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Understanding Quotes (231 quotes)

Dicere enim bene nemo potest, nisi qui prudenter intelligit.
No one can speak well, unless he thoroughly understands his subject.
Brutus VI., 23. In Thomas Benfield Harbottle, Dictionary of Quotations (classical) (3rd Ed., 1906), 45.
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Enlightenment is man's emergence from his self-incurred immaturity. Immaturity is the inability to use one's own understanding without the guidance of another. This immaturity is self-incurred if its cause is not lack of understanding, but lack of resolution and courage to use it without the guidance of another. The motto of enlightenment is therefore: Sapere aude! Have courage to use your own understanding!
'An Answer to the Question: What is Enlightenment?', (1784). In Hans Reiss (ed.), Kant: Political Writings, trans. H. B. Nisbet (1970), 54.
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Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics.
Physicist: I'm afraid I don’t understand the method of characteristics.
Neumann: In mathematics you don't understand things. You just get used to them.
Attributed, as related by Dr. Felix Smith (Head of Molecular Physics, Stanford Research Institute) to author Gary Zukav, who quoted it in The Dancing Wu Li Masters: An Overview of the New Physics (1979, 2001), 208, footnote. The physicist (a friend of Dr. Smith) worked at Los Alamos after WW II. It should be noted that although the author uses quotation marks around the spoken remarks, that they represent the author's memory of Dr. Smith's recollection, who heard it from the physicist. Therefore the fourth-hand wording is very likely not verbatim. Webmaster finds Zukav's book seems to be the only source for this quote.
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Quand celui à qui l'on parle ne comprend pas et celui qui parle ne se comprend pas, c'est de la métaphysique
When he to whom a person speaks does not understand, and he who speaks does not understand himself, that is metaphysics.
In James Wood, Dictionary of Quotations from Ancient and Modern English and Foreign Sources (1899), 361.
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A central lesson of science is that to understand complex issues (or even simple ones), we must try to free our minds of dogma and to guarantee the freedom to publish, to contradict, and to experiment. Arguments from authority are unacceptable.
Billions and Billions: Thoughts on Life and Death at the Brink of the Millenium (1998), 190.
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A designer must always think about the unfortunate production engineer who will have to manufacture what you have designed; try to understand his problems.
On the official Raymond Loewry website.
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A visitor to Niels Bohr's country cottage, noticing a horseshoe hanging on the wall, teasing the eminent scientist about this ancient superstition. “Can it be true that you, of all people, believe it will bring you luck?'
'Of course not,' replied Bohr, 'but I understand it brings you luck whether you believe it or not.'”
As described in Clifton Fadiman (ed.), André Bernard (ed.), Bartlett's Book of Anecdotes (2000), 68.
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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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All knowledge resolves itself into probability. ... In every judgment, which we can form concerning probability, as well as concerning knowledge, we ought always to correct the first judgment deriv'd from the nature of the object, by another judgment, deriv'd from the nature of the understanding.
In A treatise of Human Nature (1888), 181-182.
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All living organisms are but leaves on the same tree of life. The various functions of plants and animals and their specialized organs are manifestations of the same living matter. This adapts itself to different jobs and circumstances, but operates on the same basic principles. Muscle contraction is only one of these adaptations. In principle it would not matter whether we studied nerve, kidney or muscle to understand the basic principles of life. In practice, however, it matters a great deal.
'Muscle Research', Scientific American, 1949, 180 (6), 22.
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All Nature is but Art, unknown to thee;
All Chance, Direction, which thou canst not see;
All Discord, Harmony, not understood;
All partial Evil, universal Good:
And, spite of Pride, in erring Reason's spite,
One truth is clear, 'Whatever IS, is RIGHT.'
'An Essay on Man' (1733-4), Epistle I. In John Butt (ed.), The Poems of Alexander Pope (1965), 515.
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All that stuff I was taught about evolution, embryology, Big Bang theory, all that is lies straight from the pit of hell. It’s lies to try to keep me and all the folks who are taught that from understanding that they need a savior.
[Revealing his anti-science views, contrary to the qualifications needed to make important public policy on matters of science.]
From speech (27 Sep 2012) to a sportman's banquet at Liberty Baptist Church, Hartwell, Georgia, as quoted in Matt Pearce, 'U.S. Rep. Paul Broun: Evolution a lie ‘from the pit of hell’', Los angeles Times (7 Oct 2012).
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All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.
Lectures on the Logic of Arithmetic (1903), Preface, 18-19.
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All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.
The Value of Science (1905), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 332.
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Although a science fair can seem like a big “pain” it can help you understand important scientific principles, such as Newton's First Law of Inertia, which states: “A body at rest will remain at rest until 8:45 p.m. the night before the science fair project is due, at which point the body will come rushing to the body's parents, who are already in their pajamas, and shout, ‘I JUST REMEMBERED THE SCIENCE FAIR IS TOMORROW AND WE GOTTA GO TO THE STORE RIGHT NOW!’”
'Science: It's Just Not Fair', Miami Herald (22 Mar 1998)
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An egg is a chemical process, but it is not a mere chemical process. It is one that is going places—even when, in our world of chance and contingency, it ends up in an omelet and not in a chicken. Though it surely be a chemical process, we cannot understand it adequately without knowing the kind of chicken it has the power to become.
'The Changing Impact of Darwin on Philosophy', Journal of the History of Ideas (1961), 22, 457.
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An expert is a man who understands everything, and nothing else.
Speech, London (16 Dec 1970), 'Israel's International Relations in an Era of Peace', (1979), 22.
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And I believe there are many Species in Nature, which were never yet taken notice of by Man, and consequently of no use to him, which yet we are not to think were created in vain; but it's likely ... to partake of the overflowing Goodness of the Creator, and enjoy their own Beings. But though in this sense it be not true, that all things were made for Man; yet thus far it is, that all the Creatures in the World may be some way or other useful to us, at least to exercise our Wits and Understandings, in considering and contemplating of them, and so afford us Subject of Admiring and Glorifying their and our Maker. Seeing them, we do believe and assert that all things were in some sense made for us, we are thereby obliged to make use of them for those purposes for which they serve us, else we frustrate this End of their Creation.
John Ray
The Wisdom of God Manifested in the Works of the Creation (1691), 169-70.
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Anyone who is not shocked by the quantum theory has not understood it.
Atomic Physics and Human Knowledge (1958). Quoted in Eric Middleton, The New Flatlanders (2007), 19.
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Archaeology gives a sense of place. It grounds us within the landscape and every place is unique. … Archaeology can also give an understanding of where we come from.
From interview with Sarah Marsh, in “Being a Council Archaeologist is ‘Like Being a Detective’”, The Guardian (6 Sep 2013).
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Art and science work in quite different ways: agreed. But, bad as it may sound, I have to admit that I cannot get along as an artist without the use of one or two sciences. ... In my view, the great and complicated things that go on in the world cannot be adequately recognized by people who do not use every possible aid to understanding.
Bertolt Brecht, John Willett (trans.), Brecht on Theatre (1964), 73.
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As for the search for truth, I know from my own painful searching, with its many blind alleys, how hard it is to take a reliable step, be it ever so small, towards the understanding of that which is truly significant.
Letter to an interested layman (13 Feb 1934). In Helen Dukas and Banesh Hoffman, Albert Einstein: The Human Side: New Glipses From His Archives (1981), 18.
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Asked in 1919 whether it was true that only three people in the world understood the theory of general relativity, [Eddington] allegedly replied: “Who's the third?”
As described in Brian Stableford, Science Fact and Science Fiction: An Encyclopedia (2006), 150.
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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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Books have always a secret influence on the understanding; we cannot at pleasure obliterate ideas; he that reads books of science, thogh without any fixed desire of improvement, will grow more knowing…
In Samuel Johnson and W. Jackson Bate (Ed.), ',The Adventurer, No. 137, Tuesday, 26 Febraury 1754.' The Selected Essays from the Rambler, Adventurer, and Idler (1968), 273.
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But, but, but ... if anybody says he can think about quantum theory without getting giddy it merely shows that he hasn't understood the first thing about it!
Quoted in Otto R. Frisch, What Little I Remember (1979), 95.
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By this we may understand, there be two sorts of knowledge, whereof the one is nothing else but sense, or knowledge original (as I have said at the beginning of the second chapter), and remembrance of the same; the other is called science or knowledge of the truth of propositions, and how things are called, and is derived from understanding.
The Elements of Law: Natural and Politic (1640), Ferdinand Tonnies edn. (1928), Part 1, Chapter 6, 18-9.
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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&rdqo; 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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Contrary to popular parlance, Darwin didn't discover evolution. He uncovered one (most would say the) essential mechanism by which it operates: natural selection. Even then, his brainstorm was incomplete until the Modern Synthesis of the early/mid-20th century when (among other things) the complementary role of genetic heredity was fully realized. Thousands upon thousands of studies have followed, providing millions of data points that support this understanding of how life on Earth has come to be as it is.
In online article, 'The Day That Botany Took on Bobby Jindal by Just Being Itself', Huffington Post (5 Aug 2013).
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Creation science has not entered the curriculum for a reason so simple and so basic that we often forget to mention it: because it is false, and because good teachers understand why it is false. What could be more destructive of that most fragile yet most precious commodity in our entire intellectual heritage—good teaching—than a bill forcing our honorable teachers to sully their sacred trust by granting equal treatment to a doctrine not only known to be false, but calculated to undermine any general understanding of science as an enterprise?.
In 'The Verdict on Creationism' The Sketical Inquirer (Winter 1987/88), 12, 186.
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Data is not information, Information is not knowledge, Knowledge is not understanding, Understanding is not wisdom.
Attributed to Cliff Stoll and Gary Schubert, in Mark R Keeler, Nothing to Hide: Privacy in the 21st Century (2006), 112. A similar quote, 'Information is not knowledge, Knowledge is not wisdom,' is in the lyrics of Frank Zappa's album, Joe's Garage, track 'Packard Goose.' The sentiment of the above quote is presented in Clifford Stoll, Silicon Snake Oil: Second Thoughts on the Information Highway (1996), 193-194. The elements of the above quote are fragmented and distributed within three paragraphs. “Data isn't information ... information is not knowledge ... doesn't mean you understand ... There's a relationship between data, information, knowledge, understanding, and wisdom. ... perhaps knowledge becomes wisdom.” [If you know a primary print source and date for Stoll and Schubert's quote, in the exact words of the summary form as above, please contact webmaster.]
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Data isn't information. ... Information, unlike data, is useful. While there’s a gulf between data and information, there’s a wide ocean between information and knowledge. What turns the gears in our brains isn't information, but ideas, inventions, and inspiration. Knowledge—not information—implies understanding. And beyond knowledge lies what we should be seeking: wisdom.
In High-Tech Heretic: Reflections of a Computer Contrarian (2000), 185-186.
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During the war years I worked on the development of radar and other radio systems for the R.A.F. and, though gaining much in engineering experience and in understanding people, rapidly forgot most of the physics I had learned.
From Autobiography in Wilhelm Odelberg (ed.), Les Prix Nobel en 1974/Nobel Lectures (1975)
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Early in my school career, I turned out to be an incorrigible disciplinary problem. I could understand what the teacher was saying as fast as she could say it, I found time hanging heavy, so I would occasionally talk to my neighbor. That was my great crime, I talked in school.
In In Memory Yet Green: the Autobiography of Isaac Asimov, 1920-1954 (1979), 73.
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EDUCATION, n. That which discloses to the wise and disguises from the foolish their lack of understanding.
The Cynic's Word Book (1906), 86. Also published later as The Devil's Dictionary.
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Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.
In How to Solve It: A New Aspect of Mathematical Method (2004), 14.
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Even today a good many distinguished minds seem unable to accept or even to understand that from a source of noise natural selection alone and unaided could have drawn all the music of the biosphere. In effect natural selection operates upon the products of chance and can feed nowhere else; but it operates in a domain of very demanding conditions, and from this domain chance is barred. It is not to chance but to these conditions that eveloution owes its generally progressive cource, its successive conquests, and the impresssion it gives of a smooth and steady unfolding.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), 118-119.
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Every sentence I utter must be understood not as an affirmation but as a question.
[A caution he gives his students, to be wary of dogmatism.]
In Bill Becker, 'Pioneer of the Atom', New York Times Sunday Magazine (20 Oct 1957), 52.
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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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Flower in the crannied wall,
I pluck you out of the crannies;—
I hold you here, root and all, in my hand,
Little flower—but if I could understand
What you are, root and all, and all in all,
I should know what God and man is.
In The Holy Grail: and Other Poems (1870), 165.
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Fractal geometry will make you see everything differently. There is a danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpet, bricks, and much else besides. Never again will your interpretation of these things be quite the same.
Fractals Everywhere (2000), 1.
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From the point of view of the pure morphologist the recapitulation theory is an instrument of research enabling him to reconstruct probable lines of descent; from the standpoint of the student of development and heredity the fact of recapitulation is a difficult problem whose solution would perhaps give the key to a true understanding of the real nature of heredity.
Form and Function: A Contribution to the History of Animal Morphology (1916), 312-3.
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Furious activity is no substitute for understanding.
In Michael Fripp, Speaking of Science: Notable Quotes on Science, Engineering, and the Environment‎ (2000), 203. Widely seen, but without further biographical information or source citation. Webmaster has not yet found a print source prior to 2000. Please contact Webmaster if you have more details. (For a similar quote in 1972, see Alastair Pilkington.)
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Good luck is science not yet classified; just as the supernatural is the natural not yet understood.
In Elbert Hubbard (ed. and publ.), The Philistine (Dec 1907), 26, No. 1, 10.
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Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand… So Greek mathematics is ‘permanent’, more permanent even than Greek literature.
In A Mathematician’s Apology (1940, 1967), 81.
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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
Science and Method (1914, 2003), 117-118.
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I am not a speed reader. I am a speed understander.
In Cris Tovani, Do I Really Have to Teach Reading? (2004), 51
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I believe scientists have a duty to share the excitement and pleasure of their work with the general public, and I enjoy the challenge of presenting difficult ideas in an understandable way.
From Autobiography in Wilhelm Odelberg (ed.), Les Prix Nobel en 1974/Nobel Lectures (1975)
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I believe that only scientists can understand the universe. It is not so much that I have confidence in scientists being right, but that I have so much in nonscientists being wrong.
Webmaster has not yet been able to confirm this attribution. If you know an original print citation, please contact Webmaster.
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I cannot think of a single field in biology or medicine in which we can claim genuine understanding, and it seems to me the more we learn about living creatures, especially ourselves, the stranger life becomes.
In 'On Science and Certainty', Discover Magazine (Oct 1980).
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I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.
Quoted in F Wilczek, B Devine, Longing for the Harmonies.
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I do not understand modern physics at all, but my colleagues who know a lot about the physics of very small things, like the particles in atoms, or very large things, like the universe, seem to be running into one queerness after another, from puzzle to puzzle.
In 'On Science and Certainty', Discover Magazine (Oct 1980).
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I esteem his understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of his work, where the author studies things of little use or when he builds on the improbable principle of attraction.
Writing about Newton's Principia. Huygens had some time earlier indicated he did not believe the theory of universal gravitation, saying it 'appears to me absurd.'
Quoted in Archana Srinivasan, Great Inventors (2007), 37.
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I have always found small mammals enough like ourselves to feel that I could understand what their lives would be like, and yet different enough to make it a sort of adventure and exploration to see what they were doing.
Echoes of Bats and Men (1959), 2.
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I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.
Max Born
My Life & My Views (1968), 48.
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I never said a word against eminent men of science. What I complain of is a vague popular philosophy which supposes itself to be scientific when it is really nothing but a sort of new religion and an uncommonly nasty one. When people talked about the fall of man, they knew they were talking about a mystery, a thing they didn’t understand. Now they talk about the survival of the fittest: they think they do understand it, whereas they have not merely no notion, they have an elaborately false notion of what the words mean.
In The Club of Queer Trades (1903, 1905), 241.
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I think the next [21st] century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don’t know how the laws fit together, and what happens under extreme conditions. But I expect we will find a complete unified theory sometime this century. The is no limit to the complexity that we can build using those basic laws.
[Answer to question: Some say that while the twentieth century was the century of physics, we are now entering the century of biology. What do you think of this?]
'"Unified Theory" Is Getting Closer, Hawking Predicts', interview in San Jose Mercury News (23 Jan 2000), 29A. Answer quoted in Ashok Sengupta, Chaos, Nonlinearity, Complexity: The Dynamical Paradigm of Nature (2006), vii. Question included in Hans-Joachim Schellnhuber, Nicholas Stern and Mario Molina , Global Sustainability: a Nobel Cause (2010), 13. Cite from Brent Davis and Dennis J. Sumara, Complexity and Education: Inquiries Into Learning, Teaching, and Research (2006), 171.
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I was sitting writing at my textbook but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gambolling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the rest of the hypothesis. Let us learn to dream, gentlemen, then perhaps we shall find the truth... But let us beware of publishing our dreams till they have been tested by waking understanding.
Kekule at Benzolfest in Berichte (1890), 23, 1302.
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I would clarify that by ‘animal’ I understand a being that has feeling and that is capable of exercising life functions through a principle called soul; that the soul uses the body's organs, which are true machines, by virtue of its being the principal cause of the action of each of the machine's parts; and that although the placement that these parts have with respect to one another does scarcely anything else through the soul's mediation than what it does in pure machines, the entire machine nonetheless needs to be activated and guided by the soul in the same way as an organ, which, although capable of rendering different sounds through the placement of the parts of which it is composed, nonetheless never does so except through the guidance of the organist.
'La Mechanique des Animaux', in Oeuvres Diverses de Physique et de Mechanique (1721), Vol. 1, 329. Quoted in Jacques Roger, Keith R. Benson (ed.), Robert Ellrich (trans.), The Life Sciences in Eighteenth-Century French Thought, (1997), 273-4.
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I would rather live in a world where my life is surrounded by mystery than live in a world so small that my mind could comprehend it.
'The Mystery of Life', Riverside Sermons (1958), 22.
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I've found out so much about electricity that I've reached the point where I understand nothing and can explain nothing.
[Describing his experiments with the Leyden jar.]
Letter to Réamur (20 Jan 1746), in AS. Proc. verb., LXV (1746), 6. Cited in J. L. Heilbron, Electricity in the 17th and 18th Centuries: a Study of Early Modern Physics (1979), 314.
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If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
Endless Horizons (1946), 27.
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If the brain were so simple that we could understand it, we would be so simple we couldn't.
Quoted by George E. Pugh, The Biological Origin of Human Values (1978), 154. In a footnote, the author writes that this quote comes his own father, around 1938. The quote is also widely seen attributed to Lyall Watson (born 1939), for example, by Larry Chang in Wisdom for the Soul: Five Millennia of Prescriptions for Spiritual Healing (2006), 539.
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If the human mind were simple enough to understand, we'd be too simple to understand it.
Pat Bahn
Bahn's conundrum to cognitive theory
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If this seems complex, the reason is because Tao is both simple and complex. It is complex when we try to understand it, and simple when we allow ourselves to experience it.
In Gary William Flake, The Computational Beauty of Nature (2000), 327.
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If we do discover a complete theory, it should be in time understandable in broad principle by everyone ... Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.
A Brief History of Time (1988), 191.
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If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
In How to Solve It: A New Aspect of Mathematical Method (2004), 15.
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If you want to understand human beings, there are plenty of people to go to besides psychologists.... Most of these people are incapable of communicating their knowledge, but those who can communicate it are novelists. They are good novelists precisely because they are good psychologists.
In Science is a Sacred Cow (1950), 128.
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In a certain sense I made a living for five or six years out of that one star [υ Sagittarii] and it is still a fascinating, not understood, star. It’s the first star in which you could clearly demonstrate an enormous difference in chemical composition from the sun. It had almost no hydrogen. It was made largely of helium, and had much too much nitrogen and neon. It’s still a mystery in many ways … But it was the first star ever analysed that had a different composition, and I started that area of spectroscopy in the late thirties.
Oral History Transcript of interview with Dr. Jesse Greenstein by Paul Wright (31 Jul 1974), on website of American Institute of Physics, about his research on strange shell stars. As quoted in J. B. Hearnshaw, The Analysis of Starlight: One Hundred and Fifty Years of Astronomical Spectroscopy (1986, 1990), 362. Hearnshaw footnoted that Berman earlier analysed the peculiar star R CrB (1935).
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In every science certain things must be accepted as first principles if the subject matter is to be understood; and these first postulates rest upon faith.
As quoted, without citation, in Ronald Keast, Dancing in the Dark: The Waltz in Wonder of Quantum Metaphysics (2009), 104-105. If you know a primary source, please contact Webmaster.
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In my understanding of God I start with certain firm beliefs. One is that the laws of nature are not broken. We do not, of course, know all these laws yet, but I believe that such laws exist. I do not, therefore, believe in the literal truth of some miracles which are featured in the Christian Scriptures, such as the Virgin Birth or water into wine. ... God works, I believe, within natural laws, and, according to natural laws, these things happen.
Essay 'Science Will Never Give Us the Answers to All Our Questions', collected in Henry Margenau, and Roy Abraham Varghese (eds.), Cosmos, Bios, Theos (1992), 66.
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In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skilful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them.
'Cosmology', in Arthur Beer (ed.), Vistas in Astronomy (1956), Vol. 2, 1722.
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In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
In How to Solve It: A New Aspect of Mathematical Method (2004), 174.
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In our day grand generalizations have been reached. The theory of the origin of species is but one of them. Another, of still wider grasp and more radical significance, is the doctrine of the Conservation of Energy, the ultimate philosophical issues of which are as yet but dimly seem-that doctrine which 'binds nature fast in fate' to an extent not hitherto recognized, exacting from every antecedent its equivalent consequent, and bringing vital as well as physical phenomena under the dominion of that law of causal connexion which, so far as the human understanding has yet pierced, asserts itself everywhere in nature.
'Address Delivered Before The British Association Assembled at Belfast', (19 Aug 1874). Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 1801.
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In studying the fate of our forest king, we have thus far considered the action of purely natural causes only; but, unfortunately, man is in the woods, and waste and pure destruction are making rapid headway. If the importance of the forests were even vaguely understood, even from an economic standpoint, their preservation would call forth the most watchful attention of government
John Muir
In The Mountains of California (1894), 198.
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In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.
Reflections: Mathematics and Creativity', New Yorker (1972), 47, No. 53, 39-45. In Douglas M. Campbell, John C. Higgins (eds.), Mathematics: People, Problems, Results (1984), Vol. 2, 7.
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In the mathematics I can report no deficience, except it be that men do not sufficiently understand this excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures, so in the mathematics that use which is collateral and intervenient is no less worthy than that which is principal and intended.
The Advancement of Learning (1605), Book 2. Reprinted in The Two Books of Francis Bacon: Of the Proficience and Advancement of Learning, Divine and Human (2009), 97.
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In the sick room, ten cents' worth of human understanding equals ten dollars' worth of medical science.
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
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Increased knowledge of heredity means increased power of control over the living thing, and as we come to understand more and more the architecture of the plant or animal we realize what can and what cannot be done towards modification or improvement.
Reginald C. Punnett, in article 'Mendelism', from Hugh Chisholm (ed.) The Encyclopædia Britannica (1911), Vol. 18, 120.
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Intelligence is an extremely subtle concept. It’s a kind of understanding that flourishes if it's combined with a good memory, but exists anyway even in the absence of good memory. It’s the ability to draw consequences from causes, to make correct inferences, to foresee what might be the result, to work out logical problems, to be reasonable, rational, to have the ability to understand the solution from perhaps insufficient information. You know when a person is intelligent, but you can be easily fooled if you are not yourself intelligent.
In Irv Broughton (ed.), The Writer's Mind: Interviews with American Authors (1990), Vol. 2, 57.
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It appears unlikely that the role of the genes in development is to be understood so long as the genes are considered as dictatorial elements in the cellular economy. It is not enough to know what a gene does when it manifests itself. One must also know the mechanisms determining which of the many gene-controlled potentialities will be realized.
'The Role of the Cytoplasm in Heredity', in William D. McElroy and Bentley Glass (eds.), A Symposium on the Chemical Basis of Heredity (1957), 162.
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It is easier to understand mankind in general than any individual man.
Maxims (1678), no. 436, trans. F. G. Stevens (1939), 137.
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It is imperative in the design process to have a full and complete understanding of how failure is being obviated in order to achieve success. Without fully appreciating how close to failing a new design is, its own designer may not fully understand how and why a design works. A new design may prove to be successful because it has a sufficiently large factor of safety (which, of course, has often rightly been called a “factor of ignorance”), but a design's true factor of safety can never be known if the ultimate failure mode is unknown. Thus the design that succeeds (ie, does not fail) can actually provide less reliable information about how or how not to extrapolate from that design than one that fails. It is this observation that has long motivated reflective designers to study failures even more assiduously than successes.
In Design Paradigms: Case Histories of Error and Judgment in Engineering (1994), 31. books.google.comHenry Petroski - 1994
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It is in moments of illness that we are compelled to recognize that we live not alone but chained to a creature of a different kingdom, whole worlds apart, who has no knowledge of us, and by whom it is impossible to make ourselves understood: our body.
'Le Côté de Guermantes', À la recherche du temps perdu (1913-27).
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It is in our genes to understand the universe if we can, to keep trying even if we cannot, and to be enchanted by the act of learning all the way.
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It is my intent to beget a good understanding between the chymists and the mechanical philosophers who have hitherto been too little acquainted with one another's learning.
The Sceptical Chymist (1661).
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It is not enough to say that we cannot know or judge because all the information is not in. The process of gathering knowledge does not lead to knowing. A child's world spreads only a little beyond his understanding while that of a great scientist thrusts outward immeasurably. An answer is invariably the parent of a great family of new questions. So we draw worlds and fit them like tracings against the world about us, and crumple them when we find they do not fit and draw new ones.
In John Steinbeck and Edward Flanders Ricketts, Sea of Cortez: a Leisurely Journal of Travel and Research (1941), 165-66.
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It is often claimed that knowledge multiplies so rapidly that nobody can follow it. I believe this is incorrect. At least in science it is not true. The main purpose of science is simplicity and as we understand more things, everything is becoming simpler. This, of course, goes contrary to what everyone accepts.
Edward Teller, Wendy Teller, Wilson Talley, Conversations on the Dark Secrets of Physics (1991, 2002), 2.
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It is structure that we look for whenever we try to understand anything. All science is built upon this search; we investigate how the cell is built of reticular material, cytoplasm, chromosomes; how crystals aggregate; how atoms are fastened together; how electrons constitute a chemical bond between atoms. We like to understand, and to explain, observed facts in terms of structure. A chemist who understands why a diamond has certain properties, or why nylon or hemoglobin have other properties, because of the different ways their atoms are arranged, may ask questions that a geologist would not think of' formulating, unless he had been similarly trained in this way of thinking about the world.
‘The Place of Chemistry In the Integration of the Sciences’, Main Currents in Modern Thought (1950), 7, 110.
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It is the nature of an hypothesis, when once a man has conceived it, that it assimilates every thing to itself, as proper nourishment; and, from the first moment of your begetting it, it generally grows the stronger by every thing you see, hear, read, or understand.
The Life and Opinions of Tristram Shandy Gentleman (1759-67), Penguin edition (1997), 121-2.
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It may be unpopular and out-of-date to say—but I do not think that a scientific result which gives us a better understanding of the world and makes it more harmonious in our eyes should be held in lower esteem than, say, an invention which reduces the cost of paving roads, or improves household plumbing.
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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It was a great step in science when men became convinced that, in order to understand the nature of things, they must begin by asking, not whether a thing is good or bad, noxious or beneficial, but of what kind it is? And how much is there of it? Quality and Quantity were then first recognised as the primary features to be observed in scientific inquiry.
'Address to the Mathematical and Physical Sections of the British Association, Liverpool, 15 Sep 1870', The Scientific Papers of James Clerk Maxwell (1890 edition, reprint 2003), Vol. 2, 217.
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It was my science that drove me to the conclusion that the world is much more complicated than can be explained by science. It is only through the supernatural that I can understand the mystery of existence.
As quoted in Sharon Begley, 'Science Finds God', Newsweek (1998).
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It's only through honesty and courage that science can work at all. The Ptolemaic understanding of the solar system was undermined and corrected by the constant pressure of more and more honest reporting.
In essay, 'The Origin of the Universe,' 6. Written after hearing Stephen Hawking's lecture (2006) at Oxford, about the origin of the universe.
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It's important to always bear in mind that life occurs in historical time. Everyone in every culture lives in some sort of historical time, though it might not be perceived in the same way an outside observer sees it. It's an interesting question, “When is now?” “Now” can be drawn from some point like this hour, this day, this month, this lifetime, or this generation. “Now” can also have occurred centuries ago; things like unfair treaties, the Trail of Tears, and the Black Hawk War, for instance, remain part of the “Now” from which many Native Americans view their place in time today. Human beings respond today to people and events that actually occurred hundreds or even thousands of years ago. Ethnohistorians have played a major role in showing how now is a social concept of time, and that time is part of all social life. I can only hope that their work will further the understanding that the study of social life is a study of change over time.
From Robert S. Grumet, 'An Interview with Anthony F. C. Wallace', Ethnohistory (Winter 1998), 45, No. 1, 127.
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Knowing how hard it is to collect a fact, you understand why most people want to have some fun analyzing it.
Quoted in Fortune (May 1960), as cited in Maxine Block, Anna Herthe Rothe and Marjorie Dent Candee, Current Biography Yearbook 1963 (1964), 161.
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Knowing is not understanding. There is a great difference between knowing and understanding: you can know a lot about something and not really understand it.
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Language is the principal tool with which we communicate; but when words are used carelessly or mistakenly, what was intended to advance mutual understanding may in fact hinder it; our instrument becomes our burden
Irving M. Copi and Carl Cohen (probably? in their Introduction to Logic), In K. Srinagesh, The Principles of Experimental Research (2006), 15.
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Linnaeus had it constantly in mind:'The closer we get to know the creatures around us, the clearer is the understanding we obtain of the chain of nature, and its harmony and system, according to which all things appear to have been created.'
In 'The Two Faces of Linnaeus', in Tore Frängsmyr (ed.), Linnaeus: The Man and his Work (1983, 1994), 16. Quoted in David Weinberger, Everything is Miscellaneous (2007), 241.
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Literary intellectuals at one pole—at the other scientists, and as the most representative, the physical scientists. Between the two a gulf of mutual incomprehension—sometimes (particularly among the young) hostility and dislike, but most of all lack of understanding.
The Two Cultures: The Rede Lecture (1959), 4.
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Magic and all that is ascribed to it is a deep presentiment of the powers of science. The shoes of swiftness, the sword of sharpness, the power of subduing the elements, of using the secret virtues of minerals, of understanding the voices of birds, are the obscure efforts of the mind in a right direction.
From 'History', collected in The Complete Works of Ralph Waldo Emerson (1903), 34.
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Man masters nature not by force but by understanding. That is why science has succeeded where magic failed: because it has looked for no spell to cast on nature.
Lecture, 'The Creative Mind' (26 Feb 1953) at Massachusetts Institute of Technology. Printed in Science and Human Values (1959), 18.
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Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.
In 'Prop. 47: The human mind possesses an adequate knowledge of the eternal and infinite essence of God', Ethic, translated by William Hale White (1883), 93-94. Collected in The English and Foreign Philosophical Library, Vol. 21.
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Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
In 'A Mathematician's Gossip', Indiscrete Thoughts (2008), 214.
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Medicine rests upon four pillars—philosophy, astronomy, alchemy, and ethics. The first pillar is the philosophical knowledge of earth and water; the second, astronomy, supplies its full understanding of that which is of fiery and airy nature; the third is an adequate explanation of the properties of all the four elements—that is to say, of the whole cosmos—and an introduction into the art of their transformations; and finally, the fourth shows the physician those virtues which must stay with him up until his death, and it should support and complete the three other pillars.
Vas Buch Paragranum (c.1529-30), in J. Jacobi (ed.), Paracelsus: Selected Writings (1951), 133-4.
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Men think epilepsy divine, mere because they do not understand it. But if they called everything divine which they do not understand, why, there would be no end of divine things.
As given in Carl SaganCosmos (1985), 145.
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More and more of out colleagues fail to understand our work because of the high specialization of research problems. We must not be discouraged if the products of our labor are not read or even known to exist. The joy of research must be found in doing since every other harvest is uncertain.
Letter to Dr. E. B. Krumhaar (11 Oct 1933), in Journal of Bacteriology (Jan 1934), 27, No. 1, 20.
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Much of the work we do as scientists involves filling in the details about matters that are basically understood already, or applying standard techniques to new specific cases. But occasionally there is a question that offers an opportunity for a really major discovery.
In Tyrannosaurus Rex and the Crater of Doom (1997), 42.
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My scientific work is motivated by an irresistible longing to understand the secrets of nature and by no other feeling. My love for justice and striving to contribute towards the improvement of human conditions are quite independent from my scientific interests.
In Helen Dukas and Banesh Hoffman, Albert Einstein, the Human Side: New Glipses from his Archives (1971) 18. In Vladimir Burdyuzha, The Future of Life and the Future of Our Civilization (2006), 374.
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Mystics understand the roots of the Tao but not its branches; scientists understand its branches but not its roots. Science does not need mysticism and mysticism does not need science; but man needs both.
In The Tao of Physics (1975), 306.
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Nature is made in such a way as to be able to be understood. Or perhaps I should put it—more correctly—the other way around, and say that we are made in such a way as to be able to understand Nature.
Attributed. (If you know a primary source, please contact webmaster.)
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Nature never makes excellent things, for mean or no uses: and it is hardly to be conceived, that our infinitely wise Creator, should make so admirable a Faculty, as the power of Thinking, that Faculty which comes nearest the Excellency of his own incomprehensible Being, to be so idlely and uselesly employ'd, at least 1/4 part of its time here, as to think constantly, without remembering any of those Thoughts, without doing any good to it self or others, or being anyway useful to any other part of Creation.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 1, Section 15, 113.
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Nearly every understanding is gained by a painful struggle in which belief and unbelief are dramatically interwoven.
In Quest: An Autobiography (1980), 200.
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No engineer can go upon a new work and not find something peculiar, that will demand his careful reflection, and the deliberate consideration of any advice that he may receive; and nothing so fully reveals his incapacity as a pretentious assumption of knowledge, claiming to understand everything.
In Railway Property: A Treatise on the Construction and Management of Railways (1866), 247.
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No one has yet been found so firm of mind and purpose as resolutely to compel himself to sweep away all theories and common notions, and to apply the understanding, thus made fair and even, to a fresh examination of particulars. Thus it happens that human knowledge, as we have it, is a mere medley and ill-digested mass, made up of much credulity and much accident, and also of the childish notions which we at first imbibed.
Aphorism 20,' Novum Organum, Book II (1620)
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No part of the world can be truly understood without a knowledge of its garment of vegetation, for this determines not only the nature of the animal inhabitants but also the occupations of the majority of human beings.
The Red Man's Continent: A Chronicle of Aboriginal America (1919), 88.
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Not all is doom and gloom. We are beginning to understand the natural world and are gaining a reverence for life - all life.
Source unverified. Please contact Webmaster if you know the primary source.
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One should not understand this compulsion to construct concepts, species, forms, purposes, laws ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible:—we thereby create a world which is calculable, simplified, comprehensible, etc., for us.
The Will to Power (Notes written 1883-1888), book 3, no. 521. Trans. W. Kaufmann and R. J. Hollingdale and ed. W. Kaufmann (1968), 282.
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Our children will enjoy in their homes electrical energy too cheap to meter. ... Transmutation of the elements, unlimited power, ability to investigate the working of living cells by tracer atoms, the secret of photosynthesis about to be uncovered, these and a host of other results, all in about fifteen short years. It is not too much to expect that our children will know of great periodic famines in the world only as matters of history, will travel effortlessly over the seas and under the and through the air with a minimum of danger and at great speeds, and will experience a life span far longer than ours, as disease yields and man comes to understand what causes him to age.
Speech at the 20th anniversary of the National Association of Science Writers, New York City (16 Sep 1954), asquoted in 'Abundant Power From Atom Seen', New York Times (17 Sep 1954) 5.
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Outside our consciousness there lies the cold and alien world of actual things. Between the two stretches the narrow borderland of the senses. No communication between the two worlds is possible excepting across the narrow strip. For a proper understanding of ourselves and of the world, it is of the highest importance that this borderland should be thoroughly explored.
Keynote Address, a tribute to Helmholtz, at the Imperial Palace, Berlin (Aug 1891). Cited in Davis Baird, R.I.G. Hughes and Alfred Nordmann, Heinrich Hertz: Classical Physicist, Modern Philosopher (1998), 157.
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Paris ... On this side of the ocean it is difficult to understand the susceptibility of American citizens on the subject and precisely why they should so stubbornly cling to the biblical version. It is said in Genesis the first man came from mud and mud is not anything very clean. In any case if the Darwinian hypothesis should irritate any one it should only be the monkey. The monkey is an innocent animal—a vegetarian by birth. He never placed God on a cross, knows nothing of the art of war, does not practice lynch law and never dreams of assassinating his fellow beings. The day when science definitely recognizes him as the father of the human race the monkey will have no occasion to be proud of his descendants. That is why it must be concluded that the American Association which is prosecuting the teacher of evolution can be no other than the Society for Prevention of Cruelty to Animals.
[A cynical article in the French press on the Scopes Monkey Trial, whether it will decide “a monkey or Adam was the grandfather of Uncle Sam.”]
Newspaper
Article from a French daily newspaper on the day hearings at the Scopes Monkey Trial began, Paris Soir (13 Jul 1925), quoted in 'French Satirize the Case', New York Times (14 Jul 1925), 3.
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People must understand that science is inherently neither a potential for good nor for evil. It is a potential to be harnessed by man to do his bidding.
Interview, Associated Press (29 Sep 1964). In Bill Swainson, Encarta Book of Quotations (2000), 833.
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Physicists only talk to physicists, economists to economists—worse still, nuclear physicists only talk to nuclear physicists and econometricians to econometricians. One wonders sometimes if science will not grind to a stop in an assemblage of walled-in hermits, each mumbling to himself words in a private language that only he can understand.
In 'The Skeleton of Science', General Systems Theory (1956). Collected in 'General Systems Theory—The Skeleton of Science', Beyond Economics: Essays on Society, Religion, and Ethics (1968), 85.
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Pure mathematics consists entirely of such asseverations as that, if such and such is a proposition is true of anything, then such and such another propositions is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is of which it is supposed to be true. … If our hypothesis is about anything and not about some one or more particular things, then our deductions constititute mathematics. Thus mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true.
'Recent Work on the Principles of Mathematics', International Monthly (1901), 4, 84. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 7.
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Reading furnishes the mind only with materials of knowledge, it is thinking makes what we read ours.
On the Conduct Of Understanding (written 1697, published posthumously 1706), collected in Works (5th Ed. 1751), Vol. 3, 387.
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Regardless of communication between man and man, speech is a necessary condition for the thinking of the individual in solitary seclusion. In appearance, however, language develops only socially, and man understands himself only once he has tested the intelligibility of his words by trial upon others.
On Language (1836), trans. Peter Heath (1988), 56.
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Relativity was a highly technical new theory that gave new meanings to familiar concepts and even to the nature of the theory itself. The general public looked upon relativity as indicative of the seemingly incomprehensible modern era, educated scientists despaired of ever understanding what Einstein had done, and political ideologues used the new theory to exploit public fears and anxieties—all of which opened a rift between science and the broader culture that continues to expand today.
'The Cultural Legacy of Relativity Theory' in Albert Einstein, Robert W. Lawson, Robert Geroch, Roger Penrose and David C. Cassidy, Relativity (2005), 226.
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Rules can seldom be safely applied without a clear understanding of the principles on which they rest.
From Field-Book for Railroad Engineers (1854), Preface, vii.
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Rules of Thumb
Thumb's First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb's Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Anonymous
In Arthur Bloch, The Complete Murphy's Law: A Definitive Collection (1991), 126. books.google.com - 1991
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Science has a simple faith, which transcends utility. Nearly all men of science, all men of learning for that matter, and men of simple ways too, have it in some form and in some degree. It is the faith that it is the privilege of man to learn to understand, and that this is his mission. If we abandon that mission under stress we shall abandon it forever, for stress will not cease. Knowledge for the sake of understanding, not merely to prevail, that is the essence of our being. None can define its limits, or set its ultimate boundaries.
Science is Not Enough (1967), 191.
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Science has to be understood in its broadest sense, as a method for apprehending all observable reality, and not merely as an instrument for acquiring specialized knowledge.
In Alfred Armand Montapert, Words of Wisdom to Live By: An Encyclopedia of Wisdom in Condensed Form (1986), 217, without citation. If you know the primary source, please contact Webmaster.
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Science is a human activity, and the best way to understand it is to understand the individual human beings who practise it. Science is an art form and not a philosophical method. The great advances in science usually result from new tools rather than from new doctrines. ... Every time we introduce a new tool, it always leads to new and unexpected discoveries, because Nature's imagination is richer than ours.
Concluding remark from 'The Scientist As Rebel' American Mathemtical Monthly (1996), 103, 805. Reprinted in The Scientist as Rebel (2006), 17-18, identified as originally written for a lecture (1992), then published as an essay in the New York Review.
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Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking; love has found.
The Works of Honoré de Balzac (1896), Vol. 19, 80.
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Science provides an understanding of a universal experience, and arts provides a universal understanding of a personal experience.
In online transcript of TED talk, 'Mae Jemison on teaching arts and sciences together' (2002).
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Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined. Its validity is of the same order as that of ordinary perception; memory, and understanding. Its test is found, like theirs, in actual intuition, which sometimes consists in perception and sometimes in intent. The flight of science is merely longer from perception to perception, and its deduction more accurate of meaning from meaning and purpose from purpose. It generates in the mind, for each vulgar observation, a whole brood of suggestions, hypotheses, and inferences. The sciences bestow, as is right and fitting, infinite pains upon that experience which in their absence would drift by unchallenged or misunderstood. They take note, infer, and prophesy. They compare prophesy with event, and altogether they supply—so intent are they on reality—every imaginable background and extension for the present dream.
The Life of Reason, or the Phases of Human Progress (1954), 393.
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Scientific progress is the discovery of a more and more comprehensive simplicity... The previous successes give us confidence in the future of science: we become more and more conscious of the fact that the universe is cognizable.
In O. Godart and M. Heller (eds.), Cosmology of Lemaitre (1985), 162.
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Scientists often invent words to fill the holes in their understanding.These words are meant as conveniences until real understanding can be found. ... Words such as dimension and field and infinity ... are not descriptions of reality, yet we accept them as such because everyone is sure someone else knows what the words mean.
In God's Debris: A Thought Experiment (2004), 20-21.
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Scientists themselves readily admit that they do not fully understand the consequences of our many-faceted assault upon the interwoven fabric of atmosphere, water, land and life in all its biological diversity. But things could also turn out to be worse than the current scientific best guess. In military affairs, policy has long been based on the dictum that we should be prepared for the worst case. Why should it be so different when the security is that of the planet and our long-term future?
Speech, 'Global Security Lecture' at Cambridge University (28 Apr 1993).
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Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.
Particle Physics and an Introduction to Field Theory (1981), 177.
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Some of the scientists, I believe, haven’t they been changing their opinion a little bit on global warming? There’s a lot of differing opinions and before we react I think it’s best to have the full accounting, full understanding of what’s taking place.
Presidential Debate (2000). In Historic Documents of 2000 (2001), 823.
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Subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement.
In The Tao of Physics (1975), 68.
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Such propositions are therefore called Eternal Truths, not because they are Eternal Truths, not because they are External Propositions actually formed, and antecedent to the Understanding, that at any time makes them; nor because they are imprinted on the Mind from any patterns, that are any where out of the mind, and existed before: But because, being once made, about abstract Ideas, so as to be true, they will, whenever they can be supposed to be made again at any time, past or to come, by a Mind having those Ideas, always actually be true. For names being supposed to stand perpetually for the same ideas, and the same ideas having immutably the same habitudes one to another, Propositions concerning any abstract Ideas that are once true, must needs be eternal Verities.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 11, Section 14, 638-9.
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Suppose there is something which a person cannot understand. He happens to notice the similarity of this something to some other thing which he understands quite well. By comparing them he may come to understand the thing which he could not understand up to that moment. If his understanding turns out to be appropriate and nobody else has ever come to such an understanding, he can claim that his thinking was really creative.
Creativity and Intuition: A Physicist Looks at East and West (1973), 114.

The Ideas of primary Qualities of Bodies, are Resemblances of them, and their Patterns do really exist in the Bodies themselves; but the Ideas, produced in us by these Secondary Qualities, have no resemblance of them at all. There is nothing like our Ideas, existing in the Bodies themselves. They are in Bodies, we denominate from them, only a Power to produce those Sensations in us: And what is Sweet, Blue or Warm in Idea, is but the certain Bulk, Figure, and Motion of the insensible parts in the Bodies themselves, which we call so.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 8, Section 15, 137.
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The chemical differences among various species and genera of animals and plants are certainly as significant for the history of their origins as the differences in form. If we could define clearly the differences in molecular constitution and functions of different kinds of organisms, there would be possible a more illuminating and deeper understanding of question of the evolutionary reactions of organisms than could ever be expected from morphological considerations.
'Uber das Vorkommen von Haemoglobin in den Muskeln der Mollusken und die Verbreitung desselben in den lebenden Organismen', Pflügers Archiv für die gesamte Physiologie des Menschen und der Tiere, 1871, 4, 318-9. Trans. Joseph S. Fruton, Proteins, Enzymes, Genes: The Interplay of Chemistry and Biology (1999), 270.
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The effort to understand the universe is one of the very few things that lifts human life above the level of farce, and gives it some of the grace of tragedy.
In The First Three Minutes (1977), 155.
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The engineer is the key figure in the material progress of the world. It is his engineering that makes a reality of the potential value of science by translating scientific knowledge into tools, resources, energy and labor to bring them to the service of man ... To make contribution of this kind the engineer requires the imagination to visualize the needs of society and to appreciate what is possible as well as the technological and broad social age understanding to bring his vision to reality.
In Philip Sporn, Foundations of Engineering: Cornell College of Engineering Lectures, Spring 1963 (1964), 22.
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The equation of evolution with progress represents our strongest cultural impediment to a proper understanding of this greatest biological revolution in the history of human thought.
Leonardo's Mountain of Clams and the Diet of Worms: Essays on Natural History (1998), 173.
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The experimenter who does not know what he is looking for will never understand what he finds.
Attributed. Also seen as, “He who does not know what he is looking for will not lay hold of what he has found when he gets it.” If you know a primary source, perhaps in the original French, please contact Webmaster.
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The eye, the window of the soul, is the chief means whereby the understanding can most fully and abundantly appreciate the infinite works of Nature; and the ear is second.
As quoted in Daniel J. Boorstin, The Discoverers (1983), 350.
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The feeling of understanding is as private as the feeling of pain. The act of understanding is at the heart of all scientific activity; without it any ostensibly scientific activity is as sterile as that of a high school student substituting numbers into a formula. For this reason, science, when I push the analysis back as far as I can, must be private.
Reflections of a Physicist (1950), 72.
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The graceful minuet-dance of fancy must give place to the toilsome, thorny pilgrimage of understanding.
On the transition from the age of romance to that of science.
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 431:5.

The great basic thought that the world is not to be comprehended as a complex of ready-made things, but as a complex of processes, in which the things apparently stable no less than their mind-images in our heads, the concepts, go through an uninterrupted change of coming into being and passing away, in which, in spite of all seeming accidents and of all temporary retrogression, a progressive development asserts itself in the end—this great fundamental thought has, especially since the time of Hegel, so thoroughly permeated ordinary consciousness that in this generality it is scarcely ever contradicted.
Ludwig Feuerbach and the Outcome of Classical German Philosophy (1886). C. P. Dutt (ed.) (1934), 54.
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The human understanding is moved by those things most which strike and enter the mind simultaneously and suddenly, and so fill the imagination; and then it feigns and supposes all other things to be somehow, though it cannot see how, similar to those few things by which it is surrounded.
Translation of Novum Organum, XLVII. In Francis Bacon, James Spedding, The Works of Francis Bacon (1864), Vol. 8, 80.
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The hybridoma technology was a by-product of basic research. Its success in practical applications is to a large extent the result of unexpected and unpredictable properties of the method. It thus represents another clear-cut example of the enormous practical impact of an investment in research which might not have been considered commercially worthwhile, or of immediate medical relevance. It resulted from esoteric speculations, for curiosity’s sake, only motivated by a desire to understand nature.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and ‎Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 267-268.
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The invention of the scientific method and science is, I'm sure we'll all agree, the most powerful intellectual idea, the most powerful framework for thinking and investigating and understanding and challenging the world around us that there is, and it rests on the premise that any idea is there to be attacked. If it withstands the attack then it lives to fight another day and if it doesn't withstand the attack then down it goes. Religion doesn't seem to work like that.
From impromptu speech at a Cambridge conference (1998). Quoted in Richard Dawkins, A Devil's Chaplain: Reflections on Hope, Lies, Science, and Love (2004), 168. In Douglas Adams, The Salmon of Doubt: Hitchhiking the Galaxy One Last Time (2002), 141.
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The known is finite, the unknown infinite; intellectually we stand on an islet in the midst of an illimitable ocean of inexplicability. Our business in every generation is to reclaim a little more land, to add something to the extent and the solidity of our possessions. And even a cursory glance at the history of the biological sciences during the last quarter of a century is sufficient to justify the assertion, that the most potent instrument for the extension of the realm of natural knowledge which has come into men's hands, since the publication of Newton's ‘Principia’, is Darwin's ‘Origin of Species.’
From concluding remarks to a chapter by Thomas Huxley, 'On the Reception of the ‘Origin of Species’', the last chapter in Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin (1887), Vol. 1, 557.
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The largest land animal is the elephant, and it is the nearest to man in intelligence: it understands the language of its country and obeys orders, remembers duties that it has been taught, is pleased by affection and by marks of honour, nay more it possesses virtues rare even in man, honesty, wisdom, justice, also respect for the stars and reverence for the sun and moon.
Natural History, 8, I. Trans. H. Rackham, Pliny: Natural History (1947), Vol. 3, 3.
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The meaning of human life and the destiny of man cannot be separable from the meaning and destiny of life in general. 'What is man?' is a special case of 'What is life?' Probably the human species is not intelligent enough to answer either question fully, but even such glimmerings as are within our powers must be precious to us. The extent to which we can hope to understand ourselves and to plan our future depends in some measure on our ability to read the riddles of the past. The present, for all its awesome importance to us who chance to dwell in it, is only a random point in the long flow of time. Terrestrial life is one and continuous in space and time. Any true comprehension of it requires the attempt to view it whole and not in the artificial limits of any one place or epoch. The processes of life can be adequately displayed only in the course of life throughout the long ages of its existence.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 9.
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The most incomprehensible thing about the world is that it is comprehensible.
In Banesh Hoffmann and Helen Dukas, Albert Einstein: Creator and Rebel (1972, 1973), 18.

The nucleic acids, as constituents of living organisms, are comparable In importance to proteins. There is evidence that they are Involved In the processes of cell division and growth, that they participate In the transmission of hereditary characters, and that they are important constituents of viruses. An understanding of the molecular structure of the nucleic acids should be of value In the effort to understand the fundamental phenomena of life.
[Co-author with American chemist, B. Corey (1897-1971)]
'A Proposed Structure for the Nucleic Acids', Proceedings of the National Academy of Sciences (1953), 39, 84.
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The physicist is like someone who’s watching people playing chess and, after watching a few games, he may have worked out what the moves in the game are. But understanding the rules is just a trivial preliminary on the long route from being a novice to being a grand master. So even if we understand all the laws of physics, then exploring their consequences in the everyday world where complex structures can exist is a far more daunting task, and that’s an inexhaustible one I'm sure.
In Lewis Wolpert and Alison Richards, A Passion For Science (1988), 37.
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The quantum entered physics with a jolt. It didn’t fit anywhere; it made no sense; it contradicted everything we thought we knew about nature. Yet the data seemed to demand it. ... The story of Werner Heisenberg and his science is the story of the desperate failures and ultimate triumphs of the small band of brilliant physicists who—during an incredibly intense period of struggle with the data, the theories, and each other during the 1920s—brought about a revolutionary new understanding of the atomic world known as quantum mechanics.
Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb (2009), 90. Selected and contributed to this website by the author.
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The reason Dick's [Richard Feynman] physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans [Bethe] and Oppy [Oppenheimer] and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial.
Quoted in Michio Kaku and Jennifer Trainer Thompson, Beyond Einstein: the Cosmic Quest for the Theory of the Universe (1987, 1999), 56-57, citing Freeman Dyson, Disturbing the Universe (1979, 1981), 55-56.
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The senses at first let in particular Ideas, and furnish the yet empty Cabinet: And the Mind by degrees growing familiar with some of them, they are lodged in the Memory, and Names got to them.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book I, Chapter 2, Section 15, 55.
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The size and age of the Cosmos are beyond ordinary human understanding. Lost somewhere between immensity and eternity is our tiny planetary home.
Cosmos (1981), 4.
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The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them.
Address (1918) for Max Planck's 60th birthday, at Physical Society, Berlin, 'Principles of Research' in Essays in Science (1934), 4.
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The theory of the earth is the science which describes and explains changes that the terrestrial globe has undergone from its beginning until today, and which allows the prediction of those it shall undergo in the future. The only way to understand these changes and their causes is to study the present-day state of the globe in order to gradually reconstruct its earlier stages, and to develop probable hypotheses on its future state. Therefore, the present state of the earth is the only solid base on which the theory can rely.
In Albert V. Carozzi, 'Forty Years of Thinking in Front of the Alps: Saussure's (1796) Unpublished Theory of the Earth', Earth Sciences History (1989), 8 136.
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The universality of parasitism as an offshoot of the predatory habit negatives the position taken by man that it is a pathological phenomenon or a deviation from the normal processes of nature. The pathological manifestations are only incidents in a developing parasitism. As human beings intent on maintaining man's domination over nature we may regard parasitism as pathological insofar as it becomes a drain upon human resources. In our efforts to protect ourselves we may make every kind of sacrifice to limit, reduce, and even eliminate parasitism as a factor in human life. Science attempts to define the terms on which this policy of elimination may or may not succeed. We must first of all thoroughly understand the problem, put ourselves in possession of all the facts in order to estimate the cost. Too often it has been assumed that parasitism was abnormal and that it needed only a slight force to reestablish what was believed to be a normal equilibrium without parasitism. On the contrary, biology teaches us that parasitism is a normal phenomenon and if we accept this view we shall be more ready to pay the price of freedom as a permanent and ever recurring levy of nature for immunity from a condition to which all life is subject. The greatest victory of man over nature in the physical realm would undoubtedly be his own delivery from the heavy encumbrance of parasitism with which all life is burdened.
Parasitism and Disease (1934), 4.
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The universe does not exist 'out there,' independent of us. We are inescapably involved in bringing about that which appears to be happening. We are not only observers. We are participators. In some strange sense, this is a participatory universe. Physics is no longer satisfied with insights only into particles, fields of force, into geometry, or even into time and space. Today we demand of physics some understanding of existence itself.
Quoted in Denis Brian, The Voice Of Genius: Conversations with Nobel Scientists and Other Luminaries, 127.
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The universe seems to me infinitely strange and foreign. At such a moment I gaze upon it with a mixture of anguish and euphoria; separate from the universe, as though placed at a certain distance outside it; I look and I see pictures, creatures that move in a kind of timeless time and spaceless space, emitting sounds that are a kind of language I no longer understand or ever register.
‘Interviews: Brief Notes for Radio’, Notes and Counter-Notes: Writings on the Theatre (1964), 136.
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The wonderful structure of the animal system will probably never permit us to look upon it as a merely physical apparatus, yet the demands of science require that the evidently magnified principles of vitality should be reduced to their natural spheres, or if truth requires, wholly subverted in favor of those more cognizable by the human understanding. The spirit of the age will not tolerate in the devotee of science a quiet indifference. ...
In 'An Inquiry, Analogical and Experimental, into the Different Electrical conditions of Arterial and Venous Blood', New Orleans Medical and Surgical Journal (1853-4), 10, 584-602 & 738-757. As cited in George B. Roth, 'Dr. John Gorrie—Inventor of Artificial Ice and Mechanical Refrigeration', The Scientific Monthly (May 1936) 42 No. 5, 464-469.
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The word “mathematics” is a Greek word and, by origin, it means “something that has been learned or understood,” or perhaps “acquired knowledge,” or perhaps even, somewhat against grammar, “acquirable knowledge,” that is, “learnable knowledge,” that is, “knowledge acquirable by learning.”
'Why Mathematics Grows', Journal of the History of Ideas (Jan-Mar 1965), 26, No. 1, 4. In Salomon Bochner and Robert Clifford Gunning (ed.) Collected Papers of Salomon Bochner (1992), Vol. 4, 192.
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The work I have done has, already, been adequately rewarded and recognized. Imagination reaches out repeatedly trying to achieve some higher level of understanding, until suddenly I find myself momentarily alone before one new corner of nature's pattern of beauty and true majesty revealed. That was my reward.
Nobel Banquet Speech (10 Dec 1965).
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The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found.
In Floyd Merrell, Unthinking Thinking: Jorge Luis Borges, Mathematics, and the New Physics (1991), 156.
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There are two kinds of biologists, those who are looking to see if there is one thing that can be understood and those who keep saying it is very complicated and that nothing can be understood. ... You must study the simplest system you think has the properties you are interested in.
As quoted, without source, by John R. Platt in 'Science, Strong Inference', Science (16 Oct 1964), 146, No. 3642, 349.
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There is a story that once, not long after he came to Berlin, Planck forgot which room had been assigned to him for a lecture and stopped at the entrance office of the university to find out. Please tell me, he asked the elderly man in charge, 'In which room does Professor Planck lecture today?' The old man patted him on the shoulder 'Don't go there, young fellow,' he said 'You are much too young to understand the lectures of our learned Professor Planck'.
Anonymous
In Barbara Lovett Cline, Men Who Made a New Physics: Physicists and the Quantum Theory (1987), 46.
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There is a tendency to consider anything in human behavior that is unusual, not well known, or not well understood, as neurotic, psychopathic, immature, perverse, or the expression of some other sort of psychologic disturbance.
Sexual Behavior in the Human Female (1953), 195.
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There is another ground of hope that must not be omitted. Let men but think over their infinite expenditure of understanding, time, and means on matters and pursuits of far less use and value; whereof, if but a small part were directed to sound and solid studies, there is no difficulty that might not be overcome.
Translation of Novum Organum, CXI. In Francis Bacon, James Spedding, The Works of Francis Bacon (1864), Vol. 8, 144.
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There is no art or science that is too difficult for industry to attain to; it is the gift of tongues, and makes a man understood and valued in all countries, and by all nations; it is the philosopher's stone, that turns all metals, and even stones, into gold, and suffers not want to break into its dwelling; it is the northwest passage, that brings the merchant's ships as soon to him as he can desire: in a word, it conquers all enemies, and makes fortune itself pay contribution.
'Essay on Industry' (1670). In Thomas Henry Lister, Life and Administration of Edward, first Earl of Clarendon (1838), Vol. 2, 566.
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There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
'The Study of the Natural Sciences: An Introductory Lecture to the Course of Experimental Chemistry in the University of Munich, for the Winter Session of 1852-53,' as translated and republished in The Medical Times and Gazette (22 Jan 1853), N.S. Vol. 6, 82.
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There is no doubt but men of genius and leisure may carry our method to greater perfection, but, having had long experience, we have found none equal to it for the commodiousness it affords in working with the Understanding.
'Scala Intellectus', The Works of Francis Bacon (1815), Vol. 11, 13.

There is no result in nature without a cause; understand the cause and you will have no need of the experiment.
'Philosophy', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy, (1938) Vol. 1, 70.
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They [mathematicians] only take those things into consideration, of which they have clear and distinct ideas, designating them by proper, adequate, and invariable names, and premising only a few axioms which are most noted and certain to investigate their affections and draw conclusions from them, and agreeably laying down a very few hypotheses, such as are in the highest degree consonant with reason and not to be denied by anyone in his right mind. In like manner they assign generations or causes easy to be understood and readily admitted by all, they preserve a most accurate order, every proposition immediately following from what is supposed and proved before, and reject all things howsoever specious and probable which can not be inferred and deduced after the same manner.
Mathematical Lectures (1734), 65-66.
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This is all very fine, but it won't do—Anatomy—botany—Nonsense! Sir, I know an old woman in Covent Garden, who understands botany better, and as for anatomy, my butcher can dissect a joint full as well; no, young man, all that is stuff; you must go to the bedside, it is there alone you can learn disease!
Comment to Hans Sloane on Robert Boyle's letter of introduction describing Sloane as a 'ripe scholar, a good botanist, a skilful anatomist'.
Quoted in John D. Comrie, 'Life of Thomas Sydenham, M. D.', in Comrie (ed.), Selected Works of Thomas Sydenham (1922), 2.
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This is an age of science. ... All important fields of activity from the breeding of bees to the administration of an empire, call for an understanding of the spirit and the technique of modern science. The nations that do not cultivate the sciences cannot hold their own.
From Rose's private notebook (1924?), as quoted by Stanley Coben in 'The Scientific Establishment and the Transmission of Quantum Mechanics to the United States, 1919-32', The American Historical Review (Apr 1971), 76, No. 2, 449.
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Tho' there be no such Thing as Chance in the World; our Ignorance of the real Ccause of any Event has the same Influence on the Understanding, and begets a like Species of Belief or Opinion.
An Enquiry Concerning Human Understanding (1748), 93.
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Though the world does not change with a change of paradigm, the scientist afterward works in a different world... I am convinced that we must learn to make sense of statements that at least resemble these. What occurs during a scientific revolution is not fully reducible to a re-interpretation of individual and stable data. In the first place, the data are not unequivocally stable.
The Structure of Scientific Revolutions (1962), 120.
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Thoughts without content are empty, intuitions without concepts are blind... The understanding can intuit nothing, the senses can think nothing. Only through their union can knowledge arise.
Critique of Pure Reason (1781), trans. Norman Kemp Smith (1929), 93.
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Through it [Science] we believe that man will be saved from misery and degradation, not merely acquiring new material powers, but learning to use and to guide his life with understanding. Through Science he will be freed from the fetters of superstition; through faith in Science he will acquire a new and enduring delight in the exercise of his capacities; he will gain a zest and interest in life such as the present phase of culture fails to supply.
'Biology and the State', The Advancement of Science: Occasional Essays & Addresses (1890), 108-9.
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To be worthy of the name, an experimenter must be at once theorist and practitioner. While he must completely master the art of establishing experimental facts, which are the materials of science, he must also clearly understand the scientific principles which guide his reasoning through the varied experimental study of natural phenomena. We cannot separate these two things: head and hand. An able hand, without a head to direct it, is a blind tool; the head is powerless without its executive hand.
In Claude Bernard and Henry Copley Greene (trans.), An Introduction to the Study of Experimental Medicine (1927, 1957), 3.
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To make a discovery is not necessarily the same as to understand a discovery.
Inward Bound: Of Matter and Forces in the Physical World (1986), 134.
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To me, science is an expression of the human spirit, which reaches every sphere of human culture. It gives an aim and meaning to existence as well as a knowledge, understanding, love, and admiration for the world. It gives a deeper meaning to morality and another dimension to esthetics.
From a letter to his long-time associate, Jerrold Zacharias. Quoted in A tribute to I. I. Rabi, Department of Physics, Columbia University, June 1970. In John S. Rigden, in Rabi, Scientist and Citizen (2000), xxi.
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To understand God's thoughts, one must study statistics, for these are the measure of His purpose.
Nightingale held this belief, here expressed in the words written by Karl Pearson in The Life, Letters and Labours of Francis Galton (1924), Vol 2, 415.
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Truth and falsity, indeed understanding, is not necessarily something purely intellectual, remote from feelings and attitudes. ... It is in the total conduct of men rather than in their statements that truth or falsehood lives, more in what a man does, in his real reaction to other men and to things, in his will to do them justice, to live at one with them. Here lies the inner connection between truth and justice. In the realm of behavior and action, the problem recurs as to the difference between piece and part.
From 'On Truth', collected in Mary Henle (ed.), Documents of Gestalt Psychology (1961), 28.
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Truth scarce ever yet carried it by Vote any where at its first appearance: New Opinions are always suspected, and usually opposed, without any other Reason, but because they are not already common.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), The Epistle Dedicatory, 4.
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Understanding a theory has, indeed, much in common with understanding a human personality. We may know or understand a man's system of dispositions pretty well; that is to say, we may be able to predict how he would act in a number of different situations. But since there are infinitely many possible situations, of infinite variety, a full understanding of a man's dispositions does not seem to be possible.
Objective Knowledge: an Evolutionary Approach (1972), 299.
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Understanding is the reward of faith. Therefore, do not seek to understand in order to believe, but believe that thou mayest understand; since “except ye believe ye shall not understand.”
From Tractate 29, as translated by Marcus Dods in Saint Augustine (Bishop of Hippo), The Works of Aurelius Augustine: A New Translation (1873), Vol. 10, 405.
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Undeveloped though the science [of chemistry] is, it already has great power to bring benefits. Those accruing to physical welfare are readily recognized, as in providing cures, improving the materials needed for everyday living, moving to ameliorate the harm which mankind by its sheer numbers does to the environment, to say nothing of that which even today attends industrial development. And as we continue to improve our understanding of the basic science on which applications increasingly depend, material benefits of this and other kinds are secured for the future.
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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Unless you make yourself equal to God, you cannot understand God: for the like is not intelligible save to the like. Make yourself grow to a greatness beyond measure, by a bound free yourself from the body; raise yourself above all time, become Eternity; then you will understand God. Believe that nothing is impossible for you, think yourself immortal and capable of understanding all, all arts, all sciences, the nature of every living being. Mount higher than the highest height; descend lower than the lowest depth. Draw into yourself all sensations of everything created, fire and water, dry and moist, imagining that you are everywhere, on earth, in the sea, in the sky, that you are not yet born, in the maternal womb, adolescent, old, dead, beyond death. If you embrace in your thought all things at once, times, places, substances, qualities, quantities, you may understand God.
Quoted in F. A. Yales, Giordano Bruno and the Hermetic Tradition (1964), 198.
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We achieve more than we know. We know more than we understand. We understand more than we can explain.
In AI: The Tumultuous History of the Search for Artificial Intelligence (1999), 159, but without citation. If you know a primary source, please contact Webmaster.
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We are going through the body-snatching phase right now, and there are all these Burke and Hare attitudes towards geneticists-that they are playing God and that DNA is sacred. No, it's not. It's no more sacred than your toenails. Basically, we are not going to make long-term medical progress without understanding how the genes work.
[Referring to the similarity of fears and superstitions in genetics as once were associated with anatomy ]
Quoted by Sean O'Hagan, in 'End of sperm report', The Observer (14 Sep 2002).
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We cannot hope to either understand or to manage the carbon in the atmosphere unless we understand and manage the trees and the soil too.
From From Eros to Gaia (1993). In Bill Swainson, Encarta Book of Quotations (2000), 299.
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We have to understand that the world can only be grasped by action, not by contemplation. The hand is more important than the eye ... The hand is the cutting edge of the mind.
The Ascent of Man (1973), 115-6.
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We may... have to relinquish the notion, explicit or implicit, that changes of paradigm carry scientists and those who learn from them closer and closer to the truth... The developmental process described in this essay has been a process of evolution from primitive beginnings—a process whose successive stages are characterized by an increasingly detailed and refined understanding of nature. But nothing that has been or will be said makes it a process of evolution toward anything.
The Structure of Scientific Revolutions (1962), 169-70.
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We must painfully acknowledge that, precisely because of its great intellectual developments, the best of man's domesticated animals—the dog—most often becomes the victim of physiological experiments. Only dire necessity can lead one to experiment on cats—on such impatient, loud, malicious animals. During chronic experiments, when the animal, having recovered from its operation, is under lengthy observation, the dog is irreplaceable; moreover, it is extremely touching. It is almost a participant in the experiments conducted upon it, greatly facilitating the success of the research by its understanding and compliance.
'Vivisection' (1893), as translated in Daniel P. Todes, Pavlov's Physiology Factory: Experiment, Interpretation, Laboratory Enterprise (2002), 123.
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We often observe in lawyers, who as Quicquid agunt homines is the matter of law suits, are sometimes obliged to pick up a temporary knowledge of an art or science, of which they understood nothing till their brief was delivered, and appear to be much masters of it.
In The Life of Samuel Johnson (1820), Vol. 1, 218. The Latin phrase translates as “what people do.”
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We think we understand the regular reflection of light and X rays - and we should understand the reflections of electrons as well if electrons were only waves instead of particles ... It is rather as if one were to see a rabbit climbing a tree, and were to say ‘Well, that is rather a strange thing for a rabbit to be doing, but after all there is really nothing to get excited about. Cats climb trees - so that if the rabbit were only a cat, we would understand its behavior perfectly.’ Of course, the explanation might be that what we took to be a rabbit was not a rabbit at all but was actually a cat. Is it possible that we are mistaken all this time in supposing they are particles, and that actually they are waves?
Franklin Institute Journal Vol. 205, 597. Cited in New Scientist (14 Apr 1977), 66.
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We were very privileged to leave on the Moon a plaque ... saying, ‘For all Mankind’. Perhaps in the third millennium a wayward stranger will read the plaque at Tranquility Base. We’ll let history mark that this was the age in which that became a fact. I was struck this morning in New York by a proudly waved but uncarefully scribbled sign. It said, ‘Through you we touched the Moon.’ It was our privilege today to touch America. I suspect perhaps the most warm, genuine feeling that all of us could receive came through the cheers and shouts and, most of all, the smiles of our fellow Americans. We hope and think that those people shared our belief that this is the beginning of a new era—the beginning of an era when man understands the universe around him, and the beginning of the era when man understands himself.
Acceptance speech (13 Aug 1969), upon receiving the Medal of Freedom as a member of the first manned moon-landing mission. In James R. Hansen, First Man: The Life of Neil A. Armstrong (2005), 569.
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What distinguishes the language of science from language as we ordinarily understand the word? … What science strives for is an utmost acuteness and clarity of concepts as regards their mutual relation and their correspondence to sensory data.
In Out of My Later Years (1950, 1956), 112. Footnoted on page 277 as from 'The Common Language of Science', a broadcast recording for the Science Conference, London (28 Sep 1941) and published in Advancement of Science, 2, No. 5, 16.
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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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What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
Science and Method (1914, 2003), 117.
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When understanding of the universe has become widespread, when the majority of men know that the stars are not sources of light but worlds, perhaps inhabited worlds like ours, then the Christian doctrine will be convicted of absurdity.
In Adolf Hitler, Hugh Redwald Trevor-Roper, translated by Norman Cameron and R. H. Stevens, '14 October 1941', Secret Conversations (1941 - 1944) (1953), 50
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When we understand how animals are resistant to chemicals, the mechanisms are all independent of whether its natural or synthetic. And in fact, when you look at natural chemicals, half of those tested come out positive.
Paper to the American Chemical Society, 'Pollution, Pesticides and Cancer Misconceptions.' As cited by Art Drysdale, 'Latest Insider News: Natural vs. Synthetic Chemical Pesticides' (14 Feb 1999), on the mitosyfraudes.org website. Bruce Ames has written a similar sentiment in various other publications.
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Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.
How to Solve It: a New Aspect of Mathematical Method (1957), 33.
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Who then understands the reciprocal flux and reflux of the infinitely great and the infinitely small, the echoing of causes in the abysses of being, and the avalanches of creation?
Victor Hugo and Charles E. Wilbour (trans.), Les Misérables (1862), 41.
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Widespread intellectual and moral docility may be convenient for leaders in the short term, but it is suicidal for nations in the long term. One of the criteria for national leadership should therefore be a talent for understanding, encouraging, and making constructive use of vigorous criticism.
Billions and Billions: Thoughts on Life and Death at the Brink of the Millenium (1998), 189.
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Without initiation into the scientific spirit one is not in possession of the best tools humanity has so far devised for effectively directed reflection. [Without these one] fails to understand the full meaning of knowledge.
Democracy and Education: an Introduction to the Philosophy of Education (1916), 223.
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Without the sensuous faculty no object would be given to us, without understanding no object would be thought. Thoughts without content are void, intuitions without conceptions, blind.
Critique of Pure Reason, translation by John Miller Dow Meiklejohn (1899), 45.
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Wonder [admiratio astonishment, marvel] is a kind of desire for knowledge. The situation arises when one sees an effect and does not know its cause, or when the cause of the particular effect is one that exceeds his power of understanding. Hence, wonder is a cause of pleasure insofar as there is annexed the hope of attaining understanding of that which one wants to know. ... For desire is especially aroused by the awareness of ignorance, and consequently a man takes the greatest pleasure in those things which he discovers for himself or learns from the ground up.
From Summa Theologiae Question 32, 'The Causes of Pleasure,' Article 8, 'Is Pleasure Caused by Wondering.'(1a2ae 32.8). As translated in James Vincent Cunningham, Tragic Effect and Tragic Process in Some Plays of Shakespeare (1945). Also in The Collected Essays of J.V. Cunningham (1976), 72-73.
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You don't need a science degree to understand about science. You just need to think about it.
Quoted in Max Davidson, 'Bill Bryson: Have faith, science can solve our problems', Daily Telegraph (26 Sep 2010)
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You don't understand anything until you learn it more than one way.
In Rebecca Herold, Managing an Information Security and Privacy Awareness and Training Program (2005), 101.
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[About research with big particle accelerators such as the Large Hadron Collider.] I think the primary justification for this sort of science that we do is fundamental human curiosity. ... It's true, of course, that every previous generation that's made some breakthrough in understanding nature has seen those discoveries translated into new technologies, new possibilities for the human race. That may well happen with the Higgs boson. Quite frankly, at the moment I don't see how you can use the Higgs boson for anything useful.
As quoted in Alan Boyle, 'Discovery of Doom? Collider Stirs Debate', article (8 Sep 2008) on a msnbc.com web page.
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[Learning is] the actual process of broadening yourself, of knowing there's a little extra facet of the universe you know about and can think about and can understand. It seems to me that when it's time to die, and that will come to all of us, there'll be a certain pleasure in thinking that you had utilized your life well, that you had learned as much as you could, gathered in as much as possible of the universe, and enjoyed it. I mean, there's only this universe and only this one lifetime to try to grasp it. And, while it is inconceivable that anyone can grasp more than a tiny portion of it, at least do that much. What a tragedy to just pass through and get nothing out of it.
'Isaac Asimov Speaks' with Bill Moyers in The Humanist (Jan/Feb 1989), 49. Reprinted in Carl Howard Freedman (ed.), Conversations with Isaac Asimov (2005), 139.
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[Misquotation; not by Einstein.] You do not really understand something unless you can explain it to your grandmother.
No evidence exists that this was ever said or written by Einstein, yet is often seen attribued to him, for example, in Rosemarie Jarski, Words from the Wise: Over 6,000 of the Smartest Things Ever Said (2007), 515. However, see a similar quote by Ernest Rutherford about explaining to a “barmaid.”
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[On the practical applications of particle physics research with the Large Hadron Collider.] Sometimes the public says, 'What's in it for Numero Uno? Am I going to get better television reception? Am I going to get better Internet reception?' Well, in some sense, yeah. ... All the wonders of quantum physics were learned basically from looking at atom-smasher technology. ... But let me let you in on a secret: We physicists are not driven to do this because of better color television. ... That's a spin-off. We do this because we want to understand our role and our place in the universe.
As quoted in Alan Boyle, 'Discovery of Doom? Collider Stirs Debate', article (8 Sep 2008) on a msnbc.com web page. The article writer included the information that Kaku noted that past discoveries from the world of particle physics ushered in many of the innovations we enjoy today, ranging from satellite communications and handheld media players to medical PET scanners (which put antimatter to practical use)."
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[Scientists] define these [terms] in tight phrases which convey a meaning only to those who already understand it.
In Science is a Sacred Cow (1950), 31.
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[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher's assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds.
In editorial in Focus, a Journal of the Mathematical Association of America (1986), quoted in obituary by Eric Pace, New York Times (11 Jun 1992).
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[There] are cases where there is no dishonesty involved but where people are tricked into false results by a lack of understanding about what human beings can do to themselves in the way of being led astray by subjective effects, wishful thinking or threshold interactions. These are examples of pathological science. These are things that attracted a great deal of attention. Usually hundreds of papers have been published upon them. Sometimes they have lasted for fifteen or twenty years and then they gradually die away.
[Coining the term “pathological science” for the self-deceiving application of science to a phenomenon that doesn't exist.]
From a Colloquium at The Knolls Research Laboratory (18 Dec 1953). Transcribed and edited by R. N. Hall. In General Electric Laboratories, Report No. 68-C-035 (April 1968).
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[W]hen Galileo discovered he could use the tools of mathematics and mechanics to understand the motion of celestial bodies, he felt, in the words of one imminent researcher, that he had learned the language in which God recreated the universe. Today we are learning the language in which God created life. We are gaining ever more awe for the complexity, the beauty, the wonder of God's most devine and sacred gift.
From White House Announcement of the Completion of the First Survey of the Entire Human Genome Project, broadcast on the day of the publication of the first draft of the human genome. Quoted in transcript on the National Archives, Clinton White House web site, 'Text of Remarks on the Completion of the First Survey of the Entire Human Genome Project' (26 Jun 2000).
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…we are all inclined to ... direct our inquiry not by the matter itself, but by the views of our opponents; and, even when interrogating oneself, one pushes the inquiry only to the point at which one can no longer offer any opposition. Hence a good inquirer will be one who is ready in bringing forward the objections proper to the genus, and that he will be when he has gained an understanding of the differences.
Aristotle
'On the Heavens', The Works of Aristotle editted by William David Ross and John Alexander Smith (1930), Vol. 2, 15.
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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
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
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
Avicenna
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
Archimedes
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
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton