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Home > Category Index for Science Quotations > Category Index R > Category: Rule

Rule Quotes (294 quotes)

Air Chief Marshal Harris [objecting to a change in strategy recommended by statisticians]: Are we fighting this war with weapons or the slide rule?
Churchill [after puffing on his cigar]: That's a good idea. Let's try the slide rule.
During World War II, Britain lost the advantage when enemy U-boats began listening in to the aircraft radar, were forewarned, and would dive. U-boat sinkings fell to zero. Physicist Patrick S. Blackett with his Operational Research colleagues came up with a solution. Concentrate sufficient aircraft in certain areas, causing the subs to dive so frequently their air supply and batteries were exhausted, forcing them to remain on the surface and be vulnerable to attack. The strategy required diverting several squadrons from Bomber Command to Coastal Command. “Bomber” Harris voiced his objection to Churchill, who made the right choice, proved by successful results. As described by R.V. Jones, 'Churchill and Science', in Robert Blake and Wm. Roger Louis (eds.), Churchill (1996), 437.
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Dilbert: Maybe I’m unlucky in love because I’m so knowledgeable about science that I intimidate people. Their intimidation becomes low self-esteem, then they reject me to protect their egos.
Dogbert: Occam’s Razor.
Dilbert: What is “Occam's Razor”?
Dogbert: A guy named Occam had a rule about the world. Basically he said that when there are multiple explanations for something the simplest explanation is usually correct. The simplest explanation for your poor love life is that you’re immensely unattractive.
Dilbert: Maybe Occam had another rule that specifically exempted this situation, but his house burned down with all his notes. Then he forgot.
Dogbert: Occam’s Razor.
Dilbert: I’m an idiot.
Dogbert: I don’t think we can rule it out at this point.
Dilbert comic strip (11 Jul 1993).
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En un mot, pour tirer la loi de l'expérience, if faut généraliser; c'est une nécessité qui s'impose à l'observateur le plus circonspect.
In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 186.
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Hoc age ['do this'] is the great rule, whether you are serious or merry; whether ... learning science or duty from a folio, or floating on the Thames. Intentions must be gathered from acts.
In James Boswell, The Life of Samuel Johnson (1821), 139.
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Les faits scientifiques, et à fortiori, les lois sont l’œuvre artificielle du savant ; la science ne peut donc rien nous apprendre de la vérité, elle ne peut nous servir que de règle d’action.
The facts of science and, à fortiori, its laws are the artificial work of the scientist; science therefore can teach us nothing of the truth; it can only serve us as rule of action.
In La Valeur de la Science (1904), 214, translated by George Bruce Halsted, in The Value of Science (1907), 112.
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M.A. Rosanoff: Mr. Edison, please tell me what laboratory rules you want me to observe.
Edison: Hell! There ain’t no rules around here! We’re trying to accomplish somep’n.
In Martin André Rosanoff, 'Edison in His Laboratory', Harper’s Magazine (Sep 1932), 403.
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[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.
Quoted, without source, in The Grolier Library of Science Biographies (1996), Vol. 3, 191.
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A chemical compound once formed would persist for ever, if no alteration took place in surrounding conditions. But to the student of Life the aspect of nature is reversed. Here, incessant, and, so far as we know, spontaneous change is the rule, rest the exception—the anomaly to be accounted for. Living things have no inertia and tend to no equilibrium.
From Address (22 Jul 1854) delivered at St. Martin’s Hall, published as a pamphlet (1854), 7, and collected in 'Educational Value of Natural History Sciences', Lay Sermons, Addresses, and Reviews (1870), 75.
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A good teacher must know the rules; a good pupil, the exceptions.
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
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A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
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A Law of Nature, (Lex Naturalis) is a Precept, or general Rule, found out by Reason, by which a man is forbidden to do, that, which is destructive of his life, or taketh away the means of preserving the same; and to omit, that, by which he thinketh it may be best preserved
Leviathan, ch. 14 (1651).
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A machine is not a genie, it does not work by magic, it does not possess a will, and … nothing comes out which has not been put in, barring of course, an infrequent case of malfunctioning. … The “intentions” which the machine seems to manifest are the intentions of the human programmer, as specified in advance, or they are subsidiary intentions derived from these, following rules specified by the programmer. … The machine will not and cannot do any of these things until it has been instructed as to how to proceed. ... To believe otherwise is either to believe in magic or to believe that the existence of man’s will is an illusion and that man’s actions are as mechanical as the machine’s.
In Science, September 16, 1960.
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A man, as a general rule, owes very little to what he is born with—a man is what he makes of himself.
In Orison Swett Marden, 'Bell Telephone Talk: Hints on Success by Alexander G. Bell', How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 39.
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After that, I thought about what a proposition generally needs in order to be true and certain because, since I had just found one that I knew was such, I thought I should also know what this certainty consists in. Having noticed that there is nothing at all in the proposition “I think, therefore I am” [cogito ergo sum] which convinces me that I speak the truth, apart from the fact that I see very clearly that one has to exist in order to think, I judged that I could adopt as a general rule that those things we conceive very clearly and distinctly are all true. The only outstanding difficulty is in recognizing which ones we conceive distinctly.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 4, 25.
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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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Although with the majority of those who study and practice in these capacities [engineers, builders, surveyors, geographers, navigators, hydrographers, astronomers], secondhand acquirements, trite formulas, and appropriate tables are sufficient for ordinary purposes, yet these trite formulas and familiar rules were originally or gradually deduced from the profound investigations of the most gifted minds, from the dawn of science to the present day. … The further developments of the science, with its possible applications to larger purposes of human utility and grander theoretical generalizations, is an achievement reserved for a few of the choicest spirits, touched from time to time by Heaven to these highest issues. The intellectual world is filled with latent and undiscovered truth as the material world is filled with latent electricity.
In Orations and Speeches, Vol. 3 (1870), 513.
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Although [Charles Darwin] would patiently go on repeating experiments where there was any good to be gained, he could not endure having to repeat an experiment which ought, if complete care had been taken, to have told its story at first—and this gave him a continual anxiety that the experiment should not be wasted; he felt the experiment to be sacred, however slight a one it was. He wished to learn as much as possible from an experiment, so that he did not confine himself to observing the single point to which the experiment was directed, and his power of seeing a number of other things was wonderful. ... Any experiment done was to be of some use, and ... strongly he urged the necessity of keeping the notes of experiments which failed, and to this rule he always adhered.
In Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of his Published Letters (1908), 92.
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Amid all the revolutions of the globe, the economy of Nature has been uniform, ... and her laws are the only things that have resisted the general movement. The rivers and the rocks, the seas and the continents, have been changed in all their parts; but the laws which direct those changes, and the rules to which they are subject, have remained invariably the same.
Illustrations of the Huttonian Theory of the Earth (1802) collected in The Works of John Playfair (1822), Vol. 1, 415
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An autocratic system of coercion, in my opinion, soon degenerates. For force always attracts men of low morality, and I believe it to be an invariable rule that tyrants of genius are succeeded by scoundrels. For this reason I have always been passionately opposed to systems such as we see in Italy and Russia to-day.
In The World As I See It (1934), 240.
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An essential [of an inventor] is a logical mind that sees analogies. No! No! not mathematical. No man of a mathematical habit of mind ever invented anything that amounted to much. He hasn’t the imagination to do it. He sticks too close to the rules, and to the things he is mathematically sure he knows, to create anything new.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
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And as to the faculties of the mind, setting aside the arts grounded upon words, and especially that skill of proceeding upon generall, and infallible rules, called Science; which very few have, and but in few things; as being not a native faculty, born within us; nor attained, (as Prudence,) while we look after somewhat else.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 13, 183.
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And from true lordship it follows that the true God is living, intelligent, and powerful; from the other perfections, that he is supreme, or supremely perfect. He is eternal and infinite, omnipotent and omniscient; that is, he endures from eternity to eternity; and he is present from infinity to infinity; he rules all things, and he knows all things that happen or can happen.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), General Scholium, 941.
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And God made two great lights, great for their use
To man, the greater to have rule by day, The less by night…
Paradise Lost: A poem, in Twelve Books (1750), Book 7, 36-37.
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And God said, Let there be lights in the firmament of the heavens to separate the day from the night; and let them be for signs and for seasons and for days and years, and let them be lights in the firmament of the heavens to give light upon the earth.” And it was so. And God made the two great lights, the greater light to rule the day, and the lesser light to rule the night; he made the stars also.
Bible
(circa 725 B.C.)
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And there are absolutely no judgments (or rules) in Mechanics which do not also pertain to Physics, of which Mechanics is a part or type: and it is as natural for a clock, composed of wheels of a certain kind, to indicate the hours, as for a tree, grown from a certain kind of seed, to produce the corresponding fruit. Accordingly, just as when those who are accustomed to considering automata know the use of some machine and see some of its parts, they easily conjecture from this how the other parts which they do not see are made: so, from the perceptible effects and parts of natural bodies, I have attempted to investigate the nature of their causes and of their imperceptible parts.
Principles of Philosophy (1644), trans. V. R. and R. P. Miller (1983), 285-6.
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Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped onto the other (the computer).
Machinery of the Mind: Inside the New Science of Artificial Intelligence (1986), 250.
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As a general rule, the most successful man in life is the man who has the best information.
Endymion (1880), 156.
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As a rule, software systems do not work well until they have been used, and have failed repeatedly, in real applications.
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As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.
At age 36.
"Proceedings of the Royal Society of Edinburgh (1939), 59 122. In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 109-110. This quote is also on this web page in a longer version that begins, “Pure mathematics and physics are… ”.
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Astronomy affords the most extensive example of the connection of physical sciences. In it are combined the sciences of number and quantity, or rest and motion. In it we perceive the operation of a force which is mixed up with everything that exists in the heavens or on earth; which pervades every atom, rules the motion of animate and inanimate beings, and is a sensible in the descent of the rain-drop as in the falls of Niagara; in the weight of the air, as in the periods of the moon.
On the Connexion of the Physical Sciences (1858), 1.
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Being also in accord with Goethe that discoveries are made by the age and not by the individual, I should consider the instances to be exceedingly rare of men who can be said to be living before their age, and to be the repository of knowledge quite foreign to the thought of the time. The rule is that a number of persons are employed at a particular piece of work, but one being a few steps in advance of the others is able to crown the edifice with his name, or, having the ability to generalise already known facts, may become in time to be regarded as their originator. Therefore it is that one name is remembered whilst those of coequals have long been buried in obscurity.
In Historical Notes on Bright's Disease, Addison's Disease, and Hodgkin's Disease', Guy's Hospital Reports (1877), 22, 259-260.
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By a generative grammar I mean simply a system of rules that in some explicit and well-defined way assigns structural descriptions to sentences. Obviously, every speaker of a language has mastered and internalized a generative grammar that expresses his knowledge of his language. This is not to say that he is aware of the rules of the grammar or even that he can become aware of them, or that his statements about his intuitive knowledge of the language are necessarily accurate.
Aspects of the Theory of Syntax (1965), 8.
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By virtue of the way it has organized its technological base, contemporary industrial society tends to be totalitarian. For 'totalitarian' is not only a terroristic political coordination of society, but also a non-terroristic economic-technical coordination which operates through the manipulation of needs by vested interests. It thus precludes the emergence of an effective opposition against the whole. Not only a specific form of government or party rule makes for totalitarianism, but also a specific system of production and distribution which may well be compatible with a 'pluralism' of parties, newspapers, 'countervailing powers,' etc.
One Dimensional Man (1964), 3.
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Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and confirmed. They are no exception to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science.
On Growth and Form (1917), 7-8.
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Civilization is hooped together, brought
Under a rule, under the semblance of peace
By manifold illusion.
The Collected Poems of W. B. Yeats (1951), 287.
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Consider the very roots of our ability to discern truth. Above all (or perhaps I should say “underneath all”), common sense is what we depend on—that crazily elusive, ubiquitous faculty we all have to some degree or other. … If we apply common sense to itself over and over again, we wind up building a skyscraper. The ground floor of the structure is the ordinary common sense we all have, and the rules for building news floors are implicit in the ground floor itself. However, working it all out is a gigantic task, and the result is a structure that transcends mere common sense.
In Metamagical Themas: Questing for the Essence of Mind and Pattern (1985), 93–94.
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Creatures that by a rule in nature teach
The act of order to a peopled kingdom.
They have a king and officers of sorts;
Where some, like magistrates, correct at home,
Others, like merchants, venture trade abroad,
Others, like soldiers, armed in their stings,
Make boot upon the summer's velvet buds;
Which pillage they with merry march bring home
To the tent-royal of their emperor.
Who, busied in his majesty, surveys
The singing masons building roofs of gold;
The civil citizens kneading up the honey;
The poor mechanic porters crowding
Their heavy burdens at his narrow gate;
The sad-eyed justice, with his surly hum,
Delivering o'er to executors pale
The lazy yawning drone.
Henry V (1599), I, ii.
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Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
(1906). As quoted “in free translation” in Benoit B. Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 7.
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Debate is an art form. It is about the winning of arguments. It is not about the discovery of truth. There are certain rules and procedures to debate that really have nothing to do with establishing fact–which creationists have mastered. Some of those rules are: never say anything positive about your own position because it can be attacked, but chip away at what appear to be the weaknesses in your opponent’s position. They are good at that. I don’t think I could beat the creationists at debate. I can tie them. But in courtrooms they are terrible, because in courtrooms you cannot give speeches. In a courtroom you have to answer direct questions about the positive status of your belief. We destroyed them in Arkansas. On the second day of the two-week trial we had our victory party!
…...
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Dewar’s rule in his laboratory was as absolute as that of a Pharaoh, and he showed deference to no one except the ghost of Faraday whom he met occasionally all night in the gallery behind the lecture room.
In The Quest for Absolute Zero (1945, 1966), 73.
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Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomed mine
Unweave a rainbow.
Lamia 1820, II, lines 229-37. In John Barnard (ed.), John Keats. The Complete Poems (1973), 431.
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During the long ages of class rule, which are just beginning to cease, only one form of sovereignty has been assigned to all men—that, namely, over all women. Upon these feeble and inferior companions all men were permitted to avenge the indignities they suffered from so many men to whom they were forced to submit.
In “Common Sense” Applied to Woman Suffrage (1894), 180.
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During the time that [Karl] Landsteiner gave me an education in the field of imununology, I discovered that he and I were thinking about the serologic problem in very different ways. He would ask, What do these experiments force us to believe about the nature of the world? I would ask, What is the most. simple and general picture of the world that we can formulate that is not ruled by these experiments? I realized that medical and biological investigators were not attacking their problems the same way that theoretical physicists do, the way I had been in the habit of doing.
‘Molecular Disease’, Pfizer Spectrum (1958), 6:9, 234.
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Each of us has read somewhere that in New Guinea pidgin the word for 'piano' is (I use English spelling) 'this fellow you hit teeth belonging to him he squeal all same pig'. I am inclined to doubt whether this expression is authentic; it looks just like the kind of thing a visitor to the Islands would facetiously invent. But I accept 'cut grass belong head belong me' for 'haircut' as genuine... Such phrases seem very funny to us, and make us feel very superior to the ignorant foreigners who use long winded expressions for simple matters. And then it is our turn to name quite a simple thing, a small uncomplicated molecule consisting of nothing more than a measly 11 carbons, seven hydrogens, one nitrogen and six oxygens. We sharpen our pencils, consult our rule books and at last come up with 3-[(1, 3- dihydro-1, 3-dioxo-2H-isoindol-2-yl) oxy]-3-oxopropanoic acid. A name like that could drive any self-respecting Papuan to piano-playing.
The Chemist's English (1990), 3rd Edition, 57.
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Each problem that I solved became a rule which served afterwards to solve other problems.
In Discours de la Méthode (1637), collected in Œuvres, vol. VI, 20-21. As translated and cited in epigraph, George Polya, Mathematical Discovery (1981), 1.
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Ethnologists regard man as the primitive element of tribes, races, and peoples. The anthropologist looks at him as a member of the fauna of the globe, belonging to a zoölogical classification, and subject to the same laws as the rest of the animal kingdom. To study him from the last point of view only would be to lose sight of some of his most interesting and practical relations; but to be confined to the ethnologist’s views is to set aside the scientific rule which requires us to proceed from the simple to the compound, from the known to the unknown, from the material and organic fact to the functional phenomenon.
'Paul Broca and the French School of Anthropology'. Lecture delivered in the National Museum, Washington, D.C., 15 April 1882, by Dr. Robert Fletcher. In The Saturday Lectures (1882), 118.
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Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?
A Brief History of Time (1998), 190.
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Events and developments, such as … the Copernican Revolution, … occurred only because some thinkers either decided not to be bound by certain “obvious” methodological rules, or because they unwittingly broke them.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14.
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Every complete set of chromosomes contains the full code; so there are, as a rule, two copies of the latter in the fertilized egg cell, which forms the earliest stage of the future individual. In calling the structure of the chromosome fibres a code-script we mean that the all-penetrating mind, once conceived by Laplace, to which every causal connection lay immediately open, could tell from their structure whether the egg would develop, under suitable conditions, into a black cock or into a speckled hen, into a fly or a maize plant, a rhododendron, a beetle, a mouse or a woman. To which we may add, that the appearances of the egg cells are very often remarkably similar; and even when they are not, as in the case of the comparatively gigantic eggs of birds and reptiles, the difference is not so much in the relevant structures as in the nutritive material which in these cases is added for obvious reasons.
But the term code-script is, of course, too narrow. The chromosome structures are at the same time instrumental in bringing about the development they foreshadow. They are law-code and executive power?or, to use another simile, they are architect's plan and builder’s craft-in one.
In What is Life? : The Physical Aspect of the Living Cell (1944), 20-21.
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Every rule has its limits, and every concept its ambiguities. Most of all is this true in the science of life, where nothing quite corresponds to our ideas; similar ends are reached by varied means, and no causes are simple.
In Internal Factors in Evolution (1965), 13.
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Experiment is the interpreter of nature. Experiments never deceive. It is our judgment which sometimes deceives itself because it expects results which experiment refuses. We must consult experiment, varying the circumstances, until we have deduced general rules, for experiment alone can furnish reliable rules.
In Introductory College Physics by Oswald Blackwood (1939).
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Experiments on ornamental plants undertaken in previous years had proven that, as a rule, hybrids do not represent the form exactly intermediate between the parental strains. Although the intermediate form of some of the more striking traits, such as those relating to shape and size of leaves, pubescence of individual parts, and so forth, is indeed nearly always seen, in other cases one of the two parental traits is so preponderant that it is difficult or quite impossible, to detect the other in the hybrid. The same is true for Pisum hybrids. Each of the seven hybrid traits either resembles so closely one of the two parental traits that the other escapes detection, or is so similar to it that no certain distinction can be made. This is of great importance to the definition and classification of the forms in which the offspring of hybrids appear. In the following discussion those traits that pass into hybrid association entirely or almost entirely unchanged, thus themselves representing the traits of the hybrid, are termed dominating and those that become latent in the association, recessive. The word 'recessive' was chosen because the traits so designated recede or disappear entirely in the hybrids, but reappear unchanged in their progeny, as will be demonstrated later.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 9.
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For a while he [Charles S. Mellen] trampled with impunity on laws human and divine but, as he was obsessed with the delusion that two and two makes five, he fell, at last a victim to the relentless rules of humble Arithmetic.
Remember, O stranger: “Arithmetic is the first of the sciences and the mother of safety.”
In a private letter (29 Sep 1911) to Norman Hapgood, editor of Harper’s Weekly, referenced in Hapgood’s editorial, 'Arithmetic', which was quoted in Hapgood’s Preface to Louis Brandeis, Other People’s Money and How The Bankers Use It (1914), xli. Brandeis was describing Mellen, president of the New Haven Railroad, whom he correctly predicted would resign in the face of reduced dividends caused by his bad financial management. The embedded quote, “Arithmetic…”, is footnoted in Louis D. Brandeis, Letters of Louis D. Brandeis: Volume II, 1907-1912: People's Attorney (1971), 501, citing its source as from a novel by Victor Cherbuliez, Samuel Brohl and Partner (probably 1881 edition), which LDB had transcribed “into his literary notebook at an early age.”
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For since the fabric of the universe is most perfect and the work of a most wise creator, nothing at all takes place in the universe in which some rule of the maximum or minimum does not appear….
From Methodus Inveniendi Uneas Curvas (1744), 1st addition, art. 1, translated as an epigram in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics (1990), Vol. 1, 285.
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For [Richard] Feynman, the essence of the scientific imagination was a powerful and almost painful rule. What scientists create must match reality. It must match what is already known. Scientific creativity is imagination in a straitjacket.
In Genius: The Life and Science of Richard Feynman (1992), 324.
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Four circles to the kissing come,
The smaller are the benter.
The bend is just the inverse of
The distance from the centre.
Though their intrigue left Euclid dumb
There’s now no need for rule of thumb.
Since zero bend’s a dead straight line
And concave bends have minus sign,
The sum of squares of all four bends
Is half the square of their sum.
In poem, 'The Kiss Precise', Nature (20 Jun 1936), 137, 1021, as quoted, cited, explained and illustrated in Martin Gardner, The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001), 139-141.
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From a few basic rules you can generate a cosmos.
In The God Problem: How a Godless Cosmos Creates (2012), 24.
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Gather round while I sing you of Wernher von Braun,
A man whose allegiance
Is ruled by expedience.
Call him a Nazi, he won't even frown.
“ha, Nazi sch-mazi,” says Wernher von Braun.
Stanza from song, 'Wernher von Braun' on record That Was the Year That Was (Jul 1965). Collected in script to musical, Tom Foolery: The Words and Music of Tom Lehrer (1986), 35.
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Genius is supposed to be a power of producing excellences which are put of the reach of the rules of art: a power which no precepts can teach, and which no industry can acquire.
From 'A Discourse Delivered to the Students of the Royal Academy, on the Distribution of Prizes' (10 Dec 1774), in Seven Discourses Delivered in the Royal Academy (1778), 202-203.
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Given any rule, however “fundamental” or “necessary” for science, there are always circumstances when it is advisable not only to ignore the rule, but to adopt its opposite. For example, there are circumstances when it is advisable to introduce, elaborate and defend ad hoc hypotheses, or hypotheses which contradict well-established and generally accepted experimental results, or hypotheses whose content is smaller than the content of the existing and empirically adequate alternative, or self-inconsistent hypotheses, and so on.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14-15.
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Go, wondrous creature, mount where science guides.
Go, measure earth, weigh air, and state the tides;
Instruct the planets in what orbs to run,
Correct old Time, and regulate the sun;
Go, teach Eternal Wisdom how to rule,
Then drop into thyself and be a fool.
Quoted in James Wood Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 125.
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God plays dice with the universe, but they’re loaded dice. And the main objective of physics now is to find out by what rules were they loaded and how can we use them for our own ends.
Quoted in James Gleick, Chaos: Making a New Science (1987), 314.
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Great men are they who see that spiritual is stronger than any material force—that thoughts rule the world.
In James Elliot Cabot (ed.), Emerson's Complete Works: Letters and Social Aims (1883), Vol. 8, 217.
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Gödel proved that the world of pure mathematics is inexhaustible; no finite set of axioms and rules of inference can ever encompass the whole of mathematics; given any finite set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. I hope that an analogous Situation exists in the physical world. If my view of the future is correct, it means that the world of physics and astronomy is also inexhaustible; no matter how far we go into the future, there will always be new things happening, new information coming in, new worlds to explore, a constantly expanding domain of life, consciousness, and memory.
From Lecture 1, 'Philosophy', in a series of four James Arthur Lectures, 'Lectures on Time and its Mysteries' at New York University (Autumn 1978). Printed in 'Time Without End: Physics and Biology in an Open Universe', Reviews of Modern Physics (Jul 1979), 51, 449.
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He rules all things, not as the world soul but as the lord of all. And because of his dominion he is called Lord God Pantokrator. For 'god' is a relative word and has reference to servants, and godhood is the lordship of God, not over his own body as is supposed by those for whom God is the world soul, but over servants. The supreme God is an eternal, infinite, and absolutely perfect being; but a being, however perfect, without dominion is not the Lord God.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), General Scholium, 940-1.
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Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components... the syntactic component of a grammar must specify, for each sentence, a deep structure that determines its semantic interpretation and a surface structure that determines its phonetic interpretation. The first of these is interpreted by the semantic component; the second, by the phonological component.
Aspects of the Theory of Syntax (1965), 15-6.
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Here’s to the crazy ones. The misfits. The rebels. The troublemakers. The round heads in the square holes. The ones who see things differently. They’re not fond of rules. You can quote them. Disagree with them. Glorify or vilify them. But the only thing you can’t do is ignore them. Because they change things. They push the human race forward. And while some may see them as the crazy ones, we see genius. Because the people who are crazy enough to think they can change the world, are the ones who do.
In Apple Computer newspaper advertisement (1997) as quoted and cited in Tad Lathrop and Jim Pettigrew, This Business of Music Marketing and Promotion (1999), 55.
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How could science be any enemy of religion when God commanded man to be a scientist the day He told him to rule the earth and subject it?
In The Life of All Living: the philosophy of life (1929, 1942), 212.
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How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.
Max Planck, Walter Henry Johnston, The Universe in the Light of Modern Physics (1931), 58.
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Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.
From Novum Organum (1620), Book 1, Aphorism 3. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 47.
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Human societies are everywhere complex, for living at peace with ourselves requires a vast multiplicity of rules.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 18.
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I am Freeth, and I have come to apply the phase-rule to the ammonia-soda process.
First words on joining the Brunner-Mond Company in 1907.
W. F. L. Dick, A Hundred Years of Alkali in Cheshire (1973), 38.
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I am not ... asserting that humans are either genial or aggressive by inborn biological necessity. Obviously, both kindness and violence lie with in the bounds of our nature because we perpetrate both, in spades. I only advance a structural claim that social stability rules nearly all the time and must be based on an overwhelmingly predominant (but tragically ignored) frequency of genial acts, and that geniality is therefore our usual and preferred response nearly all the time ... The center of human nature is rooted in ten thousand ordinary acts of kindness that define our days.
…...
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I believed that, instead of the multiplicity of rules that comprise logic, I would have enough in the following four, as long as I made a firm and steadfast resolution never to fail to observe them.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 16.
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I came from Paris in the Spring of 1884, and was brought in intimate contact with him [Thomas Edison]. We experimented day and night, holidays not excepted. His existence was made up of alternate periods of work and sleep in the laboratory. He had no hobby, cared for no sport or amusement of any kind and lived in utter disregard of the most elementary rules of hygiene. There can be no doubt that, if he had not married later a woman of exceptional intelligence, who made it the one object of her life to preserve him, he would have died many years ago from consequences of sheer neglect. So great and uncontrollable was his passion for work.
As quoted in 'Tesla Says Edison Was an Empiricist', The New York Times (19 Oct 1931), 25.
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I concluded that I might take as a general rule the principle that all things which we very clearly and obviously conceive are true: only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive.
In Discours de la Méthode (1637), as translated by J. Veitch, A Discourse on Method (1912), 27.
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I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.
Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.
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I do not forget that Medicine and Veterinary practice are foreign to me. I desire judgment and criticism upon all my contributions. Little tolerant of frivolous or prejudiced contradiction, contemptuous of that ignorant criticism which doubts on principle, I welcome with open arms the militant attack which has a method of doubting and whose rule of conduct has the motto “More light.”
In Louis Pasteur and Harold Clarence Ernst (trans), The Germ Theory and Its Application to Medicine and Surgery, Chap. 12. Reprinted in Charles W. Eliot (ed.), The Harvard Classics: Scientific Papers: Physiology, Medicine, Surgery, Geology (1897, 1910), Vol. 38, 401-402. Cited as read before French Academy of Science (20 Apr 1878), published in Comptes Rendus de l’Académie des Sciences, 84, 1037-43.
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I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
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I had … during many years, followed a golden rule, namely, that whenever a published fact, a new observation or thought came across me, which was opposed by my general results, to make a memorandum of it without fail and at once; for I had found by experience that such facts and thoughts were far more apt to escape from memory than favorable ones.
In The Autobiography of Charles Darwin with original omissions restored, edited by Nora Barlow (1958).
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I often use the analogy of a chess game: one can learn all the rules of chess, but one doesn’t know how to play well…. The present situation in physics is as if we know chess, but we don’t know one or two rules. But in this part of the board where things are in operation, those one or two rules are not operating much and we can get along pretty well without understanding those rules. That’s the way it is, I would say, regarding the phenomena of life, consciousness and so forth.
In Superstrings: A Theory of Everything? by P. C. W. Davies and Julian Brown (1988).
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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 rejoice to see … Euclid honourably shelved or buried “deeper than did ever plummet sound” out of the schoolboys’ reach; morphology introduced into the elements of algebra; projection, correlation, and motion accepted as aids to geometry; the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrines of the imaginary and inconceivable.
From Presidential Address (1869) to the British Association, Exeter, Section A, collected in Collected Mathematical Papers of Lames Joseph Sylvester (1908), Vol. 2, 657. Also in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 93. [Note: “plummet sound” refers to ocean depth measurement (sound) from a ship using a line dropped with a weight (plummet). —Webmaster]
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I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.
Responding to the toast, 'Science!' at the Royal Academy of the Arts in 1932.)
Quoted in Lawrence Badash, 'Ernest Rutherford and Theoretical Physics,' in Robert Kargon and Peter Achinstein (eds.) Kelvin's Baltimore Lectures and Modern Theoretical Physics: Historical and Philosophical Perspectives (1987), 352.
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I think it is the general rule that the originator of a new idea is not the most suitable person to develop it, because his fears of something going wrong are really too strong…
At age 69.
The Development of Quantum Theory (1971). In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 111.
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I wasn’t aware of Chargaff’s rules when he said them, but the effect on me was quite electric because I realized immediately that if you had this sort of scheme that John Griffith was proposing, of adenine being paired with thymine, and guanine being paired with cytosine, then you should get Chargaff’s rules.
I was very excited, but I didn’t actually tell Chargaff because it was something I was doing with John Griffith. There was a sort of musical comedy effect where I forgot what the bases were and I had to go to the library to check, and I went back to John Griffith to find out which places he said. Low and behold, it turned out that John Griffith’s ideas fitted in with Chargaff’s rules!
This was very exciting, and we thought “ah ha!” and we realized—I mean what anyone who is familiar with the history of science ought to realize—that when you have one-to-one ratios, it means things go to together. And how on Earth no one pointed out this simple fact in those years, I don’t know.
From Transcript of documentary by VSM Productions, The DNA Story (1973). As excerpted on web page 'Chargaff’s Rules', Linus Pauling and the Race for DNA on website scarc.library.oregonstate.edu
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I would ... change the accepted rule that the nature of a complex molecule is determined by the nature, quantity, and position of its elementary component parts, by the following statement: the chemical nature of a complex molecule is determined by the nature of its elementary component parts, their quantity and chemical structure.
'On the Chemical Structure of Substances' 1861.
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If ... the past may be no Rule for the future, all Experience becomes useless and can give rise to no Inferences or Conclusions.
An Enquiry Concerning Human Understanding (1748), 65.
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If in a given community unchecked popular rule means unlimited waste and destruction of the natural resources—soil, fertility, waterpower, forests, game, wild-life generally—which by right belong as much to subsequent generations as to the present generation, then it is sure proof that the present generation is not yet really fit for self-control, that it is not yet really fit to exercise the high and responsible privilege of a rule which shall be both by the people and for the people. The term “for the people” must always include the people unborn as well as the people now alive, or the democratic ideal is not realized.
In A Book-Lover's Holidays in the Open (1916), 319.
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If the Commission is to enquire into the conditions “to be observed,” it is to be presumed that they will give the result of their enquiries; or, in other words, that they will lay down, or at least suggest, “rules” and “conditions to be (hereafter) observed” in the construction of bridges, or, in other words, embarrass and shackle the progress of improvement to-morrow by recording and registering as law the prejudices or errors of to-day.
[Objecting to any interference by the State with the freedom of civil engineers in the conduct of their professional work.]
Letter (13 Mar 1848) to the Royal Commission on the Application of Iron in Railway Structures. Collected in The Life of Isambard Kingdom Brunel, Civil Engineer (1870), 487. The above verbatim quote may be the original source of the following statement as seen in books and on the web without citation: “I am opposed to the laying down of rules or conditions to be observed in the construction of bridges lest the progress of improvement tomorrow might be embarrassed or shackled by recording or registering as law the prejudices or errors of today.” Webmaster has not yet found a primary source for his latter form, and suspects it may be a synopsis, rather than a verbatim quote. If you know of such a primary source, please inform Webmaster.
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If there is a lesson in our story it is that the manipulation, according to strictly self-consistent rules, of a set of symbols representing one single aspect of the phenomena may produce correct, verifiable predictions, and yet completely ignore all other aspects whose ensemble constitutes reality.
In 'Epilogue', The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959, 1968), 533.
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If we are ever in doubt what to do, it is a good rule to ask ourselves what we shall wish on the morrow that we had done.
The Pleasures of Life (1887, 2007), 21.
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If we go back to our chequer game, the fundamental laws are rules by which the chequers move. Mathematics may be applied in the complex situation to figure out what in given circumstances is a good move to make. But very little mathematics is needed for the simple fundamental character of the basic laws. They can be simply stated in English for chequers.
In The Character of Physical Law (1965), 36.
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If we lived on a planet where nothing ever changed, there would be little to do. There would be nothing to figure out. There would be no impetus for science. And if we lived in an unpredictable world, where things changed in random or very complex ways, we would not be able to figure things out. But we live in an in-between universe, where things change, but according to patterns, rules, or as we call them, laws of nature. If I throw a stick up in the air, it always falls down. If the sun sets in the west, it always rises again the next morning in the east. And so it becomes possible to figure things out. We can do science, and with it we can improve our lives.
Cosmos (1980, 1985), 32.
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If “Number rules the universe” as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.
In Men of Mathematics (1937), 16.
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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 a library we are surrounded by many hundreds of dear friends, but they are imprisoned by an enchanter in these paper and leathern boxes; and though they know us, and have been waiting two, ten, or twenty centuries for us,—some of them,—and are eager to give us a sign and unbosom themselves, it is the law of their limbo that they must not speak until spoken to; and as the enchanter has dressed them, like battalions of infantry, in coat and jacket of one cut, by the thousand and ten thousand, your chance of hitting on the right one is to be computed by the arithmetical rule of Permutation and Combination,—not a choice out of three caskets, but out of half a million caskets, all alike.
In essay 'Books', collected in Society and Solitude (1870, 1871), 171
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In an objective system … any mingling of knowledge with values is unlawful, forbidden. But [the] … “first commandment” which ensures the foundation of objective knowledge, is not itself objective. It cannot be objective: it is an ethical guideline, a rule for conduct. True knowledge is ignorant of values, but it cannot be grounded elsewhere than upon a value judgment…
In Chance and Necessity (1970), 176.
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In departing from any settled opinion or belief, the variation, the change, the break with custom may come gradually; and the way is usually prepared; but the final break is made, as a rule, by some one individual, … who sees with his own eyes, and with an instinct or genius for truth, escapes from the routine in which his fellows live. But he often pays dearly for his boldness.
In The Harveian Oration, delivered before the Royal College of Physicians of London (18 Oct 1906). Printed in 'The Growth of Truth, as Illustrated in the Discovery of the Circulation of Blood', The Lancet (27 Oct 1906), Vol. 2, Pt. 2, 1114.
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In general … science per se does not increase the destructiveness of war, since, as a rule, it strengthens the defense as much as the attack.
In 'Boredom or Doom in a Scientific World', United Nations World (Sep 1948), Vol. 2, No. 8, 14.
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In my own field, x-ray crystallography, we used to work out the structure of minerals by various dodges which we never bothered to write down, we just used them. Then Linus Pauling came along to the laboratory, saw what we were doing and wrote out what we now call Pauling's Rules. We had all been using Pauling's Rules for about three or four years before Pauling told us what the rules were.
In The Extension of Man (1972), 116.
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In my own view, some advice about what should be known, about what technical education should be acquired, about the intense motivation needed to succeed, and about the carelessness and inclination toward bias that must be avoided is far more useful than all the rules and warnings of theoretical logic.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 6.
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In nature there is no law of refraction, only different cases of refraction. The law of refraction is a concise compendious rule, devised by us for the mental reconstruction of a fact.
In The Science of Mechanics (1893), 485-486.
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In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skilful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them.
'Cosmology', in Arthur Beer (ed.), Vistas in Astronomy (1956), Vol. 2, 1722.
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In science, law is not a rule imposed from without, but an expression of an intrinsic process. The laws of the lawgiver are impotent beside the laws of human nature, as to his disillusion many a lawgiver has discovered.
Attributed. Peter McDonald, In The Oxford Dictionary of Medical Quotations (2004), 2.
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In shades of black and blue the skies do bow as darkness falls the lights go out.
Nature softly immersed in glee as all mankind drifts off to sleep.
Water breathes a sigh of relief now aquatic creatures can do as they please.
Animals whether large or small regain the natural instincts that man has fought.
The moon shines bright he’s happy too people can’t over-ride his rules.
Midnight calms the wounds of the world the break of dawn disperses new hope...
…...
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In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Bionomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 143.
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In the center of everything rules the sun; for who in this most beautiful temple could place this luminary at another better place whence it can light up the whole at once? ... In this arrangement we thus find an admirable harmony of the world, and a constant harmonious connection between the motion and the size of the orbits as could not be found otherwise.
…...
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In the field one has to face a chaos of facts, some of which are so small that they seem insignificant; others loom so large that they are hard to encompass with one synthetic glance. But in this crude form they are not scientific facts at all; they are absolutely elusive, and can be fixed only by interpretation, by seeing them sub specie aeternitatis, by grasping what is essential in them and fixing this. Only laws and gerneralizations are scientific facts, and field work consists only and exclusively in the interpretation of the chaotic social reality, in subordinating it to general rules.
Baloma (1954), 238.
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In the republic of scholarship everybody wants to rule, there are no aldermen there, and that is a bad thing: every general must, so to speak, draw up the plan, stand sentry, sweep out the guardroom and fetch the water; no one wants to work for the good of another.
Aphorism 80 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 56.
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In the world of science different levels of esteem are accorded to different kinds of specialist. Mathematicians have always been eminently respectable, and so are those who deal with hard lifeless theories about what constitutes the physical world: the astronomers, the physicists, the theoretical chemists. But the more closely the scientist interests himself in matters which are of direct human relevance, the lower his social status. The real scum of the scientific world are the engineers and the sociologists and the psychologists. Indeed, if a psychologist wants to rate as a scientist he must study rats, not human beings. In zoology the same rules apply. It is much more respectable to dissect muscle tissues in a laboratory than to observe the behaviour of a living animal in its natural habitat.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
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In things to be seen at once, much variety makes confusion, another vice of beauty. In things that are not seen at once, and have no respect one to another, great variety is commendable, provided this variety transgress not the rules of optics and geometry.
Quoted from the Parentalia in Charles Henry Bellenden Ker, Sir Christopher Wren (1828), 30. Published as a booklet in the series Lives of Eminent Persons (1833) by the Society for the Diffusion of Useful Knowledge. Also in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966).
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In this communication I wish first to show in the simplest case of the hydrogen atom (nonrelativistic and undistorted) that the usual rates for quantization can be replaced by another requirement, in which mention of “whole numbers” no longer occurs. Instead the integers occur in the same natural way as the integers specifying the number of nodes in a vibrating string. The new conception can be generalized, and I believe it touches the deepest meaning of the quantum rules.
'Quantisierung als Eigenwertproblem', Annalen der Physik (1926), 79, 361. Trans. Walter Moore, Schrödinger: Life and Thought (1989), 200-2.
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Induction is the process of generalizing from our known and limited experience, and framing wider rules for the future than we have been able to test fully. At its simplest, then, an induction is a habit or an adaptation—the habit of expecting tomorrow’s weather to be like today’s, the adaptation to the unwritten conventions of community life.
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Invention is an Heroic thing, and plac'd above the reach of a low, and vulgar Genius. It requires an active, a bold, a nimble, a restless mind: a thousand difficulties must be contemn'd with which a mean heart would be broken: many attempts must be made to no purpose: much Treasure must sometimes be scatter'd without any return: much violence, and vigour of thoughts must attend it: some irregularities, and excesses must be granted it, that would hardly be pardon'd by the severe Rules of Prudence.
The History of the Royal Society (1667), 392.
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Is not disease the rule of existence? There is not a lily pad floating on the river but has been riddled by insects. Almost every shrub and tree has its gall, oftentimes esteemed its chief ornament and hardly to be distinguished from the fruit. If misery loves company, misery has company enough. Now, at midsummer, find me a perfect leaf or fruit.
In The Writings of Henry David Thoreau (1893), Vol. 9, 458.
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It has been said that numbers rule the world; but I know that the numbers teach us, whether it is governed well or badly.
English using Google translate from the original German, “Man hat behauptet, die Welt werde durch Zahlen regiert; das aber weiss ich, dass die Zahlen uns belehren, ob sie gut oder schlecht regiert werde,” in J.P. Eckermann, entry for Sonntag den 31 Januar 1830', Gespräche mit Goethe (1836), 180. However, notice that in the original context, the sense of Zahen is “pay.” In the translation by S.M. Fuller, the full context is thus: “Goethe read in the French periodical, the ‘Times,’ an article on the enormous salaries of the English clergy, who receive more than all other ecclesiastics in Christendom put together. ‘It has been maintained,’ said Goethe, ‘that the world is governed by pay; this I know, by examining the distribution of pay, we can find out whether it is well or ill governed.’” In J.P. Eckermann and S.M. Fuller (trans.), 'Sunday, 31st January', Conversations with Goethe in the Last Years of His Life (1839), 336. Yet commonly seen on the web as “It has been said that figures rule the world. Maybe. But I am sure that figures show us whether it is being ruled well or badly.”
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It is a common rule in theoretical physics, one accepted by many physicists, that anything not forbidden by the basic laws of nature must take place.
In 'The Ultimate Speed Limit', Saturday Review of Sciences (8 Jul 1972), 56.
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It is a common rule with primitive people not to waken a sleeper, because his soul is away and might not have time to get back.
In The Golden Bough: A Study in Magic and Religion: Part II: Taboo and the Perils of the Soul (1890, 1911), 39.
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It is a safe rule to apply that, when a mathematical or philosophical author writes with a misty profoundity, he is talking nonsense.
In An Introduction to Mathematics (1911), 227.
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It is also a good rule not to put overmuch confidence in the observational results that are put forward until they are confirmed by theory.
New Pathways in Science (1935), 211.
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It is one thing to say, “Some men shall rule,” quite another to declare, “All men shall rule,” and that in virtue of the most primitive, the most rudimentary attribute they possess, that namely of sex.
In “Common Sense” Applied to Woman Suffrage (1894), 84.
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It is probable that all organisms now alive are descended from one ancestor, for the following reason. Most of our structural molecules are asymmetrical, as shown by the fact that they rotate the plane of polarized light, and often form asymmetrical crystals. But of the two possible types of any such molecule, related to one another like a right and left boot, only one is found throughout living nature. The apparent exceptions to this rule are all small molecules which are not used in the building of the large structures which display the phenomena of life.
In 'The Origin of Life', The Inequality of Man: And Other Essays (1932), 157.
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It is the rule which says that the other rules of scientific procedure must be designed in such a way that they do not protect any statement in science against falsification. (1959)
The Logic of Scientific Discovery: Logik Der Forschung (2002), 33.
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It is … genius which has given motion and progress to society; prevented the ossification of the human heart and brain; and though, in its processes, it may not ever have followed the rules laid down in primers, it has, at least, saved history from being the region of geology, and our present society from being a collection of fossil remains.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 204.
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It need scarcely be pointed out that with such a mechanism complete isolation of portion of a species should result relatively rapidly in specific differentiation, and one that is not necessarily adaptive. The effective inter­group competition leading to adaptive advance may be between species rather than races. Such isolation is doubtless usually geographic in character at the outset but may be clinched by the development of hybrid sterility. The usual difference of the chromosome complements of related species puts the importance of chromosome aberration as an evolutionary process beyond question, but, as I see it, this importance is not in the character differences which they bring (slight in balanced types), but rather in leading to the sterility of hybrids and thus making permanent the isolation of two groups.
How far do the observations of actual species and their subdivisions conform to this picture? This is naturally too large a subject for more than a few suggestions.
That evolution involves non-adaptive differentiation to a large extent at the subspecies and even the species level is indicated by the kinds of differences by which such groups are actually distinguished by systematics. It is only at the subfamily and family levels that clear-cut adaptive differences become the rule. The principal evolutionary mechanism in the origin of species must thus be an essentially nonadaptive one.
In Proceedings of the Sixth International Congress of Genetics: Ithaca, New York, 1932 (1932) Vol. 1, 363-364.
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It surely can be no offence to state, that the progress of science has led to new views, and that the consequences that can be deduced from the knowledge of a hundred facts may be very different from those deducible from five. It is also possible that the facts first known may be the exceptions to a rule and not the rule itself, and generalisations from these first-known facts, though useful at the time, may be highly mischievous, and impede the progress of the science if retained when it has made some advance.
Sections and Views Illustrative of Geological Phenomena (1830), viii.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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It [an ethical problem with in vitro fertilization] depends on whether you're talking ethics from the standpoint of some religious denomination or from just truly religious people. The Jewish or Catholic faiths, for example, have their own rules. But just religious people, who will make very devoted parents, have no problem with in vitro fertilization.
From address to the annual meeeting of the American Fertility Society in San Francisco (5 Feb 1979), as quoted in a UPI news article, reprinted in, for example, 'Steptoe Discusses Test Tube Ethics', The Milwaukee Journal (6 Feb 1979), 5. As reported, each sentence was separated in its own quote marks, separated by “Dr. Patrick Steptoe said” and “he said,” so the quote may not have been delivered as a single statement.
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It’s very good jam, said the Queen.
“Well, I don’t want any to-day, at any rate.”
“You couldn’t have it if you did want it,” the Queen said.
“The rule is jam tomorrow and jam yesterday but never jam to-day.”
“It must come sometimes to “jam to-day,” Alice objected.
“No it can’t,” said the Queen.
“It’s jam every other day; to-day isn’t any other day, you know.”
“I don’t understand you,” said Alice. “It’s dreadfully confusing.”
From Through the Looking Glass. In Alice’s Adventures in Wonderland And, Through the Looking Glass (1898), 149.
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Let every student of nature take this as his rule, that whatever the mind seizes upon with particular satisfaction is to be held in suspicion.
Novum Organum (1620). In Jerome Kagan, Three Seductive Ideas (1998).
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Let me arrest thy thoughts; wonder with me, why plowing, building, ruling and the rest, or most of those arts, whence our lives are blest, by cursed Cain’s race invented be, and blest Seth vexed us with Astronomy.
…...
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Logic does not pretend to teach the surgeon what are the symptoms which indicate a violent death. This he must learn from his own experience and observation, or from that of others, his predecessors in his peculiar science. But logic sits in judgment on the sufficiency of that observation and experience to justify his rules, and on the sufficiency of his rules to justify his conduct. It does not give him proofs, but teaches him what makes them proofs, and how he is to judge of them.
In A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation (1843), Vol. 1, 11.
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Logic has borrowed the rules of geometry without understanding its power. … I am far from placing logicians by the side of geometers who teach the true way to guide the reason. … The method of avoiding error is sought by every one. The logicians profess to lead the way, the geometers alone reach it, and aside from their science there is no true demonstration.
From De l’Art de Persuader, (1657). Pensées de Pascal (1842), Part 1, Article 3, 41-42. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202. From the original French, “La logique a peut-être emprunté les règles de la géométrie sans en comprendre la force … je serai bien éloigné de les mettre en parallèle avec les géomètres, qui apprennent la véritable méthode de conduire la raison. … La méthode de ne point errer est recherchée de tout le monde. Les logiciens font profession d'y conduire, les géomètres seuls y arrivent; et, hors de leur science …, il n'y a point de véritables démonstrations ….”
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Mammals in general seem to live, at best, as long as it takes their hearts to count a billion. To this general rule, man himself is the most astonishing exception.
(1965). In Isaac Asimov’s Book of Science and Nature Quotations (1988), 336.
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Mathematics is a game played according to certain simple rules with meaningless marks on paper.
Given as narrative, without quotation marks, in Eric Temple Bell, Mathematics, Queen and Servant of Science (1951, 1961), 21.
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Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics.
In 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97.
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Mathematics is the science of skillful operations with concepts and rules invented just for this purpose.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 536.
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Mathematics … belongs to every inquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by observation. In its pure and simple form the syllogism cannot be directly compared with all experience, or it would not have required an Aristotle to discover it. It must be transmuted into all the possible shapes in which reasoning loves to clothe itself. The transmutation is the mathematical process in the establishment of the law.
From Memoir (1870) read before the National Academy of Sciences, Washington, printed in 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97-98.
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Mathematics, indeed, is the very example of brevity, whether it be in the shorthand rule of the circle, c = πd, or in that fruitful formula of analysis, e = -1, —a formula which fuses together four of the most important concepts of the science,—the logarithmic base, the transcendental ratio π, and the imaginary and negative units.
In 'The Poetry of Mathematics', The Mathematics Teacher (May 1926), 19, No. 5, 293.
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Men will never disappoint us if we observe two rules: (i) To find out what they are; (2) to expect them to be just that.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 175.
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Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
Co-authored with Leopold Infeld.
The Evolution of Physics: The Growth of Ideas from the Early Concepts to Relativity and Quanta (1938), 29. Infeld was a Polish physicist (1898-1968).
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My colleagues in elementary particle theory in many lands [and I] are driven by the usual insatiable curiosity of the scientist, and our work is a delightful game. I am frequently astonished that it so often results in correct predictions of experimental results. How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature?
Nobel Banquet Speech (10 Dec 1969), in Wilhelm Odelberg (ed.),Les Prix Nobel en 1969 (1970).
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My mind seems to have become a kind of machine for grinding general laws out of large collections of facts, but why this should have caused the atrophy of that part of the brain that alone on which the higher tastes depend, I cannot conceive. A man with a mind more highly organised or better constituted than mine would not, I suppose, have thus suffered, and if I had to live my life over again, I would have made a rule to read some poetry and listen to some music at least once every week; for perhaps the parts of my brain now atrophied would thus have been kept alive through use.
In Charles Darwin and Francis Darwin (ed.), Charles Darwin: His Life Told in an Autobiographical Chapter, and in a Selected Series of His Published Letters (1892), 51.
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My thoughts … are like persons met upon a journey; I think them very agreeable at first but soon find, as a rule, that I am tired of them.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 216.
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Nature provides exceptions to every rule.
In the Boston Dial (Jul 1843), 4, No. 1, 43.
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Neither in the subjective nor in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free from the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multiplied necessity that we call mathematics.
How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.
In Number: The Language of Science; a Critical Survey Written for the Cultured Non-Mathematician (1937), 244-245.
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No national sovereignty rules in outer space. Those who venture there go as envoys of the entire human race. Their quest, therefore, must be for all mankind, and what they find should belong to all mankind.
In 'The President’s News Conference at the LBJ Ranch' (29 Aug 1965). Collected in Public Papers of the Presidents of the United States: Lyndon B. Johnson: 1965 (1966), 945.
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No scientist or student of science, need ever read an original work of the past. As a general rule, he does not think of doing so. Rutherford was one of the greatest experimental physicists, but no nuclear scientist today would study his researches of fifty years ago. Their substance has all been infused into the common agreement, the textbooks, the contemporary papers, the living present.
Attempting to distinguish between science and the humanities in which original works like Shakespeare's must be studied verbatim. 'The Case of Leavis and the Serious Case', (1970), reprinted in Public Affairs (1971), 94.
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Nonconformists travel as a rule in bunches. You rarely find a nonconformist who goes it alone. And woe to him inside a nonconformist clique who does not conform with nonconformity.
In Reflections on the Human Condition (1973), 33.
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Not everything is an idea. Otherwise psychology would contain all the sciences within it or at least it would be the highest judge over all the sciences. Otherwise psychology would rule over logic and mathematics. But nothing would be a greater misunderstanding of mathematics than its subordination to psychology.
In Elmer Daniel Klemke, Essays on Frege (1968), 531.
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Number rules the universe
Motto of the Pythagoreans as given in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 19.
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Numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.
In 'Mathematics and the Laws of Nature', The Armchair Science Reader (1959), 301.
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Oddly enough, eccentrics are happier and healthier than conformists. A study of 1,000 people found that eccentrics visit a doctor an average of just once every eight years, while conformists go twice a year. Eccentrics apparently enjoy better health because they feel less pressured to follow society’s rules, said the researcher who did the study at Royal Edinburgh Hospital in Scotland.
Eccentrics (1995).Study results in SELF magazine - 1992 National Enquirer.
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Of beasts, it is confess’d, the ape
Comes nearest us in human shape;
Like man he imitates each fashion,
And malice is his ruling passion.
In Poetical Essay, 'The Logicians Refuted', The Scots Magazine (1759),-21, 525.
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One can do noble acts without ruling earth and sea: for even with moderate advantages, one can act virtuously.
Aristotle
In Nicomachean Ethics, Book 10, Chap. 8. Great Books of the Western World (1952), Vol. 9, 433.
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One of the main purposes of scientific inference is to justify beliefs which we entertain already; but as a rule they are justified with a difference. Our pre-scientific general beliefs are hardly ever without exceptions; in science, a law with exceptions can only be tolerated as a makeshift. Scientific laws, when we have reason to think them accurate, are different in form from the common-sense rules which have exceptions: they are always, at least in physics, either differential equations, or statistical averages. It might be thought that a statistical average is not very different from a rule with exceptions, but this would be a mistake. Statistics, ideally, are accurate laws about large groups; they differ from other laws only in being about groups, not about individuals. Statistical laws are inferred by induction from particular statistics, just as other laws are inferred from particular single occurrences.
The Analysis of Matter (1927), 191.
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Only one rule in medical ethics need concern you - that action on your part which best conserves the interests of your patient.
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ORGANIC LIFE beneath the shoreless waves
Was born and nurs'd in Ocean's pearly caves;
First, forms minute, unseen by spheric glass,
Move on the mud, or pierce the watery mass;
These, as successive generations bloom,
New powers acquire, and larger limbs assume;
Whence countless groups of vegetation spring,
And breathing realms of fin, and feet, and wing.
Thus the tall Oak, the giant of the wood,
Which bears Britannia's thunders on the flood;
The Whale, unmeasured monster of the main,
The lordly Lion, monarch of the plain,
The Eagle soaring in the realms of air,
Whose eye undazzled drinks the solar glare,
Imperious man, who rules the bestial crowd,
Of language, reason, and reflection proud,
With brow erect, who scorns this earthy sod,
And styles himself the image of his God;
Arose from rudiments of form and sense,
An embryon point, or microscopic ens!
The Temple of Nature (1803), canto 1, lines 295-314, pages 26-8.
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Orgel's First Rule: Whenever a spontaneous process is too slow or too inefficient a protein will evolve to speed it up or make it more efficient.
In Jack D. Dunitz and Gerald F. Joyce, 'Leslie Eleazer Orgel', Biographical Memoirs of Fellows of the Royal Society (2013), Vol. 59, 286.
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Our ambition should be to rule ourselves, the true kingdom for each one of us; and true progress is to know more, and be more, and to do more.
The Use of Life (1895, 1923), 260.
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Our commercial and mercantile law was no sudden invention. It was not the work of a day, or of one set of minds… In the incipient, the early existence of this system, a single maxim obtained force, others succeeded; one rule of right formed a nucleus around which other kindred rules might cling; the necessities of trade originated customs, customs ripened into law; a few feeble decisions of courts laid the foundation for others; the wisdom and experience of each succeeding generation improved upon the wisdom and experience of generations that were past; and thus the edifice arose, perfect in its parts, beautiful in its proportions.
From biographical preface by T. Bigelow to Austin Abbott (ed.), Official Report of the Trial of Henry Ward Beecher (1875), Vol. 1, xi-xii.
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Our highest claim to respect, as a nation, rests not in the gold, nor in the iron and the coal, nor in inventions and discoveries, nor in agricultural productions, nor in our wealth, grown so great that a war debt of billions fades out under ministrations of the revenue collector without fretting the people; nor, indeed, in all these combined. That claim finds its true elements in our systems of education and of unconstrained religious worship; in our wise and just laws, and the purity of their administration; in the conservative spirit with which the minority submits to defeat in a hotly-contested election; in a free press; in that broad humanity which builds hospitals and asylums for the poor, sick, and insane on the confines of every city; in the robust, manly, buoyant spirit of a people competent to admonish others and to rule themselves; and in the achievements of that people in every department of thought and learning.
From his opening address at an annual exhibition of the Brooklyn Industrial Institute. As quoted in biographical preface by T. Bigelow to Austin Abbott (ed.), Official Report of the Trial of Henry Ward Beecher (1875), Vol. 1, xiv.
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Our school education ignores, in a thousand ways, the rules of healthy development; and the results … are gained very generally at the cost of physical and mental health.
Lecture (2 Dec 1959) delivered in Clinton Hall, New York City. Published in 'Medicine as a Profession for Women', The English Woman’s Journal (1 May 1860), 5, No. 27, 148. (Prepared together with Emily Blackwell.) The Blackwells recognized the connection between health and learning. They also wanted that teachers (of whom 90% were women) should “diffuse among women the physiological and sanitary knowledge which they will need.”
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Part of the strength of science is that it has tended to attract individuals who love knowledge and the creation of it.
Just as important to the integrity of science have been the unwritten rules of the game. These provide recognition and approbation for work which is imaginative and accurate, and apathy or criticism for the trivial or inaccurate. … Thus, it is the communication process which is at the core of the vitality and integrity of science.
Editorial, 'The Roots of Scientific Integrity', Science (1963), 3561. In Bulletin of the Atomic Scientists (May 1965), 29.
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Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.
Quoted in a space filler, without citation, in The Pentagon: A Mathematics Magazine for Students (Fall 1951), 11, No. 1, 12. Primary source needed (can you help).
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Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.
Anonymous
In Wieslaw Krawcewicz, Bindhyachal Rai, Calculus with Maple Labs (2003), 328. In this book, and also in Julian Havil, Nonplussed!: Mathematical Proof of Implausible Ideas? (2007), 68, the quote is attributed to Ian Ellis, but most sources vite it as Anonymous.
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Physicists are, as a general rule, highbrows. They think and talk in long, Latin words, and when they write anything down they usually include at least one partial differential and three Greek letters.
In 'A Newsman Looks at Physicists', Physics Today (May 1948), 1, No. 1, 15.
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Poor teaching leads to the inevitable idea that the subject [mathematics] is only adapted to peculiar minds, when it is the one universal science and the one whose four ground-rules are taught us almost in infancy and reappear in the motions of the universe.
In Mathematical Teaching (1907), 19.
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Pope has elegantly said a perfect woman's but a softer man. And if we take in the consideration, that there can be but one rule of moral excellence for beings made of the same materials, organized after the same manner, and subjected to similar laws of Nature, we must either agree with Mr. Pope, or we must reverse the proposition, and say, that a perfect man is a woman formed after a coarser mold.
Letter XXII. 'No Characteristic Difference in Sex'. In Letters on Education with Observations on Religious and Metaphysical Subjects (1790), 128.
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Primates stand at a turning point in the course of evolution. Primates are to the biologist what viruses are to the biochemist. They can be analysed and partly understood according to the rules of a simpler discipline, but they also present another level of complexity: viruses are living chemicals, and primates are animals who love and hate and think.
'The Evolution of Primate Behavior: A survey of the primate order traces the progressive development of intelligence as a way of life', American Scientist (1985), 73, 288.
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Psychology … tells us that we rarely work through reasons and evidence in a systematic way; weighing information carefully and suspending the impulse to draw conclusions. Instead, much of the time we use mental shortcuts or rules of thumb that save us mental effort. These habits often work reasonably well, but they also can lead us to conclusions we might dismiss if we applied more thought.
As co-author with Kathleen Hall Jamieson, in unSpun: Finding Facts in a World of Disinformation (2007), 70.
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Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. … Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical application, its importance in physics being proportional to its interest in mathematics.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 124.
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Reason is the only ability that makes it possible for humans to rule the Earth and to ruin it.
…...
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Remember a networked learning machine’s most basic rule: strengthen the connections to those who succeed, weaken them to those who fail.
In 'The Conformity Police', Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 83.
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Remember this, the rule for giving an extempore lecture is—let the the mind rest from the subject entirely for an interval preceding the lecture, after the notes are prepared; the thoughts will ferment without your knowing it, and enter into new combinations; but if you keep the mind active upon the subject up to the moment, the subject will not ferment but stupefy.
In Letter (10 Jul 1854) to William Rowan Hamilton, collected in Robert Perceval Graves, Life of Sir William Rowan Hamilton (1882-89), Vol. 3, 487.
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Round about the accredited and orderly facts of every science there ever floats a sort of dust-cloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to … Anyone will renovate his science who will steadily look after the irregular phenomena, and when science is renewed, its new formulas often have more of the voice of the exceptions in them than of what were supposed to be the rules.
In 'The Hidden Self', Scribner’s Magazine (1890), Vol. 7, 361.
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Rules are made for people who aren’t willing to make up their own.
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Rules can seldom be safely applied without a clear understanding of the principles on which they rest.
From Field-Book for Railroad Engineers (1854), Preface, vii.
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Rules of Thumb
Thumb’s First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb’s Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Anonymous
In Arthur Bloch, The Complete Murphy's Law: A Definitive Collection (1991), 126.
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Science is a game we play with God, to find out what his rules are.
…...
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Science is a game—but a game with reality, a game with sharpened knives … If a man cuts a picture carefully into 1000 pieces, you solve the puzzle when you reassemble the pieces into a picture; in the success or failure, both your intelligences compete. In the presentation of a scientific problem, the other player is the good Lord. He has not only set the problem but also has devised the rules of the game—but they are not completely known, half of them are left for you to discover or to deduce. The experiment is the tempered blade which you wield with success against the spirits of darkness—or which defeats you shamefully. The uncertainty is how many of the rules God himself has permanently ordained, and how many apparently are caused by your own mental inertia, while the solution generally becomes possible only through freedom from its limitations.
Quoted in Walter Moore, Schrödinger: Life and Thought (1989), 348.
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Science is a set of rules that keep the scientists from lying to each other.
Quoted in Alexander Kohn, False Prophets (1986, 1997), 2.
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Science is complex and chilling. The mathematical language of science is understood by very few. The vistas it presents are scary—an enormous universe ruled by chance and impersonal rules, empty and uncaring, ungraspable and vertiginous. How comfortable to turn instead to a small world, only a few thousand years old, and under God's personal; and immediate care; a world in which you are His peculiar concern.
The 'Threat' of Creationism. In Ashley Montagu (ed.), Science and Creationism (1984), 192.
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Science means simplification. It substitutes a single rule for a million miscellaneous observations.
In Chats on Science (1924), 4.
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Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
Appended to his entry in Who’s Who. In Alan Lindsay Mackay, A Dictionary of Scientific Quotations (1991), 163.
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Science, like life, feeds on its own decay. New facts burst old rules; then newly divined conceptions bind old and new together into a reconciling law.
The Will to Believe and Other Essays in Popular Philosophy, 1910
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Scientific method is often defined as if it were a set procedure, to be learned, like a recipe, as if anyone could like a recipe, as if anyone could become a scientist simply by learning the method. This is as absurd ... [so I shall not] discuss scientific method, but rather the methods of scientists. We proceed by common sense and ingenuity. There are no rules, only the principles of integrity and objectivity, with a complete rejection of all authority except that of fact.
In Science in the Making (1957), 8.
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Since the princes take the Earth for their own, it’s fair that the philosophers reserve the sky for themselves and rule there, but they should never permit the entry of others.
Conversations on the Plurality of Words (1686), trans. H. A. Hargreaves (1990), 51.
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Some may claim that is it unscientific to speak of the operations of nature as “miracles.” But the point of the title lies in the paradox of finding so many wonderful things … subservient to the rule of law.
In Nature’s Miracles: Familiar Talks on Science (1899), Vol. 1, Introduction, v.
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Some say that science dictates, or at least its old rules said, that it is impossible for bumblebees to fly. This may be a myth, but wouldn't you like to think that every time you look at the bees, you are seeing that there is no such thing as the impossible?
Joe Rukin
Look at the Bees (2006).
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Suppose it were perfectly certain that the life and fortune of every one of us would, one day or other, depend upon his winning or losing a game of chess. Don't you think that we should all consider it to be a primary duty to learn at least the names and the moves of the pieces; to have a notion of a gambit, and a keen eye for all the means of giving and getting out of check? Do you not think that we should look with a disapprobation amounting to scorn upon the father who allowed his son, or the state which allowed its members, to grow up without knowing a pawn from a knight?
Yet, it is a very plain and elementary truth that the life, the fortune, and the happiness of every one of us, and, more or less, of those who are connected with us, do depend upon our knowing something of the rules of a game infinitely more difficult and complicated than chess. It is a game which has been played for untold ages, every man and woman of us being one of the two players in a game of his or her own. The chess-board is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance. To the man who plays well the highest stakes are paid with that sort of overflowing generosity with which the strong shows delight in strength. And one who plays ill is checkmated—without haste, but without remorse.
Address to the South London Working Men’s College. 'A Liberal Education; and Where to Find It', in David Masson, (ed.), Macmillan’s Magazine (Mar 1868), 17, 369. Also in 'A Liberal Education and Where to Find it' (1868). In Collected Essays (1893), Vol. 3, 82.
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That is the way of the scientist. He will spend thirty years in building up a mountain range of facts with the intent to prove a certain theory; then he is so happy with his achievement that as a rule he overlooks the main chief fact of all—that all his accumulation proves an entirely different thing.
'The Bee'. In What is Man? and Other Essays? (1917), 283.
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The chess-board is the world; the pieces are the phenomena of the universe; the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, just and patient. But we know, to our cost, that he never overlooks a mistake, or makes the slightest allowance for ignorance.
'A Liberal Education', Lay Sermons, Addresses, and Reviews (1870). Collected in Science & Education: Essays (1893), 82.
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the Courts of Justice had once ruled that a man carrying bagpipes was a man carrying a weapon—so inspiring was the music of the pipers to the clans in battle.
The Reader
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The days of my youth extend backward to the dark ages, for I was born when the rush-light, the tallow-dip or the solitary blaze of the hearth were common means of indoor lighting, and an infrequent glass bowl, raised 8 or 10 feet on a wooden post, and containing a cup full of evil-smelling train-oil with a crude cotton wick stuck in it, served to make the darkness visible out of doors. In the chambers of the great, the wax candle or, exceptionally, a multiplicity of them, relieved the gloom on state occasions, but as a rule, the common people, wanting the inducement of indoor brightness such as we enjoy, went to bed soon after sunset.
Reminiscence written by Swan “in his old age”, as quoted in Kenneth Raydon Swan, Sir Joseph Swan (1946), 1-2.
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The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.
'On Formally Undecidable Propositions of Principia Mathematica and Related Systems I' (193 1), in S. Feferman (ed.), Kurt Gödel Collected Works: Publications 1929-1936 (1986), Vol. I, 145.
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The difficulties connected with my criterion of demarcation (D) are important, but must not be exaggerated. It is vague, since it is a methodological rule, and since the demarcation between science and nonscience is vague. But it is more than sharp enough to make a distinction between many physical theories on the one hand, and metaphysical theories, such as psychoanalysis, or Marxism (in its present form), on the other. This is, of course, one of my main theses; and nobody who has not understood it can be said to have understood my theory.
The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the 'means of production' would lead to social, political, and ideological developments, rather than the other way round.
But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin's and Stalin's ideology that Russia must push forward with its industrialization ('Socialism is dictatorship of the proletariat plus electrification') which promoted the new development of the means of production.
Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).
However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.
Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler's break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)
The point is very clear. Neither Freud nor Adler excludes any particular person's acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud's theory; the theory was compatible with everything that could happen—even without any special immunization treatment.
Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.
'The Problem of Demarcation' (1974). Collected in David Miller (ed.) Popper Selections (1985), 127-128.
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The distinction is, that the science or knowledge of the particular subject-matter furnishes the evidence, while logic furnishes the principles and rules of the estimation of evidence.
In A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation (1843), Vol. 1, 11.
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The economic anarchy of capitalist society as it exists today is, in my opinion, the real source of the evil. We see before us a huge community of producers the members of which are unceasingly striving to deprive each other of the fruits of their collective labor–not by force, but on the whole in faithful compliance with legally established rules.
…...
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The elements of human nature are the learning rules, emotional reinforcers, and hormonal feedback loops that guide the development of social behaviour into certain channels as opposed to others. Human nature is not just the array of outcomes attained in existing societies. It is also the potential array that might be achieved through conscious design by future societies. By looking over the realized social systems of hundreds of animal species and deriving the principles by which these systems have evolved, we can be certain that all human choices represent only a tiny subset of those theoretically possible. Human nature is, moreover, a hodgepodge of special genetic adaptations to an environment largely vanished, the world of the Ice­Age hunter-gatherer.
In On Human Nature (1978), 196.
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The examples which a beginner should choose for practice should be simple and should not contain very large numbers. The powers of the mind cannot be directed to two things at once; if the complexity of the numbers used requires all the student’s attention, he cannot observe the principle of the rule which he is following.
In Study and Difficulties of Mathematics (1902), chap. 3.
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The fact that the proof of a theorem consists in the application of certain simple rules of logic does not dispose of the creative element in mathematics, which lies in the choice of the possibilities to be examined.
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), 15.
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The first and most fundamental rule is: Consider social facts as things.
The Rules of Sociological Method (1895), 8th edition, trans. Sarah A. Solovay and John M. Mueller, ed. George E. G. Catlin (1938, 1964 edition), 14.
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The first fundamental rule of historical science and research, when by these is sought a knowledge of the general destinies of mankind, is to keep these and every object connected with them steadily in view, without losing ourselves in the details of special inquiries and particular facts, for the multitude and variety of these subjects is absolutely boundless; and on the ocean of historical science the main subject easily vanishes from the eye.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 8.
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The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.
In How to Solve It: A New Aspect of Mathematical Method (2004), 172.
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The first rule of intelligent tinkering is to save all the parts.
With co-author John P. Holdren, in Saturday Review (5 June 1971), 54, 59. Ehrlich is making his own paraphrase of an earlier quote, citing Aldo Leopold: “To keep every cog and wheel is the first precaution of intelligent tinkering.” See the Aldo Leopold Quotes page of this website. These refer to the importance of supporting an ecosystem by keeping all its parts - saving all the species.
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The first rule to proper diet? Ask them what they want and then give it to them. There are few exceptions.
Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).
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The first two rules of science are: 1. The truth at any price including the price of your life. 2. Look at things right under your nose as if you’ve never seen them before, then proceed from there.
In The God Problem: How a Godless Cosmos Creates (2012), 16.
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The focal points of our different reflections have been called “science”’ or “art” according to the nature of their “formal” objects, to use the language of logic. If the object leads to action, we give the name of “art” to the compendium of rules governing its use and to their technical order. If the object is merely contemplated under different aspects, the compendium and technical order of the observations concerning this object are called “science.” Thus metaphysics is a science and ethics is an art. The same is true of theology and pyrotechnics.
Definition of 'Art', Encyclopédie (1751). Translated by Nelly S. Hoyt and Thomas Cassirer (1965), 4.
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The game of chess has always fascinated mathematicians, and there is reason to suppose that the possession of great powers of playing that game is in many features very much like the possession of great mathematical ability. There are the different pieces to learn, the pawns, the knights, the bishops, the castles, and the queen and king. The board possesses certain possible combinations of squares, as in rows, diagonals, etc. The pieces are subject to certain rules by which their motions are governed, and there are other rules governing the players. … One has only to increase the number of pieces, to enlarge the field of the board, and to produce new rules which are to govern either the pieces or the player, to have a pretty good idea of what mathematics consists.
In Book review, 'What is Mathematics?', Bulletin American Mathematical Society (May 1912), 18, 386-387.
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The golden rule is that there are no golden rules.
…...
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The great rule: If the little bit you have is nothing special in itself, at least find a way of saying it that is a little bit special.
Aphorism 55 in Notebook E, as translated by R.J. Hollingdale in Aphorisms (1990).
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The greatest slave is not he who is ruled by a despot, great though that evil be, but he who is in the thrall of his own moral ignorance, selfishness, and vice.
In Self-help: With Illustrations of Character and Conduct (1859, 1861), 17.
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The greatest spiritual revolutionary Western history, Saint Francis, proposed what he thought was an alternative Christian view of nature and man’s relation to it: he tried to substitute the idea of the equality of creatures, including man, for the idea of man’s limitless rule of creation. He failed. Both our present science and our present technology are so tinctured with orthodox Christian arrogance toward nature that no solution for our ecologic crisis can be expected from them alone. Since the roots of our trouble are so largely religious, the remedy must also be essentially religious, whether we call it that or not. We must rethink and refeel our nature and destiny. The profoundly religious, but heretical, sense of the primitive Franciscans for the spiritual autonomy of all parts of nature may point a direction. I propose Francis as a patron saint for ecologists.
In The Historical Roots of our Ecologic Crisis (1967), 1207.
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The history of psychiatry to the present day is replete with examples of loose thinking and a failure to apply even the simplest rules of logic. “A Court of Statistical Appeal” has now been equated with scientific method.
Myre Sim
Quoted in book review by Myre Sim about 'Ending the Cycle of Abuse', The Canadian Journal of Psychiatry (May 1997), 42:4, 425.
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The hypotheses which we accept ought to explain phenomena which we have observed. But they ought to do more than this; our hypotheses ought to foretell phenomena which have not yet been observed; ... because if the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.
Philosophy of the Inductive Sciences (1847), Vol. 2, 62-63.
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The idea of a method that contains firm, unchanging, and absolutely binding principles for conducting the business of science meets considerable difficulty when confronted with the results of historical research. We find, then, that there is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time or another.
Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14.
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The laws of nature are the rules according to which the effects are produced; but there must be a cause which operates according to these rules. The laws of navigation never navigated a ship. The rules of architecture never built a house.
'Essay I: On Active Power In General: Chapter 6: On the Efficient Causes of the Phenomena of Nature', Essays on the Active Powers of Man (1785), Chap. 6, 47.
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The logic of the subject [algebra], which, both educationally and scientifically speaking, is the most important part of it, is wholly neglected. The whole training consists in example grinding. What should have been merely the help to attain the end has become the end itself. The result is that algebra, as we teach it, is neither an art nor a science, but an ill-digested farrago of rules, whose object is the solution of examination problems. … The result, so far as problems worked in examinations go, is, after all, very miserable, as the reiterated complaints of examiners show; the effect on the examinee is a well-known enervation of mind, an almost incurable superficiality, which might be called Problematic Paralysis—a disease which unfits a man to follow an argument extending beyond the length of a printed octavo page.
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 447-448.
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The man in the street will, therefore, twist the statement that the scientist has come to the end of meaning into the statement that the scientist has penetrated as far as he can with the tools at his command, and that there is something beyond the ken of the scientist. This imagined beyond, which the scientist has proved he cannot penetrate, will become the playground of the imagination of every mystic and dreamer. The existence of such a domain will be made the basis of an orgy of rationalizing. It will be made the substance of the soul; the spirits of the dead will populate it; God will lurk in its shadows; the principle of vital processes will have its seat here; and it will be the medium of telepathic communication. One group will find in the failure of the physical law of cause and effect the solution of the age-long problem of the freedom of the will; and on the other hand the atheist will find the justification of his contention that chance rules the universe.
Reflections of a Physicist (1950),102-3.
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The marriage of reason and nightmare which has dominated the 20th century has given birth to an ever more ambiguous world. Across the communications landscape move the specters of sinister technologies and the dreams that money can buy. Thermonuclear weapons systems and soft drink commercials coexist in an overlit realm ruled by advertising and pseudoevents, science and pornography. Over our lives preside the great twin leitmotifs of the 20th century—sex and paranoia.
Crash (1973, 1995), catalogue notes. In J. G. Ballard, The Kindness of Women (2007), 221.
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The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen.
In Ian Stewart, Why Beauty is Truth (2007), 279.
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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 more a man is imbued with the ordered regularity of all events the firmer becomes his conviction that there is no room left by the side of this ordered regularity for causes of a different nature. For him neither the rule of human nor the rule of divine will exists as an independent cause of natural events. To be sure, the doctrine of a personal God interfering with natural events could never be refuted, in the real sense, by science, for this doctrine can always take refuge in those domains in which scientific knowledge has not yet been able to set foot.
…...
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The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it.
In 'Uses of Mathesis', Bibliotheca Sacra (Jul 1875), 32, 505.
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The other line of argument, which leads to the opposite conclusion, arises from looking at artificial automata. Everyone knows that a machine tool is more complicated than the elements which can be made with it, and that, generally speaking, an automaton A, which can make an automaton B, must contain a complete description of B, and also rules on how to behave while effecting the synthesis. So, one gets a very strong impression that complication, or productive potentiality in an organization, is degenerative, that an organization which synthesizes something is necessarily more complicated, of a higher order, than the organization it synthesizes. This conclusion, arrived at by considering artificial automaton, is clearly opposite to our early conclusion, arrived at by considering living organisms.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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The physicist is like someone who’s watching people playing chess and, after watching a few games, he may have worked out what the moves in the game are. But understanding the rules is just a trivial preliminary on the long route from being a novice to being a grand master. So even if we understand all the laws of physics, then exploring their consequences in the everyday world where complex structures can exist is a far more daunting task, and that’s an inexhaustible one I'm sure.
In Lewis Wolpert and Alison Richards, A Passion For Science (1988), 37.
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The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits—he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher—the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do—and if a man does his best, what else can you ask of him?
The Rise of Scientific Philosophy (1951, 1973), 248-9. Collected in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 376.
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The principles of logic and mathematics are true universally simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.
Language, Truth and Logic (1960), 77.
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The psychopaths are always around. In calm times we study them, but in times of upheaval, they rule over us.
Gestalten und Gedanken (1963), 94, trans. P. Lerner.
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The question of the origin of the hypothesis belongs to a domain in which no very general rules can be given; experiment, analogy and constructive intuition play their part here. But once the correct hypothesis is formulated, the principle of mathematical induction is often sufficient to provide the proof.
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), 15.
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The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc’d to a Mathematical Reasoning, and when they cannot, it’s a sign our Knowledge of them is very small and confus’d; and where a mathematical reasoning can be had, it’s as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.
Of the Laws of Chance, or, a Method of the Hazards of Game (1692), Preface.
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The reader will find no figures in this work. The methods which I set forth do not require either constructions or geometrical or mechanical reasonings: but only algebraic operations, subject to a regular and uniform rule of procedure.
From the original French, “On ne trouvera point de Figures dans set Ouvrage. Les méthodes que j’y expose ne demandent ni constructions, ni raisonnements géométriqus ou méchaniques, mais seulement des opérations algébriques, assujetties à une march régulière et uniforme.” In 'Avertissement', Mécanique Analytique (1788, 1811), Vol. 1, i. English version as given in Cornelius Lanczos, The Variational Principles of Mechanics (1966), Vol. 1, 347.
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The reason it is so hard to attain to something good in any of the arts and sciences is that it involves attaining to a certain stipulated point; to do something badly according to a predetermined rule would be just as hard, if indeed it would then still deserve to be called bad.
Aphorism 53 in Notebook C (1772-1773), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 42.
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The rule for life in the sea can be summed up in the well known expression “big fish eat little fish”. … Research shows that great losses occur in the fish cycle because small fish are eaten by larger ones, and in many cases the larger fish are not fit for human consumption.
In 'Man Explores the Sea', Journal of the Royal Society of Arts (Sep 1963), 111, No. 5086, 787-789.
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The rules of scientific investigation always require us, when we enter the domains of conjecture, to adopt that hypothesis by which the greatest number of known facts and phenomena may be reconciled.
In The Physical Geography of the Sea (1855), 123.
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The simple rule about weapons is that if thery can be built, they will be built.
Accidental Empires (1992), 79.
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The steam-engine in its manifold applications, the crime-decreasing gas-lamp, the lightning conductor, the electric telegraph, the law of storms and rules for the mariner's guidance in them, the power of rendering surgical operations painless, the measures for preserving public health, and for preventing or mitigating epidemics,—such are among the more important practical results of pure scientific research, with which mankind have been blessed and States enriched.
President's Address to the British Association, Leeds (1858). In Charles W. Vincent and James Mason (eds.), The Year-book of Facts in Science and Art (1859), title page.
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The subsequent course of nature, teaches, that God, indeed, gave motion to matter; but that, in the beginning, he so guided the various motion of the parts of it, as to contrive them into the world he design'd they should compose; and establish'd those rules of motion, and that order amongst things corporeal, which we call the laws of nature. Thus, the universe being once fram'd by God, and the laws of motion settled, and all upheld by his perpetual concourse, and general providence; the same philosophy teaches, that the phenomena of the world, are physically produced by the mechanical properties of the parts of matter; and, that they operate upon one another according to mechanical laws. 'Tis of this kind of corpuscular philosophy, that I speak.
'The Excellence and Grounds of the Mechanical Philosophy', In P. Shaw (ed.), The Philosophical Works of Robert Boyle (1725), Vol. 1, 187.
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The surveyor ought to work in solitude. He must no more admit company while mapping than a writer admits visitors to his study while writing. This applies even to geological company, nay, even to the company of a skilled fellow-surveyor... The two authors of this book [Edward Greenly and Howell Williams] once thought that it would be pleasant to have a day's mapping together, and decided to break through their rule. The result was a ludicrous paralysis. The commonest operation seemed a mountain of difficulty. Next day the senior author (whose ground it was) swept an india-rubber over every line and went out again, when, hey presto! And all was clear.
Edward Greenly and Howell Williams, Methods in Geological Surveying (1930), 375-6.
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The teaching of elementary mathematics should be conducted so that the way should be prepared for the building upon them of the higher mathematics. The teacher should always bear in mind and look forward to what is to come after. The pupil should not be taught what may be sufficient for the time, but will lead to difficulties in the future. … I think the fault in teaching arithmetic is that of not attending to general principles and teaching instead of particular rules. … I am inclined to attack Teaching of Mathematics on the grounds that it does not dwell sufficiently on a few general axiomatic principles.
In John Perry (ed.), Discussion on the Teaching of Mathematics (1901), 33. The discussion took place on 14 Sep 1901 at the British Association at Glasgow, during a joint meeting of the mathematics and physics sections with the education section. The proceedings began with an address by John Perry. Professor Hudson was the first speak in the Discussion which followed.
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There are those whose sole claim to profundity is the discovery of exceptions to the rules.
Maxim 2838 in Maxims for a Modern Man (1965), 321.
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There are three ruling ideas, three so to say, spheres of thought, which pervade the whole body of mathematical science, to some one or other of which, or to two or all three of them combined, every mathematical truth admits of being referred; these are the three cardinal notions, of Number, Space and Order.
Arithmetic has for its object the properties of number in the abstract. In algebra, viewed as a science of operations, order is the predominating idea. The business of geometry is with the evolution of the properties of space, or of bodies viewed as existing in space.
In 'A Probationary Lecture on Geometry, York British Association Report (1844), Part 2; Collected Mathematical Papers, Vol. 2, 5.
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There cannot be a body of rules without a rationale, and this rationale constitutes the science.
In A Treatise on the Methods of Observation and Reasoning in (1852), 148.
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There is one class of mind that loves to lean on rules and definitions, and another that discards them as far as possible. A faddist will generally ask for a definition of faddism, and one who is not a faddist will be impatient of being asked to give one.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.
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There is one class of mind that loves to lean on rules and definitions, and another that discards them as far as possible. A faddist will generally ask for a definition of faddism, and one who is not a faddist will be impatient of being asked to give one.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.
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There is only one cardinal rule: One must always listen to the patient.
Quoted by Walter Clemons, 'Listening to the Lost', Newsweek (20 Aug 1984).