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Result Quotes (677 quotes)

... an analysis that puts the final link in the chain, for here we see correlations between cytological evidence and genetic results that are so strong and obvious that their validity cannot be denied. This paper has been called a landmark in experimental genetics. It is more than that—it is a cornerstone.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931), demonstrating that the exchange of genetic information that occurs during the production of sex cells is accompanied by an exchange of chromosomal material.
Classic Papers in Genetics (1959), 156.
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... I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
Quoted in Sir Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), 541. Science and Method (1908) 51-52, 392.
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...I believe there exists, & I feel within me, an instinct for the truth, or knowledge or discovery, of something of the same nature as the instinct of virtue, & that our having such an instinct is reason enough for scientific researches without any practical results ever ensuing from them.
The Correspondence of Charles Darwin, Vol. 4. (1847-50)
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...the genes almost always accurately reproduce. If they don't, you get one of the following results: One, monsters—that is, grossly malformed babies resulting from genetic mistakes. Years ago most monsters died, but now many can be saved. This has made possible the National Football League.
Found widely quoted on the web, but without a print source. Please contact webmaster if you know the primary source.
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...the life of the planet began the long, slow process of modulating and regulating the physical conditions of the planet. The oxygen in today's atmosphere is almost entirely the result of photosynthetic living, which had its start with the appearance of blue-green algae among the microorganisms.
In Late Night Thoughts on Listening to Mahler's Ninth Symphony(1984), 74.
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Als Physiker, der sein ganzes Leben der nüchternen Wissenschaft, der Erforschung der Materie widmete, bin ich sicher von dem Verdacht frei, für einen Schwarmgeist gehalten zu werden. Und so sage ich nach meinen Erforschungen des Atoms dieses: Es gibt keine Materie an sich. Alle Materie entsteht und besteht nur durch eine Kraft, welche die Atomteilchen in Schwingung bringt und sie zum winzigsten Sonnensystem des Alls zusammenhält. Da es im ganzen Weltall aber weder eine intelligente Kraft noch eine ewige Kraft gibt - es ist der Menschheit nicht gelungen, das heißersehnte Perpetuum mobile zu erfinden - so müssen wir hinter dieser Kraft einen bewußten intelligenten Geist annehmen. Dieser Geist ist der Urgrund aller Materie.
As a man who has devoted his whole life to the most clear headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.
Lecture, 'Das Wesen der Materie' [The Essence/Nature/Character of Matter], Florence, Italy (1944). Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797. Excerpt in Gregg Braden, The Spontaneous Healing of Belief: Shattering the Paradigm of False Limits (2009), 334-35. Note: a number of books showing this quote cite it as from Planck's Nobel Prize acceptance speech (1918), which the Webmaster has checked, and does not see this quote therein.
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Conclusions
I. A curve has been found representing the frequency distribution of standard deviations of samples drawn from a normal population.
II. A curve has been found representing the frequency distribution of values of the means of such samples, when these values are measured from the mean of the population in terms of the standard deviation of the sample…
IV. Tables are given by which it can be judged whether a series of experiments, however short, have given a result which conforms to any required standard of accuracy or whether it is necessary to continue the investigation.
'The Probable Error of a Mean', Biometrika, 1908, 6, 25.
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Man is the result of slow growth; that is why he occupies the position he does in animal life. What does a pup amount to that has gained its growth in a few days or weeks, beside a man who only attains it in as many years.
In Orison Swett Marden, 'Bell Telephone Talk: Hints on Success by Alexander G. Bell', How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 35.
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[About the demand of the Board of Regents of the University of California that professors sign non-Communist loyalty oaths or lose their jobs within 65 days.] No conceivable damage to the university at the hands of hypothetical Communists among us could possibly have equaled the damage resulting from the unrest, ill-will and suspicion engendered by this series of events.
As quoted in 'Professors in West Call Oath “Indignity”', New York Times (26 Feb 1950), 38.
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[In refutation of evolution] There is not enough evidence, consistent evidence to make it as fact, and I say that because for theory to become a fact, it needs to consistently have the same results after it goes through a series of tests. The tests that they put—that they use to support evolution do not have consistent results. Now too many people are blindly accepting evolution as fact. But when you get down to the hard evidence, it’s merely a theory.
[In favor of the teaching of creationism alongside evolution in schools.]
From interview by Miles O'Brien on CNN (30 Mar 1996). Reported from transcript, via Nexis, in New York Magazine (15 Sep 2010).
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[In refutation of evolution] They use carbon dating ... to prove that something was millions of years old. Well, we have the eruption of Mt. Saint Helens and the carbon dating test that they used then would have to then prove that these were hundreds of millions of years younger, when what happened was they had the exact same results on the fossils and canyons that they did the tests on that were supposedly 100 millions of years old. And it’s the kind of inconsistent tests like this that they’re basing their “facts” on.
[Citing results from a solitary young-Earth creationist, questioning whether the lava dome at Mount St. Helens is really a million years old.]
From interview by Miles O''Brien on CNN (30 Mar 1996). Reported from transcript, via Nexis, in New York Magazine (15 Sep 2010).
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[When recording electrical impulses from a frog nerve-muscle preparation seemed to show a tiresomely oscillating electrical artefact—but only when the muscle was hanging unsupported.] The explanation suddenly dawned on me ... a muscle hanging under its own weight ought, if you come to think of it, to be sending sensory impulses up the nerves coming from the muscle spindles ... That particular day’s work, I think, had all the elements that one could wish for. The new apparatus seemed to be misbehaving very badly indeed, and I suddenly found it was behaving so well that it was opening up an entire new range of data ... it didn’t involve any particular hard work, or any particular intelligence on my part. It was just one of those things which sometimes happens in a laboratory if you stick apparatus together and see what results you get.
From 'Memorable experiences in research', Diabetes (1954), 3, 17-18. As cited in Alan McComa, Galvani's Spark: The Story of the Nerve Impulse (2011), 102-103.
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A general course in mathematics should be required of all officers for its practical value, but no less for its educational value in training the mind to logical forms of thought, in developing the sense of absolute truthfulness, together with a confidence in the accomplishment of definite results by definite means.
In 'Mathematics at West Point and Annapolis', United States Bureau of Education, Bulletin 1912, No. 2, 11.
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A casual glance at crystals may lead to the idea that they were pure sports of nature, but this is simply an elegant way of declaring one's ignorance. With a thoughtful examination of them, we discover laws of arrangement. With the help of these, calculation portrays and links up the observed results. How variable and at the same time how precise and regular are these laws! How simple they are ordinarily, without losing anything of their significance! The theory which has served to develop these laws is based entirely on a fact, whose existence has hitherto been vaguely discerned rather than demonstrated. This fact is that in all minerals which belong to the same species, these little solids, which are the crystal elements and which I call their integrant molecules, have an invariable form, in which the faces lie in the direction of the natural fracture surfaces corresponding to the mechanical division of the crystals. Their angles and dimensions are derived from calculations combined with observation.
Traité de mineralogie ... Publié par le conseil des mines (1801), Vol. 1, xiii-iv, trans. Albert V. and Marguerite Carozzi.
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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 few of the results of my activities as a scientist have become embedded in the very texture of the science I tried to serve—this is the immortality that every scientist hopes for. I have enjoyed the privilege, as a university teacher, of being in a position to influence the thought of many hundreds of young people and in them and in their lives I shall continue to live vicariously for a while. All the things I care for will continue for they will be served by those who come after me. I find great pleasure in the thought that those who stand on my shoulders will see much farther than I did in my time. What more could any man want?
In 'The Meaning of Death,' in The Humanist Outlook edited by A. J. Ayer (1968) [See Gerald Holton and Sir Isaac Newton].
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A moment's consideration of this case shows what a really great advance in the theory and practise of breeding has been obtained through the discovery of Mendel's law. What a puzzle this case would have presented to the biologist ten years ago! Agouti crossed with chocolate gives in the second filial generation (not in the first) four varieties, viz., agouti, chocolate, black and cinnamon. We could only have shaken our heads and looked wise (or skeptical).
Then we had no explanation to offer for such occurrences other than the 'instability of color characters under domestication,' the 'effects of inbreeding,' 'maternal impressions.' Serious consideration would have been given to the proximity of cages containing both black and cinnamon-agouti mice.
Now we have a simple, rational explanation, which anyone can put to the test. We are able to predict the production of new varieties, and to produce them.
We must not, of course, in our exuberance, conclude that the powers of the hybridizer know no limits. The result under consideration consists, after all, only in the making of new combinations of unit characters, but it is much to know that these units exist and that all conceivable combinations of them are ordinarily capable of production. This valuable knowledge we owe to the discoverer and to the rediscoverers of Mendel's law.
'New Colour Variety of the Guinea Pig', Science, 1908, 28, 250-252.
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A philosopher once said, ‘It is necessary for the very existence of science that the same conditions always produce the same results’. Well, they don’t!
…...
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A pound of energy with an ounce of talent will achieve greater results than a pound of talent with an ounce of energy.
In Getting on in the World; Or, Hints on Success in Life (1873), 55.
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A professor … may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered. This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. … The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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A rose is the visible result of an infinitude of complicated goings on in the bosom of the earth and in the air above, and similarly a work of art is the product of strange activities in the human mind.
In Since Cezanne (1922), 40.
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A scientific invention consists of six (or some number) ideas, five of which are absurd but which, with the addition of the sixth and enough rearrangement of the combinations, results in something no one has thought of before.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 66.
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A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.
From 'On Some Recent Tendencies in Geometrical Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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A surplus of ideas is as dangerous as a drought. The tendency to jump from idea to idea spreads your energy horizontally rather than vertically. As a result you'll struggle to make progress.
In 'The Action Method', Making Ideas Happen (2012).
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A vital phenomenon can only be regarded as explained if it has been proven that it appears as the result of the material components of living organisms interacting according to the laws which those same components follow in their interactions outside of living systems.
Gesammelte Schriften (1904), Vol. 3, 767. Trans. Paul F. Cranefield, 'The Organic Physics of 1847 and the Biophysics of Today', Journal of the History of Medicine and Allied Sciences, 1957, 12, 410.
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A … difference between most system-building in the social sciences and systems of thought and classification of the natural sciences is to be seen in their evolution. In the natural sciences both theories and descriptive systems grow by adaptation to the increasing knowledge and experience of the scientists. In the social sciences, systems often issue fully formed from the mind of one man. Then they may be much discussed if they attract attention, but progressive adaptive modification as a result of the concerted efforts of great numbers of men is rare.
The Study of Man (1941), 19-20.
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Abraham Maslow, felt … [an] instinctive revolt against the “atmosphere” of Freudian psychology, with its emphasis on sickness and neurosis, and decided that he might obtain some equally interesting results if he studied extremely healthy people.
In Introduction to the New Existentialism (1966), 15.
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Accurate and minute measurement seems to the non-scientific imagination, a less lofty and dignified work than looking for something new. But nearly all the grandest discoveries of science have been but the rewards of accurate measurement and patient long-continued labour in the minute sifting of numerical results.
Presidential inaugural address, to the General Meeting of the British Association, Edinburgh (2 Aug 1871). In Report of the Forty-First Meeting of the British Association for the Advancement of Science (1872), xci.
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Act as if you are going to live for ever and cast your plans way ahead. You must feel responsible without time limitations, and the consideration of whether you may or may not be around to see the results should never enter your thoughts.
In Theodore Rockwell, The Rickover Effect: How One Man Made A Difference (2002), 342.
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After an orange cloud—formed as a result of a dust storm over the Sahara and caught up by air currents—reached the Philippines and settled there with rain, I understood that we are all sailing in the same boat.
In Jack Hassard and Julie Weisberg , Environmental Science on the Net: The Global Thinking Project (1999), 40.
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After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Atombau und Spektrallinien (1919), viii, Atomic Structure and Spectral Lines, trans. Henry L. Brose (1923), viii.
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Again and again in reading even his [William Thomson] most abstract writings one is struck by the tenacity with which physical ideas control in him the mathematical form in which he expressed them. An instance of this is afforded by … an example of a mathematical result that is, in his own words, “not instantly obvious from the analytical form of my solution, but which we immediately see must be the case by thinking of the physical meaning of the result.”
As given in Life of Lord Kelvin (1910), Vol. 2, 1136. The ellipsis gives the reference to the quoted footnote, to a passage in his Mathematical and Physical Papers, Vol. 1, 457. [Note: William Thomson, later became Lord Kelvin. —Webmaster]
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All living forms are the results of physical influences which are still in operation, and vary only in degree and direction
Entry for Gottfried Reinhold Treviranus in Encyclopedia Britannica (1911), Vol. 27, 256.
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All palaetiological sciences, all speculations which attempt to ascend from the present to the remote past, by the chain of causation, do also, by an inevitable consequence, urge us to look for the beginning of the state of things which we thus contemplate; but in none of these cases have men been able, by the aid of science, to arrive at a beginning which is homogeneous with the known course of events. The first origin of language, of civilization, of law and government, cannot be clearly made out by reasoning and research; and just as little, we may expect, will a knowledge of the origin of the existing and extinct species of plants and animals, be the result of physiological and geological investigation.
In History of the Inductive Sciences (1837), Vol. 3, 581.
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All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work which follows the inspiration, and in which the results of the inspiration are verified and the consequences deduced.
Science and Method (1914, 2003), 62.
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All the events which occur upon the earth result from Law: even those actions which are entirely dependent on the caprices of the memory, or the impulse of the passions, are shown by statistics to be, when taken in the gross, entirely independent of the human will. As a single atom, man is an enigma; as a whole, he is a mathematical problem. As an individual, he is a free agent; as a species, the offspring of necessity.
In The Martyrdom of Man (1876), 185-186.
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All the human culture, all the results of art, science and technology that we see before us today, are almost exclusively the creative product of the Aryan. This very fact admits of the not unfounded inference that he alone was the founder of all higher humanity, therefore representing the prototype of all that we understand by the word 'man.' He is the Prometheus of mankind from whose shining brow the divine spark of genius has sprung at all times, forever kindling anew that fire of knowledge which illuminated the night of silent mysteries and thus caused man to climb the path to mastery over the other beings of the earth ... It was he who laid the foundations and erected the walls of every great structure in human culture.
Mein Kampf (1925-26), American Edition (1943), 290. In William Lawrence Shirer, The Rise and Fall of the Third Reich (1990), 86-87.
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All things on the earth are the result of chemical combination. The operation by which the commingling of molecules and the interchange of atoms take place we can imitate in our laboratories; but in nature they proceed by slow degrees, and, in general, in our hands they are distinguished by suddenness of action. In nature chemical power is distributed over a long period of time, and the process of change is scarcely to be observed. By acts we concentrate chemical force, and expend it in producing a change which occupies but a few hours at most.
In chapter 'Chemical Forces', The Poetry of Science: Or, Studies of the Physical Phenomena of Nature (1848), 235-236. Charles Dicken used this quote, with his own sub-head of 'Relative Importance Of Time To Man And Nature', to conclude his review of the book, published in The Examiner (1848).
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Almost all the greatest discoveries in astronomy have resulted from what we have elsewhere termed Residual Phenomena, of a qualitative or numerical kind, of such portions of the numerical or quantitative results of observation as remain outstanding and unaccounted for, after subducting and allowing for all that would result from the strict application of known principles.
Outlines of Astronomy (1876), 626.
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Although I must say that research problems I worked on were frequently the result of serendipity and often grew out of my interest in some species or some environment which I found to be particularly appealing—marine birds and tropical islands for example.
Bartholomew, April 1993, unpublished remarks when receiving the Miller Award from the Cooper Ornithological Society.
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Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.
In Charles S. Peirce, ‎Charles Hartshorne (ed.), ‎Paul Weiss (ed.), Collected Papers of Charles Sanders Peirce (1931), Vol. 4, 197.
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An experiment is never a failure solely because it fails to achieve predicted results. An experiment is a failure only when it also fails adequately to test the hypothesis in question, when the data it produces don’t prove anything one way or another.
In Zen and the Art of Motorcycle Maintenance: An Inquiry Into Values (1974), 102.
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An induction shock results in a contraction or fails to do so according to its strength; if it does so at all, it produces in the muscle at that time the maximal contraction that can result from stimuli of any strength.
Über die Eigentümlichkeiten der Reizbarkeit welche die Muskelfasern des Herzen zeigen', Ber. süchs. Akad. Wiss., Math.-nat Klasse, 1871, 23, 652-689. Trans. Edwin Clarke and C. D. O'Malley, The Human Brain and Spinal Cord (1968), 218.
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Anaximenes ... said that infinite air was the principle, from which the things that are becoming, and that are, and that shall be, and gods and things divine, all come into being, and the rest from its products. The form of air is of this kind: whenever it is most equable it is invisible to sight, but is revealed by the cold and the hot and the damp and by movement. It is always in motion; for things that change do not change unless there be movement. Through becoming denser or finer it has different appearances; for when it is dissolved into what is finer it becomes fire, while winds, again, are air that is becoming condensed, and cloud is produced from air by felting. When it is condensed still more, water is produced; with a further degree of condensation earth is produced, and when condensed as far as possible, stones. The result is that the most influential components of the generation are opposites, hot and cold.
Hippolytus, Refutation, 1.7.1. In G. S. Kirk, J. E. Raven and M. Schofield (eds.), The Presocratic Philosophers: A Critical History with a Selection of Texts (1983), p. 145.
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Any chemist reading this book can see, in some detail, how I have spent most of my mature life. They can become familiar with the quality of my mind and imagination. They can make judgements about my research abilities. They can tell how well I have documented my claims of experimental results. Any scientist can redo my experiments to see if they still work—and this has happened! I know of no other field in which contributions to world culture are so clearly on exhibit, so cumulative, and so subject to verification.
From Design to Discovery (1990), 119-20.
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Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.
From Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838), as translated by Nathaniel T. Bacon in 'Preface', Researches Into Mathematical Principles of the Theory of Wealth (1897), 4. From the original French, “Quiconque connaît la notation algébrique, lit d'un clin-d'œil dans une équation le résultat auquel on parvient péniblement par des règles de fausse position, dans l'arithmétique de Banque.”
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As a result of the phenomenally rapid change and growth of physics, the men and women who did their great work one or two generations ago may be our distant predecessors in terms of the state of the field, but they are our close neighbors in terms of time and tastes. This may be an unprecedented state of affairs among professionals; one can perhaps be forgiven if one characterizes it epigrammatically with a disastrously mixed metaphor; in the sciences, we are now uniquely privileged to sit side-by-side with the giants on whose shoulders we stand.
In 'On the Recent Past of Physics', American Journal of Physics (1961), 29, 807.
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As an adult she had her organs removed one by one. Now she is a mere shell with symptoms where her organs used to be.
Written as an intern on one of his patient's charts; commentary on the result of surgical treatment of non-organic disease.
In Barry G. Firkin, Judith A. Whitworth, Dictionary of Medical Eponyms (1966), 267.
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As modern physics started with the Newtonian revolution, so modern philosophy starts with what one might call the Cartesian Catastrophe. The catastrophe consisted in the splitting up of the world into the realms of matter and mind, and the identification of “mind” with conscious thinking. The result of this identification was the shallow rationalism of l’esprit Cartesien, and an impoverishment of psychology which it took three centuries to remedy even in part.
The Act of Creation (1964), 148.
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As pure truth is the polar star of our science [mathematics], so it is the great advantage of our science over others that it awakens more easily the love of truth in our pupils. … If Hegel justly said, “Whoever does not know the works of the ancients, has lived without knowing beauty,” Schellbach responds with equal right, “Who does not know mathematics, and the results of recent scientific investigation, dies without knowing truth.”
Max Simon
From Didaktik und Methodik des Rechnens und der Mathematik (1908), 37. As quoted and translated in J.W.A. Young, Teaching of Mathematics in the Elementary and the Secondary School (1907), 44. From the original German, “Wenn Hegel mit Recht sagt: ‘Wer die Werke der Alten nicht kennt, der hat gelebt, ohne die Schönheit gekannt zu haben’, so erwidert Schellbach mit nicht minderem Recht: ‘Wer die Math. und die Resultate der neueren Naturforschung nicht gekannt hat, der stirbt, ohne die Wahrheit zu kennen.’”
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As science is more and more subject to grave misuse as well as to use for human benefit it has also become the scientist's responsibility to become aware of the social relations and applications of his subject, and to exert his influence in such a direction as will result in the best applications of the findings in his own and related fields. Thus he must help in educating the public, in the broad sense, and this means first educating himself, not only in science but in regard to the great issues confronting mankind today.
Message to University Students Studying Science', Kagaku Asahi 11, no. 6 (1951), 28-29. Quoted in Elof Axel Carlson, Genes, Radiation, and Society: The Life and Work of H. J. Muller (1981), 371.
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As soon as we got rid of the backroom attitude and brought our apparatus fully into the Department with an inexhaustible supply of living patients with fascinating clinical problems, we were able to get ahead really fast. Any new technique becomes more attractive if its clinical usefulness can be demonstrated without harm, indignity or discomfort to the patient... Anyone who is satisfied with his diagnostic ability and with his surgical results is unlikely to contribute much to the launching of a new medical science. He should first be consumed with a divine discontent with things as they are. It greatly helps, of course, to have the right idea at the right time, and quite good ideas may come, Archimedes fashion, in one's bath..
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Asian Homo erectus died without issue and does not enter our immediate ancestry (for we evolved from African populations); Neanderthal people were collateral cousins, perhaps already living in Europe while we emerged in Africa... In other words, we are an improbable and fragile entity, fortunately successful after precarious beginnings as a small population in Africa, not the predictable end result of a global tendency. We are a thing, an item of history, not an embodiment of general principles.
Wonderful Life (1989), 319.
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Astronomy was not studied by Kepler, Galileo, or Newton for the practical applications which might result from it, but to enlarge the bounds of knowledge, to furnish new objects of thought and contemplation in regard to the universe of which we form a part; yet how remarkable the influence which this science, apparently so far removed from the sphere of our material interests, has exerted on the destinies of the world!
In 'Report of the Secretary', Annual Report of the Board of Regents of the Smithsonian Institution for 1859 (1860), 15.
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At last such field studies have been put on a sound basis which should result in the hunting of information rather than specimens.
Concluding line of review (of Hiram Bingham’s 1932 book, Gorillas in a Native Habitat), in journal, Ecology (1933), 14, No. 3, 320. Note that the quote is authored by the reviewer, W.C. Allee, and any source attributing it directly to Bingham himself is incorrect.
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At no period of [Michael Faraday’s] unmatched career was he interested in utility. He was absorbed in disentangling the riddles of the universe, at first chemical riddles, in later periods, physical riddles. As far as he cared, the question of utility was never raised. Any suspicion of utility would have restricted his restless curiosity. In the end, utility resulted, but it was never a criterion to which his ceaseless experimentation could be subjected.
'The Usefulness of Useless Knowledge', Harper's Magazine (Jun/Nov 1939), No. 179, 546. In Hispania (Feb 1944), 27, No. 1, 77.
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Bad science contributes to the steady dumbing down of our nation. Crude beliefs get transmitted to political leaders and the result is considerable damage to society. We see this happening now in the rapid rise of the religious right and how it has taken over large segments of the Republican Party.
As quoted in Kendrick Frazier, 'A Mind at Play: An Interview with Martin Gardner', Skeptical Inquirer (Mar/Apr 1998), 22, No. 2, 37.
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Basic research may seem very expensive. I am a well-paid scientist. My hourly wage is equal to that of a plumber, but sometimes my research remains barren of results for weeks, months or years and my conscience begins to bother me for wasting the taxpayer’s money. But in reviewing my life’s work, I have to think that the expense was not wasted.
Basic research, to which we owe everything, is relatively very cheap when compared with other outlays of modern society. The other day I made a rough calculation which led me to the conclusion that if one were to add up all the money ever spent by man on basic research, one would find it to be just about equal to the money spent by the Pentagon this past year.
In The Crazy Ape (1971).
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Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit.
'The Meaning and Limits of Exact Science', Science (30 Sep 1949), 110, No. 2857, 325. Advance reprinting of chapter from book Max Planck, Scientific Autobiography (1949), 110.
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Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world could have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility. … Our modern power of easy reckoning with decimal fractions is the most miraculous result of a perfect notation.
In Introduction to Mathematics (1911), 59.
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Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611. [The French phrase, à peu près means “approximately”. —Webmaster]
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Blood mixture and the result drop in the racial level is the sole cause of the dying out of old cultures; for men do not perish as a result of lost wars, but by the loss of that force of resistance which is continued only in pure blood. All who are not of good race in this world are chaff.
Mein Kampf (1925-26), American Edition (1943), 296. In William Lawrence Shirer, The Rise and Fall of the Third Reich (1990), 88.
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Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.
The Anatomy of Science (1926), 158-9.
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But as no two (theoreticians) agree on this (skin friction) or any other subject, some not agreeing today with what they wrote a year ago, I think we might put down all their results, add them together, and then divide by the number of mathematicians, and thus find the average coefficient of error. (1908)
In Artificial and Natural Flight (1908), 3. Quoted in John David Anderson, Jr., Hypersonic and High Temperature Gas Dynamics (2000), 335.
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But from the time I was in college I learned that there is nothing one could imagine which is so strange and incredible that it was not said by some philosopher; and since that time, I have recognized through my travels that all those whose views are different from our own are not necessarily, for that reason, barbarians or savages, but that many of them use their reason either as much as or even more than we do. I also considered how the same person, with the same mind, who was brought up from infancy either among the French or the Germans, becomes different from what they would have been if they had always lived among the Chinese or among the cannibals, and how, even in our clothes fashions, the very thing that we liked ten years ago, and that we may like again within the next ten years, appears extravagant and ridiculous to us today. Thus our convictions result from custom and example very much more than from any knowledge that is certain... truths will be discovered by an individual rather than a whole people.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 14-5.
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But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.
In Editor’s Preface to Augustus De Morgan and Thomas J. McCormack (ed.), Elementary Illustrations of the Differential and Integral Calculus (1899), v.
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But science and technology are only one of the avenues toward reality; others are equally needed to comprehend the full significance of our existence. Indeed, these other avenues are necessary for the prevention of thoughtless and inhuman abuses of the results of science.
In The Privilege of Being a Physicist (1989).
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By destroying the biological character of phenomena, the use of averages in physiology and medicine usually gives only apparent accuracy to the results. From our point of view, we may distinguish between several kinds of averages: physical averages, chemical averages and physiological and pathological averages. If, for instance, we observe the number of pulsations and the degree of blood pressure by means of the oscillations of a manometer throughout one day, and if we take the average of all our figures to get the true or average blood pressure and to learn the true or average number of pulsations, we shall simply have wrong numbers. In fact, the pulse decreases in number and intensity when we are fasting and increases during digestion or under different influences of movement and rest; all the biological characteristics of the phenomenon disappear in the average. Chemical averages are also often used. If we collect a man's urine during twenty-four hours and mix all this urine to analyze the average, we get an analysis of a urine which simply does not exist; for urine, when fasting, is different from urine during digestion. A startling instance of this kind was invented by a physiologist who took urine from a railroad station urinal where people of all nations passed, and who believed he could thus present an analysis of average European urine! Aside from physical and chemical, there are physiological averages, or what we might call average descriptions of phenomena, which are even more false. Let me assume that a physician collects a great many individual observations of a disease and that he makes an average description of symptoms observed in the individual cases; he will thus have a description that will never be matched in nature. So in physiology, we must never make average descriptions of experiments, because the true relations of phenomena disappear in the average; when dealing with complex and variable experiments, we must study their various circumstances, and then present our most perfect experiment as a type, which, however, still stands for true facts. In the cases just considered, averages must therefore be rejected, because they confuse, while aiming to unify, and distort while aiming to simplify. Averages are applicable only to reducing very slightly varying numerical data about clearly defined and absolutely simple cases.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 134-135.
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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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Cavendish gave me once some bits of platinum for my experiments, and came to see my results on the decomposition of the alkalis, and seemed to take an interest in them; but he encouraged no intimacy with any one, and received nobody at his own house. … He was acute, sagacious, and profound, and, I think, the most accomplished British philosopher of his time.
As quoted in Victor Robinson, Pathfinders in Medicine (1912), 143.
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Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.
In Proceedings of London Royal Society (1895), 58, 11-12.
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Characteristically skeptical of the idea that living things would faithfully follow mathematical formulas, [Robert Harper] seized upon factors in corn which seemed to blend in the hybrid—rather than be represented by plus or minus signs, and put several seasons into throwing doubt upon the concept of immutable hypothetical units of inheritance concocted to account for selected results.
In 'Robert Almer Harper', National Academy Biographical Memoirs (1948), 25, 233-234.
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Charles Babbage proposed to make an automaton chess-player which should register mechanically the number of games lost and gained in consequence of every sort of move. Thus, the longer the automaton went on playing game, the more experienced it would become by the accumulation of experimental results. Such a machine precisely represents the acquirement of experience by our nervous organization.
In ‘Experimental Legislation’, Popular Science (Apr 1880), 16, 754-5.
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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 yet, indeed, a mere embryon. Its principles are contested; experiments seem contradictory; their subjects are so minute as to escape our senses; and their result too fallacious to satisfy the mind. It is probably an age too soon to propose the establishment of a system.
Letter to Rev. James Madison (Paris, 19 Jul 1788). In Thomas Jefferson and John P. Foley (ed.), The Jeffersonian Cyclopedia (1900), 135. From H.A. Washington, The Writings of Thomas Jefferson (1853-54). Vol 2, 431.
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Chemistry works with an enormous number of substances, but cares only for some few of their properties; it is an extensive science. Physics on the other hand works with rather few substances, such as mercury, water, alcohol, glass, air, but analyses the experimental results very thoroughly; it is an intensive science. Physical chemistry is the child of these two sciences; it has inherited the extensive character from chemistry. Upon this depends its all-embracing feature, which has attracted so great admiration. But on the other hand it has its profound quantitative character from the science of physics.
In Theories of Solutions (1912), xix.
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Collective unity is not the result of the brotherly love of the faithful for each other. The loyalty of the true believer is to the whole—the church, party, nation—and not to his fellow true believer. True loyalty between individuals is possible only in a loose and relatively free society.
In The True Believer (1951), 122
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Common sense is in spite of, not as the result of, education.
Anonymous
“Anonymous” because although commonly seen attributed to Victor Hugo, the quote cannot be found in his works.
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Common sense is only the application of theories which have grown and been formulated unconsciously as result of experience.
From 'For Mans Use of God's Gifts', collected in Robert C. Goodpasture (ed.), Engineers and Ivory Towers (1952), 107.
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Common sense … has the very curious property of being more correct retrospectively than prospectively. It seems to me that one of the principal criteria to be applied to successful science is that its results are almost always obvious retrospectively; unfortunately, they seldom are prospectively. Common sense provides a kind of ultimate validation after science has completed its work; it seldom anticipates what science is going to discover.
Quoted in A. De Reuck, M. Goldsmith and J. Knight (eds.), Decision Making in National Science Policy (1968), 96.
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Computers and rocket ships are examples of invention, not of understanding. … All that is needed to build machines is the knowledge that when one thing happens, another thing happens as a result. It’s an accumulation of simple patterns. A dog can learn patterns. There is no “why” in those examples. We don’t understand why electricity travels. We don’t know why light travels at a constant speed forever. All we can do is observe and record patterns.
In God's Debris: A Thought Experiment (2004), 22.
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Consider the very roots of our ability to discern truth. Above all (or perhaps I should say “underneath all”), common sense is what we depend on—that crazily elusive, ubiquitous faculty we all have to some degree or other. … If we apply common sense to itself over and over again, we wind up building a skyscraper. The ground floor of the structure is the ordinary common sense we all have, and the rules for building news floors are implicit in the ground floor itself. However, working it all out is a gigantic task, and the result is a structure that transcends mere common sense.
In Metamagical Themas: Questing for the Essence of Mind and Pattern (1985), 93–94.
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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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During the eighteenth and nineteenth centuries we can see the emergence of a tension that has yet to be resolved, concerning the attitude of scientists towards the usefulness of science. During this time, scientists were careful not to stress too much their relationships with industry or the military. They were seeking autonomy for their activities. On the other hand, to get social support there had to be some perception that the fruits of scientific activity could have useful results. One resolution of this dilemma was to assert that science only contributed at the discovery stage; others, industrialists for example, could apply the results. ... Few noted the ... obvious paradox of this position; that, if scientists were to be distanced from the 'evil' effects of the applications of scientific ideas, so too should they receive no credit for the 'good' or socially beneficial, effects of their activities.
Co-author with Philip Gummett (1947- ), -British social scientist
Science, Technology and Society Today (1984), Introduction, 4.
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Each part of the project had a specific task. These tasks were carefully allocated and supervised so that the sum of their parts would result in the accomplishment of our over-all mission.
In And Now It Can Be Told: The Story Of The Manhattan Project (1962), 414.
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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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Einstein’s results again turned the tables and now very few philosophers or scientists still think that scientific knowledge is, or can be, proven knowledge.
In 'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London 1965 (1970), Vol. 4, 92.
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England was nothing, compared to continental nations until she had become commercial … until about the middle of the last century, when a number of ingenious and inventive men, without apparent relation to each other, arose in various parts of the kingdom, succeeded in giving an immense impulse to all the branches of the national industry; the result of which has been a harvest of wealth and prosperity, perhaps without a parallel in the history of the world.
In Lives of the Engineers (1862, 1874), xvii.
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Erasmus Darwin held that every so often you should try a damn-fool experiment. He played the trombone to his tulips. This particular result was, in fact, negative.
In 'The Mathematician’s Art of Work' (1967), collected in Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 194. Webmaster has looked for a primary source to verify this statement and so far has found none. Can you help?
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Every good thought you think is contributing its share to the ultimate result of your life.
…...
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Every improvement that is put upon the real estate is the result of an idea in somebody's head. The skyscraper is another idea; the railroad is another; the telephone and all those things are merely symbols which represent ideas. An andiron, a wash-tub, is the result of an idea that did not exist before.
Speaking to a committee considering a new Copyright Bill (6 Dec 1906). In Mark Twain and William Dean Howells (ed.), Mark Twain’s Speeches? (1910), 320. An andiron is a metal bar, used in a pair, as a stand for logs in a fireplace. The Copyright Bill proposed to give authors, artists and musicians copyright for the term of his life and for 50 years thereafter. John Philip Sousa spoke for the musicians.
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Every well established truth is an addition to the sum of human power, and though it may not find an immediate application to the economy of every day life, we may safely commit it to the stream of time, in the confident anticipation that the world will not fail to realize its beneficial results.
In 'Report of the Secretary', Annual Report of the Board of Regents of the Smithsonian Institution for 1856 (1857), 20.
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Everything material which is the subject of knowledge has number, order, or position; and these are her first outlines for a sketch of the universe. If our feeble hands cannot follow out the details, still her part has been drawn with an unerring pen, and her work cannot be gainsaid. So wide is the range of mathematical sciences, so indefinitely may it extend beyond our actual powers of manipulation that at some moments we are inclined to fall down with even more than reverence before her majestic presence. But so strictly limited are her promises and powers, about so much that we might wish to know does she offer no information whatever, that at other moments we are fain to call her results but a vain thing, and to reject them as a stone where we had asked for bread. If one aspect of the subject encourages our hopes, so does the other tend to chasten our desires, and he is perhaps the wisest, and in the long run the happiest, among his fellows, who has learned not only this science, but also the larger lesson which it directly teaches, namely, to temper our aspirations to that which is possible, to moderate our desires to that which is attainable, to restrict our hopes to that of which accomplishment, if not immediately practicable, is at least distinctly within the range of conception.
From Presidential Address (Aug 1878) to the British Association, Dublin, published in the Report of the 48th Meeting of the British Association for the Advancement of Science (1878), 31.
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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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Evolution is a blind giant who rolls a snowball down a hill. The ball is made of flakes—circumstances. They contribute to the mass without knowing it. They adhere without intention, and without foreseeing what is to result. When they see the result they marvel at the monster ball and wonder how the contriving of it came to be originally thought out and planned. Whereas there was no such planning, there was only a law: the ball once started, all the circumstances that happened to lie in its path would help to build it, in spite of themselves.
'The Secret History of Eddypus', in Mark Twain and David Ketterer (ed.), Tales of Wonder (2003), 222-23.
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Examples ... show how difficult it often is for an experimenter to interpret his results without the aid of mathematics.
Quoted in E. T. Bell, Men of Mathematics, xvi.
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Experience is never at fault; it is only your judgment that is in error in promising itself such results from experience as are not caused by our experiments. For having given a beginning, what follows from it must necessarily be a natural development of such a beginning, unless it has been subject to a contrary influence, while, if it is affected by any contrary influence, the result which ought to follow from the aforesaid beginning will be found to partake of this contrary influence in a greater or less degree in proportion as the said influence is more or less powerful than the aforesaid beginning.
'Philosophy', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938), Vol. 1, 70.
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Experiment is the interpreter of nature. Experiments never deceive. It is our judgment which sometimes deceives itself because it expects results which experiment refuses. We must consult experiment, varying the circumstances, until we have deduced general rules, for experiment alone can furnish reliable rules.
In Introductory College Physics by Oswald Blackwood (1939).
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Experiments may be of two kinds: experiments of simple fact, and experiments of quantity. ...[In the latter] the conditions will ... vary, not in quality, but quantity, and the effect will also vary in quantity, so that the result of quantitative induction is also to arrive at some mathematical expression involving the quantity of each condition, and expressing the quantity of the result. In other words, we wish to know what function the effect is of its conditions. We shall find that it is one thing to obtain the numerical results, and quite another thing to detect the law obeyed by those results, the latter being an operation of an inverse and tentative character.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 1892), 439.
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Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
A simple system representing cellular convection is solved numerically. All of the solutions are found to be unstable, and almost all of them are nonperiodic.
The feasibility of very-long-range weather prediction is examined in the light of these results
Abstract from his landmark paper introducing Chaos Theory in relation to weather prediction, 'Deterministic Nonperiodic Flow', Journal of the Atmospheric Science (Mar 1963), 20, 130.
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For nature by the same cause, provided it remain in the same condition, always produces the same effect, so that either coming-to-be or passing-away will always result.
Aristotle
On Generation and Corruption, 336a, 27-9. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 551.
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For the truth of the conclusions of physical science, observation is the supreme Court of Appeal. It does not follow that every item which we confidently accept as physical knowledge has actually been certified by the Court; our confidence is that it would be certified by the Court if it were submitted. But it does follow that every item of physical knowledge is of a form which might be submitted to the Court. It must be such that we can specify (although it may be impracticable to carry out) an observational procedure which would decide whether it is true or not. Clearly a statement cannot be tested by observation unless it is an assertion about the results of observation. Every item of physical knowledge must therefore be an assertion of what has been or would be the result of carrying out a specified observational procedure.
In ’Scientific Epistemology', The Philosophy of Physical Science (1938, 2012), 9.
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Forces of nature act in a mysterious manner. We can but solve the mystery by deducing the unknown result from the known results of similar events.
In The Words of Gandhi (2001), 87.
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Fortunately Nature herself seems to have prepared for us the means of supplying that want which arises from the impossibility of making certain experiments on living bodies. The different classes of animals exhibit almost all the possible combinations of organs: we find them united, two and two, three and three, and in all proportions; while at the same time it may be said that there is no organ of which some class or some genus is not deprived. A careful examination of the effects which result from these unions and privations is therefore sufficient to enable us to form probable conclusions respecting the nature and use of each organ, or form of organ. In the same manner we may proceed to ascertain the use of the different parts of the same organ, and to discover those which are essential, and separate them from those which are only accessory. It is sufficient to trace the organ through all the classes which possess it, and to examine what parts constantly exist, and what change is produced in the respective functions of the organ, by the absence of those parts which are wanting in certain classes.
Letter to Jean Claude Mertrud. In Lectures on Comparative Anatomy (1802), Vol. I, xxiii--xxiv.
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Four college students taking a class together, had done so well through the semester, and each had an “A”. They were so confident, the weekend before finals, they went out partying with friends. Consequently, on Monday, they overslept and missed the final. They explained to the professor that they had gone to a remote mountain cabin for the weekend to study, but, unfortunately, they had a flat tire on the way back, didn’t have a spare, and couldn’t get help for a long time. As a result, they missed the final. The professor kindly agreed they could make up the final the following day. When they arrived the next morning, he placed them each in separate rooms, handed each one a test booklet, and told them to begin. The the first problem was simple, worth 5 points. Turning the page they found the next question, written: “(For 95 points): Which tire?”
Anonymous
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Fourier’s Theorem … is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth’s crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, 28.
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Further study of the division phenomena requires a brief discussion of the material which thus far I have called the stainable substance of the nucleus. Since the term nuclear substance could easily result in misinterpretation..., I shall coin the term chromatin for the time being. This does not indicate that this substance must be a chemical compound of a definite composition, remaining the same in all nuclei. Although this may be the case, we simply do not know enough about the nuclear substances to make such an assumption. Therefore, we will designate as chromatin that substance, in the nucleus, which upon treatment with dyes known as nuclear stains does absorb the dye. From my description of the results of staining resting and dividing cells... it follows that the chromatin is distributed throughout the whole resting nucleus, mostly in the nucleoli, the network, and the membrane, but also in the ground-substance. In nuclear division it accumulates exclusively in the thread figures. The term achromatin suggests itself automatically for the unstainable substance of the nucleus. The terms chromatic and achromatic which will be used henceforth are thus explained.
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Galileo was no idiot. Only an idiot could believe that science requires martyrdom—that may be necessary in religion, but in time a scientific result will establish itself.
As quoted, without citation, in Harold Eves, Mathematical Circles Squared (1971). Collected in Bill Swainson, The Encarta Book of Quotations (2000), 361.
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General practice is at least as difficult, if it is to be carried on well and successfully, as any special practice can be, and probably more so; for the G.P. has to live continually, as it were, with the results of his handiwork.
The Corner of Harley Street: Being Some Familiar Correspondence of Peter Harding, M. D., Ch. 26.
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Geologists have not been slow to admit that they were in error in assuming that they had an eternity of past time for the evolution of the earth's history. They have frankly acknowledged the validity of the physical arguments which go to place more or less definite limits to the antiquity of the earth. They were, on the whole, disposed to acquiesce in the allowance of 100 millions of years granted to them by Lord Kelvin, for the transaction of the whole of the long cycles of geological history. But the physicists have been insatiable and inexorable. As remorseless as Lear's daughters, they have cut down their grant of years by successive slices, until some of them have brought the number to something less than ten millions. In vain have the geologists protested that there must somewhere be a flaw in a line of argument which tends to results so entirely at variance with the strong evidence for a higher antiquity, furnished not only by the geological record, but by the existing races of plants and animals. They have insisted that this evidence is not mere theory or imagination, but is drawn from a multitude of facts which become hopelessly unintelligible unless sufficient time is admitted for the evolution of geological history. They have not been able to disapprove the arguments of the physicists, but they have contended that the physicists have simply ignored the geological arguments as of no account in the discussion.
'Twenty-five years of Geological Progress in Britain', Nature, 1895, 51, 369.
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Geology is part of that remarkable dynamic process of the human mind which is generally called science and to which man is driven by an inquisitive urge. By noticing relationships in the results of his observations, he attempts to order and to explain the infinite variety of phenomena that at first sight may appear to be chaotic. In the history of civilization this type of progressive scientist has been characterized by Prometheus stealing the heavenly fire, by Adam eating from the tree of knowledge, by the Faustian ache for wisdom.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 454.
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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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Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison which we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome, but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.
From Essai d’une nouvelle théorie de la résistance des fluides (1752), translated as an epigram in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics (1990), Vol. 1, 33.
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Given any rule, however “fundamental” or “necessary” for science, there are always circumstances when it is advisable not only to ignore the rule, but to adopt its opposite. For example, there are circumstances when it is advisable to introduce, elaborate and defend ad hoc hypotheses, or hypotheses which contradict well-established and generally accepted experimental results, or hypotheses whose content is smaller than the content of the existing and empirically adequate alternative, or self-inconsistent hypotheses, and so on.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14-15.
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Goethe said that he who cannot draw on 3,000 years of learning is living hand to mouth. It could just as well be said that individuals who do tap deeply into this rich cultural legacy are wealthy indeed. Yet the paradox is that much of this wisdom is buried in a sea of lesser books or like lost treasure beneath an ocean of online ignorance and trivia. That doesn’t mean that with a little bit of diligence you can’t tap into it. Yet many people, perhaps most, never take advantage of all this human experience. They aren’t obtaining knowledge beyond what they need to know for work or to get by. As a result, their view of our amazing world is diminished and their lives greatly circumscribed.
In An Embarrassment of Riches: Tapping Into the World's Greatest Legacy of Wealth (2013), 65.
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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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Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence and fulfills the duty to express the results of his thoughts in clear form.
…...
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Gyroscope, n.: A wheel or disk mounted to spin rapidly about an axis and also free to rotate about one or both of two axes perpendicular to each other and the axis of spin so that a rotation of one of the two mutually perpendicular axes results from application of torque to the other when the wheel is spinning and so that the entire apparatus offers considerable opposition depending on the angular momentum to any torque that would change the direction of the axis of spin.
Webster's New Collegiate Dictionary (8th Ed., 1973), 513. (Webmaster comments: A definition which is perfectly easy to understand. Right?)
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Here about the beach I wandered, nourishing a youth sublime
With the fairy tales of science, and the long result of Time.
'Locksley Hall' (1842), collected in Alfred Tennyson and William James Rolfe (ed.) The Poetic and Dramatic Works of Alfred, Lord Tennyson (1898), 90.
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Here I shall present, without using Analysis [mathematics], the principles and general results of the Théorie, applying them to the most important questions of life, which are indeed, for the most part, only problems in probability. One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth—induction and analogy—are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.
Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 1.
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His [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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Historically the most striking result of Kant's labors was the rapid separation of the thinkers of his own nation and, though less completely, of the world, into two parties;—the philosophers and the scientists.
The Order of Nature: An Essay (1917), 69.
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Hitherto the conception of chemical transmission at nerve endings and neuronal synapses, originating in Loewi’s discovery, and with the extension that the work of my colleagues has been able to give to it, can claim one practical result, in the specific, though alas only short, alleviation of the condition of myasthenia gravis, by eserine and its synthetic analogues.
'Some recent extensions of the chemical transmission of the effects of nerve impulses', Nobel Lecture, 12 December 1936. In Nobel Lectures: Physiology or Medicine 1922-1941 (1965), 412-3.
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How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.
Max Planck, Walter Henry Johnston, The Universe in the Light of Modern Physics (1931), 58.
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However much the pits may be apparent, yet none, as far as can be comprehended by the senses, passes through the septum of the heart from the right ventricle into the left. I have not seen even the most obscure passages by which the septum of the ventricles is pervious, although they are mentioned by professors of anatomy since they are convinced that blood is carried from the right ventricle into the left. As a result—as I shall declare more openly elsewhere—I am in no little doubt regarding the function of the heart in this part.
In De Humani Corporis Fabrica Libri Septem [Seven Books on the Structure of the Human Body] (revised ed. 1555), 734. Quoted and trans. in Charles Donald O'Malley, Andreas Vesalius of Brussels, 1514-1564 (1964), 281.
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I am a believer in unconscious cerebration. The brain is working all the time, though we do not know it. At night it follows up what we think in the daytime. When I have worked a long time on one thing, I make it a point to bring all the facts regarding it together before I retire; I have often been surprised at the results… We are thinking all the time; it is impossible not to think.
In Orison Swett Marden, 'Bell Telephone Talk: Hints on Success by Alexander G. Bell', How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 33.
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I am afraid I am not in the flight for “aerial navigation”. I was greatly interested in your work with kites; but I have not the smallest molecule of faith in aerial navigation other than ballooning or of expectation of good results from any of the trials we hear of. So you will understand that I would not care to be a member of the aëronautical Society.
Letter (8 Dec 1896) to Baden Powell. This is the full text of the letter. An image of the handwritten original is on the zapatopi.net website
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I am delighted that I have found a new reaction to demonstrate even to the blind the structure of the interstitial stroma of the cerebral cortex. I let the silver nitrate react with pieces of brain hardened in potassium dichromate. I have already obtained magnificent results and hope to do even better in the future.
Letter to Nicolo Manfredi, 16 Feb 1873. Archive source. Quoted in Paolo Mazzarello, The Hidden Structure: A Scientific Biography of Camillo Golgi, trans. and ed. Henry A. Buchtel and Aldo Badiani (1999), 63.
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I believe it to be of particular importance that the scientist have an articulate and adequate social philosophy, even more important than the average man should have a philosophy. For there are certain aspects of the relation between science and society that the scientist can appreciate better than anyone else, and if he does not insist on this significance no one else will, with the result that the relation of science to society will become warped, to the detriment of everybody.
Reflections of a Physicist (1950), 287.
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I believe—and human psychologists, particularly psychoanalysts should test this—that present-day civilized man suffers from insufficient discharge of his aggressive drive. It is more than probable that the evil effects of the human aggressive drives, explained by Sigmund Freud as the results of a special death wish, simply derive from the fact that in prehistoric times intra-specific selection bred into man a measure of aggression drive for which in the social order today he finds no adequate outlet.
On Aggression, trans. M. Latzke (1966), 209.
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I built the solenoid and with great expectations late one evening I pressed the switch which sent a current of 40 amperes through the coil. The result was spectacular—a deafening explosion, the apparatus disappeared, all windows were blown in or out, a wall caved in, and thus ended my pioneering experiment on liquid hydrogen cooled coils! [Recalling the result of his experiment, on 31 Mar 1930, to maximize the magnetic field by cooling the coils of an electromagnet in liquid hydrogen to reduce their resistance.]
'Magnets I have Known', Lecture Notes in Physics (1983), 177, 542-548. Quoted from his memoirs in M.J.M. Leask, 'Obituary: Professor Nicholas Kurti', The Independent (27 Nov 1998).
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I can see him now at the blackboard, chalk in one hand and rubber in the other, writing rapidly and erasing recklessly, pausing every few minutes to face the class and comment earnestly, perhaps on the results of an elaborate calculation, perhaps on the greatness of the Creator, perhaps on the beauty and grandeur of Mathematics, always with a capital M. To him mathematics was not the handmaid of philosophy. It was not a humanly devised instrument of investigation, it was Philosophy itself, the divine revealer of TRUTH.
Writing as a Professor Emeritus at Harvard University, a former student of Peirce, in 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 5.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I cannot anyhow be contented to view this wonderful universe, and especially the nature of man, and to conclude that everything is the result of brute force. I am inclined to look at everything as resulting from designed laws, with the details, whether good or bad, left to the working out of what we call chance. Not that this notion at all satisfies me. I feel most deeply that the whole subject is too profound for the human intellect. A dog might as well speculate on the mind of Newton. Let each man hope and believe what he can.
Letter to Asa Gray (22 May 1860). In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 236.
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I consider the differences between man and animals in propensities, feelings, and intellectual faculties, to be the result of the same cause as that which we assign for the variations in other functions, viz. difference of organization; and that the superiority of man in rational endowments is not greater than the more exquisite, complicated, and perfectly developed structure of his brain, and particularly of his ample cerebral hemispheres, to which the rest of the animal kingdom offers no parallel, nor even any near approximation, is sufficient to account for.
Lectures on Physiology, Zoology, and the Natural History of Man (1819), 237.
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I distinguish two kinds of "applied" research: problem-solving research — government or commercially initiated, centrally managed and institutionally coupled to a plan for application of the results, useful science—investigator-initiated, competitively evaluated and widely communicated. Then we have basic science—useful also, also investigator-initiated, competitively evaluated and widely communicated.
In Confessions of a Technophile (1994), 31.
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I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are permutations and aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of number which it requires a mind like mine to perceive. For instance, if you add a sum from the bottom up, and then from the top down, the result is always different. Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.
Letter to Mrs Arthur Severn (Jul 1878), collected in The Letters of a Noble Woman (Mrs. La Touche of Harristown) (1908), 50. Also in 'Gleanings Far and Near', Mathematical Gazette (May 1924), 12, 95.
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I do not believe that science per se is an adequate source of happiness, nor do I think that my own scientific outlook has contributed very greatly to my own happiness, which I attribute to defecating twice a day with unfailing regularity. Science in itself appears to me neutral, that is to say, it increases men’s power whether for good or for evil. An appreciation of the ends of life is something which must be superadded to science if it is to bring happiness, but only the kind of society to which science is apt to give rise. I am afraid you may be disappointed that I am not more of an apostle of science, but as I grow older, and no doubt—as a result of the decay of my tissues, I begin to see the good life more and more as a matter of balance and to dread all over-emphasis upon anyone ingredient.
Letter to W. W. Norton, Publisher (27 Jan 1931). In The Autobiography of Bertrand Russell, 1914-1944 (1968), Vol. 2, 200.
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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 had made up my mind to find that for which I was searching even if it required the remainder of my life. After innumerable failures I finally uncovered the principle for which I was searching, and I was astounded at its simplicity. I was still more astounded to discover the principle I had revealed not only beneficial in the construction of a mechanical hearing aid but it served as well as means of sending the sound of the voice over a wire. Another discovery which came out of my investigation was the fact that when a man gives his order to produce a definite result and stands by that order it seems to have the effect of giving him what might be termed a second sight which enables him to see right through ordinary problems. What this power is I cannot say; all I know is that it exists and it becomes available only when a man is in that state of mind in which he knows exactly what he wants and is fully determined not to quit until he finds it.
As quoted, without citation, in Mack R. Douglas, Making a Habit of Success: How to Make a Habit of Succeeding, How to Win With High Self-Esteem (1966, 1994), 38. Note: Webmaster is dubious of a quote which seems to appear in only one source, without a citation, decades after Bell’s death. If you know a primary source, please contact Webmaster.
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I had … during many years, followed a golden rule, namely, that whenever a published fact, a new observation or thought came across me, which was opposed by my general results, to make a memorandum of it without fail and at once; for I had found by experience that such facts and thoughts were far more apt to escape from memory than favorable ones.
In The Autobiography of Charles Darwin with original omissions restored, edited by Nora Barlow (1958).
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I have always loved to begin with the facts, to observe them, to walk in the light of experiment and demonstrate as much as possible, and to discuss the results.
Quoted in Francesco Rodolico, 'Arduino', In Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1970), Vol. 1, 234.
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I have always supported women’s rights. I moved the admission of women to my college, Gonville and Caius College, Cambridge. The results were wholly good.
From TV show interview with Piers Morgan, on ITV, 'Good Morning Britain'. As quoted in Sarah Knapton, 'Five Most Powerful People in Britain are Women, says Prof Stephen Hawking', Daily Telegraph (20 Mar 2017).
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I have been scientifically studying the traits and dispositions of the “lower animals” (so-called,) and contrasting them with the traits and dispositions of man. I find the result profoundly humiliating to me. For it obliges me to renounce my allegiance to the Darwinian theory of the Ascent of Man from the Lower Animals; since it now seems plain to me that that theory ought to be vacated in favor of a new and truer one, this new and truer one to be named the Descent of Man from the Higher Animals.
From 'Man's Place in the Animal World' (1896) in What is Man?: and Other Philosophical Writings (1973), 81.
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I have devoted my whole life to the study of Nature, and yet a single sentence may express all that I have done. I have shown that there is a correspondence between the succession of Fishes in geological times and the different stages of their growth in the egg,—this is all. It chanced to be a result that was found to apply to other groups and has led to other conclusions of a like nature.
In Methods of Study in Natural History (1863), 23.
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I have had my results for a long time: but I do not yet know how I am to arrive at them.
Quoted in A. Arber, The Mind and the Eye (1954).
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I have long since come to see that no one deserves either praise or blame for the ideas that come to him, but only for the actions resulting therefrom. Ideas and beliefs are certainly not voluntary acts. They come to us—we hardly know how or whence, and once they have got possession of us we can not reject or change them at will. It is for the common good that the promulgation of ideas should be free—uninfluenced by either praise or blame, reward or punishment. But the actions which result from our ideas may properly be so treated, because it is only by patient thought and work, that new ideas, if good and true, become adopted and utilized; while, if untrue or if not adequately presented to the world, they are rejected or forgotten.
In 'The Origin of the Theory of Natural Selection', Popular Science Monthly (1909), 74, 400.
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Srinivasa Ramanujan quote: I have not trodden through a conventional university course, but I am striking out a new path for mys
I have not trodden through a conventional university course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling.”
First letter to G.H. Hardy (16 Jan 1913). In Collected Papers of Srinivasa Ramanujan (1927), xxiii. Hardy notes he did “seem to remember his telling me that his friends had given him some assistance” in writing the letter because Ramanujan's “knowledge of English, at that stage of his life, could scarcely have been sufficient.”
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I have paid special attention to those Properties of the Positive Rays which seem to throw light on the problems of the structure of molecules and atoms and the question of chemical combination … I am convinced that as yet we are only at the beginning of the harvest of results which will elucidate the process of chemical combination, and thus bridge over the most serious gap which now exists between Physics and Chemistry.
Rays of Positive Electricity and their Application to Chemical Analyses (1921), v.
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I have satisfied myself that the [cosmic] rays are not generated by the formation of new matter in space, a process which would be like water running up a hill. Nor do they come to any appreciable amount from the stars. According to my investigations the sun emits a radiation of such penetrative power that it is virtually impossible to absorb it in lead or other substances. ... This ray, which I call the primary solar ray, gives rise to a secondary radiation by impact against the cosmic dust scattered through space. It is the secondary radiation which now is commonly called the cosmic ray, and comes, of course, equally from all directions in space. [The article continues: The phenomena of radioactivity are not the result of forces within the radioactive substances but are caused by this ray emitted by the sun. If radium could be screened effectively against this ray it would cease to be radioactive, he said.]
Quoted in 'Tesla, 75, Predicts New Power Source', New York Times (5 Jul 1931), Section 2, 1.
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I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.
Letter to Heinrich Schumacher (17 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
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I hope that in due time the chemists will justify their proceedings by some large generalisations deduced from the infinity of results which they have collected. For me I am left hopelessly behind and I will acknowledge to you that through my bad memory organic chemistry is to me a sealed book. Some of those here, [August] Hoffman for instance, consider all this however as scaffolding, which will disappear when the structure is built. I hope the structure will be worthy of the labour. I should expect a better and a quicker result from the study of the powers of matter, but then I have a predilection that way and am probably prejudiced in judgment.
Letter to Christian Schönbein (9 Dec 1852), The Letters of Faraday and Schoenbein, 1836-1862 (1899), 209-210.
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I like a deep and difficult investigation when I happen to have made it easy to myself, if not to all others; and there is a spirit of gambling in this, whether, as by the cast of a die, a calculation è perte de vue shall bring out a beautiful and perfect result or shall be wholly thrown away. Scientific investigations are a sort of warfare carried on in the closet or on the couch against all one's contemporaries and predecessors; I have often gained a signal victory when I have been half asleep, but more frequently have found, upon being thoroughly awake, that the enemy had still the advantage of me, when I thought I had him fast in a corner, and all this you see keeps me alive.
Letter to Hudson Gurney, quoted in George Peacock, The Life of Thomas Young (1855), 239.
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I like to summarize what I regard as the pedestal-smashing messages of Darwin’s revolution in the following statement, which might be chanted several times a day, like a Hare Krishna mantra, to encourage penetration into the soul: Humans are not the end result of predictable evolutionary progress, but rather a fortuitous cosmic afterthought, a tiny little twig on the enormously arborescent bush of life, which, if replanted from seed, would almost surely not grow this twig again, or perhaps any twig with any property that we would care to call consciousness.
…...
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I noticed affixed to a laboratory door the following words: “Les théories passent. Le Grenouille reste. [The theories pass. The frog remains.] &mdashJean Rostand, Carnets d’un biologiste.” There is a risk that in the less severe discipline of criticism the result may turn out to be different; the theories will remain but the frog may disappear.
In An Appetite for Poetry (1989), 5.
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I pass with relief from the tossing sea of Cause and Theory to the firm ground of Result and Fact.
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I recall my own emotions: I had just been initiated into the mysteries of the complex number. I remember my bewilderment: here were magnitudes patently impossible and yet susceptible of manipulations which lead to concrete results. It was a feeling of dissatisfaction, of restlessness, a desire to fill these illusory creatures, these empty symbols, with substance. Then I was taught to interpret these beings in a concrete geometrical way. There came then an immediate feeling of relief, as though I had solved an enigma, as though a ghost which had been causing me apprehension turned out to be no ghost at all, but a familiar part of my environment.
In Tobias Dantzig and Joseph Mazur (ed.), 'The Two Realities', Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 254.
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I said that there is something every man can do, if he can only find out what that something is. Henry Ford has proved this. He has installed in his vast organization a system for taking hold of a man who fails in one department, and giving him a chance in some other department. Where necessary every effort is made to discover just what job the man is capable of filling. The result has been that very few men have had to be discharged, for it has been found that there was some kind of work each man could do at least moderately well. This wonderful system adopted by my friend Ford has helped many a man to find himself. It has put many a fellow on his feet. It has taken round pegs out of square holes and found a round hole for them. I understand that last year only 120 workers out of his force of 50,000 were discharged.
As quoted from an interview by B.C. Forbes in The American Magazine (Jan 1921), 10.
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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 sometimes ask myself how it came about that I was the one to develop the theory of relativity. The reason, I think, is that a normal adult never stops to think about the problem of space and time. These are things which he has thought of as a child. But my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had already grown up.
In Ronald W. Clark, Einstein: The Life and Times (1971), 10.
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I specifically paused to show that, if there were such machines with the organs and shape of a monkey or of some other non-rational animal, we would have no way of discovering that they are not the same as these animals. But if there were machines that resembled our bodies and if they imitated our actions as much as is morally possible, we would always have two very certain means for recognizing that, none the less, they are not genuinely human. The first is that they would never be able to use speech, or other signs composed by themselves, as we do to express our thoughts to others. For one could easily conceive of a machine that is made in such a way that it utters words, and even that it would utter some words in response to physical actions that cause a change in its organs—for example, if someone touched it in a particular place, it would ask what one wishes to say to it, or if it were touched somewhere else, it would cry out that it was being hurt, and so on. But it could not arrange words in different ways to reply to the meaning of everything that is said in its presence, as even the most unintelligent human beings can do. The second means is that, even if they did many things as well as or, possibly, better than anyone of us, they would infallibly fail in others. Thus one would discover that they did not act on the basis of knowledge, but merely as a result of the disposition of their organs. For whereas reason is a universal instrument that can be used in all kinds of situations, these organs need a specific disposition for every particular action.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 5, 40.
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I started studying law, but this I could stand just for one semester. I couldn’t stand more. Then I studied languages and literature for two years. After two years I passed an examination with the result I have a teaching certificate for Latin and Hungarian for the lower classes of the gymnasium, for kids from 10 to 14. I never made use of this teaching certificate. And then I came to philosophy, physics, and mathematics. In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.
From interview on his 90th birthday. In D J Albers and G L Alexanderson (eds.), Mathematical People: Profiles and Interviews (1985), 245-254.
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I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.
Science and Method (1908), trans. Francis Maitland (1914), 53-4.
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I think one’s feelings waste themselves in words; they ought all to be distilled into actions, and into actions which bring results.
Letter to Mary Clarke (1844), quoted in Sir Edward Tyas Cook in The Life of Florence Nightingale (1914), 94.
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I undertake my scientific research with the confident assumption that the earth follows the laws of nature which God established at creation. … My studies are performed with the confidence that God will not capriciously confound scientific results by “slipping in” a miracle.
Quoted in Lenny Flank, Deception by Design: The Intelligent Design Movement in America (2007), 81. Also seen as cited from Arthur Newell Strahler, Science and Earth History: the Evolution/Creation Controversy (1987), 40-41.
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I use the word “attraction” here in a general sense for any endeavor whatever of bodies to approach one another, whether that endeavor occurs as a result of the action of the bodies either drawn toward one other or acting on one another by means of spirits emitted or whether it arises from the action of aether or of air or of any medium whatsoever—whether corporeal or incorporeal—in any way impelling toward one another the bodies floating therein. I use the word “impulse” in the same general sense, considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Book I, Section II, Scholium, 588.
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I well know what a spendidly great difference there is [between] a man and a bestia when I look at them from a point of view of morality. Man is the animal which the Creator has seen fit to honor with such a magnificent mind and has condescended to adopt as his favorite and for which he has prepared a nobler life; indeed, sent out for its salvation his only son; but all this belongs to another forum; it behooves me like a cobbler to stick to my last, in my own workshop, and as a naturalist to consider man and his body, for I know scarcely one feature by which man can be distinguished from apes, if it be not that all the apes have a gap between their fangs and their other teeth, which will be shown by the results of further investigation.
T. Fredbärj (ed.), Menniskans Cousiner (Valda Avhandlingar av Carl von Linné nr, 21) (1955), 4. Trans. Gunnar Broberg, 'Linnaeus's Classification of Man', in Tore Frängsmyr (ed.), Linnaeus: The Man and his Work (1983), 167.
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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 won’t let anyone take us backward, deny our economy the benefits of harnessing a clean energy future, or force our children to endure the catastrophe that would result from unchecked climate change.
In Hillary Clinton, 'Hillary Clinton: America Must Lead at Paris Climate Talks', Time (29 Nov 2015)
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I would picture myself as a virus, or as a cancer cell, for example, and try to sense what it would be like to be either. I would also imagine myself as the immune system, and I would try to reconstruct what I would do as an immune system engaged in combating a virus or cancer cell. When I had played through a series of such scenarios on a particular problem and had acquired new insights, I would design laboratory experiments accordingly… Based upon the results of the experiment, I would then know what question to ask next… When I observed phenomena in the laboratory that I did not understand, I would also ask questions as if interrogating myself: “Why would I do that if I were a virus or a cancer cell, or the immune system?” Before long, this internal dialogue became second nature to me; I found that my mind worked this way all the time.
In Anatomy of Reality: Merging of Intuition and Reason (1983), 7, footnote b, as quoted and cited in Roger Frantz, Two Minds: Intuition and Analysis in the History of Economic Thought (2006), 7.
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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 gold medals and prizes were awarded to institutions instead of individuals, the Peter Bent Brigham Hospital of 30 years ago would have qualified. The ruling board and administrative structure of that hospital did not falter in their support of the quixotic objective of treating end-stage renal disease despite a long list of tragic failures that resulted from these early efforts.
In Tore Frängsmyr and Jan E. Lindsten (eds.), Nobel Lectures: Physiology Or Medicine: 1981-1990 (1993), 558.
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If I have succeeded in discovering any truths in the sciences…, I can declare that they are but the consequences and results of five or six principal difficulties which I have surmounted, and my encounters with which I reckoned as battles in which victory declared for me.
In Discours de la Méthode (1637), as translated by J. Veitch, A Discourse on Method (1912), 53. Also seen translated as, “If I found any new truths in the sciences…, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.”
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If materialism is true, it seems to me that we cannot know that it is true. If my opinions are the result of the chemical processes going on in my brain, they are determined by the laws of chemistry, not those of logic.
The Inequality of Man (1932), 162.
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If one in twenty does not seem high enough odds, we may, if we prefer it, draw the line at one in fifty (the 2 per cent. point), or one in a hundred (the 1 per cent. point). Personally, the writer prefers to set a low standard of significance at the 5 per cent. point, and ignore entirely all results which fail to reach this level. A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance.
'The Arrangement of Field Experiments', The Journal of the Ministry of Agriculture, 1926, 33, 504.
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If one small and odd lineage of fishes had not evolved fins capable of bearing weight on land (though evolved for different reasons in lakes and seas,) terrestrial vertebrates would never have arisen. If a large extraterrestrial object—the ultimate random bolt from the blue—had not triggered the extinction of dinosaurs 65 million years ago, mammals would still be small creatures, confined to the nooks and crannies of a dinosaur's world, and incapable of evolving the larger size that brains big enough for self-consciousness require. If a small and tenuous population of protohumans had not survived a hundred slings and arrows of outrageous fortune (and potential extinction) on the savannas of Africa, then Homo sapiens would never have emerged to spread throughout the globe. We are glorious accidents of an unpredictable process with no drive to complexity, not the expected results of evolutionary principles that yearn to produce a creature capable of understanding the mode of its own necessary construction.
Full House: The Spread of Excellence from Plato to Darwin (1996), 216.
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If science is to progress, what we need is the ability to experiment, honesty in reporting results—the results must be reported without somebody saying what they would like the results to have been—and finally—an important thing—the intelligence to interpret the results.
In The Character of Physical Law (1965, 2001), 148.
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If the Commission is to enquire into the conditions “to be observed,” it is to be presumed that they will give the result of their enquiries; or, in other words, that they will lay down, or at least suggest, “rules” and “conditions to be (hereafter) observed” in the construction of bridges, or, in other words, embarrass and shackle the progress of improvement to-morrow by recording and registering as law the prejudices or errors of to-day.
[Objecting to any interference by the State with the freedom of civil engineers in the conduct of their professional work.]
Letter (13 Mar 1848) to the Royal Commission on the Application of Iron in Railway Structures. Collected in The Life of Isambard Kingdom Brunel, Civil Engineer (1870), 487. The above verbatim quote may be the original source of the following statement as seen in books and on the web without citation: “I am opposed to the laying down of rules or conditions to be observed in the construction of bridges lest the progress of improvement tomorrow might be embarrassed or shackled by recording or registering as law the prejudices or errors of today.” Webmaster has not yet found a primary source for his latter form, and suspects it may be a synopsis, rather than a verbatim quote. If you know of such a primary source, please inform Webmaster.
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If the kind of controversy which so often springs up between modernism and traditionalism in religion were applied to more commonplace affairs of life we might see some strange results. …It arises, let us say, from a passage in an obituary notice which mentions that the deceased had loved to watch the sunsets from his peaceful country home.. …it is forgotten that what the deceased man looked out for each evening was an experience and not a creed.
Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 84-85.
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If the results of the present study on the chemical nature of the transforming principle are confirmed, then nucleic acids must be regarded as possessing biological specificity the chemical basis of which is as yet undetermined.
Oswald T. Avery (1877-1955), Colin Macleod (1909-72) and Maclyn McCarty (1911-2005), ‘Studies in the Chemical Nature of the Substance Inducing Transformation of Pneumococcal Types', Journal of Experimental Medicine 1944, 79, 155.
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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 ascribe the ejection of the proton to a Compton recoil from a quantum of 52 x 106 electron volts, then the nitrogen recoil atom arising by a similar process should have an energy not greater than about 400,000 volts, should produce not more than about 10,000 ions, and have a range in the air at N.T.P. of about 1-3mm. Actually, some of the recoil atoms in nitrogen produce at least 30,000 ions. In collaboration with Dr. Feather, I have observed the recoil atoms in an expansion chamber, and their range, estimated visually, was sometimes as much as 3mm. at N.T.P.
These results, and others I have obtained in the course of the work, are very difficult to explain on the assumption that the radiation from beryllium is a quantum radiation, if energy and momentum are to be conserved in the collisions. The difficulties disappear, however, if it be assumed that the radiation consists of particles of mass 1 and charge 0, or neutrons. The capture of the a-particle by the Be9 nucleus may be supposed to result in the formation of a C12 nucleus and the emission of the neutron. From the energy relations of this process the velocity of the neutron emitted in the forward direction may well be about 3 x 109 cm. per sec. The collisions of this neutron with the atoms through which it passes give rise to the recoil atoms, and the observed energies of the recoil atoms are in fair agreement with this view. Moreover, I have observed that the protons ejected from hydrogen by the radiation emitted in the opposite direction to that of the exciting a-particle appear to have a much smaller range than those ejected by the forward radiation.
This again receives a simple explanation on the neutron hypothesis.
'Possible Existence of a Neutron', Letter to the Editor, Nature, 1932, 129, 312.
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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 we knew all the laws of Nature, we should need only one fact or the description of one actual phenomenon to infer all the particular results at that point. Now we know only a few laws, and our result is vitiated, not, of course, by any confusion or irregularity in Nature, but by our ignorance of essential elements in the calculation. Our notions of law and harmony are commonly confined to those instances which we detect, but the harmony which results from a far greater number of seemingly conflicting, but really concurring, laws which we have not detected, is still more wonderful. The particular laws are as our points of view, as to the traveler, a mountain outline varies with every step, and it has an infinite number of profiles, though absolutely but one form. Even when cleft or bored through, it is not comprehended in its entireness.
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If we work, it is less to obtain those positive results the common people think are our only interest, than to feel that aesthetic emotion and communicate it to those able to experience it.
From the original French, “Si nous travaillons, c’est moins pour obtenir ces résultats auxquels le vulgaire nous croit uniquement attachés, que pour ressentir cette émotion esthétique et la communiquer à ceux qui sont capables de l’éprouver,” quoted in Henri Poincaré,'Notice sur Halphen', Journal de l’École Polytechnique (1890), 60, 143, cited in Oeuvres de G.H. Halphen (1916), Vol. 1, xxiv. As translated in Armand Borel, 'On the Place of Mathematics in Culture', in Armand Borel: Œvres: Collected Papers (1983), Vol. 4, 421.
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If you don’t know anything about computers, just remember that they are machines that do exactly what you tell them but often surprise you in the result.
The Blind Watchmaker (1996), 51.
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If your result needs a statistician then you should design a better experiment.
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If, unwarned by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means, I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results.
In Passages from the Life of a Philosopher (1864), 450.
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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 all cases when a particular agent or cause is to be studied, experiments should be arranged in such a way as to lead if possible to results depending on it alone ; or, if this cannot be done, they should be arranged so as to increase the effects due to the cause to be studied till these so far exceed the unavoidable concomitants, that the latter may be considered as only disturbing, not essentially modifying the effects of the principal agent.
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, 305.
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In all chemical investigations, it has justly been considered an important object to ascertain the relative weights of the simples which constitute a compound. But unfortunately the enquiry has terminated here; whereas from the relative weights in the mass, the relative weights of the ultimate particles or atoms of the bodies might have been inferred, from which their number and weight in various other compounds would appear, in order to assist and to guide future investigations, and to correct their results. Now it is one great object of this work, to shew the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle.
If there are two bodies, A and B, which are disposed to combine, the following is the order in which the combinations may take place, beginning with the most simple: namely,
1 atom of A + 1 atom of B = 1 atom of C, binary
1 atom of A + 2 atoms of B = 1 atom of D, ternary
2 atoms of A + 1 atom of B = 1 atom of E, ternary
1 atom of A + 3 atoms of B = 1 atom of F, quaternary
3 atoms of A and 1 atom of B = 1 atom of G, quaternary
A New System of Chemical Philosophy (1808), Vol. 1, 212-3.
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In all likelihood, it is the local conditions of society, which determine the form of the disease, and we can so far think of it as a fairly general result, that the simplest form is the more common, the more paltry and unbalanced the food, and the worse the dwellings are.
From the original German, “Aller Wahrscheinlichkeit nach sind es die lokalen Verhältnisse der Gesellschaft, welche die Form der Krankheit bestimmen, und wir können bis jetzt als ein ziemlich allgemeines Resultathinstellen, daß die einfache Form umso häufiger ist, je armseliger und einseitiger die Nahrungsmittel und je schlechter die Wohnungen sind,” in 'Mittheilungen über die in Oberschlesien herrschende Typhus-Epidemie', R. Virchow and B. Reinhardt, Archiv für pathologische Anatomie und Physiologie und für klinische Medicin (1848), 2, No. 2, 248. English version by Webmaster with Google translate.
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In deriving a body from the water type I intend to express that to this body, considered as an oxide, there corresponds a chloride, a bromide, a sulphide, a nitride, etc., susceptible of double compositions, or resulting from double decompositions, analogous to those presented by hydrochloric acid, hydrobromic acid, sulphuretted hydrogen, ammonia etc., or which give rise to the same compounds. The type is thus the unit of comparison for all the bodies which, like it, are susceptible of similar changes or result from similar changes.
Traité de Chimie Organique, 1856, 4, 587. Trans. J. R. Partington, A History of Chemistry, (1970), Vol. 4, 456.
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In discussing the state of the atmosphere following a nuclear exchange, we point especially to the effects of the many fires that would be ignited by the thousands of nuclear explosions in cities, forests, agricultural fields, and oil and gas fields. As a result of these fires, the loading of the atmosphere with strongly light absorbing particles in the submicron size range (1 micron = 10-6 m) would increase so much that at noon solar radiation at the ground would be reduced by at least a factor of two and possibly a factor of greater than one hundred.
Paul J. Crutzen -and John W. Birks (1946-, American chemist), 'The Atmosphere after a Nuclear War: Twilight at Noon', Ambio, 1982, 11, 115.
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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 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 history an additional result is commonly produced by human actions beyond that which they aim at and obtain—that which they immediately recognize and desire. They gratify their own interest; but something further is thereby accomplished, latent in the actions in question, though not present to their consciousness, and not included in their design. … This may be called the cunning of reason.
From Vorlesungen über die philosophie der weltgeschichte (1837), as translated from the Third German Edition by J. Sibree (1857), in The Philosophy of History (1857, 1861), 28-29 & 34. Hegel coined the expression List der Vernunft translated as the cunning of reason. In Hegel’s philosophical view, the expression represents a process by which a certain purpose is realized in the history of mankind that is not conscious to the acting man.
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In Institutions of a lower grade [secondary schools], it [geology] receives far less attention than its merits deserve. Why should not a science, whose facts possess a thrilling interest; whose reasonings are admirably adapted for mental discipline, and often severely tax the strongest powers; and whose results are, many of them, as grand and ennobling as those of Astronomy itself; … why should not such a science be thought as essential in education as the kindred branches of Chemistry and Astronomy?
In 'Preface', Elementary Geology (1840, 1841), vi.
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In many ways, unexpected results are what have most inspired my photography.
As quoted, without source, in Gus Kayafas and Estelle Jussim, Stopping Time: The Photographs of Harold Edgerton (1987), 9.
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In my first publication I might have claimed that I had come to the conclusion, as a result of serious study of the literature and deep thought, that valuable antibacterial substances were made by moulds and that I set out to investigate the problem. That would have been untrue and I preferred to tell the truth that penicillin started as a chance observation. My only merit is that I did not neglect the observation and that I pursued the subject as a bacteriologist. My publication in 1929 was the starting-point of the work of others who developed penicillin especially in the chemical field.
'Penicillin', Nobel Lecture, 11 Dec 1945. In Nobel Lectures: Physiology or Medicine 1942-1962 (1964), 83.
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In my opinion, there is absolutely no trustworthy proof that talents have been improved by their exercise through the course of a long series of generations. The Bach family shows that musical talent, and the Bernoulli family that mathematical power, can be transmitted from generation to generation, but this teaches us nothing as to the origin of such talents. In both families the high-watermark of talent lies, not at the end of the series of generations, as it should do if the results of practice are transmitted, but in the middle. Again, talents frequently appear in some member of a family which has not been previously distinguished.
In 'On Heredity', Essays upon Heredity and Kindred Biological Problems (1889), Vol. 1, 95-96.
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In October 1838, that is, fifteen months after I had begun my systematic enquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be, preserved, and unfavourable ones to be destroyed. The result of this would be the formation of new species. Here, then, I had at last got a theory by which to work; but I was so anxious to avoid prejudice, that I determined not for some time to write even the briefest sketch of it.
In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 40.
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In order that the facts obtained by observation and experiment may be capable of being used in furtherance of our exact and solid knowledge, they must be apprehended and analysed according to some Conceptions which, applied for this purpose, give distinct and definite results, such as can be steadily taken hold of and reasoned from.
Philosophy of the Inductive Sciences (1840), Vol. 2, 205.
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In order to form for one's self a just notion of the operations which result in the production of thought, it is necessary to conceive of the brain as a peculiar organ, specially designed for the production thereof, just as the stomach is designed to effect digestion, the liver to filter the bile, the parotids and the maxillary and sublingual glands to prepare the salivary juices.
Rapports du Physique et du Moral de l'Homme (1805), 2nd edition, Vol. 1, 152-3. Translated in Robert M. Young, Mind, Brain and Adaptation in the Nineteenth Century (1970), 20.
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In physical science the discovery of new facts is open to every blockhead with patience, manual dexterity, and acute senses; it is less effectually promoted by genius than by co-operation, and more frequently the result of accident than of design.
In Review of 'An Account of the Life, Lectures, and Writings of William Cullen, M.D. Professor of the Practice of Physic in the University of Edinburgh', The Edinburgh Review (1832), 55, 461.
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In point of fact, no conclusive disproof of a theory can ever be produced; for it is always possible to say that the experimental results are not reliable or that the discrepancies which are asserted to exist between the experimental results and the theory are only apparent and that they will disappear with the advance of our understanding. If you insist on strict proof (or strict disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are.
The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 28.
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In scientific investigations it is grievously wrong to pander to the public’s impatience for results, or to let them think that for discovery it is necessary only to set up a great manufactory and a system of mass production. If in treatment team work is effective, in research it is the individual who counts first and above all. No great thought has ever sprung from anything but a single mind, suddenly conceiving. Throughout the whole world there has been too violent a forcing of the growth of ideas; too feverish a rush to perform experiments and publish conclusions. A year of vacation for calm detachment with all the individual workers thinking it all over in a desert should be proclaimed.
In Viewless Winds: Being the Recollections and Digressions of an Australian Surgeon (1939), 286.
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In teaching man, experimental science results in lessening his pride more and more by proving to him every day that primary causes, like the objective reality of things, will be hidden from him forever and that he can only know relations.
…...
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In that pure enjoyment experienced on approaching to the ideal, in that eagerness to draw aside the veil from the hidden truth, and even in that discord which exists between the various workers, we ought to see the surest pledges of further scientific success. Science thus advances, discovering new truths, and at the same time obtaining practical results.
In The Principles of Chemistry (1891), Vol. 1, preface, footnote, ix, as translated from the Russian 5th edition by George Kamensky, edited by A. J. Greenaway.
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In the course of the history of the earth innumerable events have occurred one after another, causing changes of states, all with certain lasting consequences. This is the basis of our developmental law, which, in a nutshell, claims that the diversity of phenomena is a necessary consequence of the accumulation of the results of all individual occurrences happening one after another... The current state of the earth, thus, constitutes the as yet most diverse final result, which of course represents not a real but only a momentary end-point.
Ober das Entwicklung der Erde, (1867), 5-6.
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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 Ele