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Understand Quotes (606 quotes)

...That day in the account of creation, or those days that are numbers according to its recurrence, are beyond the experience and knowledge of us mortal earthbound men. And if we are able to make any effort towards an understanding of those days, we ought not to rush forward with an ill considered opinion, as if no other reasonable and plausible interpretation could be offered.
iv.44
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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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Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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Les hommes ne sont pas faits pour savoir; les hommes ne sont pas faits pour comprendre … et nos illusions croissent avec nos connaissances.
Men are not created to know, men are not created to understand … and our illusions increase with our knowledge.
From the fictional Dr. Trublet in Histoire Comique (1900), 212. As translated in Lewis P. Shanks, Anatole France (1919), 165. Shanks comments that Anatole France was writing, not as “an idealist of science, but as a skeptic content to accept truths merely pragmatic. … Trublet has lost faith in absolute truth.”
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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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Nisi credideritis, non intelligitis.
Unless you believe, you will not understand.
De Ubero Arbitrio (On Free Choice of the Will) [386], Book I, chapter 2, section 4 (Augustine quoting from Isaiah 7:9).
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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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Ron Hutcheson, a Knight-Ridder reporter: [Mr. President, what are your] personal views [about the theory of] intelligent design?
President George W. Bush: [Laughing. You're] doing a fine job of dragging me back to the past [days as governor of Texas]. ... Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught...”
Hutcheson: Both sides ought to be properly taught?
President: Yes ... so people can understand what the debate is about.
Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?
President: I think that part of education is to expose people to different schools of thought, and I'm not suggesting—you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.
Hutcheson: So we've got to give these groups—...
President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]
From conversation with reporters at the White House (1 Aug 2005), as quoted by Matthew Cooper in 'Fanning the Controversy Over “Intelligent Design”', Time (3 Aug 2005). The Time writer stated, “The president has gone farther in questioning the widely-taught theories of evolution and natural selection than any president since Ronald Reagan, who advocated teaching creationism in public schools alongside evolution.” Just a few months later, in the nation's first case on that point, on 20 Dec 2005, “a federal judge [John E. Jones] ruled it was unconstitutional for a Pennsylvania school district to present intelligent design as an alternative in high school biology courses, because it is a religious viewpoint,” as reported by Laurie Goodstein in 'Judge Rejects Teaching Intelligent Design', New York Times (21 Dec 2005). Goodstein also wrote “Judge Jones, a Republican appointed by President Bush, concluded that intelligent design was not science,” and that “the evidence in the trial proved that intelligent design was 'creationism relabeled.' The Supreme Court has already ruled that creationism ... cannot be taught as science in a public school.”
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Salviati: …Now you see how easy it is to understand.
Sagredo: So are all truths, once they are discovered; the point is in being able to discover them.
[Commonly seen merged in a paraphrase as: All truths are easy to understand once they are discovered; the point is to discover them.]
Lines of two characters in Dialogue Concerning the Two Chief World Systems (1632), as translated by S. Drake (1967). As quoted and cited in Barnaby Sheppard, The Logic of Infinity (2014), 398 & 440 footnote. Galileo’s work is written as a series of dialogues over four days between Salviati (supporting the Copernican system), Sagredo (a neutral layman) and Simplicio (supporting the Ptolemaic system).
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The Charms of Statistics.—It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence. Some people hate the very name of statistics, but I find them full of beauty and interest. Whenever they are not brutalised, but delicately handled by the higher methods, and are warily interpreted, their power of dealing with complicated phenomena is extraordinary. They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man.
Natural Inheritance (1889), 62-3.
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To Wheeler's comment, If you haven't found something strange during the day, it hasn't been much of a day, a student responded, I can't believe that space is that crummy. Wheeler replied: To disagree leads to study, to study leads to understanding, to understand is to appreciate, to appreciate is to love. So maybe I'll end up loving your theory.
Quoted in Charles Birch, Biology and the Riddle of Life (1999), 10.
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A cell has a history; its structure is inherited, it grows, divides, and, as in the embryo of higher animals, the products of division differentiate on complex lines. Living cells, moreover, transmit all that is involved in their complex heredity. I am far from maintaining that these fundamental properties may not depend upon organisation at levels above any chemical level; to understand them may even call for different methods of thought; I do not pretend to know. But if there be a hierarchy of levels we must recognise each one, and the physical and chemical level which, I would again say, may be the level of self-maintenance, must always have a place in any ultimate complete description.
'Some Aspects of Biochemistry', The Irish Journal of Medical Science (1932), 79, 346.
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A 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 good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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A hundred years ago, Auguste Compte, … a great philosopher, said that humans will never be able to visit the stars, that we will never know what stars are made out of, that that's the one thing that science will never ever understand, because they're so far away. And then, just a few years later, scientists took starlight, ran it through a prism, looked at the rainbow coming from the starlight, and said: “Hydrogen!” Just a few years after this very rational, very reasonable, very scientific prediction was made, that we'll never know what stars are made of.
Quoted in Nina L. Diamond, Voices of Truth (2000), 332.
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Sigmund Freud quote: A layman will no doubt find it hard to understand how pathological disorders of the body and mind can be el
A layman will no doubt find it hard to understand how pathological disorders of the body and mind can be eliminated by 'mere' words. He will feel that he is being asked to believe in magic. And he will not be so very wrong, for the words which we use in our everyday speech are nothing other than watered-down magic. But we shall have to follow a roundabout path in order to explain how science sets about restoring to words a part at least of their former magical power.
Psychical (or Mental) Treatment (1905), In James Strachey (ed.), The Standard Edition of the Complete Psychological Works of Sigmund Freud (1953), Vol. 7, 283.
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A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
War and Peace (1869), Book 11, Chap. 1.
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A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 140-141.
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A scientist strives to understand the work of Nature. But with our insufficient talents as scientists, we do not hit upon the truth all at once. We must content ourselves with tracking it down, enveloped in considerable darkness, which leads us to make new mistakes and errors. By diligent examination, we may at length little by little peel off the thickest layers, but we seldom get the core quite free, so that finally we have to be satisfied with a little incomplete knowledge.
Lecture to the Royal Swedish Academy of Science, 23 May 1764. Quoted in J. A. Schufle 'Torbern Bergman, Earth Scientist', Chymia, 1967, 12, 78.
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A troubling question for those of us committed to the widest application of intelligence in the study and solution of the problems of men is whether a general understanding of the social sciences will be possible much longer. Many significant areas of these disciplines have already been removed by the advances of the past two decades beyond the reach of anyone who does not know mathematics; and the man of letters is increasingly finding, to his dismay, that the study of mankind proper is passing from his hands to those of technicians and specialists. The aesthetic effect is admittedly bad: we have given up the belletristic “essay on man” for the barbarisms of a technical vocabulary, or at best the forbidding elegance of mathematical syntax.
Opening paragraph of 'The Study of Man: Sociology Learns the Language of Mathematics' in Commentary (1 Sep 1952). Reprinted in James Roy Newman, The World of Mathematics (1956), Vol. 2, 1294.
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A vision of the whole of life!. Could any human undertaking be ... more grandiose? This attempt stands without rival as the most audacious enterprise in which the mind of man has ever engaged ... Here is man, surrounded by the vastness of a universe in which he is only a tiny and perhaps insignificant part—and he wants to understand it.
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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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Above, far above the prejudices and passions of men soar the laws of nature. Eternal and immutable, they are the expression of the creative power they represent what is, what must be, what otherwise could not be. Man can come to understand the: he is incapable of changing them.
In Cours d’economie Politique (1896-97)
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After an orange cloud—formed as a result of a dust storm over the Sahara and caught up by air currents—reached the Philippines and settled there with rain, I understood that we are all sailing in the same boat.
In Jack Hassard and Julie Weisberg , Environmental Science on the Net: The Global Thinking Project (1999), 40.
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After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Atombau und Spektrallinien (1919), viii, Atomic Structure and Spectral Lines, trans. Henry L. Brose (1923), viii.
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Again and again in reading even his [William Thomson] most abstract writings one is struck by the tenacity with which physical ideas control in him the mathematical form in which he expressed them. An instance of this is afforded by … an example of a mathematical result that is, in his own words, “not instantly obvious from the analytical form of my solution, but which we immediately see must be the case by thinking of the physical meaning of the result.”
As given in Life of Lord Kelvin (1910), Vol. 2, 1136. The ellipsis gives the reference to the quoted footnote, to a passage in his Mathematical and Physical Papers, Vol. 1, 457. [Note: William Thomson, later became Lord Kelvin. —Webmaster]
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Alexander the king of the Macedonians, began like a wretch to learn geometry, that he might know how little the earth was, whereof he had possessed very little. Thus, I say, like a wretch for this, because he was to understand that he did bear a false surname. For who can be great in so small a thing? Those things that were delivered were subtile, and to be learned by diligent attention: not which that mad man could perceive, who sent his thoughts beyond the ocean sea. Teach me, saith he, easy things. To whom his master said: These things be the same, and alike difficult unto all. Think thou that the nature of things saith this. These things whereof thou complainest, they are the same unto all: more easy things can be given unto none; but whosoever will, shall make those things more easy unto himself. How? With uprightness of mind.
In Thomas Lodge (trans.), 'Epistle 91', The Workes of Lucius Annaeus Seneca: Both Morrall and Naturall (1614), 383. Also in Robert Édouard Moritz, Memorabilia Mathematica (1914), 135.
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All knowledge and understanding of the Universe was no more than playing with stones and shells on the seashore of the vast imponderable ocean of truth.
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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 of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics ... It has survived all tests and there is no reason to believe that there is any flaw in it.... We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.
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All of physics is either impossible or trivial. It is impossible until you understand it, and then it becomes trivial.
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All that science can achieve is a perfect knowledge and a perfect understanding of the action of natural and moral forces.
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All the human culture, all the results of art, science and technology that we see before us today, are almost exclusively the creative product of the Aryan. This very fact admits of the not unfounded inference that he alone was the founder of all higher humanity, therefore representing the prototype of all that we understand by the word 'man.' He is the Prometheus of mankind from whose shining brow the divine spark of genius has sprung at all times, forever kindling anew that fire of knowledge which illuminated the night of silent mysteries and thus caused man to climb the path to mastery over the other beings of the earth ... It was he who laid the foundations and erected the walls of every great structure in human culture.
Mein Kampf (1925-26), American Edition (1943), 290. In William Lawrence Shirer, The Rise and Fall of the Third Reich (1990), 86-87.
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All the real true knowledge we have of Nature is intirely experimental, insomuch that, how strange soever the assertion seems, we may lay this down as the first fundamental unerring rule in physics, That it is not within the compass of human understanding to assign a purely speculative reason for any one phaenomenon in nature.
In The Procedure, Extent, and Limits of Human Understanding (1728, 1729), 205-206.
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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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All true science must aim at objective truth, and that means that the human observer must never allow himself to get emotionally mixed up with his subject-matter. His concern is to understand the universe, not to improve it. Detachment is obligatory.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
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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 engineer, a physicist and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard.
After some observations and rough calculations the engineer realizes the situation and starts laughing.
A few minutes later the physicist understands too and chuckles to himself happily, as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.
Anonymous
In 'Zero Gravity: The Lighter Side of Science' APS News (Jun 2003), 12 No. 6.
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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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An important fact, an ingenious aperçu, occupies a very great number of men, at first only to make acquaintance with it; then to understand it; and afterwards to work it out and carry it further.
In The Maxims and Reflections of Goethe (1906), 189.
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An informed appraisal of life absolutely require(s) a full understanding of life’s arena–the universe. … By deepening our understanding of the true nature of physical reality, we profoundly reconfigure our sense of ourselves and our experience of the universe.
In The Fabric of the Cosmos: Space, Time, and the Texture of Reality (2007), 5.
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And let me adde, that he that throughly understands the nature of Ferments and Fermentations, shall probably be much better able than he that Ignores them, to give a fair account of divers Phænomena of severall diseases (as well Feavers and others) which will perhaps be never throughly understood, without an insight into the doctrine of Fermentation.
Essay 2, 'Offering some Particulars relating to the Pathologicall Part of Physick', in the Second Part of Some Considerations Touching The Usefulnesse of Naturall Philosophy (1663, 1664), 43.
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And yet I think that the Full House model does teach us to treasure variety for its own sake–for tough reasons of evolutionary theory and nature’s ontology, and not from a lamentable failure of thought that accepts all beliefs on the absurd rationale that disagreement must imply disrespect. Excellence is a range of differences, not a spot. Each location on the range can be occupied by an excellent or an inadequate representative– and we must struggle for excellence at each of these varied locations. In a society driven, of ten unconsciously, to impose a uniform mediocrity upon a former richness of excellence–where McDonald’s drives out the local diner, and the mega-Stop & Shop eliminates the corner Mom and Pop–an understanding and defense of full ranges as natural reality might help to stem the tide and preserve the rich raw material of any evolving system: variation itself.
…...
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Anthropology has reached that point of development where the careful investigation of facts shakes our firm belief in the far-reaching theories that have been built up. The complexity of each phenomenon dawns on our minds, and makes us desirous of proceeding more cautiously. Heretofore we have seen the features common to all human thought. Now we begin to see their differences. We recognize that these are no less important than their similarities, and the value of detailed studies becomes apparent. Our aim has not changed, but our method must change. We are still searching for the laws that govern the growth of human culture, of human thought; but we recognize the fact that before we seek for what is common to all culture, we must analyze each culture by careful and exact methods, as the geologist analyzes the succession and order of deposits, as the biologist examines the forms of living matter. We see that the growth of human culture manifests itself in the growth of each special culture. Thus we have come to understand that before we can build up the theory of the growth of all human culture, we must know the growth of cultures that we find here and there among the most primitive tribes of the Arctic, of the deserts of Australia, and of the impenetrable forests of South America; and the progress of the civilization of antiquity and of our own times. We must, so far as we can, reconstruct the actual history of mankind, before we can hope to discover the laws underlying that history.
The Jesup North Pacific Expedition: Memoir of the American Museum of Natural History (1898), Vol. 1, 4.
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Any artist or novelist would understand—some of us do not produce their best when directed. We expect the artist, the novelist and the composer to lead solitary lives, often working at home. While a few of these creative individuals exist in institutions or universities, the idea of a majority of established novelists or painters working at the “National Institute for Painting and Fine Art” or a university “Department of Creative Composition” seems mildly amusing. By contrast, alarm greets the idea of a creative scientist working at home. A lone scientist is as unusual as a solitary termite and regarded as irresponsible or worse.
Homage to Gala: The Life of an Independent Scholar (2000), 2.
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Any fool can know. The point is to understand.
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Any man who is intelligent must, on considering that health is of the utmost value to human beings, have the personal understanding necessary to help himself in diseases, and be able to understand and to judge what physicians say and what they administer to his body, being versed in each of these matters to a degree reasonable for a layman.
Affections, in Hippocrates, trans. P. Potter (1988), Vol. 5, 7.
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Any one, if he will only observe, can find some little thing he does not understand as a starter for an investigation.
From Address (22 May 1914) to the graduating class of the Friends’ School, Washington, D.C. Printed in 'Discovery and Invention', The National Geographic Magazine (1914), 25, 650.
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Anyone who sits on top of the largest hydrogen-oxygen fueled system in the world; knowing they’re going to light the bottom, and doesn’t get a little worried, does not fully understand the situation.
Response to question whether he was worried about embarking on the first space shuttle flight. As quoted on the nmspacemuseum.org website of the New Mexico Museum of Space History.
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Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.
From Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838), as translated by Nathaniel T. Bacon in 'Preface', Researches Into Mathematical Principles of the Theory of Wealth (1897), 4. From the original French, “Quiconque connaît la notation algébrique, lit d'un clin-d'œil dans une équation le résultat auquel on parvient péniblement par des règles de fausse position, dans l'arithmétique de Banque.”
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As language-using organisms, we participate in the evolution of the Universe most fruitfully through interpretation. We understand the world by drawing pictures, telling stories, conversing. These are our special contributions to existence. It is our immense good fortune and grave responsibility to sing the songs of the Cosmos.
Epigraph, without citation, in Michael Dowd, Thank God for Evolution: How the Marriage of Science and Religion Will Transform Your Life and Our World (2008), 103.
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As was predicted at the beginning of the Human Genome Project, getting the sequence will be the easy part as only technical issues are involved. The hard part will be finding out what it means, because this poses intellectual problems of how to understand the participation of the genes in the functions of living cells.
Loose Ends from Current Biology (1997), 71.
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At first it seems obvious, but the more you think about it the stranger the deductions from this axiom seem to become; in the end you cease to understand what is meant by it.
As quoted, without citation, in Stories about Sets (1968), 84.
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At terrestrial temperatures matter has complex properties which are likely to prove most difficult to unravel; but it is reasonable to hope that in the not too distant future we shall be competent to understand so simple a thing as a star.
The Internal Constitution of Stars, Cambridge. (1926, 1988), 393.
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Available energy is energy which we can direct into any desired channel. Dissipated energy is energy which we cannot lay hold of and direct at pleasure, such as the energy of the confused agitation of molecules which we call heat. Now, confusion, like the correlative term order, is not a property of material things in themselves, but only in relation to the mind which perceives them. A memorandum-book does not, provided it is neatly written, appear confused to an illiterate person, or to the owner who understands it thoroughly, but to any other person able to read it appears to be inextricably confused. Similarly the notion of dissipated energy could not occur to a being who could not turn any of the energies of nature to his own account, or to one who could trace the motion of every molecule and seize it at the right moment. It is only to a being in the intermediate stage, who can lay hold of some forms of energy while others elude his grasp, that energy appears to be passing inevitably from the available to the dissipated state.
'Diffusion', Encyclopaedia Britannica (1878). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 646.
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Basic research at universities comes in two varieties: research that requires big bucks and research that requires small bucks. Big bucks research is much like government research and in fact usually is government research but done for the government under contract. Like other government research, big bucks academic research is done to understand the nature and structure of the universe or to understand life, which really means that it is either for blowing up the world or extending life, whichever comes first. Again, that's the government's motivation. The universities' motivation for conducting big bucks research is to bring money in to support professors and graduate students and to wax the floors of ivy-covered buildings. While we think they are busy teaching and learning, these folks are mainly doing big bucks basic research for a living, all the while priding themselves on their terrific summer vacations and lack of a dress code.
Smalls bucks research is the sort of thing that requires paper and pencil, and maybe a blackboard, and is aimed primarily at increasing knowledge in areas of study that don't usually attract big bucks - that is, areas that don't extend life or end it, or both. History, political science, and romance languages are typically small bucks areas of basic research. The real purpose of small bucks research to the universities is to provide a means of deciding, by the quality of their small bucks research, which professors in these areas should get tenure.
Accidental Empires (1992), 78.
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Bell’s theorem is easy to understand but hard to believe.
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Biology today is moving in the direction of chemistry. Much of what is understood in the field is based on the structure of molecules and the properties of molecules in relation to their structure. If you have that basis, then biology isn’t just a collection of disconnected facts.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 737.
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Both social and biosocial factors are necessary to interpret crosscultural studies, with the general proviso that one’s research interest determines which elements, in what combinations, are significant for the provision of understanding.
…...
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Break the chains of your prejudices and take up the torch of experience, and you will honour nature in the way she deserves, instead of drawing derogatory conclusions from the ignorance in which she has left you. Simply open your eyes and ignore what you cannot understand, and you will see that a labourer whose mind and knowledge extend no further than the edges of his furrow is no different essentially from the greatest genius, as would have been proved by dissecting the brains of Descartes and Newton; you will be convinced that the imbecile or the idiot are animals in human form, in the same way as the clever ape is a little man in another form; and that, since everything depends absolutely on differences in organisation, a well-constructed animal who has learnt astronomy can predict an eclipse, as he can predict recovery or death when his genius and good eyesight have benefited from some time at the school of Hippocrates and at patients' bedsides.
Machine Man (1747), in Ann Thomson (ed.), Machine Man and Other Writings (1996), 38.
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But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.
…...
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But no Anglo-Saxon can understand relativity.
Said at a dinner in 1910, teasing Ernest Rutherford, who replied, 'No, they have too much sense.'
Quoted in Richard Reeves, A Force of Nature: The Frontier Genius of Ernest Rutherford (2007), 66.
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But psychology is a more tricky field, in which even outstanding authorities have been known to run in circles, ‘describing things which everyone knows in language which no one understands.’
From The Scientific Analysis of Personality (1965), 18.
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But when on shore, and wandering in the sublime forests, surrounded by views more gorgeous than even Claude ever imagined, I enjoy a delight which none but those who have experienced it can understand. If it is to be done, it must be by studying Humboldt.
From letter to W.D. Fox (May 1832), in Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin: Including an Autobiographical Chapter (1887), Vol. 1, 207.
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By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.
From his memoir 'Erdmagnetismus und Magnetometer' in Collected Works (1877), Vol. 5, 315-316. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 411.
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By science, then, I understand the consideration of all subjects, whether of a pure or mixed nature, capable of being reduced to measurement and calculation. All things comprehended under the categories of space, time and number properly belong to our investigations; and all phenomena capable of being brought under the semblance of a law are legitimate objects of our inquiries.
In Report of the British Association for the Advancement of Science (1833), xxviii.
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By the year 2070 we cannot say, or it would be imbecile to do so, that any man alive could understand Shakespearean experience better than Shakespeare, whereas any decent eighteen-year-old student of physics will know more physics than Newton.
'The Case of Leavis and the Serious Case’, Times Literary Supplement (9 Jul 1970), 737-740. Collected in Public Affairs (1971), 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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Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.
In Proceedings of London Royal Society (1895), 58, 11-12.
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Chaos theory is a new theory invented by scientists panicked by the thought that the public were beginning to understand the old ones.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 273.
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Chemistry is the study of material transformations. Yet a knowledge of the rate, or time dependence, of chemical change is of critical importance for the successful synthesis of new materials and for the utilization of the energy generated by a reaction. During the past century it has become clear that all macroscopic chemical processes consist of many elementary chemical reactions that are themselves simply a series of encounters between atomic or molecular species. In order to understand the time dependence of chemical reactions, chemical kineticists have traditionally focused on sorting out all of the elementary chemical reactions involved in a macroscopic chemical process and determining their respective rates.
'Molecular Beam Studies of Elementary Chemical Processes', Nobel Lecture, 8 Dec 1986. In Nobel Lectures: Chemistry 1981-1990 (1992), 320.
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Commenting on Archimedes, for whom he also had a boundless admiration, Gauss remarked that he could not understand how Archimedes failed to invent the decimal system of numeration or its equivalent (with some base other than 10). … This oversight Gauss regarded as the greatest calamity in the history of science.
In Men of Mathematics (1937), 256.
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Common sense … is to the judgment what genius is to the understanding.
In Igerne and Other Writings of Arthur Handly Marks (1897), 349.
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Computers and rocket ships are examples of invention, not of understanding. … All that is needed to build machines is the knowledge that when one thing happens, another thing happens as a result. It’s an accumulation of simple patterns. A dog can learn patterns. There is no “why” in those examples. We don’t understand why electricity travels. We don’t know why light travels at a constant speed forever. All we can do is observe and record patterns.
In God's Debris: A Thought Experiment (2004), 22.
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Considering the difficulties represented by the lack of water, by extremes of temperature, by the full force of gravity unmitigated by the buoyancy of water, it must be understood that the spread to land of life forms that evolved to meet the conditions of the ocean represented the greatest single victory won by life over the inanimate environment.
(1965). In Isaac Asimov’s Book of Science and Nature Quotations (1988), 194.
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Contrary to the legend, Darwin's finches do not appear to have inspired his earliest theoretical views on evolution, even after he finally became an evolutionist in 1837; rather it was his evolutionary views that allowed him, retrospectively, to understand the complex case of the finches.
Quoted in Stephen Gould, The Flamingo's Smile (1987), 356. From Frank J. Sulloway, 'Darwin's Conversion: The Beagle Voyage and its Aftermath'. Journal of the History of Biology (1982), 15, 327-398.
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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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Deprived, therefore, as regards this period, of any assistance from history, but relieved at the same time from the embarrassing interference of tradition, the archaeologist is free to follow the methods which have been so successfully pursued in geology—the rude bone and stone implements of bygone ages being to the one what the remains of extinct animals are to the other. The analogy may be pursued even further than this. Many mammalia which are extinct in Europe have representatives still living in other countries. Our fossil pachyderms, for instance, would be almost unintelligible but for the species which still inhabit some parts of Asia and Africa; the secondary marsupials are illustrated by their existing representatives in Australia and South America; and in the same manner, if we wish clearly to understand the antiquities of Europe, we must compare them with the rude implements and weapons still, or until lately, used by the savage races in other parts of the world. In fact, the Van Diemaner and South American are to the antiquary what the opossum and the sloth are to the geologist.
Pre-historic Times, as Illustrated by Ancient Remains, and the Manners and Customs of Modern Savages, (2nd ed. 1869, 1890), 429-430.
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Descriptive anatomy is to physiology what geography is to history, and just as it is not enough to know the typography of a country to understand its history, so also it is not enough to know the anatomy of organs to understand their functions.
Lectures on the Phenomena of Life Common to Animals and Plants (1878), trans. Hebbel E. Hoff, Roger Guillemin and Lucienne Guillemin (1974), 7.
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Dirichlet was not satisfied to study Gauss’ Disquisitiones arithmetical once or several times, but continued throughout life to keep in close touch with the wealth of deep mathematical thoughts which it contains by perusing it again and again. For this reason the book was never placed on the shelf but had an abiding place on the table at which he worked. … Dirichlet was the first one, who not only fully understood this work, but made it also accessible to others.
In Dirichlet, Werke, Bd. 2, 315. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 159.
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Doctors coin money when they do procedures—family practice doesn’t have any procedures. A urologist has cystoscopies, a gastroenterologist has gastroscopies, a dermatologist has biopsies. They can do three or four of those and make five or six hundred dollars in a single day. We get nothing for the use of our time to understand the lives of our patients. Technology is rewarded in medicine, it seems to me, and not thinking.
Quoted in John McPhee, 'Heirs of General Practice,' New Yorker (23 Jul 1984), 40-85. In David Barton Smith and Arnold D. Kaluzny, The White Labyrinth (2000), 227.
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Does it mean, if you don’t understand something, and the community of physicists don’t understand it, that means God did it? Is that how you want to play this game? Because if it is, here’s a list of the things in the past that the physicists—at the time—didn’t understand … [but now we do understand.] If that’s how you want to invoke your evidence for God, then God is an ever-receding pocket of scientific ignorance, that’s getting smaller and smaller and smaller, as time moves on. So just be ready for that to happen, if that’s how you want to come at the problem. That’s simply the “God of the Gaps” argument that’s been around for ever.
From interview, The Science Studio video series of The Science Network website, episode 'The Moon, the Tides and why Neil DeGrasse Tyson is Colbert’s God' (20 Jan 2011), time 26:58-27:55.
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Dreams are true interpreters of our inclinations; but there is art required to categorize and understand them.
In The Works of Michael de Montaigne (1849), 536.
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Each thing in the world has names or unnamed relations to everything else. Relations are infinite in number and kind. To be is to be related. It is evident that the understanding of relations is a major concern of all men and women. Are relations a concern of mathematics? They are so much its concern that mathematics is sometimes defined to be the science of relations.
In Mole Philosophy and Other Essays (1927), 94-95.
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Each worldview was a cultural product, but evolution is true and separate creation is not ... Worldviews are social constructions, and they channel the search for facts. But facts are found and knowledge progresses, however fitfully. Fact and theory are intertwined, and all great scientists understand the interaction.
…...
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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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Egad, I think the interpreter is the hardest to be understood of the two!
In 'The Critic: Or, A Tragedy Rehearsed', Act 1, Scene 2, as collected in Thomas Moore (ed.), The Works of the Late Right Honourable Richard Brinsley Sheridan (1833), 181.
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ENGINEER, in the military art, an able expert man, who, by a perfect knowledge in mathematics, delineates upon paper, or marks upon the ground, all sorts of forts, and other works proper for offence and defence. He should understand the art of fortification, so as to be able, not only to discover the defects of a place, but to find a remedy proper for them; as also how to make an attack upon, as well as to defend, the place. Engineers are extremely necessary for these purposes: wherefore it is requisite that, besides being ingenious, they should be brave in proportion. When at a siege the engineers have narrowly surveyed the place, they are to make their report to the general, by acquainting him which part they judge the weakest, and where approaches may be made with most success. Their business is also to delineate the lines of circumvallation and contravallation, taking all the advantages of the ground; to mark out the trenches, places of arms, batteries, and lodgments, taking care that none of their works be flanked or discovered from the place. After making a faithful report to the general of what is a-doing, the engineers are to demand a sufficient number of workmen and utensils, and whatever else is necessary.
In Encyclopaedia Britannica or a Dictionary of Arts and Sciences (1771), Vol. 2, 497.
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Engineering is quite different from science. Scientists try to understand nature. Engineers try to make things that do not exist in nature. Engineers stress invention. To embody an invention the engineer must put his idea in concrete terms, and design something that people can use. That something can be a device, a gadget, a material, a method, a computing program, an innovative experiment, a new solution to a problem, or an improvement on what is existing. Since a design has to be concrete, it must have its geometry, dimensions, and characteristic numbers. Almost all engineers working on new designs find that they do not have all the needed information. Most often, they are limited by insufficient scientific knowledge. Thus they study mathematics, physics, chemistry, biology and mechanics. Often they have to add to the sciences relevant to their profession. Thus engineering sciences are born.
Y.C. Fung and P. Tong, Classical and Computational Solid Mechanics (2001), 1.
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Error is often nourished by good sense. … The meaning is, that the powers of the understanding are frequently employed to defend favourite errors; and that a man of sense frequently fortifies himself in his prejudices, or in false opinions which he received without examination, by such arguments as would not have occurred to a fool.
In Maxims, Characters, and Reflections, Critical, Satyrical and Moral (2nd ed., 1757), 9. The meaning is given as a footnote.
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Euclid and Archimedes are allowed to be knowing, and to have demonstrated what they say: and yet whosoever shall read over their writings without perceiving the connection of their proofs, and seeing what they show, though he may understand all their words, yet he is not the more knowing. He may believe, indeed, but does not know what they say, and so is not advanced one jot in mathematical knowledge by all his reading of those approved mathematicians.
In Conduct of the Understanding, sect. 24.
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Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members. On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112-113.
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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 day we are interacting with the economy, whether we want to or not, and whether we know it or not. To have a level of control over our lives, we need to understand the connections between money and events and ourselves.
As quoted in brochure for PBS TV financial news series, Adam Smith’s Money World.
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Every discovery, every enlargement of the understanding, begins as an imaginative preconception of what the truth might be. The imaginative preconception—a “hypothesis”—arises by a process as easy or as difficult to understand as any other creative act of mind; it is a brainwave, an inspired guess, a product of a blaze of insight. It comes anyway from within and cannot be achieved by the exercise of any known calculus of discovery.
In Advice to a Young Scientist (1979), 84.
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Every natural scientist who thinks with any degree of consistency at all will, I think, come to the view that all those capacities that we understand by the phrase psychic activities (Seelenthiitigkeiten) are but functions of the brain substance; or, to express myself a bit crudely here, that thoughts stand in the same relation to the brain as gall does to the liver or urine to the kidneys. To assume a soul that makes use of the brain as an instrument with which it can work as it pleases is pure nonsense; we would then be forced to assume a special soul for every function of the body as well.
Carl Vogt
In Physiologische Briefe für Gelbildete aIle Stünde (1845-1847), 3 parts, 206. as translated in Frederick Gregory, Scientific Materialism in Nineteenth Century Germany (1977), 64.
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Every proposition which we can understand must be composed wholly of constituents with which we are acquainted.
From 'Knowledge by Acquaintance', in Mysticism and Logic: And Other Essays (1918), 219.
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Every species of plant and animal is determined by a pool of germ plasm that has been most carefully selected over a period of hundreds of millions of years. We can understand now why it is that mutations in these carefully selected organisms almost invariably are detrimental.The situation can be suggested by a statement by Dr. J.B.S. Haldane: “My clock is not keeping perfect time. It is conceivable that it will run better if I shoot a bullet through it; but it is much more probable that it will stop altogether.” Professor George Beadle, in this connection, has asked: “What is the chance that a typographical error would improve Hamlet?”
In No More War! (1958), Chap. 4, 53.
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Everyone working in science, no matter their politics, has a stake in cleaning up the mess revealed by the East Anglia emails. Science is on the credibility bubble. If it pops, centuries of what we understand to be the role of science go with it.
Newspaper
In D. Henninger, 'Climategate: Science is Dying', Wall Street Journal (Dec 2009), A21.
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Everything that the human race has done and thought is concerned with the satisfaction of deeply felt needs and the assuagement of pain. One has to keep this constantly in mind if one wishes to understand spiritual movements and their development. Feeling and longing are the motive force behind all human endeavor and human creation, in however exalted a guise the latter may present themselves to us.
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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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Everywhere you look in science, the harder it becomes to understand the universe without God.
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Evolution is the conviction that organisms developed their current forms by an extended history of continual transformation, and that ties of genealogy bind all living things into one nexus. Panselectionism is a denial of history, for perfection covers the tracks of time. A perfect wing may have evolved to its current state, but it may have been created just as we find it. We simply cannot tell if perfection be our only evidence. As Darwin himself understood so well, the primary proofs of evolution are oddities and imperfections that must record pathways of historical descent–the panda’s thumb and the flamingo’s smile of my book titles (chosen to illustrate this paramount principle of history).
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Faced with a new mutation in an organism, or a fundamental change in its living conditions, the biologist is frequently in no position whatever to predict its future prospects. He has to wait and see. For instance, the hairy mammoth seems to have been an admirable animal, intelligent and well-accoutered. Now that it is extinct, we try to understand why it failed. I doubt that any biologist thinks he could have predicted that failure. Fitness and survival are by nature estimates of past performance.
In Scientific American (Sep 1958). As cited in '50, 100 & 150 years ago', Scientific American (Sep 2008), 299, No. 3, 14.
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Faced with the widespread destruction of the environment, people everywhere are coming to understand that we cannot continue to use the goods of the earth as we have in the past … [A] new ecological awareness is beginning to emerge which rather than being downplayed, ought to be encouraged to develop into concrete programs and initiatives. (8 Dec 1989)
The Ecological Crisis: A Common Responsibility. Quoted in Al Gore, Earth in the Balance: Ecology and the Human Spirit (2000), 262.
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Facts are to the mind the same thing as food to the body. On the due digestion of facts depends the strength and wisdom of the one, just as vigor and health depend on the other. The wisest in council, the ablest in debate, and the most agreeable in the commerce of life is that man who has assimilated to his understanding the greatest number of facts.
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Faraday, … by his untiring faithfulness in keeping his diary, contributes to our understanding the objects of his scientific research in magnetism, electricity and light, but he also makes us understand the scientist himself, as a living subject, the mind in action.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 2.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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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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For man being the minister and interpreter of nature, acts and understands so far as he has observed of the order, the works and mind of nature, and can proceed no further; for no power is able to loose or break the chain of causes, nor is nature to be conquered but by submission: whence those twin intentions, human knowledge and human power, are really coincident; and the greatest hindrance to works is the ignorance of causes.
In The Great lnstauration.
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For, in mathematics or symbolic logic, reason can crank out the answer from the symboled equations—even a calculating machine can often do so—but it cannot alone set up the equations. Imagination resides in the words which define and connect the symbols—subtract them from the most aridly rigorous mathematical treatise and all meaning vanishes. Was it Eddington who said that we once thought if we understood 1 we understood 2, for 1 and 1 are 2, but we have since found we must learn a good deal more about “and”?
In 'The Biological Basis of Imagination', American Thought: 1947 (1947), 81.
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Formal thought, consciously recognized as such, is the means of all exact knowledge; and a correct understanding of the main formal sciences, Logic and Mathematics, is the proper and only safe foundation for a scientific education.
In Number and its Algebra (1896), 134.
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Freeman’s gift? It’s cosmic. He is able to see more interconnections between more things than almost anybody. He sees the interrelationships, whether it’s in some microscopic physical process or in a big complicated machine like Orion. He has been, from the time he was in his teens, capable of understanding essentially anything that he’s interested in. He’s the most intelligent person I know.
As quoted in Kenneth Brower, 'The Danger of Cosmic Genius', The Atlantic (Dec 2010). Webmaster note: The Orion Project was a study of the possibility of nuclear powered propulsion of spacecraft.
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Fullness of knowledge always means some understanding of the depths of our ignorance; and that is always conducive to humility and reverence.
In 'What I Believe: Living Philosophies II', The Forum (Oct 1929), 82, No. 4, 199.
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Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it is the truth.
In a lecture, after establishing the relation eπ/2 = ii in a lecture, “which evidently had a strong hold on his imagination. He dropped his chalk and rubber, put his hands in his pockets, and after contemplating the formula a few minutes turned to his class and said [this quote] very slowly and impressively.” As quoted in W. E. Byerly (writing as a Professor Emeritus at Harvard University, but a former student of Peirce), 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 6.
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Geometry may sometimes appear to take the lead of analysis, but in fact precedes it only as a servant goes before his master to clear the path and light him on his way. The interval between the two is as wide as between empiricism and science, as between the understanding and the reason, or as between the finite and the infinite.
From 'Astronomical Prolusions', Philosophical Magazine (Jan 1866), 31, No. 206, 54, collected in Collected Mathematical Papers of James Joseph Sylvester (1908), Vol. 2, 521.
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God is able to do more than man can understand.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 156
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God was always invented to explain mystery. God is always invented to explain those things that you do not understand. Now, when you finally discover how something works … you don't need him anymore. But … you leave him to create the universe because we haven't figured that out yet.
Interview, collected in Paul C. W. Davies and Julian R. Brown (eds.) Superstrings: A Theory of Everything? (1988), 208-209.
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Good scholars struggle to understand the world in an integral way (pedants bite off tiny bits and worry them to death). These visions of reality ... demand our respect, for they are an intellectual’s only birthright. They are often entirely wrong and always flawed in serious ways, but they must be understood honorably and not subjected to mayhem by the excision of patches.
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Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence and fulfills the duty to express the results of his thoughts in clear form.
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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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Guide to understanding a net.addict’s day: Slow day: didn’t have much to do, so spent three hours on usenet. Busy day: managed to work in three hours of usenet. Bad day: barely squeezed in three hours of usenet.
Anonymous
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He had seen too much of the cosmos to have any great faith in man's ability to understand it.
Ghetto (1954)
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He is a learned man that understands one subject, a very learned man that understands two.
In Hialmer Day Gould, New Practical Spelling (1905), 14.
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He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.
Quoted, without citation, in Max Dehn, 'Mathematics, 300 B.C.-200 B.C.', The American Mathematical Monthly (Jan 1944), 51, No. 1, 31.
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He who wishes to explain Generation must take for his theme the organic body and its constituent parts, and philosophize about them; he must show how these parts originated, and how they came to be in that relation in which they stand to each other. But he who learns to know a thing not only from its phenomena, but also its reasons and causes; and who, therefore, not by the phenomena merely, but by these also, is compelled to say: “The thing must be so, and it cannot be otherwise; it is necessarily of such a character; it must have such qualities; it is impossible for it to possess others”—understands the thing not only historically but truly philosophically, and he has a philosophic knowledge of it. Our own Theory of Generation is to be such a philosphic comprehension of an organic body, a very different one from one merely historical. (1764)
Quoted as an epigraph to Chap. 2, in Ernst Haeckel, The Evolution of Man, (1886), Vol 1, 25.
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He [Lord Bacon] appears to have been utterly ignorant of the discoveries which had just been made by Kepler’s calculations … he does not say a word about Napier’s Logarithms, which had been published only nine years before and reprinted more than once in the interval. He complained that no considerable advance had been made in Geometry beyond Euclid, without taking any notice of what had been done by Archimedes and Apollonius. He saw the importance of determining accurately the specific gravities of different substances, and himself attempted to form a table of them by a rude process of his own, without knowing of the more scientific though still imperfect methods previously employed by Archimedes, Ghetaldus and Porta. He speaks of the εὕρηκα of Archimedes in a manner which implies that he did not clearly appreciate either the problem to be solved or the principles upon which the solution depended. In reviewing the progress of Mechanics, he makes no mention either of Archimedes, or Stevinus, Galileo, Guldinus, or Ghetaldus. He makes no allusion to the theory of Equilibrium. He observes that a ball of one pound weight will fall nearly as fast through the air as a ball of two, without alluding to the theory of acceleration of falling bodies, which had been made known by Galileo more than thirty years before. He proposed an inquiry with regard to the lever,—namely, whether in a balance with arms of different length but equal weight the distance from the fulcrum has any effect upon the inclination—though the theory of the lever was as well understood in his own time as it is now. … He speaks of the poles of the earth as fixed, in a manner which seems to imply that he was not acquainted with the precession of the equinoxes; and in another place, of the north pole being above and the south pole below, as a reason why in our hemisphere the north winds predominate over the south.
From Spedding’s 'Preface' to De Interpretations Naturae Proœmium, in The Works of Francis Bacon (1857), Vol. 3, 511-512. [Note: the Greek word “εὕρηκα” is “Eureka” —Webmaster.]
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Heraclitus son of Bloson (or, according to some, of Herakon) of Ephesus. This man was at his prime in the 69th Olympiad. He grew up to be exceptionally haughty and supercilious, as is clear also from his book, in which he says: “Learning of many things does not teach intelligence; if so it would have taught Hesiod and Pythagoras, and again Xenophanes and Hecataeus.” … Finally he became a misanthrope, withdrew from the world, and lived in the mountains feeding on grasses and plants. However, having fallen in this way into a dropsy he came down to town and asked the doctors in a riddle if they could make a drought out of rainy weather. When they did not understand he buried himself in a cow-stall, expecting that the dropsy would be evaporated off by the heat of the manure; but even so he failed to effect anything, and ended his life at the age of sixty.
Diogenes Laertius 9.1. In G. S. Kirk, E. Raven, and M. Schofield (eds.), The Presocratic philosophers: A Critical History with a Selection of Texts (1983), 181.
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How far will chemistry and physics … help us understand the appeal of a painting?
Colour: Why the World Isn’t Grey (1983). Quoted in Sidney Perkowitz, Empire of Light (1999), 1.
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Human evolution is nothing else but the natural continuation, at a collective level, of the perennial and cumulative process of “psychogenetic” arrangement of matter which we call life. … The whole history of mankind has been nothing else (and henceforth it will never be anything else) but an explosive outburst of ever-growing cerebration. … Life, if fully understood, is not a freak in the universe—nor man a freak in life. On the contrary, life physically culminates in man, just as energy physically culminates in life.
(1952). As quoted in Stephen Jay Gould, Hen's Teeth and Horse's Toes: Further Reflections in Natural History (1984, 1994), 246.
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I am afraid I am not in the flight for “aerial navigation”. I was greatly interested in your work with kites; but I have not the smallest molecule of faith in aerial navigation other than ballooning or of expectation of good results from any of the trials we hear of. So you will understand that I would not care to be a member of the aëronautical Society.
Letter (8 Dec 1896) to Baden Powell. This is the full text of the letter. An image of the handwritten original is on the zapatopi.net website
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I am never content until I have constructed a mechanical model of the subject I am studying. If I succeed in making one, I understand. Otherwise, I do not. [Attributed; source unverified.]
Note: Webmaster has been unable to verify this quotation allegedly from his Baltimore Lectures. Is is widely quoted, usually without citation. A few instances indicate the quote came from a guest lecture, Johns Hopkins University, Baltimore (1884). The lecture notes were published in Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light (1904). Webmaster has found no citation giving a page number, and has been unable to find the quote in that text. Anyone with more specific information, please contact Webmaster.
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I am not insensible to natural beauty, but my emotional joys center on the improbable yet sometimes wondrous works of that tiny and accidental evolutionary twig called Homo sapiens. And I find, among these works, nothing more noble than the history of our struggle to understand nature—a majestic entity of such vast spatial and temporal scope that she cannot care much for a little mammalian afterthought with a curious evolutionary invention, even if that invention has, for the first time in so me four billion years of life on earth, produced recursion as a creature reflects back upon its own production and evolution. Thus, I love nature primarily for the puzzles and intellectual delights that she offers to the first organ capable of such curious contemplation.
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I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
In 'Ueber das Lehrziel im mathemalischen Unterricht der höheren Realanstalten', Jahresbericht der Deutschen Mathematiker Vereinigung, 2, 192. (The Annual Report of the German Mathematical Association. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 73.
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I am satisfied with the mystery of life’s eternity and with a knowledge, a sense, of the marvelous structure of existence–as well as the humble attempt to understand even a tiny portion of the Reason that manifests itself in nature.
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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 can never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand.
From stenographic report by A.S. Hathaway of the Lecture 20 Kelvin presented at Johns Hopkins University, Baltimore, on 'Molecular Dynamics and the Wave Theory of Light' (1884), 270-271. (Hathaway was a Mathematics fellow there.) This remark is not included in the first typeset publication—a revised version, printed twenty years later, in 1904, as Lord Kelvin’s Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. The original notes were reproduced by the “papyrograph” process. They are excerpted in Pierre Maurice Marie Duhem, Essays in the History and Philosophy of Science (1996), 55.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I can understand your aversion to the use of the term ‘religion’ to describe an emotional and psychological attitude which shows itself most clearly in Spinoza ... I have not found a better expression than ‘religious’ for the trust in the rational nature of reality that is, at least to a certain extent, accessible to human reason.
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I cannot separate land and sea: to me they interfinger like a pattern in a moss agate, positive and negative shapes irrevocably interlocked. My knowledge of this peninsula depends on that understanding: of underwater canyons that are continuations of the land, of the shell fossils far inland that measure continuations of the sea in eons past.
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I cannot tell you the efforts to which I was condemned to understand something of the diagrams of Descriptive Geometry, which I detest.
Epigraph, without citation, in E.T. Bell, Men of Mathematics (1937, 1965), 181.
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I can’t explain it, but spiritually it makes sense— though I don’t understand how it does make sense.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 120
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I can’t think of any definition of the words mathematician or scientist that would apply to me. I think of myself as a journalist who knows just enough about mathematics to be able to take low-level math and make it clear and interesting to nonmathematicians. Let me say that I think not knowing too much about a subject is an asset for a journalist, not a liability. The great secret of my column is that I know so little about mathematics that I have to work hard to understand the subject myself. Maybe I can explain things more clearly than a professional mathematician can.
In Scot Morris, 'Interview: Martin Gardner', Omni, 4, No. 4 (Jan 1982), 68.
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I can’t understand why men make all this fuss about Everest—it’s only a mountain.
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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 decided to study science and, on arrival at Cambridge, became extremely excited and interested in biochemistry when I first heard about it…. It seemed to me that here was a way to really understand living matter and to develop a more scientific basis to many medical problems.
From biographical sketch in Wilhelm Odelberg (ed.) Les Prix Nobel. The Nobel Prizes 1980, (1981).
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I didn’t arrive at my understanding of the fundamental laws of the universe through my rational mind.
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I do believe that a scientist is a freelance personality. We’re driven by an impulse which is one of curiosity, which is one of the basic instincts that a man has. So we are … driven … not by success, but by a sort of passion, namely the desire of understanding better, to possess, if you like, a bigger part of the truth. I do believe that science, for me, is very close to art.
From 'Asking Nature', collected in Lewis Wolpert and Alison Richards (eds.), Passionate Minds: The Inner World of Scientists (1997), 197.
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I do not see how a man can work on the frontiers of physics and write poetry at the same time. They are in opposition. In science you want to say something that nobody knew before, in words which everyone can understand. In poetry you are bound to say ... something that everyone knows already in words that nobody can understand.
Commenting to him about the poetry J. Robert Oppenheimer wrote.
Quoted in Steven George Krantz, Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians (2005), 169
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I do not study to understand the transit of the stars. My soul has never sought for responses from ghosts. I detest all sacrilegious rites.
Confessions [c.397], Book X, chapter 35 (56), trans. H. Chadwick (1991),212.
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I do not think it is possible really to understand the successes of science without understanding how hard it is—how easy it is to be led astray, how difficult it is to know at any time what is the next thing to be done.
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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 don’t pretend to understand the universe–it’s much bigger than I am.
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I don’t pretend to understand the Universe—it’s a great deal bigger than I am. … People ought to be modester.
Quoted in William Allingham's diary entry for 28 Dec 1868, from a conversation with Carlyle that day. In Helen Allingham and D. Radford (eds.), William Allingham: A Diary (1907), 196.
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I don’t understand why people insist on pitting concepts of evolution and creation against each other. Why can’t they see that spiritualism and science are one? That bodies evolve and souls evolve and the universe is a fluid package that marries them both in a wonderful package called a human being.
The Art of Racing in the Rain. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 43
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I have a friendly feeling towards pigs generally, and consider them the most intelligent of beasts, not excepting the elephant and the anthropoid ape—the dog is not to be mentioned in this connection. I also like his disposition and attitude towards all other creatures, especially man. He is not suspicious, or shrinkingly submissive, like horses, cattle, and sheep; nor an impudent devil-may-care like the goat; nor hostile like the goose; nor condescending like the cat; nor a flattering parasite like the dog. He views us from a totally different, a sort of democratic, standpoint as fellow-citizens and brothers, and takes it for granted, or grunted, that we understand his language, and without servility or insolence he has a natural, pleasant, camerados-all or hail-fellow-well-met air with us.
In The Book of a Naturalist (1919), 295-296.
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I have always assumed, and I now assume, that he [Robert Oppenheimer] is loyal to the United States. I believe this, and I shall believe it until I see very conclusive proof to the opposite. … [But] I thoroughly disagreed with him in numerous issues and his actions frankly appeared to me confused and complicated. To this extent I feel that I would like to see the vital interests of this country in hands which I understand better, and therefore trust more.
After Teller paid tribute to Oppenheimer’s talents, especially his “very outstanding achievement” as the wartime organizer and director of Los Alamos, Teller continued his testimony to the Gray board hearings (28 Apr 1954) in the Atomic Energy Commission building, “In the Matter of J. Robert Oppenheimer.” The subject quotes were excerpted from Teller’s answers to their questions. As given in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 72-74.
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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 always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly.
In 'The Queen of mathematics', The World of Mathematics (1956), 515.
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I have always tried to fit knowledge that I acquired into my understanding of the world. … When something comes along that I don’t understand, that I can’t fit in, that bothers me, I think about it, mull over it, and perhaps ultimately do some work with it. That’s perhaps the reason that I’ve been able to make discoveries in molecular biology.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 739.
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I have before mentioned mathematics, wherein algebra gives new helps and views to the understanding. If I propose these it is not to make every man a thorough mathematician or deep algebraist; but yet I think the study of them is of infinite use even to grown men; first by experimentally convincing them, that to make anyone reason well, it is not enough to have parts wherewith he is satisfied, and that serve him well enough in his ordinary course. A man in those studies will see, that however good he may think his understanding, yet in many things, and those very visible, it may fail him. This would take off that presumption that most men have of themselves in this part; and they would not be so apt to think their minds wanted no helps to enlarge them, that there could be nothing added to the acuteness and penetration of their understanding.
In The Conduct of the Understanding, Sect. 7.
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I have deeply regretted that I did not proceed far enough [as a Cambridge undergraduate] at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense.
In Charles Darwin and Francis Darwin (ed.), 'Autobiography', The Life and Letters of Charles Darwin (1887, 1896), Vol. 1, 40.
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I have never really had dreams to fulfil…. You just want to go on looking at these ecosystems and trying to understand them and they are all fascinating. To achieve a dream suggests snatching a prize from the top of a tree and running off with it, and that’s the end of it. It isn’t like that. … What you are trying to achieve is understanding and you don’t do that just by chasing dreams.
From interview with Michael Bond, 'It’s a Wonderful Life', New Scientist (14 Dec 2002), 176, No. 2373, 52.
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I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, “Oh, I see. That’s how it must be.” This is a sign that they explain it to themselves from within their own system.
Lichtenberg: A Doctrine of Scattered Occasions: Reconstructed From: Reconstructed From His Aphorisms and Reflections (1959), 291.
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I heard … xenon was a good anesthesia. … I thought, “How can xenon, which doesn’t form any chemical compounds, serve as a general anesthetic? … I lay awake at night for a few minutes before going to sleep, and during the next couple of weeks each night I would think, “…how do anesthetic agents work?" Then I forgot to do it after a while, but I’d trained my unconscious mind to keep this question alive and to call [it] to my consciousness whenever a new idea turned up…. So seven years went by. [One day I] put my feet up on the desk and started reading my mail, and here was a letter from George Jeffrey … an x-ray crystallographer, on his determination of the structure of a hydrate crystal. Immediately I sat up, took my feet off the desk, and said, “I understand anesthesia!” … I spent a year [and] determined the structure of chloroform hydrate, and then I wrote my paper published in June of 1961.
Interview with George B. Kauffman and Laurie M. Kauffman, in 'Linus Pauling: Reflections', American Scientist (Nov-Dec 1994), 82, No. 6, 522-523.
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I like relativity and quantum theories
because I don't understand them
and they make me feel as if space shifted about
like a swan that
can't settle,
refusing to sit still and be measured;
and as if the atom were an impulsive thing
always changing its mind.
'Relativity', David Herbert Lawrence, The Works of D.H. Lawrence (1994), 437.
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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 read once that the true mark of a pro—at anything—is that he understands, loves, and is good at even the drudgery of his profession.
In I Want to be a Mathematician: an Automathography (1985), 37.
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I read them. Not to grade them. No, I read them to see how I am doing. Where am I failing? What don’t they understand? Why do they give wrong answers? Why do they have some point of view that I don’t think is right? Where am I failing? Where do I need to build up.
In The Essential Deming.
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I regard sex as the central problem of life. And now that the problem of religion has practically been settled, and that the problem of labor has at least been placed on a practical foundation, the question of sex—with the racial questions that rest on it—stands before the coming generations as the chief problem for solution. Sex lies at the root of life, and we can never learn to reverence life until we know how to understand sex.
Studies in the Psychology of Sex (1897), Vol. 1, xxx.
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I remember my first look at the great treatise of Maxwell’s when I was a young man… I saw that it was great, greater and greatest, with prodigious possibilities in its power… I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly… It will be understood that I preach the gospel according to my interpretation of Maxwell.
From translations of a letter (24 Feb 1918), cited in Paul J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age (2002), 24. Nahin footnotes that the words are not verbatim, but are the result of two translations. Heaviside's original letter in English was quoted, translated in to French by J. Bethenode, for the obituary he wrote, "Oliver Heaviside", in Annales des Posies Telegraphs (1925), 14, 521-538. The quote was retranslated back to English in Nadin's book. Bethenode footnoted that he made the original translation "as literally as possible in order not to change the meaning." Nadin assures that the retranslation was done likewise. Heaviside studyied Maxwell's two-volume Treatise on Electricity and Magnetism.
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I respect Kirkpatrick both for his sponges and for his numinous nummulosphere. It is easy to dismiss a crazy theory with laughter that debars any attempt to understand a man’s motivation–and the nummulosphere is a crazy theory. I find that few men of imagination are not worth my attention. Their ideas may be wrong, even foolish, but their methods often repay a close study ... The different drummer often beats a fruitful tempo.
…...
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I returned and saw under the sun that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.
Bible
Ecclesiastes 9:11. As given in the King James Version.
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I said that there is something every man can do, if he can only find out what that something is. Henry Ford has proved this. He has installed in his vast organization a system for taking hold of a man who fails in one department, and giving him a chance in some other department. Where necessary every effort is made to discover just what job the man is capable of filling. The result has been that very few men have had to be discharged, for it has been found that there was some kind of work each man could do at least moderately well. This wonderful system adopted by my friend Ford has helped many a man to find himself. It has put many a fellow on his feet. It has taken round pegs out of square holes and found a round hole for them. I understand that last year only 120 workers out of his force of 50,000 were discharged.
As quoted from an interview by B.C. Forbes in The American Magazine (Jan 1921), 10.
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I shall conclude, for the time being, by saying that until Philosophers make observations (especially of mountains) that are longer, more attentive, orderly, and interconnected, and while they fail to recognize the two great agents, fire and water, in their distinct affects, they will not be able to understand the causes of the great natural variety in the disposition, structure, and other matter that can be observed in the terrestrial globe in a manner that truly corresponds to the facts and to the phenomena of Nature.
'Aleune Osservazioni Orittologiche fatte nei Monti del Vicentino', Giomale d’Italia, 1769, 5, 411, trans. Ezio Vaccari.
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I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first compleat and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.
An Attempt to Prove the Motion of the Earth from Observations (1674), 27-8. Based on a Cutlerian Lecture delivered by Hooke at the Royal Society four years earlier.
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I should like to compare this rearrangement which the proteins undergo in the animal or vegetable organism to the making up of a railroad train. In their passage through the body parts of the whole may be left behind, and here and there new parts added on. In order to understand fully the change we must remember that the proteins are composed of Bausteine united in very different ways. Some of them contain Bausteine of many kinds. The multiplicity of the proteins is determined by many causes, first through the differences in the nature of the constituent Bausteine; and secondly, through differences in the arrangement of them. The number of Bausteine which may take part in the formation of the proteins is about as large as the number of letters in the alphabet. When we consider that through the combination of letters an infinitely large number of thoughts may be expressed, we can understand how vast a number of the properties of the organism may be recorded in the small space which is occupied by the protein molecules. It enables us to understand how it is possible for the proteins of the sex-cells to contain, to a certain extent, a complete description of the species and even of the individual. We may also comprehend how great and important the task is to determine the structure of the proteins, and why the biochemist has devoted himself with so much industry to their analysis.
'The Chemical Composition of the Cell', The Harvey Lectures (1911), 7, 45.
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I strive that in public dissection the students do as much as possible so that if even the least trained of them must dissect a cadaver before a group of spectators, he will be able to perform it accurately with his own hands; and by comparing their studies one with another they will properly understand, this part of medicine.
In De Humani Corporis Fabrica Libri Septem [Seven Books on the Structure of the Human Body] (1543), 547. Quoted and trans. in Charles Donald O'Malley, Andreas Vesalius of Brussels, 1514-1564 (1964), 144.
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I suppose that I tend to be optimistic about the future of physics. And nothing makes me more optimistic than the discovery of broken symmetries. In the seventh book of the Republic, Plato describes prisoners who are chained in a cave and can see only shadows that things outside cast on the cave wall. When released from the cave at first their eyes hurt, and for a while they think that the shadows they saw in the cave are more real than the objects they now see. But eventually their vision clears, and they can understand how beautiful the real world is. We are in such a cave, imprisoned by the limitations on the sorts of experiments we can do. In particular, we can study matter only at relatively low temperatures, where symmetries are likely to be spontaneously broken, so that nature does not appear very simple or unified. We have not been able to get out of this cave, but by looking long and hard at the shadows on the cave wall, we can at least make out the shapes of symmetries, which though broken, are exact principles governing all phenomena, expressions of the beauty of the world outside.
In Nobel Lecture (8 Dec 1989), 'Conceptual Foundations of the Unified Theory of Weak and Electromagnetic Interactions.' Nobel Lectures: Physics 1971-1980 (1992), 556.
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I then shouted into M [the mouthpiece] the following sentence: “Mr. Watson—Come here—I want to see you.” To my delight he came and declared that he had heard and understood what I said. I asked him to repeat the words. He answered “You said—‘Mr. Watson—-come here—I want to see you.’” We then changed places and I listened at S [the reed receiver] while Mr. Watson read a few passages from a book into the mouth piece M. It was certainly the case that articulate sounds proceeded from S. The effect was loud but indistinct and muffled. If I had read beforehand the passage given by Mr. Watson I should have recognized every word. As it was I could not make out the sense—but an occasional word here and there was quite distinct. I made out “to” and “out” and “further”; and finally the sentence “Mr. Bell do you understand what I say? Do—you—un—der—stand—what—I—say” came quite clearly and intelligibly. No sound was audible when the armature S was removed.
Notebook, 'Experiments made by A. Graham Bell, vol. I'. Entry for 10 March 1876. Quoted in Robert V. Bruce, Bell: Alexander Graham Bell and the Conquest of Solitude (1973), 181.
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I think I can safely say that nobody understands quantum mechanics.
'Probability and Uncertainty—the Quantum Mechanical View of Nature', the sixth of his Messenger Lectures (1964), Cornell University. Collected in The Character of Physical Law (1967), 129. Often misquoted in various ways, for example, “If people say they understand quantum mechanics they’re lying,” in Ari Ben-Menahem, Historical Encyclopedia of Natural and Mathematical Sciences (2009), 5699.
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I think that intelligence does not emerge from a handful of very beautiful principles—like physics. It emerges from perhaps a hundred fundamentally different kinds of mechanisms that have to interact just right. So, even if it took only four years to understand them, it might take four hundred years to unscramble the whole thing.
As quoted from an interview with author Jeremy Bernstein, in Science Observed: Essays Out of My Mind (1982), 44.
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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 try to make a point not to talk about things I don’t understand—at least the things I do not understand at all.
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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I want to argue that the ‘sudden’ appearance of species in the fossil record and our failure to note subsequent evolutionary change within them is the proper prediction of evolutionary theory as we understand it ... Evolutionary ‘sequences’ are not rungs on a ladder, but our retrospective reconstruction of a circuitous path running like a labyrinth, branch to branch, from the base of the bush to a lineage now surviving at its top.
…...
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I want you to understand I shall not hold you to any [medieval] code of faithfulness to me nor shall I consider myself bound to you similarly.
From note to her husband-to-be, George P. Putnam, on the morning of their wedding (7 Feb 1931). As quoted in Mary S. Lovell, The Sound of Wings (1989), 166. Earhart’s misspelling as “midaevil” in the original note has been corrected to “medieval” above.
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I wanted to be a scientist from my earliest school days. The crystallizing moment came when I first caught on that stars are mighty suns, and how staggeringly far away they must be to appear to us as mere points of light. I’m not sure I even knew the word science then, but I was gripped by the prospect of understanding how things work, of helping to uncover deep mysteries, of exploring new worlds.
In 'With Science on Our Side', Washington Post (9 Jan 1994).
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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 have my son mind and understand business, read little history, study the mathematics and cosmography; these are good, with subordination to the things of God. … These fit for public services for which man is born.
In Letters and Speeches of Oliver Cromwell (1899), Vol. 1, 371.
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I would not have it inferred ... that I am, as yet, an advocate for the hypothesis of chemical life. The doctrine of the vitality of the blood, stands in no need of aid from that speculative source. If it did, I would certainly abandon it. For, notwithstanding the fashionableness of the hypothesis in Europe, and the ascendancy it has gained over some minds in this country [USA], it will require stubborn facts to convince me that man with all his corporeal and intellectual attributes is nothing but hydro-phosphorated oxyde of azote ... When the chemist declares, that the same laws which direct the crystallization of spars, nitre and Glauber's salts, direct also the crystallization of man, he must pardon me if I neither understand him, nor believe him.
Medical Theses (1805), 391-2, footnote.
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I would picture myself as a virus, or as a cancer cell, for example, and try to sense what it would be like to be either. I would also imagine myself as the immune system, and I would try to reconstruct what I would do as an immune system engaged in combating a virus or cancer cell. When I had played through a series of such scenarios on a particular problem and had acquired new insights, I would design laboratory experiments accordingly… Based upon the results of the experiment, I would then know what question to ask next… When I observed phenomena in the laboratory that I did not understand, I would also ask questions as if interrogating myself: “Why would I do that if I were a virus or a cancer cell, or the immune system?” Before long, this internal dialogue became second nature to me; I found that my mind worked this way all the time.
In Anatomy of Reality: Merging of Intuition and Reason (1983), 7, footnote b, as quoted and cited in Roger Frantz, Two Minds: Intuition and Analysis in the History of Economic Thought (2006), 7.
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I would teach the world that science is the best way to understand the world, and that for any set of observations, there is only one correct explanation. Also, science is value-free, as it explains the world as it is. Ethical issues arise only when science is applied to technology – from medicine to industry.
Response to question “What is the one thing everyone should learn about science?” in 'Life Lessons' The Guardian (7 Apr 2005).
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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 a lion could talk, we could not understand him.
In Philosophical Investigations (1953), trans. G. E. M. Anscombe, 223.
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If at this moment I am not a worn-out, debauched, useless carcass of a man, if it has been or will be my fate to advance the cause of science, if I feel that I have a shadow of a claim on the love of those about me, if in the supreme moment when I looked down into my boy’s grave my sorrow was full of submission and without bitterness, it is because these agencies have worked upon me, and not because I have ever cared whether my poor personality shall remain distinct forever from the All from whence it came and whither it goes.
And thus, my dear Kingsley, you will understand what my position is. I may be quite wrong, and in that case I know I shall have to pay the penalty for being wrong. But I can only say with Luther, “Gott helfe mir, ich kann nichts anders [God help me, I cannot do otherwise].”
In Letter (23 Sep 1860) to Charles Kingsley, Life and Letters of Thomas Henry Huxley (1901), 237.
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If I choose to impose individual blame for all past social ills, there will be no one left to like in some of the most fascinating periods of our history. For example ... if I place every Victorian anti-Semite beyond the pale of my attention, my compass of available music and literature will be pitifully small. Though I hold no shred of sympathy for active persecution, I cannot excoriate individuals who acquiesced passively in a standard societal judgment. Rail instead against the judgment, and try to understand what motivates men of decent will.
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If I do not understand a thing, I keep it before me and I wait.
Gull’s restatement of a Newton quote, as given by the Editor in Preface to Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xvi.
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If in physics there’s something you don’t understand, you can always hide behind the uncharted depths of nature. You can always blame God. You didn’t make it so complex yourself. But if your program doesn’t work, there is no one to hide behind. You cannot hide behind an obstinate nature. If it doesn’t work, you’ve messed up.
…...
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If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
In Gottfried Wilhelm Leibnitz and Alfred Gideon Langley (trans.), New Essays Concerning Human Understanding (1896), 413-414.
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If it were customary to send daughters to school like sons, and if they were then taught the natural sciences, they would learn as thoroughly and understand the subtleties of all the arts and sciences as well as sons. And by chance there happen to be such women, for, as I touched on before, just as women have more delicate bodies than men, weaker and less able to perform many tasks, so do they have minds that are freer and sharper whenever they apply themselves.
The Book of the City of Ladies (1405), part 1, section 27. Trans. Earl Jeffrey Richards (1982), 63.
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If physical science is dangerous, as I have said, it is dangerous because it necessarily ignores the idea of moral evil; but literature is open to the more grievous imputation of recognizing and understanding it too well.
In 'Duties of the Church Towards Knowledge', The Idea of a University Defined and Illustrated (1852, 1873), Discourse 9, 229.
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If the brain were simple enough for us to understand it, we would be too simple to understand it.
Ken Hill
…...
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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 from 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 there’s one thing in physics I feel more responsible for than any other, it’s this perception of how everything fits together. I like to think of myself as having a sense of judgment. I’m willing to go anywhere, talk to anybody, ask any question that will make headway. I confess to being an optimist about things, especially about someday being able to understand how things are put together. So many young people are forced to specialize in one line or another that a young person can’t afford to try and cover this waterfront — only an old fogy who can afford to make a fool of himself. If I don't, who will?
Stated during a 1983 interview. Quoted in Dennis Overbye, 'John A. Wheeler, Physicist Who Coined the Term Black Hole, Is Dead at 96', New York Times (14 Apr 2008).
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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 to-day you ask a physicist what he has finally made out the æther or the electron to be, the answer will not be a description in terms of billiard balls or fly-wheels or anything concrete; he will point instead to a number of symbols and a set of mathematical equations which they satisfy. What do the symbols stand for? The mysterious reply is given that physics is indifferent to that; it has no means of probing beneath the symbolism. To understand the phenomena of the physical world it is necessary to know the equations which the symbols obey but not the nature of that which is being symbolised. …this newer outlook has modified the challenge from the material to the spiritual world.
Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 30.
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If we are correct in understanding how evolution actually works, and provided we can survive the complications of war, environmental degradation, and possible contact with interstellar planetary travelers, we will look exactly the same as we do now. We won’t change at all. The species is now so widely dispersed that it is not going to evolve, except by gradualism.
In Pamela Weintraub, The Omni Interviews (1984), 75.
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If you enquire about him [J.J. Sylvester], you will hear his genius universally recognized but his power of teaching will probably be said to be quite deficient. Now there is no man living who is more luminary in his language, to those who have the capacity to comprehend him than Sylvester, provided the hearer is in a lucid interval. But as the barn yard fowl cannot understand the flight of the eagle, so it is the eaglet only who will be nourished by his instruction.
Letter (18 Sep 1875) to Daniel C. Gilman. In Daniel C. Gilman Papers, Ms. 1, Special Collections Division, Milton S. Eisenhower Library, Johns Hopkins University. As quoted in Karen Hunger Parshall, 'America’s First School of Mathematical Research: James Joseph Sylvester at The Johns Hopkins University 1876—1883', Archive for History of Exact Sciences (1988), 38, No. 2, 167.
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If you had come to me a hundred years ago, do you think I should have dreamed of the telephone? Why, even now I cannot understand it! I use it every day, I transact half my correspondence by means of it, but I don’t understand it. Thnk of that little stretched disk of iron at the end of a wire repeating in your ear not only sounds, but words—not only words, but all the most delicate and elusive inflections and nuances of tone which separate one human voice from another! Is not that something of a miracle?
Quoted in Harold Begbie in Pall Mall magazine (Jan 1903). In Albert Shaw, The American Monthly Review of Reviews (1903), 27, 232.
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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 achieve conservation, the first thing you have to do is persuade people that the natural world is precious, beautiful, worth saving and complex. If people don’t understand that and don’t believe that in their hearts, conservation doesn't stand a chance. That’s the first step, and that is what I do.
From interview with Michael Bond, 'It’s a Wonderful Life', New Scientist (14 Dec 2002), 176, No. 2373, 48.
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If you want to really understand about a tumor, you've got be be a tumor.
Quoted in Evelyn Fox Keller, A Feeling for the Organism: The Life and Work of Barbara McClintock (1984), 207.
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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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If you’re telling a story, it’s very tempting to personalise an animal. To start with, biologists said this fascination with one individual was just television storytelling. But they began to realise that, actually, it was a new way to understand behaviour–following the fortunes of one particular animal could be very revealing and have all kinds of implications in terms of the ecology and general behaviour of the animals in that area.
From interview with Alice Roberts, 'Attenborough: My Life on Earth', The Biologist (Aug 2015), 62, No. 4, 15.
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Imagine life as a game in which you are juggling five balls in the air. You name them - work, family, health, friends, and spirit - and you’re keeping all of these in the air. You will soon understand that work is a rubber ball. If you drop it, it will bounce back. But the other four balls - family, health, friends, and spirit are made of glass. If you drop one of these, they will be irrevocably scuffed, marked, nicked, damaged, or even shattered. They will never be the same. You must understand that and strive for balance in your life.
…...
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Imagine that … the world is something like a great chess game being played by the gods, and we are observers of the game. … If we watch long enough, we may eventually catch on to a few of the rules…. However, we might not be able to understand why a particular move is made in the game, merely because it is too complicated and our minds are limited…. We must limit ourselves to the more basic question of the rules of the game.
If we know the rules, we consider that we “understand” the world.
In 'Basic Physics', The Feynman Lectures on Physics (1964, 2013), Vol. 1, 2-1.
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In 1906 I indulged my temper by hurling invectives at Neo-Darwinians in the following terms. “I really do not wish to be abusive [to Neo-Darwinians]; but when I think of these poor little dullards, with their precarious hold of just that corner of evolution that a blackbeetle can understand—with their retinue of twopenny-halfpenny Torquemadas wallowing in the infamies of the vivisector’s laboratory, and solemnly offering us as epoch-making discoveries their demonstrations that dogs get weaker and die if you give them no food; that intense pain makes mice sweat; and that if you cut off a dog’s leg the three-legged dog will have a four-legged puppy, I ask myself what spell has fallen on intelligent and humane men that they allow themselves to be imposed on by this rabble of dolts, blackguards, imposters, quacks, liars, and, worst of all, credulous conscientious fools.”
In Back to Methuselah: A Metabiological Pentateuch (1921), lxi
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In a crystal we have the clear evidence of the existence of a formative life-principle, and though we cannot understand the life of a crystal, it is none the less a living being.
In 'The Problem of Increasing Human Energy: With Special Reference to the Harnessing of the Sun’s Energy', Century Illustrated Magazine (Jun 1900), 60, No. 2, 180.
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In a strange way, Marcion understood the situation better than the more conventional followers of the church, for Lucifer is merely one of the faces of a larger force. Evil is a by-product, a component, of creation.
In 'Who is Lucifer?', The Lucifer Principle: A Scientific Expedition Into the Forces of History (1997), 2.
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In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements. Clearly, then, systematic knowledge of nature must start with an attempt to settle questions about principles.
Aristotle
In Physics Book 1, Chap 1, as translated in J.L. Ackrill, A New Aristotle Reader (1988), 81.
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In all our academies we attempt far too much. ... In earlier times lectures were delivered upon chemistry and botany as branches of medicine, and the medical student learned enough of them. Now, however, chemistry and botany are become sciences of themselves, incapable of comprehension by a hasty survey, and each demanding the study of a whole life, yet we expect the medical student to understand them. He who is prudent, accordingly declines all distracting claims upon his time, and limits himself to a single branch and becomes expert in one thing.
Quoted in Johann Hermann Baas, Henry Ebenezer Handerson (trans.), Outlines of the History of Medicine and the Medical Profession (1889), 842-843.
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In all spheres of science, art, skill, and handicraft it is never doubted that, in order to master them, a considerable amount of trouble must be spent in learning and in being trained. As regards philosophy, on the contrary, there seems still an assumption prevalent that, though every one with eyes and fingers is not on that account in a position to make shoes if he only has leather and a last, yet everybody understands how to philosophize straight away, and pass judgment on philosophy, simply because he possesses the criterion for doing so in his natural reason.
From Phänomenologie des Geistes (1807) as translated by J.B. Baillie in 'Preface', The Phenomenology of Mind (1910), Vol. 1, 67.
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In attempting to understand the elements out of which mental phenomena are compounded, it is of the greatest importance to remember that from the protozoa to man there is nowhere a very wide gap either in structure or in behaviour. From this fact it is a highly probable inference that there is also nowhere a very wide mental gap.
Lecture II, 'Instinct and Habit', The Analysis of Mind
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In biology, nothing is clear, everything is too complicated, everything is a mess, and just when you think you understand something, you peel off a layer and find deeper complications beneath. Nature is anything but simple.
The Hot Zone
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In fact, we will have to give up taking things for granted, even the apparently simple things. We have to learn to understand nature and not merely to observe it and endure what it imposes on us. Stupidity, from being an amiable individual defect, has become a social crime.
The Origin of Life (1967), 163.
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In mathematics, … and in natural philosophy since mathematics was applied to it, we see the noblest instance of the force of the human mind, and of the sublime heights to which it may rise by cultivation. An acquaintance with such sciences naturally leads us to think well of our faculties, and to indulge sanguine expectations concerning the improvement of other parts of knowledge. To this I may add, that, as mathematical and physical truths are perfectly uninteresting in their consequences, the understanding readily yields its assent to the evidence which is presented to it; and in this way may be expected to acquire the habit of trusting to its own conclusions, which will contribute to fortify it against the weaknesses of scepticism, in the more interesting inquiries after moral truth in which it may afterwards engage.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 3, 182.
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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 place of science, the Eskimo has only magic to bridge the gap between what he can understand and what is not known. Without magic, his life would be one long panic.
In Man’s Rise to Civilization (1968), 48.
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In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite.
As quoted, without citation, in Robert Jungk and James Cleugh (trans.), Brighter Than a Thousand Suns: A Personal History of the Atomic Scientists (1958), 22. The writing of poetry by Robert Oppenheimer was being remarked upon by Dirac, as he was talking with him.
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In the end, we conserve only what we love. We will love only what we understand. We will understand only what we are taught.
…...
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In the light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion, and the final emergence into the light—only those who have experienced it can understand that.
Quoted in Banesh Hoffmann and Helen Dukas, Albert Einstein: Creator and Rebel (1972), 124.
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In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the 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.
As translated in John Fauvel and Jeremy Gray (eds.) A History of Mathematics: A Reader (1987), 290-291. From De Augmentis, Book 3, 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 medical field [scientific ignorance] could lead to horrendous results. People who don’t understand the difference between a controlled experiment and claims by some quack may die as a result of not taking medical science seriously. One of the most damaging examples of pseudoscience is false memory syndrome. I’m on the board of a foundation exposing this problem.
As quoted by Lawrence Toppman, 'Mastermind', The Charlotte Observer (20 Jun 1993), 6E. As quoted and cited in Dana Richards, 'Martin Gardner: A “Documentary”', collected in Elwyn R. Berlekamp and Tom Rodgers (ed.) The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner (1999), 11.
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In the next twenty centuries … humanity may begin to understand its most baffling mystery—where are we going? The earth is, in fact, traveling many thousands of miles per hour in the direction of the constellation Hercules—to some unknown destination in the cosmos. Man must understand his universe in order to understand his destiny. Mystery, however, is a very necessary ingredient in our lives. Mystery creates wonder and wonder is the basis for man’s desire to understand. Who knows what mysteries will be solved in our lifetime, and what new riddles will become the challenge of the new generation? Science has not mastered prophesy. We predict too much for the next year yet far too little for the next ten. Responding to challenges is one of democracy’s great strengths. Our successes in space can be used in the next decade in the solution of many of our planet’s problems.
In a speech to a Joint Meeting of the Two Houses of Congress to Receive the Apollo 11 Astronauts (16 Sep 1969), in the Congressional Record.
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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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Increasingly, our leaders must deal with dangers that threaten the entire world, where an understanding of those dangers and the possible solutions depend on a good grasp of science. The ozone layer, the greenhouse effect, acid rain, questions of diet and of heredity--all require scientific literacy. Can Americans choose the proper leaders and support the proper programs if they are scientifically illiterate?
articles.latimes.com/1989-03-31/news/vw-543_1_scientific-literacy
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Indeed, if one understands by algebra the application of arithmetic operations to composite magnitudes of all kinds, whether they be rational or irrational number or space magnitudes, then the learned Brahmins of Hindostan are the true inventors of algebra.
In Geschichte der Mathematik im Altertum und im Mittelalter (1874), 195. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 284. From the original German, “Ja, wenn man unter Algebra die Anwendung arithmetischer Operationen auf zusammengesetzte Grössen aller Art, mögen sie rationale oder irrationale Zahl- oder Raumgrössen sein, versteht, so sind die gelehrten Brahmanen Hindustans die wahren Erfinder der Algebra.”
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Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
…...
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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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Inventions and discoveries are of two kinds. The one which we owe to chance, such as those of the mariner’s compass, gunpowder, and in general almost all the discoveries we have made in the arts. The other which we owe to genius: and here we ought to understand by the word discovery, a new combination, or a new relation perceived between certain objects or ideas. A person obtains the title of a man of genius, if the ideas which result from this combination form one grand whole, are fruitful in truths, and are of importance with respect to mankind.
From the original French, “Les inventions ou les découvertes sont de deux espèces. Il en est que nous devons au hazard; telles sont la boussole, la poudre à canon, & généralement presque toutes les découvertes que nous avons faites dans les arts. Il en est d'autres que nous devons au génie: &, par ce mot de découverte, on doit alors entendre une nouvelle combinaison, un rapport nouveau aperçu entre certains objets ou certaines idées. On obtient le titre d'homme de génie, si les idées qui résultent de ce rapport forment un grand ensemble, sont fécondes en vérités & intéressantes pour l'humanité,” in 'Du Génie', L’Esprit (1758), Discourse 4, 476. English version from Claude Adrien Helvétius and William Mudford (trans.), 'Of Genius', De l’Esprit or, Essays on the Mind and its several Faculties (1759), Essay 4, Chap. 1, 241-242.
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It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space and no matter how tiny a region of time … I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the chequer board with all its apparent complexities. But this speculation is of the same nature as those other people make—“I like it”,“I don't like it”—and it is not good to be too prejudiced about these things.
In The Character of Physical Law (1965, 2001), 57.
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It feels unacceptable to many people even to think of having a cosmology based on science. … They see fanciful origin stories as spicing up the culture. … Aspects of many origin stories can enrich our understanding of the scientific picture, but they cannot take its place.
As co-author with Nancy Ellen Abrams, in The View from the Center of the Universe: Discovering Our Extraordinary Place in the Cosmos (2006), 85.
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It has always seemed to me extreme presumptuousness on the part of those who want to make human ability the measure of what nature can and knows how to do, since, when one comes down to it, there is not one effect in nature, no matter how small, that even the most speculative minds can fully understand.
…...
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It has been said that computing machines can only carry out the processes that they are instructed to do. This is certainly true in the sense that if they do something other than what they were instructed then they have just made some mistake. It is also true that the intention in constructing these machines in the first instance is to treat them as slaves, giving them only jobs which have been thought out in detail, jobs such that the user of the machine fully understands what in principle is going on all the time. Up till the present machines have only been used in this way. But is it necessary that they should always be used in such a manner? Let us suppose we have set up a machine with certain initial instruction tables, so constructed that these tables might on occasion, if good reason arose, modify those tables. One can imagine that after the machine had been operating for some time, the instructions would have altered out of all recognition, but nevertheless still be such that one would have to admit that the machine was still doing very worthwhile calculations. Possibly it might still be getting results of the type desired when the machine was first set up, but in a much more efficient manner. In such a case one would have to admit that the progress of the machine had not been foreseen when its original instructions were put in. It would be like a pupil who had learnt much from his master, but had added much more by his own work. When this happens I feel that one is obliged to regard the machine as showing intelligence.
Lecture to the London Mathematical Society, 20 February 1947. Quoted in B. E. Carpenter and R. W. Doran (eds.), A. M. Turing's Ace Report of 1946 and Other Papers (1986), 122-3.
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