aphorism 22 in Notebook B (1768-1771), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 21.
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There is as much difference between a collection of mentally free citizens and a community molded by modern methods of propaganda as there is between a heap of raw materials and a battleship.
From An Outline of Intellectual Rubbish (1937, 1943), 9. Collected in The Basic Writings of Bertrand Russell (2009), 61.
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There is, however, no universal recipe for scientific advance. It is a matter of groping forward into terra incognita of the outer world by means of methods which should be adapted to the circumstances.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 455.
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This example illustrates the differences in the effects which may be produced by research in pure or applied science. A research on the lines of applied science would doubtless have led to improvement and development of the older methods—the research in pure science has given us an entirely new and much more powerful method. In fact, research in applied science leads to reforms, research in pure science leads to revolutions, and revolutions, whether political or industrial, are exceedingly profitable things if you are on the winning side.
In Lord Rayleigh, The Life of Sir J. J. Thomson (1943), 199
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This method is, to define as the number of a class the class of all classes similar to the given class. Membership of this class of classes (considered as a predicate) is a common property of all the similar classes and of no others; moreover every class of the set of similar classes has to the set of a relation which it has to nothing else, and which every class has to its own set. Thus the conditions are completely fulfilled by this class of classes, and it has the merit of being determinate when a class is given, and of being different for two classes which are not similar. This, then, is an irreproachable definition of the number of a class in purely logical terms.
The Principles of Mathematics (1903), 115.
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Though Hippocrates understood not the Circulation of the Blood, yet by accurately observing the Effects of the Disease, which he looked upon as an unknown Entity, and by remarking the Endeavours of Nature, by which the Disease tended to either Health or Recovery, did from thence deduce a proper Method of Cure, namely by assisting the salutary Endeavours of Nature, and by resisting those of the Disease; and thus Hippocrates, ignorant of the Causes, cured Disease as well as ourselves, stocked with so many Discoveries.
In Dr. Boerhaave's Academical Lectures on the Theory of Physic (1746), Vol. 6, 352.
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Time is that which is measured by a clock. This is a sound way of looking at things. A quantity like time, or any other physical measurement, does not exist in a completely abstract way. We find no sense in talking about something unless we specify how we measure it. It is the definition by the method of measuring a quantity that is the one sure way of avoiding talking nonsense about this kind of thing.
From Relativity and Common Sense: A New Approach to Einstein (1980), 65.
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To bring scientific investigation to a happy end once appropriate methods have been determined, we must hold firmly in mind the goal of the project. The object here is to focus the train of thought on more and more complex and accurate associations between images based on observation and ideas slumbering in the unconscious.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 33.
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To demonstrate experimentally that a microscopic organism actually is the cause of a disease and the agent of contagion, I know no other way, in the present state of Science, than to subject the microbe (the new and happy term introduced by M. Sédillot) to the method of cultivation out of the body.
Paper read to the French Academy of Sciences (29 Apr 1878), published in Comptes Rendus de l'Academie des Sciences, 86, 1037-43, as translated by H.C.Ernst. Collected in Charles W. Eliot (ed.) The Harvard Classics, Vol. 38; Scientific Papers: Physiology, Medicine, Surgery, Geology (1910), 364.
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We have all heard of the puzzle given to Archimedes…. His finding that the crown was of gold was a discovery; but he invented the method of determining the density of solids. Indeed, discoverers must generally be inventors; though inventors are not necessarily discoverers.
From 'How Discoveries Are Made', Cassell's Magazine, Illustrated (May 1908), 629.
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We may best hope to understand the nature and conditions of real knowledge, by studying the nature and conditions of the most certain and stable portions of knowledge which we already possess: and we are most likely to learn the best methods of discovering truth, by examining how truths, now universally recognised, have really been discovered.
In The Philosophy of the Inductive Sciences (1840), Vol. I, 3-4.
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We regard as 'scientific' a method based on deep analysis of facts, theories, and views, presupposing unprejudiced, unfearing open discussion and conclusions. The complexity and diversity of all the phenomena of modern life, the great possibilities and dangers linked with the scientific-technical revolution and with a number of social tendencies demand precisely such an approach, as has been acknowledged in a number of official statements.
Progress, Coexistence and Intellectual Freedom (1968), 25.
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You frequently state, and in your letter you imply, that I have developed a completely one-sided outlook and look at everything and think of everything in terms of science. Obviously my method of thought and reasoning is influenced by a scientific training—if that were not so my scientific training will have been a waste and a failure.
Letter to her father, Ellis Franklin, undated, perhaps summer 1940 while she was an undergraduate at Cambridge. Excerpted in Brenda Maddox, The Dark Lady of DNA (2002), 60.
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[Having already asserted his opposition to communism in every respect by signing the regents' oath, his answer to a question why a non-Communist professor should refuse to take a non-Communist oath as a condition of University employment was that to do so would imply it was] up to an accused person to clear himself. ... That sort of thing is going on in Washington today and is a cause of alarm to thoughtful citizens. It is the method used in totalitarian countries. It sounds un-American to people who don’t like to be pushed around. If someone says I ought to do a certain thing the burden should be on him to show I why I should, not on me to show why I should not.
As quoted in 'Educator Scores Oath For Faculty', New York Times (16 Apr 1950), 31.
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[Regarding evolution believers:] Their business is not with the possible, but the actual—not with a world which might be, but with a world that is. This they explore with a courage not unmixed with reverence, and according to methods which, like the quality of a tree, are tested by their fruits. They have but one desire—to know the truth. They have but one fear—to believe a lie.
'Scientific Use of the Imagination', Discourse Delivered Before the British Association at Liverpool, (16 Sep 1870). Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 134.
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[Society's rights to employ the scopolamine (“truth serum”) drug supersede those of a criminal.] It therefore stands to reason, that where there is a safe and humane method existing to evoke the truth from the consciousness of a suspect society is entitled to have that truth.
Quoted from presentation at the first annual meeting of the Eastern Society of Anesthetists at the Hotel McAlpin, as reported in '“Truth Serum” Test Proves Its Power', New York Times (22 Oct 1924), 14.
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[The infinitely small] neither have nor can have theory; it is a dangerous instrument in the hands of beginners [ ... ] anticipating, for my part, the judgement of posterity, I would dare predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.
Annales des Mathematiques Pures et Appliquées (1814-5), 5, 148.
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[To give insight to statistical information] it occurred to me, that making an appeal to the eye when proportion and magnitude are concerned, is the best and readiest method of conveying a distinct idea.
In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 2.
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In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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