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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Instruction Quotes (51 quotes)
Instructed Quotes, Instructive Quotes, Instructing Quotes, Instruct Quotes


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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Neque enim ingenium sine disciplina aut disciplina sine ingenio perfectum artificem potest efficere
For neither talent without instruction nor instruction without talent can produce the perfect craftsman.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 3. As in Frank Granger (trans.), Vitruvius: De Architectura (1931), 8-9. Also translated as “Neither natural ability without instruction nor instruction without natural ability can make the perfect artist.” In Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 3.
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Ut ager quamvis fertilis sine cultura fructuosus esse non potest, sic sine doctrina animus.
A mind without instruction can no more bear fruit than can a field, however fertile, without cultivation.
In Hannis Taylor and Mary Lillie Taylor Hunt, Cicero: a Sketch of His Life and Works (2nd Ed., 1918), 597.
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A fear of intellectual inadequacy, of powerlessness before the tireless electronic wizards, has given rise to dozens of science-fiction fantasies of computer takeovers. ... Other scientists too are apprehensive. D. Raj Reddy, a computer scientist at Pittsburgh’s Carnegie-Mellon University, fears that universally available microcomputers could turn into formidable weapons. Among other things, says Reddy, sophisticated computers in the wrong hands could begin subverting a society by tampering with people’s relationships with their own computers—instructing the other computers to cut off telephone, bank and other services, for example.
Magazine
An early prediction of DDoS (Distributed Denial of Service), viruses and worms like Stuxnet. As stated, without further citation, in 'The Age of Miracle Chips', Time (20 Feb 1978), 44. The article introduces a special section on 'The Computer Society.' Please contact Webmaster if you know a primary source.
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A lecturer should … give them [the audience] full reason to believe that all his powers have been exerted for their pleasure and instruction.
In Letter to his friend Benjamin Abbott (11 Jun 1813), collected in Bence Jones, Life and Letters of Faraday, Vol. 1, 73. Faraday was age 21, less than a year since completing his bookbinder apprenticeship, and had decided upon “giving up trade and taking to science.” From several letters, various opinions about lecturing were gathered in an article, 'Faraday on Scientific Lecturing', Norman Locker (ed.), Nature (23 Oct 1873), 8, 524.
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All living things need their instruction manual (even nonliving things like viruses) and that is all they need, carried in one very small suitcase.
In The Center of Life: A Natural History of the Cell (1977, 1978), 8.
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Among all the liberal arts, the first is logic, and specifically that part of logic which gives initial instruction about words. … [T]he word “logic” has a broad meaning, and is not restricted exclusively to the science of argumentative reasoning. [It includes] Grammar [which] is “the science of speaking and writing correctly—the starting point of all liberal studies.”
In John of Salisbury and Daniel D. McGarry (trans.), 'Whence grammar gets its name', The Metalogicon (2009), 37. It is footnoted: Isidore, Etym., i, 5, §1.
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As a child, I received instruction both in the Bible and in the Talmud. I am a Jew, but I am enthralled by the luminous figure of the Nazarene.
…...
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But indeed, the English generally have been very stationary in latter times, and the French, on the contrary, so active and successful, particularly in preparing elementary books, in the mathematical and natural sciences, that those who wish for instruction, without caring from what nation they get it, resort universally to the latter language.
Letter (29 Jan 1824) to Patrick K. Rodgers. Collected in Andrew A. Lipscomb (ed.), The Writings of Thomas Jefferson (1904), Vol. 16, 2.
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Each and every loss becomes an instance of ultimate tragedy–something that once was, but shall never be known to us. The hump of the giant deer–as a nonfossilizable item of soft anatomy–should have fallen into the maw of erased history. But our ancestors provided a wondrous rescue, and we should rejoice mightily. Every new item can instruct us; every unexpected object possesses beauty for its own sake; every rescue from history’s great shredding machine is–and I don’t know how else to say this–a holy act of salvation for a bit of totality.
…...
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Education is like a diamond with many facets: It includes the basic mastery of numbers and letters that give us access to the treasury of human knowledge, accumulated and refined through the ages; it includes technical and vocational training as well as instruction in science, higher mathematics, and humane letters.
In Proclamation 5463, for Education Day (19 Apr 1986). Collected in Public Papers of the Presidents of the United States: Ronald Reagan, 1986 (1988), 490.
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Education is not the piling on of learning, information, data, facts, skills, or abilities—that's training or instruction—but is rather making visible what is hidden as a seed.
The Education of the Heart (1996), Introduction, 3.
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Engineering is the art or science of utilizing, directing or instructing others in the utilization of the principles, forces, properties and substance of nature in the production, manufacture, construction, operation and use of things ... or of means, methods, machines, devices and structures ...
(1920}
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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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Every physical fact, every expression of nature, every feature of the earth, the work of any and all of those agents which make the face of the world what it is, and as we see it, is interesting and instructive. Until we get hold of a group of physical facts, we do not know what practical bearings they may have, though right-minded men know that they contain many precious jewels, which science, or the expert hand of philosophy will not fail top bring out, polished, and bright, and beautifully adapted to man's purposes.
In The Physical Geography of the Sea (1855), 209-210. Maury was in particular referring to the potential use of deep-sea soundings.
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He that could teach mathematics well, would not be a bad teacher in any of [physics, chemistry, biology or psychology] unless by the accident of total inaptitude for experimental illustration; while the mere experimentalist is likely to fall into the error of missing the essential condition of science as reasoned truth; not to speak of the danger of making the instruction an affair of sensation, glitter, or pyrotechnic show.
In Education as a Science (1879), 298.
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He that would learn by experiments, ought to proceed from particulars to generals; but the method of instructing academically, proceeds from generals to particulars
As quoted in Thomas Steele Hall, A Source Book in Animal Biology (1951), 486.
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I am particularly fond of (Emmanuel Mendes da Costa’s) Natural History of Fossils because treatise, more than any other work written in English, records a short episode expressing one of the grand false starts in the history of natural science–and nothing can be quite so informative and instructive as a juicy mistake.
…...
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I do present you with a man of mine [Hortensio]
Cunning in music and the mathematics
To instruct her fully in those sciences.
In The Taming of the Shrew (1594), Act 2, Scene 1, in The Plays of William Shakespeare (1813), 242.
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I really see no harm which can come of giving our children a little knowledge of physiology. ... The instruction must be real, based upon observation, eked out by good explanatory diagrams and models, and conveyed by a teacher whose own knowledge has been acquired by a study of the facts; and not the mere catechismal parrot-work which too often usurps the place of elementary teaching.
Science and Culture (1882), 92.
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I should object to any experimentation which can justly be called painful, for the purpose of elementary instruction ... [but I regret] a condition of the law which permits a boy to troll for pike, or set lines with live frog bait, for idle amusement; and, at the same time, lays the teacher of that boy open to the penalty of fine and imprisonment, if he uses the same animal for the purpose of exhibiting one of the most beautiful and instructive of physiological spectacles, the circulation in the web of the foot. ... [Maybe the frog is] inconvenienced by being wrapped up in a wet rag, and having his toes tied out ... But you must not inflict the least pain on a vertebrated animal for scientific purposes (though you may do a good deal in that way for gain or for sport) without due licence of the Secretary of State for the Home Department, granted under the authority of the Vivisection Act.
... [Yet, in] 1877, two persons may be charged with cruelty to animals. One has impaled a frog, and suffered the creature to writhe about in that condition for hours; the other has pained the animal no more than one of us would be pained by tying strings round his fingers, and keeping him in the position of a hydropathic patient. The first offender says, 'I did it because I find fishing very amusing,' and the magistrate bids him depart in peace; nay, probably wishes him good sport. The second pleads, 'I wanted to impress a scientific truth, with a distinctness attainable in no other way, on the minds of my scholars,' and the magistrate fines him five pounds.
I cannot but think that this is an anomalous and not wholly creditable state of things.
'On Elementary Instruction in Physiology'. Science and Culture (1882), 92.
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I wish they would use English instead of Greek words. When I want to know why a leaf is green, they tell me it is coloured by “chlorophyll,” which at first sounds very instructive; but if they would only say plainly that a leaf is coloured green by a thing which is called “green leaf,” we should see more precisely how far we had got.
The word “chlorophyll” is formed from the Greek words for “green” “leaf.” In The Queen of the Air: a Study of the Greek Myths of Cloud and Storm (1869, 1889), 51.
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In addition to instructing them in the holy Scriptures, they also taught their pupils poetry, astronomy, and the calculation of the church calendar.
Bede
Referring to the teaching methods of Theodore, Archbishop of Canterbury, and Hadrian, abbot of Canterbury (A.D. 669).
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In Science the paramount appeal is to the Intellect—its purpose being instruction; in Art, the paramount appeal is to the Emotions—its purpose being pleasure.
In The Principles of Success in Literature (1901), 63.
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In this country, science is almost exclusively prosecuted by those engaged in the laborious and exhaustive employment of imparting instruction. Science among us brings comparatively little emolument and is accompanied with but little honor.
In Letter (3 Feb 1873) to the Committee of Arrangements, in Proceedings of the Farewell Banquet to Professor Tyndall (4 Feb 1873), 19. Reprinted as 'On the Importance of the Cultivation of Science', The Popular Science Monthly (1873), Vol. 2, 646.
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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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It is easier to believe than to be scientifically instructed.
In The Conduct of the Understanding (1794, 1801), 58.
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It is possible to read books on Natural History with intelligence and profit, and even to make good observations, without a scientific groundwork of biological instruction; and it is possible to arrive at empirical facts of hygiene and medical treatment without any physiological instruction. But in all three cases the absence of a scientific basis will render the knowledge fragmentary and incomplete; and this ought to deter every one from offering an opinion on debatable questions which pass beyond the limit of subjective observations. The psychologist who has not prepared himself by a study of the organism has no more right to be heard on the genesis of the psychical states, or of the relations between body and mind, than one of the laity has a right to be heard on a question of medical treatment.
The Physical Basis of Mind (1877), 4.
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It is rigid dogma that destroys truth; and, please notice, my emphasis is not on the dogma, but on the rigidity. When men say of any question, “This is all there is to be known or said of the subject; investigation ends here,” that is death. It may be that the mischief comes not from the thinker but for the use made of his thinking by late-comers. Aristotle, for example, gave us our scientific technique … yet his logical propositions, his instruction in sound reasoning which was bequeathed to Europe, are valid only within the limited framework of formal logic, and, as used in Europe, they stultified the minds of whole generations of mediaeval Schoolmen. Aristotle invented science, but destroyed philosophy.
Dialogues of Alfred North Whitehead, as recorded by Lucien Price (1954, 2001), 165.
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It seems to me, he says, that the test of “Do we or not understand a particular subject in physics?” is, “Can we make a mechanical model of it?” I have an immense admiration for Maxwell’s model of electromagnetic induction. He makes a model that does all the wonderful things that electricity docs in inducing currents, etc., and there can be no doubt that a mechanical model of that kind is immensely instructive and is a step towards a definite mechanical theory of electromagnetism.
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), 132. (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), 54-55.
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Isaac Asimov quote It’s the bees and the flowers.
Macro photo of bee by Forest Wander (cc by-sa 2.0) (source)
I’m tired of that stupid phrase, “the birds and the bees” which is supposed to represent “the facts of life” or the beginnings of the sex instruction of the young. … Well for heaven’s sake, has anyone ever tried to explain sex by talking about the birds and the bees? What have the birds and the bees to do with it? IT’S THE BEES AND THE FLOWERS. Will you get that through your head? IT’S THE BEES AND THE FLOWERS. The bee travels to one flower and picks up pollen from the stamens. The pollen contains the male sex cells of the plant. The bee then travels to another flower (of the same species) and the pollen brushes off onto the pistil, which contains the female sex cells of the plant. … Now in the human being … we don’t rely on bees to do it for us.
From Isaac Asimov’s letter in 'Hue and Cry' letter column in magazine, James L. Quinn (ed.), IF: Worlds of Science Fiction (Dec 1957), 7, No. 6, 119
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Mere instruction to memorise data is empty. The attempt to enforce conventional mediocrity on the young is criminal.
As quoted, without citation, in Ronald William Clark, The Life of Bertrand Russell (1976), 423.
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Money. It has such an inherent power to run itself clear of taint that human ingenuity cannot devise the means of making it work permanent mischief, any more than means can be found of torturing people beyond what they can bear. Even if a man founds a College of Technical Instruction, the chances are ten to one that no one will be taught anything and that it will have been practically left to a number of excellent professors who will know very well what to do with it.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.
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Now if we want poets to interpret physical science as Milton and Shelley did (Shelley and Keats were the last English poets who were at all up-to-date in their chemical knowledge), we must see that our possible poets are instructed, as their masters were, in science and economics.
In Daedalus or Science and the Future (1924). Reprinted in Haldane's Daedalus Revisited (1995), 31.
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Recently, we’ve reported that we have made all five bases, the compounds that spell out the instructions for all life and are a part of the nucleic acids, RNA and DNA. Not only did we make all five bases but we found them in a meteorite! So that these two things coming together really assure us that the molecules necessary for life can be found in the absence of life. This was the biggest stumbling block.
In Space World (1985), 5, 25.
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The errors of a wise man are literally more instructive than the truths of a fool. The wise man travels in lofty, far-seeing regions; the fool in low-lying, high-fenced lanes; retracing the footsteps of the former, to discover where he diviated, whole provinces of the universe are laid open to us; in the path of the latter, granting even that he has not deviated at all, little is laid open to us but two wheel-ruts and two hedges.
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 425:26.
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The fact is that up to now the free society has not been good for the intellectual. It has neither accorded him a superior status to sustain his confidence nor made it easy for him to acquire an unquestioned sense of social usefulness. For he derives his sense of usefulness mainly from directing, instructing, and planning-from minding other people’s business-and is bound to feel superfluous and neglected where people believe themselves competent to manage individual and communal affairs, and are impatient of supervision and regulation. A free society is as much a threat to the intellectual’s sense of worth as an automated economy is to the workingman’s sense of worth. Any social order that can function with a minimum of leadership will be anathema to the intellectual.
In 'Concerning Individual Freedom', The Ordeal of Change (1963), 141.
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The Hypotenuse has a square on,
which is equal Pythagoras instructed,
to the sum of the squares on the other two sides
If a triangle is cleverly constructed.
From lyrics of song Sod’s Law.
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The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adhering to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depends upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.
Address to the University of Cambridge upon being elected Lucasian Professor of Mathematics (14 Mar 1664). In Mathematical Lectures (1734), xxviii.
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The science of constructing a commonwealth, or renovating it, or reforming it, is, like every other experimental science, not to be taught a priori. Nor is it a short experience that can instruct us in that practical science, because the real effects of moral causes are not always immediate.
Reflections on the Revolution in France, p. 53, ed. Pocock (1790).
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The universe came into being in a big bang, before which, Einstein’s theory instructs us, there was no before. Not only particles and fields of force had to come into being at the big bang, but the laws of physics themselves, and this by a process as higgledy-piggledy as genetic mutation or the second law of thermodynamics.
In 'The Computer and the Universe', International Journal of Theoretical Physics (1982), 21, 565.
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The wise are instructed by reason; ordinary minds by experience; the stupid, by necessity; and brutes by instinct.
In Charles Simmons, A Laconic Manual and Brief Remarker (1852), 273.
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Those who intend to practise Midwifery, ought first of all to make themselves masters of anatomy, and acquire a competent knowledge in surgery and physic; because of their connections with the obstetric art, if not always, at least in many cases. He ought to take the best opportunities he can find of being well instructed; and of practising under a master, before he attempts to deliver by himself. ... He should also embrace every occasion of being present at real labours, ... he will assist the poor as well as the rich, behaving always with charity and compassion.
In A Treatise on the Theory and Practice of Midwifery (1766), 440-441.
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To the manufacturer, chemistry has lately become fruitful of instruction and assistance. In the arts of brewing, tanning, dying, and bleaching, its doctrines are important guides. In making soap, glass, pottery, and all metallic wares, its principles are daily applied, and are capable of a still more useful application, as they become better understood.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer, and mercantile community (1827), 9.
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What more powerful form of study of mankind could there be than to read our own instruction book?
From White House Announcement of the Completion of the First Survey of the Entire Human Genome Project, broadcast on the day of the publication of the first draft of the human genome. Quoted in transcript on the National Archives, Clinton White House web site, 'Text of Remarks on the Completion of the First Survey of the Entire Human Genome Project' (26 Jun 2000).
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What politicians do not understand is that [Ian] Wilmut discovered not so much a technical trick as a new law of nature. We now know that an adult mammalian cell can fire up all the dormant genetic instructions that shut down as it divides and specializes and ages, and thus can become a source of new life. You can outlaw technique; you cannot repeal biology.
Writing after Wilmut's successful cloning of the sheep, Dolly, that research on the cloning of human beings cannot be suppressed.
'A Special Report on Cloning'. Charles Krauthammer in Time (10 Mar 1997).
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When we seek a textbook case for the proper operation of science, the correction of certain error offers far more promise than the establishment of probable truth. Confirmed hunches, of course, are more upbeat than discredited hypotheses. Since the worst traditions of ‘popular’ writing falsely equate instruction with sweetness and light, our promotional literature abounds with insipid tales in the heroic mode, although tough stories of disappointment and loss give deeper insight into a methodology that the celebrated philosopher Karl Popper once labeled as ‘conjecture and refutation.’
…...
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When you wish to instruct, be brief; that men's minds take in quickly what you say, learn its lesson, and retain it faithfully. Every word that is unnecessary only pours over the side of a brimming mind.
In Norbert Guterman, The Anchor Book of Latin Quotations (1990), 193.
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Young men, … Live in the serene peace of laboratories and libraries. Say to yourselves first: “What have I done for my instruction?” and, as you gradually advance, “What have I done for my country?”
Acceptance speech (27 Dec 1892) when awarded a 70th birthday commemorative medal by the Academy of Sciences in the great theatre of the Sorbonne, as translated in René Vallery-Radot and Mrs R.L. Devonshire (trans.), The Life of Pasteur (1902), Vol. 2, 297-298. Pasteur addressed an audience that included “deep masses of students” and “boys from the lycées.”
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[Decoding the human genome sequence] is the most significant undertaking that we have mounted so far in an organized way in all of science. I believe that reading our blueprints, cataloguing our own instruction book, will be judged by history as more significant than even splitting the atom or going to the moon.
Interview (23 May 1998), 'Cracking the Code to Life', Academy of Achievement web site.
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[The object of education is] to train the mind to ascertain the sequence of a particular conclusion from certain premises, to detect a fallacy, to correct undue generalisation, to prevent the growth of mistakes in reasoning. Everything in these must depend on the spirit and the manner in which the instruction itself is conveyed and honoured. If you teach scientific knowledge without honouring scientific knowledge as it is applied, you do more harm than good. I do think that the study of natural science is so glorious a school for the mind, that with the laws impressed on all these things by the Creator, and the wonderful unity and stability of matter, and the forces of matter, there cannot be a better school for the education of the mind.
Giving Evidence (18 Nov 1862) to the Public Schools Commission. As quoted in John L. Lewis, 125 Years: The Physical Society & The Institute of Physics (1999), 168-169.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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Sophie Germain
Gertrude Elion
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James Chadwick
Marcel Proust
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Carl Gauss
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- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
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Bible
Thomas Huxley
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Bertrand Russell
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- 70 -
Samuel Morse
John Wheeler
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Robert Fulton
Pierre Laplace
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Thomas Edison
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Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
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Martin Fischer
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Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
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John Dalton
- 40 -
Pierre Fermat
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JJ Thomson
Thomas Kuhn
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Archimedes
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- 30 -
Andreas Vesalius
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Richard Feynman
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- 20 -
Carl Sagan
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- 10 -
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