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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index I > Category: Insight

Insight Quotes (27 quotes)

[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 drop from the nose of Fleming, who had a cold, fell onto an agar plate where large yellow colonies of a contaminant had grown, and lysosyme was discovered. He made this important discovery because when he saw that the colonies of the contaminant were fading, his mind went straight to the right cause of the phenomenon he was observing—that the drop from his nose contained a lytic substance. And also immediately, he thought that this substance might be present in many secretions and tissues of the body. And he found this was so—the substance was in tears, saliva, leucocytes, skin, fingernails, mother's milk—thus very widely distributed in amounts and also in plants.
Personal recollections of Alexander Fleming by Lady Amelia Fleming. Quoted in Molecular Cloning (2001), Vol. 1, 153.
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I would... establish the conviction that Chemistry, as an independent science, offers one of the most powerful means towards the attainment of a higher mental cultivation; that the study of Chemistry is profitable, not only inasmuch as it promotes the material interests of mankind, but also because it furnishes us with insight into those wonders of creation which immediately surround us, and with which our existence, life, and development, are most closely connected.
Familiar Letters on Chemistry (1859), 4th edn., 1.
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If it were possible for us to have so deep an insight into a man's character as shown both in inner and in outer actions, that every, even the least, incentive to these actions and all external occasions which affect them were so known to us that his future conduct could be predicted with as great a certainty as the occurrence of a solar or lunar eclipse, we could nevertheless still assert that the man is free.
Critique of Practical Reason (1788). In L. W. Beck (ed. & trans.), Critique of Practical Reason and Other Writings in Moral Philosophy (1949), 204-5.
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If the task of scientific methodology is to piece together an account of what scientists actually do, then the testimony of biologists should be heard with specially close attention. Biologists work very close to the frontier between bewilderment and understanding.
Biology is complex, messy and richly various, like real life; it travels faster nowadays than physics or chemistry (which is just as well, since it has so much farther to go), and it travels nearer to the ground. It should therefore give us a specially direct and immediate insight into science in the making.
Induction and Intuition in Scientific Thought (1969), 1.
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In some strange way, any new fact or insight that I may have found has not seemed to me as a “discovery” of mine, but rather something that had always been there and that I had chanced to pick up.
Truth and Beauty: Aesthetics and Motivations in Science (1987, 1990), Preface, ix.
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Insight is not the same as scientific deduction, but even at that it may be more reliable than statistics.
In Science is a Sacred Cow (1950), 123.
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It is often held that scientific hypotheses are constructed, and are to be constructed, only after a detailed weighing of all possible evidence bearing on the matter, and that then and only then may one consider, and still only tentatively, any hypotheses. This traditional view however, is largely incorrect, for not only is it absurdly impossible of application, but it is contradicted by the history of the development of any scientific theory. What happens in practice is that by intuitive insight, or other inexplicable inspiration, the theorist decides that certain features seem to him more important than others and capable of explanation by certain hypotheses. Then basing his study on these hypotheses the attempt is made to deduce their consequences. The successful pioneer of theoretical science is he whose intuitions yield hypotheses on which satisfactory theories can be built, and conversely for the unsuccessful (as judged from a purely scientific standpoint). Co-author with British astronomer, Raymond Arthur Lyttleton (1911-95).
'The Internal Constitution of the Stars', Occasional Notes of the Royal Astronomical Society 1948, 12, 90.
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It is the lone worker who makes the first advance in a subject: the details may be worked out by a team, but the prime idea is due to the enterprise, thought, and perception of an individual.
In Angela Cran, James Robertson, Dictionary of Scottish Quotations (1996),
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I’ve always been inspired by Dr. Martin Luther King, who articulated his Dream of an America where people are judged not by skin color but “by the content of their character.” In the scientific world, people are judged by the content of their ideas. Advances are made with new insights, but the final arbitrator of any point of view are experiments that seek the unbiased truth, not information cherry picked to support a particular point of view.
In letter (1 Feb 2013) to Energy Department employees announcing his decision not to serve a second term.
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Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power. (1943)
In Béla Bollobás, Littlewood's Miscellany (1986), Foreward, 22.
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Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework.
In Principles of Electrodynamics (1972, 1987), 105.
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My original decision to devote myself to science was a direct result of the discovery which has never ceased to fill me with enthusiasm since my early youth—the comprehension of the far from obvious fact that the laws of human reasoning coincide with the laws governing the sequences of the impressions we receive from the world about us; that, therefore, pure reasoning can enable man to gain an insight into the mechanism of the latter. In this connection, it is of paramount importance that the outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life.
'A Scientific Autobiography' (1948), in Scientific Autobiography and Other Papers, trans. Frank Gaynor (1950), 13.
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My “"thinking”" time was devoted mainly to activities that were essentially clerical or mechanical: searching, calculating, plotting, transforming, determining the logical or dynamic consequences of a set of assumptions or hypotheses, preparing the way for a decision or an insight. Moreover ... the operations that fill most of the time allegedly devoted to technical thinking are operations that can be performed more effectively by machines than by men.
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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No generalizing beyond the data, no theory. No theory, no insight. And if no insight, why do research.
'Developing Theory About the Development of Theory,' in Ken G. Smith and Michael A. Hitt, Great Minds in Management: the Theory of Process Development (2005), 361.
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Questions of personal priority, however interesting they may be to the persons concerned, sink into insignificance in the prospect of any gain of deeper insight into the secrets of nature.
As quoted in Silvanus Phillips Thompson, The Life of Lord Kelvin (1910), Vol. 2, 602.
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Science as an intellectual exercise enriches our culture, and is in itself ennobling. ... Though to the layman, the world revealed by the chemist may seem more commonplace, it is not so to him. Each new insight into how the atoms in their interactions express themselves in structure and transformations, not only of inanimate matter, but particularly also of living matter, provides a thrill.
Speech at the Nobel Banquet (10 Dec 1983) for his Nobel Prize in Chemistry. In Wilhelm Odelberg (ed.), Les Prix Nobel: The Nobel Prizes (1984), 43.
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The eye of the master will do more work than both his hands.
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 426:34.

The lives of scientists, considered as Lives, almost always make dull reading. For one thing, the careers of the famous and the merely ordinary fall into much the same pattern, give or take an honorary degree or two, or (in European countries) an honorific order. It could be hardly otherwise. Academics can only seldom lead lives that are spacious or exciting in a worldly sense. They need laboratories or libraries and the company of other academics. Their work is in no way made deeper or more cogent by privation, distress or worldly buffetings. Their private lives may be unhappy, strangely mixed up or comic, but not in ways that tell us anything special about the nature or direction of their work. Academics lie outside the devastation area of the literary convention according to which the lives of artists and men of letters are intrinsically interesting, a source of cultural insight in themselves. If a scientist were to cut his ear off, no one would take it as evidence of a heightened sensibility; if a historian were to fail (as Ruskin did) to consummate his marriage, we should not suppose that our understanding of historical scholarship had somehow been enriched.
'J.B.S: A Johnsonian Scientist', New York Review of Books (10 Oct 1968), reprinted in Pluto's Republic (1982), and inThe Strange Case of the Spotted Mice and Other Classic Essays on Science (1996), 86.
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The stimulus of competition, when applied at an early age to real thought processes, is injurious both to nerve-power and to scientific insight.
In The Preparation of the Child for Science (1904), 44.
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The suppression of uncomfortable ideas may be common in religion or in politics, but it is not the path to knowledge; it has no in the endeavor of science. We do not know in advance who will discover fundamental insights.
In Cosmos (1985), 74.
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There is, however, no genius so gifted as not to need control and verification. ... [T]he brightest flashes in the world of thought are incomplete until they have been proved to have their counterparts in the world of fact. Thus the vocation of the true experimentalist may be defined as the continued exercise of spiritual insight, and its incessant correction and realisation. His experiments constitute a body, of which his purified intuitions are, as it were, the soul.
In 'Vitality', Scientific Use of the Imagination and Other Essays (1872), 43.
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We have learned that there is an endocrinology of elation and despair, a chemistry of mystical insight, and, in relation to the autonomic nervous system, a meteorology and even... an astro-physics of changing moods.
Literature and Science (1963), 90.
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What has been learned in physics stays learned. People talk about scientific revolutions. The social and political connotations of revolution evoke a picture of a body of doctrine being rejected, to be replaced by another equally vulnerable to refutation. It is not like that at all. The history of physics has seen profound changes indeed in the way that physicists have thought about fundamental questions. But each change was a widening of vision, an accession of insight and understanding. The introduction, one might say the recognition, by man (led by Einstein) of relativity in the first decade of this century and the formulation of quantum mechanics in the third decade are such landmarks. The only intellectual casualty attending the discovery of quantum mechanics was the unmourned demise of the patchwork quantum theory with which certain experimental facts had been stubbornly refusing to agree. As a scientist, or as any thinking person with curiosity about the basic workings of nature, the reaction to quantum mechanics would have to be: “Ah! So that’s the way it really is!” There is no good analogy to the advent of quantum mechanics, but if a political-social analogy is to be made, it is not a revolution but the discovery of the New World.
From Physics Survey Committee, U.S. National Academy of Sciences, National Research Council, 'The Nature of Physics', in report Physics in Perspective (1973), 61-62. As cited in I. Bernard Cohen, Revolution in Science (1985), 554-555.
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When Galileo caused balls, the weights of which he had himself previously determined, to roll down an inclined plane; when Torricelli made the air carry a weight which he had calculated beforehand to be equal to that of a definite volume of water; or in more recent times, when Stahl changed metal into lime, and lime back into metal, by withdrawing something and then restoring it, a light broke upon all students of nature. They learned that reason has insight only into that which it produces after a plan of its own, and that it must not allow itself to be kept, as it were, in nature's leading-strings, but must itself show the way with principles of judgement based upon fixed laws, constraining nature to give answer to questions of reason's own determining. Accidental observations, made in obedience to no previously thought-out plan, can never be made to yield a necessary law, which alone reason is concerned to discover.
Critique of Pure Reason (1781), trans. Norman Kemp Smith (1929), 20.
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[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
From interview with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 13.
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[W]e have made a thing, a most terrible weapon, that has altered abruptly and profoundly the nature of the world. We have made a thing that, by all standards of the world we grew up in, is an evil thing. And by doing so, by our participation in making it possible to make these things, we have raised again the question of whether science is good for man, of whether it is good to learn about the world, to try to understand it, to try to control it, to help give to the world of men increased insight, increased power. Because we are scientists, we must say an unalterable yes to these questions; it is our faith and our commitment, seldom made explicit, even more seldom challenged, that knowledge is a good in itself, knowledge and such power as must come with it.
Speech to the American Philosophical Society (Jan 1946). 'Atomic Weapons', printed in Proceedings of the American Philosophical Society, 90(1), 7-10. In Deb Bennett-Woods, Nanotechnology: Ethics and Society (2008), 23. Identified as a speech to the society in Kai Bird, Martin J. Sherwin, American Prometheus: the Triumph and Tragedy of J. Robert Oppenheimer‎ (2005), 323.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
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John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton

New Book

The Simpsons and their Mathematical Secrets,
by Simon Singh

Cleverly embedded in many Simpsons plots are subtle references to mathematics, because the show's brilliant comedy writers with advanced degrees in math or science. Singh offers an entirely new insight into the most successful show in television history.