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Home > Category Index for Science Quotations > Category Index E > Category: Error

Error Quotes (321 quotes)


'...no pleasure is comparable to the standing upon the vantage ground of truth … and to see the errors … in the vale below:' so always that this prospect be with pity, and not with swelling or pride.
Quoting an unnamed poet and adding a comment.
I. Of Truth,' Essays (1597). In Francis Bacon and Basil Montagu, The Works of Francis Bacon, Lord Chancellor of England (1852), 11
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04.23 The cautious seldom err.
Confucius
In James Legge (trans.), 'The Confucian Analects', The Chinese Classics: Life and Teachings of Confucius (1861), Vol. 1, Book 4: Le Jin, Chap. 23, 35.
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Compounds formed by chemical attraction, possess new properties different from those of their component parts... chemists have long believed that the contrary took place in their combination. They thought, in fact, that the compounds possessed properties intermediate between those of their component parts; so that two bodies, very coloured, very sapid, or insapid, soluble or insoluble, fusible or infusible, fixed or volatile, assumed in chemical combination, a shade or colour, or taste, solubility or volatility, intermediate between, and in some sort composed of, the same properties which were considered in their principles. This is an illusion or error which modern chemistry is highly interested to overthrow.
Quoted in A General System of Chemical Knowledge (1804), Vol. I, trans. W. Nicholson, 102-3.
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Error of confounding cause and effect.—There is no more dangerous error than confounding consequence with cause: I call it the intrinsic depravity of reason. … I take an example: everybody knows the book of the celebrated Comaro, in which he recommends his spare diet as a recipe for a long and happy life,—for a virtuous life also. Few books have been read so much… I believe hardly any book … has caused so much harm, has shortened so many lives, as this well-meant curiosity. The source of this mischief is in confounding consequence with cause. The candid Italian saw in his diet the cause of his long life, while the prerequisite to long life, the extraordinary slowness of the metabolic process, small consumption, was the cause of his spare diet. He was not at liberty to eat little or much; his frugality—was not of “free will;” he became sick when he ate more.
From 'The Four Great Errors', The Twilight of the Idols (1888), collected in Thomas Common (trans.), The Works of Friedrich Nietzsche (1896), Vol. 11, 139.
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Error has made man so deep, sensitive, and inventive that he has put forth such blossoms as religions and arts. Pure knowledge could not have been capable of it.
Human, All-To-Human, Vol. 1, 44-45. (1878), 140. In Willard Huntington Wright, What Nietzsche Taught? (1917), 78.
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Goldsmith: If you put a tub full of blood into a stable, the horses are like to go mad.
Johnson: I doubt that.
Goldsmith: Nay, sir, it is a fact well authenticated.
Thrale: You had better prove it before you put it into your book on natural history. You may do it in my stable if you will.
Johnson: Nay, sir, I would not have him prove it. If he is content to take his information from others, he may get through his book with little trouble, and without much endangering his reputation. But if he makes experiments for so comprehensive a book as his, there would be no end to them; his erroneous assertions would then fall upon himself: and he might be blamed for not having made experiments as to every particular.
In James Boswell, The Life of Samuel Johnson, LL.D.: Comprehending an Account of His Studies and Numerous Works (1785, 1830), 229-230.
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Il ne peut y avoir de langage plus universel et plus simple, plus exempt d’erreurs et d’obscurités, c'est-à-dire plus digne d'exprimer les rapports invariables des êtres naturels.
There cannot be a language more universal and more simple, more free from errors and obscurities, … more worthy to express the invariable relations of all natural things. [About mathematical analysis.]
From Théorie Analytique de la Chaleur (1822), xiv, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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La science, mon garçon, est faite d’erreurs, mais d’erreurs qu’il est bon de commettre, car elles mènent peu à peu à la vérité.
Science, my boy, is composed of errors, but errors that it is right to make, for they lead step by step to the truth.
Journey to the Centre of the Earth, translated by William Butcher (1992, 2008), 146.
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La vérité ne diffère de l'erreur qu'en deux points: elle est un peu plus difficile à prouver et beaucoup plus difficile à faire admettre. (Dec 1880)
Truth is different from error in two respects: it is a little harder to prove and more difficult to admit.
In Recueil d'Œuvres de Léo Errera: Botanique Générale (1908), 193. Google translation by Webmaster.
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Non enim omnis error stultitia est dicenda
We must not say every mistake is a foolish one.
De Divinatione II., 22, 79. In Thomas Benfield Harbottle, Dictionary of Quotations (classical) (3rd Ed., 1906), 169.
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To the Memory of Fourier
Fourier! with solemn and profound delight,
Joy born of awe, but kindling momently
To an intense and thrilling ecstacy,
I gaze upon thy glory and grow bright:
As if irradiate with beholden light;
As if the immortal that remains of thee
Attuned me to thy spirit’s harmony,
Breathing serene resolve and tranquil might.
Revealed appear thy silent thoughts of youth,
As if to consciousness, and all that view
Prophetic, of the heritage of truth
To thy majestic years of manhood due:
Darkness and error fleeing far away,
And the pure mind enthroned in perfect day.
In R. Graves, Life of W. R. Hamilton (1882), Vol. l, 696.
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Wenn sich für ein neues Fossil kein, auf eigenthümliche Eigenschaften desselben hinweisender, Name auffinden lassen Will; als in welchem Falle ich mich bei dem gegenwärtigen zu befinden gestehe; so halte ich es für besser, eine solche Benennung auszuwählen, die an sich gar nichts sagt, und folglich auch zu keinen unrichtigen Begriffen Anlass geben kann. Diesem zufolge will ich den Namen für die gegenwärtige metallische Substanz, gleichergestalt wie bei dem Uranium geschehen, aus der Mythologie, und zwar von den Ursöhnen der Erde, den Titanen, entlehnen, und benenne also dieses neue Metallgeschlecht: Titanium.
Wherefore no name can be found for a new fossil [element] which indicates its peculiar and characteristic properties (in which position I find myself at present), I think it is best to choose such a denomination as means nothing of itself and thus can give no rise to any erroneous ideas. In consequence of this, as I did in the case of Uranium, I shall borrow the name for this metallic substance from mythology, and in particular from the Titans, the first sons of the earth. I therefore call this metallic genus TITANIUM.
Martin Heinrich Klaproth. Original German edition, Beiträge Zur Chemischen Kenntniss Der Mineralkörper (1795), Vol. 1 , 244. English edition, translator not named, Analytical Essays Towards Promoting the Chemical Knowledge of Mineral Substances (1801), Vol. 1, 210. Klaproth's use of the term fossil associates his knowledge of the metal as from ore samples dug out of a mine.
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A conflict arises when a religious community insists on the absolute truthfulness of all statements recorded in the Bible. This means an intervention on the part of religion into the sphere of science; this is where the struggle of the Church against the doctrines of Galileo and Darwin belongs. On the other hand, representatives of science have often made an attempt to arrive at fundamental judgments with respect to values and ends on the basis of scientific method, and in this way have set themselves in opposition to religion. These conflicts have all sprung from fatal errors.
…...
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A game is on, at the other end of this infinite distance, and heads or tails will turn up. What will you wager? According to reason you cannot leave either; according to reason you cannot leave either undone... Yes, but wager you must; there is no option, you have embarked on it. So which will you have. Come. Since you must choose, let us see what concerns you least. You have two things to lose: truth and good, and two things to stake: your reason and your will, your knowledge and your happiness. And your nature has two things to shun: error and misery. Your reason does not suffer by your choosing one more than the other, for you must choose. That is one point cleared. But your happiness? Let us weigh gain and loss in calling heads that God is. Reckon these two chances: if you win, you win all; if you lose, you lose naught. Then do not hesitate, wager that He is.
Pensées (1670), Section I, aphorism 223. In H. F. Stewart (ed.), Pascal's Pensées (1950), 117-119.
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A hallucination is a fact, not an error; what is erroneous is a judgment based upon it.
The Monist (Apr 1914), 24:2, 173.
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A man’s errors are what make him amiable.
As quoted in Adam Wooléver (ed.), A Treasury of Wisdom, Wit and Humor, Odd Comparisons and Proverbs (1876), 128. The quote is identified as from last number of his Journal of Art in his 77th year, in François duc de La Rochefoucauld, Moral Reflections, Sentences and Maxims (1851), 70, footnote.
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A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
War and Peace (1869), Book 11, Chap. 1.
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A new truth is a truth, an old error is an error.
In Poor Richard's Almanack (1734).
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A school teacher probably never enjoys anything she reads, she is so intently looking for errors.
In Sinner Sermons: A Selection of the Best Paragraphs of E. W. Howe (1926), 38.
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A scientist strives to understand the work of Nature. But with our insufficient talents as scientists, we do not hit upon the truth all at once. We must content ourselves with tracking it down, enveloped in considerable darkness, which leads us to make new mistakes and errors. By diligent examination, we may at length little by little peel off the thickest layers, but we seldom get the core quite free, so that finally we have to be satisfied with a little incomplete knowledge.
Lecture to the Royal Swedish Academy of Science, 23 May 1764. Quoted in J. A. Schufle 'Torbern Bergman, Earth Scientist', Chymia, 1967, 12, 78.
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A subtle thought that is in error may yet give rise to fruitful inquiry that can establish truths of great value.
In Steven D. Price, 1001 Smartest Things Ever Said (2005), 163.
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A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; Whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest till he gets over every rub.
Letter (25 May 1694) to Nathaniel Hawes. In J. Edleston (ed.), Correspondence of Sir Isaac Newton and Professor Cotes (1850), 284.
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A week or so after I learned that I was to receive the Miller Award, our president, Marty Morton, phoned and asked me if I would utter a few words of scientific wisdom as a part of the ceremony. Unfortunately for me, and perhaps for you, I agreed to do so. In retrospect I fear that my response was a serious error, because I do not feel wise. I do not know whether to attribute my response to foolhardiness, to conceit, to an inordinate susceptibility to flattery, to stupidity, or to some combination of these unfortunate attributes all of which I have been told are recognizable in my personality. Personally, I tend to favor stupidity, because that is a condition over which I have little control.
Bartholomew, April 1993, unpublished remarks when receiving the Miller Award from the Cooper Ornithological Society.
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All err the more dangerously because each follows a truth. Their mistake lies not in following a falsehood but in not following another truth.
From Pensées, as translated in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966), 325. From the original French, “Tous errent d'autant plus dangereusement qu’ils suivent chacun une vérité. Leur faute n’est pas de suivre une fausseté, mais de ne pas suivre une autre vérité,” in Oeuvres Complètes (1864), Vol. 1, 363.
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All Men are liable to Error, and most Men are in many Points, by Passion or Interest, under Temptation to it.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 20, Section 17, 718.
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All our knowledge merely helps us to die a more painful death than the animals that know nothing. A day will come when science will turn upon its error and no longer hesitate to shorten our woes. A day will come when it will dare and act with certainty; when life, grown wiser, will depart silently at its hour, knowing that it has reached its term.
Our Eternity, translated by Alexander Teixeira de Mattos (1913), 24.
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All sorts of computer errors are now turning up. You'd be surprised to know the number of doctors who claim they are treating pregnant men.
Anonymous
Official of the Quebec Health Insurance Board, on Use of Computers in Quebec Province's Comprehensive Medical-care system. F. 19, 4:5. In Barbara Bennett and Linda Amster, Who Said What (and When, and Where, and How) in 1971: December-June, 1971 (1972), Vol. 1, 38. (Later sources cite Isaac Asimov.)
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Almost every major systematic error which has deluded men for thousands of years relied on practical experience. Horoscopes, incantations, oracles, magic, witchcraft, the cures of witch doctors and of medical practitioners before the advent of modern medicine, were all firmly established through the centuries in the eyes of the public by their supposed practical successes. The scientific method was devised precisely for the purpose of elucidating the nature of things under more carefully controlled conditions and by more rigorous criteria than are present in the situations created by practical problems.
Personal Knowledge (1958), 183.
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Almost everyone... seems to be quite sure that the differences between the methodologies of history and of the natural sciences are vast. For, we are assured, it is well known that in the natural sciences we start from observation and proceed by induction to theory. And is it not obvious that in history we proceed very differently? Yes, I agree that we proceed very differently. But we do so in the natural sciences as well.
In both we start from myths—from traditional prejudices, beset with error—and from these we proceed by criticism: by the critical elimination of errors. In both the role of evidence is, in the main, to correct our mistakes, our prejudices, our tentative theories—that is, to play a part in the critical discussion, in the elimination of error. By correcting our mistakes, we raise new problems. And in order to solve these problems, we invent conjectures, that is, tentative theories, which we submit to critical discussion, directed towards the elimination of error.
The Myth of the Framework: In Defence of Science and Rationality (1993), 140.
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Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in infering that he is an inexact man. Every careful measurement in science is always given with the probable error ... every observer admits that he is likely wrong, and knows about how much wrong he is likely to be.
In The Scientific Outlook (1931, 2009), 42.
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An error is the more dangerous in proportion to the degree of truth which it contains.
Entry for 26 Dec 1852 in Amiel’s Journal: The Journal Intime of Henri-Frédéric Amiel, trans. Humphry Ward (1893), 34.
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An error that ascribes to a man what was actually the work of a woman has more lives than a cat.
In Letter, Westminster Gazette (14 Mar 1909). As cited in Joan Mason, 'Hertha Ayrton (1854-1923) and the Admission of Women to the Royal Society of London', Notes and Records of the Royal Society of London (Jul 1991), 45, No. 2, 201-220. Ayrton wrote so that Marie Curie should be recognized for the discovery of radium, rather than being attributed to Pierre Curie.
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And even your atom, my dear mechanists and physicists—how much error, how much rudimentary psychology is still residual in your atom!
From 'The Four Great Errors', The Twilight of the Idols (1888), collected in Thomas Common (trans.), The Works of Friedrich Nietzsche (1896), Vol. 11, 139.
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And from this such small difference of eight minutes [of arc] it is clear why Ptolemy, since he was working with bisection [of the linear eccentricity], accepted a fixed equant point… . For Ptolemy set out that he actually did not get below ten minutes [of arc], that is a sixth of a degree, in making observations. To us, on whom Divine benevolence has bestowed the most diligent of observers, Tycho Brahe, from whose observations this eight-minute error of Ptolemy’s in regard to Mars is deduced, it is fitting that we accept with grateful minds this gift from God, and both acknowledge and build upon it. So let us work upon it so as to at last track down the real form of celestial motions (these arguments giving support to our belief that the assumptions are incorrect). This is the path I shall, in my own way, strike out in what follows. For if I thought the eight minutes in [ecliptic] longitude were unimportant, I could make a sufficient correction (by bisecting the [linear] eccentricity) to the hypothesis found in Chapter 16. Now, because they could not be disregarded, these eight minutes alone will lead us along a path to the reform of the whole of Astronomy, and they are the matter for a great part of this work.
Astronomia Nova, New Astronomy (1609), ch. 19, 113-4, Johannes Kepler Gesammelte Werke (1937-), Vol. 3, 177-8.
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Another error is a conceit that … the best has still prevailed and suppressed the rest: so as, if a man should begin the labor of a new search, he were but like to light upon somewhat formerly rejected, and by rejection brought into oblivion; as if the multitude, or the wisest for the multitude’s sake, were not ready to give passage rather to that which is popular and superficial, than to that which is substantial and profound: for the truth is, that time seemeth to be of the nature of a river or stream, which carrieth down to us that which is light and blown up, and sinketh and drowneth that which is weighty and solid.
Advancement of Learning, Book 1. Collected in The Works of Francis Bacon (1826), Vol 1, 36.
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Another source of fallacy is the vicious circle of illusions which consists on the one hand of believing what we see, and on the other in seeing what we believe.
Attributed. Peter McDonald, In The Oxford Dictionary of Medical Quotations (2004), 2.
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Any experiment may be regarded as forming an individual of a 'population' of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this population.
Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experiments belong. In a great number of cases the question finally turns on the value of a mean, either directly, or as the mean difference between the two qualities.
If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty:— (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals.
'The Probable Error of a Mean', Biometrika, 1908, 6, 1.
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Any one who has studied the history of science knows that almost every great step therein has been made by the “anticipation of Nature,” that is, by the invention of hypotheses, which, though verifiable, often had very little foundation to start with; and, not unfrequently, in spite of a long career of usefulness, turned out to be wholly erroneous in the long run.
In 'The Progress of Science 1837-1887' (1887), Collected Essays (1901), Vol. 1, 62.
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Are not all Hypotheses erroneous, in which Light is supposed to consist in Pression or Motion, propagated through a fluid Medium? For in all these Hypotheses the Phaenomena of Light have been hitherto explain'd by supposing that they arise from new Modifications of the Rays; which is an erroneous Supposition.
Opticks, 2nd edition (1718), Book 3, Query 28, 337.
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Art has a double face, of expression and illusion, just like science has a double face: the reality of error and the phantom of truth.
'The Lie of the Truth'. (1938) translated by Phil Powrie (1989). In Carol A. Dingle, Memorable Quotations (2000), 61.
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As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries—not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.
From A Logical Point of View (1953), 44. [Note: “qua” means “in the character or role of,” thus “qua lay physicist” means “in the role of lay physicist,” or perhaps even (?) “putting on my lay physicist hat.” —Webmaster]
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As in the experimental sciences, truth cannot be distinguished from error as long as firm principles have not been established through the rigorous observation of facts.
Ésur la maladie des vers ásoie (1870), 39.
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At the entrance to the observatory Stjerneborg located underground, Tycho Brahe built a Ionic portal. On top of this were three sculptured lions. On both sides were inscriptions and on the backside was a longer inscription in gold letters on a porfyr stone: Consecrated to the all-good, great God and Posterity. Tycho Brahe, Son of Otto, who realized that Astronomy, the oldest and most distinguished of all sciences, had indeed been studied for a long time and to a great extent, but still had not obtained sufficient firmness or had been purified of errors, in order to reform it and raise it to perfection, invented and with incredible labour, industry, and expenditure constructed various exact instruments suitable for all kinds of observations of the celestial bodies, and placed them partly in the neighbouring castle of Uraniborg, which was built for the same purpose, partly in these subterranean rooms for a more constant and useful application, and recommending, hallowing, and consecrating this very rare and costly treasure to you, you glorious Posterity, who will live for ever and ever, he, who has both begun and finished everything on this island, after erecting this monument, beseeches and adjures you that in honour of the eternal God, creator of the wonderful clockwork of the heavens, and for the propagation of the divine science and for the celebrity of the fatherland, you will constantly preserve it and not let it decay with old age or any other injury or be removed to any other place or in any way be molested, if for no other reason, at any rate out of reverence to the creator’s eye, which watches over the universe. Greetings to you who read this and act accordingly. Farewell!
(Translated from the original in Latin)
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Authority. Man cannot exist without it, and yet it brings in its train just as much of error as of truth. It perpetuates one by one things which should pass away one by one; it rejects that which should be preserved and allows it to pass away; and it is chiefly to blame for mankind’s want of progress.
In The Maxims and Reflections of Goethe (1906), 188.
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Behold the mighty dinosaur,
Famous in prehistoric lore,
Not only for his power and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains—
One in his head (the usual place),
The other at his spinal base.
Thus he could reason 'A priori'
As well as 'A posteriori'.
No problem bothered him a bit
He made both head and tail of it.
So wise was he, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along.
If something slipped his forward mind
'Twas rescued by the one behind.
And if in error he was caught
He had a saving afterthought.
As he thought twice before he spoke
He had no judgment to revoke.
Thus he could think without congestion
Upon both sides of every question.
Oh, gaze upon this model beast
Defunct ten million years at least.
'The Dinosaur: A Poem' (1912). In E. H. Colbert (ed.), The Dinosaur Book (1951), 78.
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Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611. [The French phrase, à peu près means “approximately”. —Webmaster]
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Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.
'Mathematical Problems', Bulletin of the American Mathematical Society (Jul 1902), 8, 441.
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Buffon, who, with all his theoretical ingenuity and extraordinary eloquence, I suspect had little actual information in the science on which he wrote so admirably For instance, he tells us that the cow sheds her horns every two years; a most palpable error. ... It is wonderful that Buffon who lived so much in the country at his noble seat should have fallen into such a blunder I suppose he has confounded the cow with the deer.
In The Life of Samuel Johnson, LL.D. (1826), Vol. 3, 70, footnote.
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But as no two (theoreticians) agree on this (skin friction) or any other subject, some not agreeing today with what they wrote a year ago, I think we might put down all their results, add them together, and then divide by the number of mathematicians, and thus find the average coefficient of error. (1908)
In Artificial and Natural Flight (1908), 3. Quoted in John David Anderson, Jr., Hypersonic and High Temperature Gas Dynamics (2000), 335.
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But I believe that there is no philosophical high-road in science, with epistemological signposts. No, we are in a jungle and find our way by trial and error, building our road behind us as we proceed. We do not find signposts at cross-roads, but our own scouts erect them, to help the rest.
Max Born
In Experiment and Theory in Physics (1943), 44.
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But the greatest error of all the rest is the mistaking or misplacing of the last or farthest end of knowledge: for men have entered into a desire of learning and knowledge, sometimes upon a natural curiosity and inquisitive appetite; sometimes to entertain their minds with variety and delight; sometimes for ornament and reputation; and sometimes to enable them to victory of wit and contradiction; and most times for lucre and profession; and seldom sincerely to give a true account of their gift of reason, to the benefit and use of men...
The First Book of Francis Bacon of the Proficience and Advancement of Learning (1605). In Francis Bacon and Basil Montagu, The Works of Francis Bacon, Lord Chancellor of England (1852), 174
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But when great and ingenious artists behold their so inept performances, not undeservedly do they ridicule the blindness of such men; since sane judgment abhors nothing so much as a picture perpetrated with no technical knowledge, although with plenty of care and diligence. Now the sole reason why painters of this sort are not aware of their own error is that they have not learnt Geometry, without which no one can either be or become an absolute artist; but the blame for this should be laid upon their masters, who are themselves ignorant of this art.
In The Art of Measurement (1525). As quoted in Albrecht Dürer and R.T. Nichol (trans.), 'Preface', Of the Just Shaping of Letters (1965), Book 3, 1-2.
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But, as Bacon has well pointed out, truth is more likely to come out of error, if this is clear and definite, than out of confusion, and my experience teaches me that it is better to hold a well-understood and intelligible opinion, even if it should turn out to be wrong, than to be content with a muddle-headed mixture of conflicting views, sometimes miscalled impartiality, and often no better than no opinion at all.
Principles of General Physiology (1915), x.
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But, further, no animal can live upon a mixture of pure protein, fat and carbohydrate, and even when the necessary inorganic material is carefully supplied, the animal still cannot flourish. The animal body is adjusted to live either upon plant tissues or the tissues of other animals, and these contain countless substances other than the proteins, carbohydrates and fats... In diseases such as rickets, and particularly in scurvy, we have had for long years knowledge of a dietetic factor; but though we know how to benefit these conditions empirically, the real errors in the diet are to this day quite obscure. They are, however, certainly of the kind which comprises these minimal qualitative factors that I am considering.
'The Analyst and the Medical Man', The Analyst (1906), 31, 395-6.
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By teaching us how to cultivate each ferment in its purity—in other words, by teaching us how to rear the individual organism apart from all others,—Pasteur has enabled us to avoid all these errors. And where this isolation of a particular organism has been duly effected it grows and multiplies indefinitely, but no change of it into another organism is ever observed. In Pasteur’s researches the Bacterium remained a Bacterium, the Vibrio a Vibrio, the Penicillium a Penicillium, and the Torula a Torula. Sow any of these in a state of purity in an appropriate liquid; you get it, and it alone, in the subsequent crop. In like manner, sow smallpox in the human body, your crop is smallpox. Sow there scarlatina, and your crop is scarlatina. Sow typhoid virus, your crop is typhoid—cholera, your crop is cholera. The disease bears as constant a relation to its contagium as the microscopic organisms just enumerated do to their germs, or indeed as a thistle does to its seed.
In 'Fermentation, and its Bearings on Surgery and Medicine', Essays on the Floating­Matter of the Air in Relation to Putrefaction and Infection (1881), 264.
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Common sense … may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do.
In Science and Common Sense (1951), 32-33.
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Complex organisms cannot be construed as the sum of their genes, nor do genes alone build particular items of anatomy or behavior by them selves. Most genes influence several aspects of anatomy and behavior–as they operate through complex interactions with other genes and their products, and with environmental factors both within and outside the developing organism. We fall into a deep error, not just a harmful oversimplification, when we speak of genes ‘for’ particular items of anatomy or behavior.
…...
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Crooked things may be as stiff and unflexible as streight: and Men may be as positive and peremptory in Error as in Truth.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 19, Section 11, 703.
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DISCUSSION, n. A method of confirming others in their errors.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  72.
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Dissections daily convince us of our ignorance of disease, and cause us to blush at our prescriptions. What mischief have we done under the belief of false facts and false theories! We have assisted in multiplying diseases; we have done more; we have increased their mortality. ... I am pursuing Truth, and am indifferent whither I am led, if she is my only leader.
From a public lecture by Rush. Quoted by Isaac Jennings, in Medical Reform; a Treatise on Man's Physical Being and Disorders (1847), 33.
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Endowed with two qualities, which seemed incompatible with each other, a volcanic imagination and a pertinacity of intellect which the most tedious numerical calculations could not daunt, Kepler conjectured that the movements of the celestial bodies must be connected together by simple laws, or, to use his own expression, by harmonic laws. These laws he undertook to discover. A thousand fruitless attempts, errors of calculation inseparable from a colossal undertaking, did not prevent him a single instant from advancing resolutely toward the goal of which he imagined he had obtained a glimpse. Twenty-two years were employed by him in this investigation, and still he was not weary of it! What, in reality, are twenty-two years of labor to him who is about to become the legislator of worlds; who shall inscribe his name in ineffaceable characters upon the frontispiece of an immortal code; who shall be able to exclaim in dithyrambic language, and without incurring the reproach of anyone, “The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his words.”
In 'Eulogy on Laplace', in Smithsonian Report for the year 1874 (1875), 131-132.
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Error has indeed long darkened the horizon of medical science; and albeit there have been lightnings like coruscations of genius from time to time, still they have passed away, and left the atmosphere as dark as before.
Memoirs of John Abernethy (1854), 293.
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Error held as truth has much the effect of truth. In politics and religion this fact upsets many confident predictions.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 177.
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Error is often nourished by good sense. … The meaning is, that the powers of the understanding are frequently employed to defend favourite errors; and that a man of sense frequently fortifies himself in his prejudices, or in false opinions which he received without examination, by such arguments as would not have occurred to a fool.
In Maxims, Characters, and Reflections, Critical, Satyrical and Moral (2nd ed., 1757), 9. The meaning is given as a footnote.
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Error of opinion may be tolerated where reason is left free to combat it.
From his First Inaugural Address (4 Mar 1801). In Annals of the Congress of the United States (1801), 11, 583.
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Error, never can be consistent, nor can truth fail of having support from the accurate examination of every circumstance.
'Theory of the Earth', Transactions of the Royal Society of Edinburgh (1788), 1, 259.
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Errors, like straws, upon the surface flow;
He who would search for pearls must dive below.
Prologue, All For Love: Or, The World Well Lost (1678), collected in The Modern British Drama, (1811), Vol. 1, 337.
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Even mistaken hypotheses and theories are of use in leading to discoveries. This remark is true in all the sciences. The alchemists founded chemistry by pursuing chimerical problems and theories which are false. In physical science, which is more advanced than biology, we might still cite men of science who make great discoveries by relying on false theories. It seems, indeed, a necessary weakness of our mind to be able to reach truth only across a multitude of errors and obstacles.
An Introduction to the Study of Experimental Medicine (1865, translation 1927, 1957), 170.
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Eventually, we reach … the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial.
In Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202. The lecture series was delivered at Yale University in Fall 1935. Part of a longer quote on this page that begins: “The explorations of space…”.
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Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error.
In 'Lecture 7', Lectures on the History of Moral Philosophy in England (1852), 101.
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Every species of plant and animal is determined by a pool of germ plasm that has been most carefully selected over a period of hundreds of millions of years. We can understand now why it is that mutations in these carefully selected organisms almost invariably are detrimental.The situation can be suggested by a statement by Dr. J.B.S. Haldane: “My clock is not keeping perfect time. It is conceivable that it will run better if I shoot a bullet through it; but it is much more probable that it will stop altogether.” Professor George Beadle, in this connection, has asked: “What is the chance that a typographical error would improve Hamlet?”
In No More War! (1958), Chap. 4, 53.
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Everybody firmly believes in it [Nomal Law of Errors] because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.
…...
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Everyone believes in the law of errors, the experimenters because they think it is a mathematical theorem, and the mathematicians because they think it is an experimental fact.
Remark to Henri Poincaré about the Gaussian curve. From the original French, “Les expérimentateurs s’imaginent que c’est un théorème de mathématique, et les mathématiciens d’être un fait expérimental”, in Henri Poincaré, Calcul des Probabilités (1896), 149. Poincaré introduces it as, “me disait un jour M. Lippmann” (Mr. Lippman told me one day). Quote above as translated in F. Downton, 'Review: Nonparametric Methods in Statistics', The Mathematical Gazette (Feb 1959), 43, No. 343, 67.
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Evolution triumphs because it turns to natural selection, the plodding accumulation of error.
Almost Like a Whale: The Origin of Species Updated (1999), 9.
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Experience is never at fault; it is only your judgment that is in error in promising itself such results from experience as are not caused by our experiments. For having given a beginning, what follows from it must necessarily be a natural development of such a beginning, unless it has been subject to a contrary influence, while, if it is affected by any contrary influence, the result which ought to follow from the aforesaid beginning will be found to partake of this contrary influence in a greater or less degree in proportion as the said influence is more or less powerful than the aforesaid beginning.
'Philosophy', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938), Vol. 1, 70.
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Experiment adds to knowledge, Credulity leads to error.
Anonymous
Arabic Proverb.
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False facts are highly injurious to the progress of science, for they often long endure; but false views, if supported by some evidence, do little harm, as every one takes a salutary pleasure in proving their falseness; and when this is done, one path towards error is closed and the road to truth is often at the same time opened.
The Descent of Man (1871), Vol. 2, 385.
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Falsity cannot keep an idea from being beautiful; there are certain errors of such ingenuity that one could regret their not ranking among the achievements of the human mind.
Pensées d'un Biologiste (1939). Translated in The Substance of Man (1962), 89.
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Finally, I aim at giving denominations to things, as agreeable to truth as possible. I am not ignorant that words, like money, possess an ideal value, and that great danger of confusion may be apprehended from a change of names; in the mean time it cannot be denied that chemistry, like the other sciences, was formerly filled with improper names. In different branches of knowledge, we see those matters long since reformed: why then should chemistry, which examines the real nature of things, still adopt vague names, which suggest false ideas, and favour strongly of ignorance and imposition? Besides, there is little doubt but that many corrections may be made without any inconvenience.
Physical and Chemical Essays (1784), Vol. I, xxxvii.
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For FRICTION is inevitable because the Universe is FULL of God's works.
For the PERPETUAL MOTION is in all works of Almighty GOD.
For it is not so in the engines of man, which are made of dead materials, neither indeed can be.
For the Moment of bodies, as it is used, is a false term—bless God ye Speakers on the Fifth of November.
For Time and Weight are by their several estimates.
For I bless GOD in the discovery of the LONGITUDE direct by the means of GLADWICK.
For the motion of the PENDULUM is the longest in that it parries resistance.
For the WEDDING GARMENTS of all men are prepared in the SUN against the day of acceptation.
For the wedding Garments of all women are prepared in the MOON against the day of their purification.
For CHASTITY is the key of knowledge as in Esdras, Sir Isaac Newton & now, God be praised, in me.
For Newton nevertheless is more of error than of the truth, but I am of the WORD of GOD.
From 'Jubilate Agno' (c.1758-1763), in N. Callan (ed.), The Collected Poems of Christopher Smart (1949), Vol. 1, 276.
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For the Members of the Assembly having before their eyes so many fatal Instances of the errors and falshoods, in which the greatest part of mankind has so long wandred, because they rely'd upon the strength of humane Reason alone, have begun anew to correct all Hypotheses by sense, as Seamen do their dead Reckonings by Cœlestial Observations; and to this purpose it has been their principal indeavour to enlarge and strengthen the Senses by Medicine, and by such outward Instruments as are proper for their particular works.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), preface sig.
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For, the great enemy of knowledge is not error, but inertness. All that we want is discussion, and then we are sure to do well, no matter what our blunders may be. One error conflicts with another; each destroys its opponent, and truth is evolved.
In History of Civilization in England (1861), Vol. 2, 408.
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Generally speaking, the errors in religion are dangerous; those in philosophy only ridiculous.
A Treatise on Human Nature (1739-40), ed. L. A. Selby-Bigge (1888), book 1, part 4, section 7, 272.
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Geologists have not been slow to admit that they were in error in assuming that they had an eternity of past time for the evolution of the earth's history. They have frankly acknowledged the validity of the physical arguments which go to place more or less definite limits to the antiquity of the earth. They were, on the whole, disposed to acquiesce in the allowance of 100 millions of years granted to them by Lord Kelvin, for the transaction of the whole of the long cycles of geological history. But the physicists have been insatiable and inexorable. As remorseless as Lear's daughters, they have cut down their grant of years by successive slices, until some of them have brought the number to something less than ten millions. In vain have the geologists protested that there must somewhere be a flaw in a line of argument which tends to results so entirely at variance with the strong evidence for a higher antiquity, furnished not only by the geological record, but by the existing races of plants and animals. They have insisted that this evidence is not mere theory or imagination, but is drawn from a multitude of facts which become hopelessly unintelligible unless sufficient time is admitted for the evolution of geological history. They have not been able to disapprove the arguments of the physicists, but they have contended that the physicists have simply ignored the geological arguments as of no account in the discussion.
'Twenty-five years of Geological Progress in Britain', Nature, 1895, 51, 369.
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Geometry enlightens the intellect and sets one’s mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
In Ibn Khaldûn, Franz Rosenthal (trans.) and N.J. Dawood (ed.), The Muqaddimah: An Introduction to History (1967, 1969), Vol. 1, 378.
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Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.
Pareto’s comment on Kepler. In John Bartlett, Familiar Quotations (12th ed. 1949), 1198. Also in Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 231.
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Great is the power of steady misrepresentation - but the history of science shows how, fortunately, this power does not endure long.
Origin of Species (1878), 421.
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Great scientific discoveries have been made by men seeking to verify quite erroneous theories about the nature of things.
From 'Wordsworth in the Tropics', in Life and Letters and the London Mercury (1928), Vol. 1, 349.
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He that believes, without having any Reason for believing, may be in love with his own Fancies; but neither seeks Truth as he ought, nor pays the Obedience due to his Maker, who would have him use those discerning Faculties he has given him, to keep him out of Mistake and Errour.
In 'Of Reason', Essay Concerning Humane Understanding (1690), Book 4, Ch. 17, Sec. 24, 347.
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He that could teach mathematics well, would not be a bad teacher in any of [physics, chemistry, biology or psychology] unless by the accident of total inaptitude for experimental illustration; while the mere experimentalist is likely to fall into the error of missing the essential condition of science as reasoned truth; not to speak of the danger of making the instruction an affair of sensation, glitter, or pyrotechnic show.
In Education as a Science (1879), 298.
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Hence, a devout Christian must avoid astrologers and all impious soothsayers, especially when they tell the truth, for fear of leading his soul into error by consorting with demons and entangling himself with the bonds of such association.
De Genesi ad Uteram (On The Uteral Interpretation of Genesis) [401/415], Book II, chapter 17, section 37, trans. J. H. Taylor (1982), Vol. I, 72-3.
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Here I most violently want you to
Avoid one fearful error, a vicious flaw.
Don’t think that our bright eyes were made that we
Might look ahead; that hips and knees and ankles
So intricately bend that we might take
Big strides, and the arms are strapped to the sturdy shoulders
And hands are given for servants to each side
That we might use them to support our lives.
All other explanations of this sort
Are twisted, topsy-turvy logic, for
Nothing what is born produces its own use.
Sight was not born before the light of the eyes,
Nor were words and pleas created before the tongue
Rather the tongue's appearance long preceded
Speech, and the ears were formed far earlier than
The sound first heard. To sum up, all the members Existed, I should think, before their use, So use has not caused them to have grown.
On the Nature of Things, trans. Anthony M. Esolen (1995), Book 4, lines 820-8, 145.
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Honorable errors do not count as failures in science, but as seeds for progress in the quintessential activity of correction.
Leonardo's Mountain of Clams and the Diet of Worms: Essays on Natural History (1998), 163.
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Hypotheses may be useful, though involving much that is superfluous, and even erroneous: for they may supply the true bond of connexion of the facts; and the superfluity and error may afterwards be pared away.
Aphorism 11, 'Aphorisms Concerning Science', The Philosophy of the Inductive Sciences (1840), Vol. 1, xxxvi.
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I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
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I beseech you in the bowels of Christ, think it possible you may be mistaken.
Letter, to General Assembly of the Church of Scotland (1650). In The Parliamentary or Constitutional History of England (1763), Vol. 19, 322.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I could never have known so well how paltry men are, and how little they care for really high aims, if I had not tested them by my scientific researches. Thus I saw that most men only care for science so far as they get a living by it, and that they worship even error when it affords them a subsistence.
Wed 12 Oct 1825. Johann Peter Eckermann, Conversations with Goethe, ed. J. K. Moorhead and trans. J. Oxenford (1971), 119-20.
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I do not maintain that the chief value of the study of arithmetic consists in the lessons of morality that arise from this study. I claim only that, to be impressed from day to day, that there is something that is right as an answer to the questions with which one is able to grapple, and that there is a wrong answer—that there are ways in which the right answer can be established as right, that these ways automatically reject error and slovenliness, and that the learner is able himself to manipulate these ways and to arrive at the establishment of the true as opposed to the untrue, this relentless hewing to the line and stopping at the line, must color distinctly the thought life of the pupil with more than a tinge of morality. … To be neighborly with truth, to feel one’s self somewhat facile in ways of recognizing and establishing what is right, what is correct, to find the wrong persistently and unfailingly rejected as of no value, to feel that one can apply these ways for himself, that one can think and work independently, have a real, a positive, and a purifying effect upon moral character. They are the quiet, steady undertones of the work that always appeal to the learner for the sanction of his best judgment, and these are the really significant matters in school work. It is not the noise and bluster, not even the dramatics or the polemics from the teacher’s desk, that abide longest and leave the deepest and stablest imprint upon character. It is these still, small voices that speak unmistakably for the right and against the wrong and the erroneous that really form human character. When the school subjects are arranged on the basis of the degree to which they contribute to the moral upbuilding of human character good arithmetic will be well up the list.
In Arithmetic in Public Education (1909), 18. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 69.
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I had made considerable advance ... in calculations on my favourite numerical lunar theory, when I discovered that, under the heavy pressure of unusual matters (two transits of Venus and some eclipses) I had committed a grievous error in the first stage of giving numerical value to my theory. My spirit in the work was broken, and I have never heartily proceeded with it since.
[Concerning his calculations on the orbital motion of the Moon.]
Private note (29 Sep 1890). In George Biddell Airy and Wilfrid Airy (ed.), Autobiography of Sir George Biddell Airy (1896), 350.
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I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain … But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.
(1891) As quoted in translation in Leo Koenigsberger and Frances A. Welby (trans.), Hermann von Helmholtz (1906), 180-181.
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I have made many mistakes myself; in learning the anatomy of the eye I dare say, I have spoiled a hatfull; the best surgeon, like the best general, is he who makes the fewest mistakes.
Quoted in James Anthony Froude, John Tulloch and Thomas Carlyle, Fraser's Magazine (Nov 1862), 66, 574.
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I have spent much time in the study of the abstract sciences; but the paucity of persons with whom you can communicate on such subjects disgusted me with them. When I began to study man, I saw that these abstract sciences are not suited to him, and that in diving into them, I wandered farther from my real object than those who knew them not, and I forgave them for not having attended to these things. I expected then, however, that I should find some companions in the study of man, since it was so specifically a duty. I was in error. There are fewer students of man than of geometry.
Thoughts of Blaise Pascal (1846), 137.
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I have taken the stand that nobody can be always wrong, but it does seem to me that I have approximated so highly that I am nothing short of a negative genius.
Wild Talents (1932). In The Complete Books of Charles Fort (1975), 1037.
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I know not what fatal calamity has invaded the sciences, for when an error is born with them and with the lapse of time becomes as it were fixed, those who profess the science will not suffer its withdrawal.
Jean Rey
Essays of Jean Rey, Doctor of Medicine, on an Enquiry into the Cause Wherefore Tin and Lead Increase in Weight on Calcination (1630). Translated in Alembic Club Reprint No. 11, (1895) 25.
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I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the “Law of Frequency of Error.” The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshaled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.
In Natural Inheritance (1894), 66.
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I know that certain minds would regard as audacious the idea of relating the laws which preside over the play of our organs to those laws which govern inanimate bodies; but, although novel, this truth is none the less incontestable. To hold that the phenomena of life are entirely distinct from the general phenomena of nature is to commit a grave error, it is to oppose the continued progress of science.
Leçons sur les Phenomenes Physiques de la Vie (1836-38), Vol. 1, 6. Trans. J. M. D. Olmsted, François Magendie (1944), 203.
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I know well there are those who would have the Study of Nature restrained wholly to Observations; without ever proceeding further. But due Consideration, and a deeper Insight into Things, would soon have undeceived and made them sensible of their error. Assuredly, that man who should spend his whole life in amassing together stone, timber, and other materials for building, without ever at the making any use, or raising any fabrick out of them, might well be reputed very fantastic and extravagant. And a like censure would be his due, who should be perpetually heaping up of natural collections without design. building a structure of philosophy out of them, or advancing some propositions that might turn to the benefit and advantage of the world. This is in reality the true and only proper end of collections, of observations, and natural history: and they are of no manner of use or value without it.
In An Attempt Toward a Natural History of the Fossils of England (1729), xiii-xiv.
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I, Galileo Galilei, son of the late Vincenzo Galilei, of Florence, aged seventy years, being brought personally to judgment, and kneeling before your Most Eminent and Most Reverend Lords Cardinals, General Inquisitors of the universal Christian republic against heretical depravity, having before my eyes the Holy Gospels, which I touch with my own hands, swear that I have always believed, and now believe, and with the help of God will in future believe, every article which the Holy Catholic and Apostolic Church of Rome holds, teaches, and preaches. But because I have been enjoined by this Holy Office altogether to abandon the false opinion which maintains that the sun is the centre and immovable, and forbidden to hold, defend, or teach the said false doctrine in any manner, and after it hath been signified to me that the said doctrine is repugnant with the Holy Scripture, I have written and printed a book, in which I treat of the same doctrine now condemned, and adduce reasons with great force in support of the same, without giving any solution, and therefore have been judged grievously suspected of heresy; that is to say, that I held and believed that the sun is the centre of the universe and is immovable, and that the earth is not the centre and is movable; willing, therefore, to remove from the minds of your Eminences, and of every Catholic Christian, this vehement suspicion rightfully entertained toward me, with a sincere heart and unfeigned faith, I abjure, curse, and detest the said errors and heresies, and generally every other error and sect contrary to Holy Church; and I swear that I will never more in future say or assert anything verbally, or in writing, which may give rise to a similar suspicion of me; but if I shall know any heretic, or anyone suspected of heresy, that I will denounce him to this Holy Office, or to the Inquisitor or Ordinary of the place where I may be; I swear, moreover, and promise, that I will fulfil and observe fully, all the penances which have been or shall be laid on me by this Holy Office. But if it shall happen that I violate any of my said promises, oaths, and protestations (which God avert!), I subject myself to all the pains and punishments which have been decreed and promulgated by the sacred canons, and other general and particular constitutions, against delinquents of this description. So may God help me, and his Holy Gospels which I touch with my own hands. I, the above-named Galileo Galilei, have abjured, sworn, promised, and bound myself as above, and in witness thereof with my own hand have subscribed this present writing of my abjuration, which I have recited word for word. At Rome, in the Convent of Minerva, June 22, 1633. I, Galileo Galilei, have abjured as above with my own hand.
Abjuration, 22 Jun 1633. In J.J. Fahie, Galileo, His Life and Work (1903), 319-321.
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If Bacon erred here [in valuing mathematics only for its uses], we must acknowledge that we greatly prefer his error to the opposite error of Plato. We have no patience with a philosophy which, like those Roman matrons who swallowed abortives in order to preserve their shapes, takes pains to be barren for fear of being homely.
In 'Lord Bacon', Edinburgh Review (Jul 1837). Collected in Critical and Miscellaneous Essays: Contributed to the Edinburgh Review (1857), Vol. 1, 396.
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If entomologists have things backward, their errors have spawned a host of others central to modern evolutionary science. … E.O. Wilson is … the founder of a rich and fruitful discipline—sociobiology. And sociobiology has … helped lay the groundwork for the dogma of the “selfish gene.”
In 'The Embryonic Meme', Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 34.
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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 the matter is one that can be settled by observation, make the observation yourself. Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted.
In An Outline of Intellectual Rubbish (1943), 22.
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If there is a wrong way to do something, then someone will do it.
[Subsequently became known as Murphy's Law: “If anything can go wrong, it will.”]
As quoted in Robert L. Forward, 'Murphy Lives!', Science (Jan-Feb 1983), 83, 78. Short form in J.A. Simpson (ed), The Concise Oxford Dictionary of Proverbs (1982).
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If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.
Feynman Lectures on Gravitation, edited by Brian Hatfield (2002), 21.
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If you get all the facts, your judgment can be right. If you don’t get all the facts, it can’t be right.
Quoted in The St. Louis Dispatch (21 Jun 1965). In Alfred J. Kolatch, Great Jewish Quotations (1996), 38.
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If you thought that science was certain well, that is just an error on your part.
…...
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If, in the course of a thousand or two thousand years, science arrives at the necessity of renewing its points of view, that will not mean that science is a liar. Science cannot lie, for it’s always striving, according to the momentary state of knowledge, to deduce what is true. When it makes a mistake, it does so in good faith. It’s Christianity that’s the liar. It’s in perpetual conflict with itself.
In Adolf Hitler, Hugh Redwald Trevor-Roper, translated by Norman Cameron and R. H. Stevens, '14 October 1941', Secret Conversations (1941 - 1944) (1953), 51
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In 1905, a physicist measuring the thermal conductivity of copper would have faced, unknowingly, a very small systematic error due to the heating of his equipment and sample by the absorption of cosmic rays, then unknown to physics. In early 1946, an opinion poller, studying Japanese opinion as to who won the war, would have faced a very small systematic error due to the neglect of the 17 Japanese holdouts, who were discovered later north of Saipan. These cases are entirely parallel. Social, biological and physical scientists all need to remember that they have the same problems, the main difference being the decimal place in which they appear.
In William G. Cochran, Frederick Mosteller and John W. Tukey, 'Principles of Sampling', Journal of the American Statistical Society, 1954, 49, 31. Collected in Selected Papers of Frederick Mosteller (2006), 290.
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In a sense Shapley’s telling me that space was transparent, which I shouldn’t have believed, illustrates a fundamental problem in science, believing what people tell you. Go and find it out for yourself. That same error has persisted in my life and in many other people’s. Authorities are not always authorities on everything; they often cling to their own mistakes.
Oral History Transcript of interview with Dr. Jesse Greenstein by Paul Wright (31 Jul 1974), on website of American Institute of Physics.
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In a sense, genetics grew up as an orphan. In the beginning botanists and zoologists were often indifferent and sometimes hostile toward it. 'Genetics deals only with superficial characters', it was often said. Biochemists likewise paid it little heed in its early days. They, especially medical biochemists, knew of Garrod's inborn errors of metabolism and no doubt appreciated them in the biochemical sense and as diseases; but the biological world was inadequately prepared to appreciate fully the significance of his investigations and his thinking. Geneticists, it should be said, tended to be preoccupied mainly with the mechanisms by which genetic material is transmitted from one generation to, the next.
'Genes and chemical reactions In Neurospora', Nobel Lecture, 11 December 1958. In Nobel Lectures: Physiology or Medicine 1942-1962 (1964), 598.
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In all science error precedes the truth, and it is better it should go first than last.
Quoted in Adam Wooléver (ed.), Encyclopædia of Quotations: A Treasury of Wisdom, Wit and Humor, Odd Comparisons and Proverbs (6th ed, 1876), 128.
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In all science, error precedes the truth, and it is better it should go first than last.
…...
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In the 1920s, there was a dinner at which the physicist Robert W. Wood was asked to respond to a toast … “To physics and metaphysics.” Now by metaphysics was meant something like philosophy—truths that you could get to just by thinking about them. Wood took a second, glanced about him, and answered along these lines: The physicist has an idea, he said. The more he thinks it through, the more sense it makes to him. He goes to the scientific literature, and the more he reads, the more promising the idea seems. Thus prepared, he devises an experiment to test the idea. The experiment is painstaking. Many possibilities are eliminated or taken into account; the accuracy of the measurement is refined. At the end of all this work, the experiment is completed and … the idea is shown to be worthless. The physicist then discards the idea, frees his mind (as I was saying a moment ago) from the clutter of error, and moves on to something else. The difference between physics and metaphysics, Wood concluded, is that the metaphysicist has no laboratory.
In 'Wonder and Skepticism', Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.
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In the field of thinking, the whole history of science from geocentrism to the Copernican revolution, from the false absolutes of Aristotle’s physics to the relativity of Galileo’s principle of inertia and to Einstein’s theory of relativity, shows that it has taken centuries to liberate us from the systematic errors, from the illusions caused by the immediate point of view as opposed to “decentered” systematic thinking.
As quoted in D. E. Berlyne, Structure and Direction in Thinking (1965), 232.
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In the social equation, the value of a single life is nil; in the cosmic equation, it is infinite… Not only communism, but any political movement which implicitly relies on purely utilitarian ethics, must become a victim to the same fatal error. It is a fallacy as naïve as a mathematical teaser, and yet its consequences lead straight to Goya’s Disasters, to the reign of the guillotine, the torture chambers of the Inquisition, or the cellars of the Lubianka.
In 'The Invisible Writing', Arrow in the Blue: An Autobiography (1952), Vol. 2, 357.
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Inborn errors of metabolism.
Inborn Errors of Metabolism. The Croonian Lectures delivered before the Royal College of Physicians of London, in June, 1908 (1909).
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Irrationally held truths may be more harmful than reasoned errors.
Science and Culture, and Other Essays (1890), 335.
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Is it not evident, in these last hundred years (when the Study of Philosophy has been the business of all the Virtuosi in Christendome) that almost a new Nature has been revealed to us? that more errours of the School have been detected, more useful Experiments in Philosophy have been made, more Noble Secrets in Opticks, Medicine, Anatomy, Astronomy, discover'd, than in all those credulous and doting Ages from Aristotle to us? So true it is that nothing spreads more fast than Science, when rightly and generally cultivated.
Of Dramatic Poesie (1684 edition), lines 258-67, in James T. Boulton (ed.) (1964), 44
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It is a profoundly erroneous truism, repeated by all copy-books and eminent people when they are making speeches, that we should cultivate habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle—they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
In An Introduction to Mathematics (1911), 61.
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It is almost as difficult to make a man unlearn his errors, as his knowledge. Mal-information is more hopeless than non-information: for error is always more busy than ignorance. Ignorance is a blank sheet on which we may write; but error is a scribbled one on which we first erase. Ignorance is contented to stand still with her back to the truth; but error is more presumptuous, and proceeds, in the same direction. Ignorance has no light, but error follows a false one. The consequence is, that error, when she retraces her footsteps, has farther to go, before we can arrive at the truth, than ignorance.
Reflection 1, in Lacon: or Many things in Few Words; Addressed to Those Who Think (1820), 15.
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It is an error to imagine that evolution signifies a constant tendency to increased perfection. That process undoubtedly involves a constant remodeling of the organism in adaptation to new conditions; but it depends on the nature of those conditions whether the direction of the modifications effected shall be upward or downward.
'The Struggle for Existence in Human Society' (1888). In Collected Essays (1894), Vol. 9, 199.
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It is curious how often erroneous theories have had a beneficial effect for particular branches of science.
The Growth of Biological Thought: Diversity, Evolution and Inheritance (1982), 847.
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It is difficult to know how to treat the errors of the age. If a man oppose them, he stands alone; if he surrender to them, they bring him neither joy nor credit.
In The Maxims and Reflections of Goethe (1906), 185.
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It is easier to perceive error than to find truth, for the former lies on the surface and is easily seen, while the latter lies in the depth, where few are willing to search for it.
…...
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It is error only, and not truth, that shrinks from inquiry.
In 'Address to the Addressers', The Political Writings of Thomas Paine (1824), Vol. 2, 284.
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It is in scientific honesty that I endorse the presentation of alternative theories for the origin of the universe, life and man in the science classroom. It would be an error to overlook the possibility that the universe was planned rather than happening by chance.
In letter to California State board of Education (14 Sep 1972).
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It is in the name of Moses that Bellarmin thunderstrikes Galileo; and this great vulgarizer of the great seeker Copernicus, Galileo, the old man of truth, the magian of the heavens, was reduced to repeating on his knees word for word after the inquisitor this formula of shame: “Corde sincera et fide non ficta abjuro maledico et detestor supradictos errores et hereses.” Falsehood put an ass's hood on science.
[With a sincere heart, and of faith unfeigned, I deny by oath, condemn and detest the aforesaid errors and heresies.]
In Victor Hugo and Lorenzo O'Rourke (trans.) Victor Hugo's Intellectual Autobiography: (Postscriptum de ma vie) (1907), 313.
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It is interesting to transport one’s self back to the times when Astronomy began; to observe how discoveries were connected together, how errors have got mixed up with truth, have delayed the knowledge of it, and retarded its progress; and, after having followed the various epochs and traversed every climate, finally to contemplate the edifice founded on the labours of successive centuries and of various nations.
Description of Bailly’s plan when writing his history of astronomy books, quoted by François Arago, trans. by William Henry Smyth, Baden Powell and Robert Grant, in 'Bailly', Biographies of Distinguished Scientific Men (1859), Vol. 1, 114. Arago first presented this biography of Bailly when he read it to the Academy of Sciences (26 Feb 1844).
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It is not error which opposes the progress of truth; it is indolence, obstinacy, the spirit of routine, every thing which favors inaction.
In Fielding Hudson Garrison, An Introduction to the History of Medicine (1929), 33.
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It is not hard to learn more. What is hard is to unlearn when you discover yourself wrong
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It is not so difficult a task as to plant new truths, as to root out old errors
Lacon: Many Things in Few Words (1820-22, 1866), 276.
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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 often assumed that because the young child is not competent to study geometry systematically he need be taught nothing geometrical; that because it would be foolish to present to him physics and mechanics as sciences it is useless to present to him any physical or mechanical principles.
An error of like origin, which has wrought incalculable mischief, denies to the scholar the use of the symbols and methods of algebra in connection with his early essays in numbers because, forsooth, he is not as yet capable of mastering quadratics! … The whole infant generation, wrestling with arithmetic, seek for a sign and groan and travail together in pain for the want of it; but no sign is given them save the sign of the prophet Jonah, the withered gourd, fruitless endeavor, wasted strength.
From presidential address (9 Sep 1884) to the General Meeting of the American Social Science Association, 'Industrial Education', printed in Journal of Social Science (1885), 19, 121. Collected in Francis Amasa Walker, Discussions in Education (1899), 132.
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It is one thing, to shew a Man that he is in an Error; and another, to put him in possession of Truth.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 7, Section 11, 602.
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It is sometimes well for a blatant error to draw attention to overmodest truths.
Pensées d'un Biologiste (1939). Translated in The Substance of Man (1962), 89.
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It is the very error of the moon;
She comes more nearer earth than she was wont,
And makes men mad.
In Othello (1622), Act 5, Scene 2, line 109-111.
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It is they who hold the secret of the mysterious property of the mind by which error ministers to truth, and truth slowly but irrevocably prevails. Theirs is the logic of discovery, the demonstration of the advance of knowledge and the development of ideas, which as the earthly wants and passions of men remain almost unchanged, are the charter of progress, and the vital spark in history.
Lecture, 'The Study of History' (11 Jun 1895) delivered at Cambridge, published as A Lecture on The Study of History (1895), 54-55.
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It may be said of many palaeontologists, as Professor Hugh Trevor-Roper said recently of 18th century historians: “Their most serious error was to measure the past by the present”.
In The Nature of the Stratigraphical Record (1973), 26.
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It often happens that men, even of the best understandings and greatest circumspection, are guilty of that fault in reasoning which the writers on logick call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that the art which affords a cure to this weakness, or defect, of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted anyone arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations ... It proceeds indeed upon mathematical principles in calculating the number of the combinations of the things proposed: but by the conclusions that are obtained by it, the sagacity of the natural philosopher, the exactness of the historian, the skill and judgement of the physician, and the prudence and foresight of the politician, may be assisted; because the business of all these important professions is but to form reasonable conjectures concerning the several objects which engage their attention, and all wise conjectures are the results of a just and careful examination of the several different effects that may possibly arise from the causes that are capable of producing them.
Ars conjectandi (1713). In F. Maseres, The Doctrine of Permutations and Combinations (1795), 36.
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It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously. I also cannot imagine some will or goal outside the human sphere has been cited as a statement that precedes the last three sentences here, but this might have originated in a paraphrase, a transcription error, or a misquotation; it does not appear in any editions of the essay which have thus far been checked.
…...
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It was found after many troublesome experiments that when the vacuum within the lamp globe was good, and the contact between the carbon and the conductor which supported it sufficient, there was no blackening of the globes, and no appreciable wasting away of the carbons. Thus was swept away a pernicious error, which, like a misleading finger post proclaiming “No road this way,” tended to bar progress along a good thoroughfare. It only remained to perfect the details of the lamp, to find the best material from which to form the carbon, and to fix this material in the lamp in the best manner. These points, I think, I have now satisfactorily settled, and you see the result in the lamp before me on the table.
In Lecture (20 Oct 1880) at Newcastle-Upon-Tyne, as quoted in United States Courts of Appeals Reports: Cases Adjudged in the United States Circuit Court of Appeals (1894), Vol. 11, 419-420.
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It’s not the critic who counts; not the man which points out how the strong man stumbles or where the doer of deeds could have done them better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again … who knows great enthusiasms, the great devotions; who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.
In Joseph A. Califano, Jr., Inside: A Public and Private Life (2005), 356.
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Just as a physicist has to examine the telescope and galvanometer with which he is working; has to get a clear conception of what he can attain with them, and how they may deceive him; so, too, it seemed to me necessary to investigate likewise the capabilities of our power of thought.
'An Autobiographical Sketch' (1891). Trans. E. Atkinson, Popular Lectures on Scientific Subjects, Second Series, New Edition (1895), 284-5.
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Kepler’s laws, although not rigidly true, are sufficiently near to the truth to have led to the discovery of the law of attraction of the bodies of the solar system. The deviation from complete accuracy is due to the facts, that the planets are not of inappreciable mass, that, in consequence, they disturb each other's orbits about the Sun, and, by their action on the Sun itself, cause the periodic time of each to be shorter than if the Sun were a fixed body, in the subduplicate ratio of the mass of the Sun to the sum of the masses of the Sun and Planet; these errors are appreciable although very small, since the mass of the largest of the planets, Jupiter, is less than 1/1000th of the Sun's mass.
In Isaac Newton and Percival Frost (ed.) Newton’s Principia: Sections I, II, III (1863), 216.
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Know then thyself, presume not God to scan;
The proper study of Mankind is Man.
Plac'd on this isthmus of a middle state,
A being darkly wise, and rudely great:
With too much knowledge for the Sceptic side,
With too much weakness for the Stoic's pride,
He hangs between; in doubt to act, or rest;
In doubt to deem himself a God, or Beast;
In doubt his Mind or Body to prefer,
Born but to die, and reas'ning but to err;
Alike in ignorance, his reason such,
Whether he thinks too little, or too much:
Chaos of Thought and Passion, all confus'd;
Still by himself abus'd, or disabus'd;
Created half to rise, and half to fall;
Great lord of all things, yet a prey to all;
Sole judge of Truth, in endless Error hurl'd:
The glory, jest, and riddle of the world!
... Superior beings, when of late they saw
A mortal Man unfold all Nature's law,
Admir'd such wisdom in an earthly shape,
And shew'd a NEWTON as we shew an Ape.
'An Essay on Man' (1733-4), Epistle II. In John Butt (ed.), The Poems of Alexander Pope (1965), 516-7.
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Knowing, henceforth, the physiognomy of the disease when allowed to run its own course, you can, without risk of error, estimate the value of the different medications which have been employed. You will discover which remedies have done no harm, and which have notably curtailed the duration of the disease; and thus for the future you will have a standard by which to measure the value of the medicine which you see employed to counteract the malady in question. What you have done in respect of one disease, you will be able to do in respect of many; and by proceeding in this way you will be able, on sure data, to pass judgment on the treatment pursued by your masters.
In Armand Trousseau, as translated by P. Victor and John Rose Cormack, Lectures on Clinical Medicine: Delivered at the Hôtel-Dieu, Paris (1873), Vol. 1, 40-41.
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Langmuir is the most convincing lecturer that I have ever heard. I have heard him talk to an audience of chemists when I knew they did not understand more than one-third of what he was saying; but they thought they did. It’s very easy to be swept off one's feet by Langmuir. You remember in [Kipling’s novel] Kim that the water jar was broken and Lurgan Sahib was trying to hypnotise Kim into seeing it whole again. Kim saved himself by saying the multiplication table [so] I have heard Langmuir lecture when I knew he was wrong, but I had to repeat to myself: “He is wrong; I know he is wrong; he is wrong”, or I should have believed like the others.
In 'How to Ripen Time', Journal of Physical Chemistry 1931, 35, 1917.
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Law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise, or at least pretends to be. Experiment is made under conditions always complex, the enunciation of the law eliminates these complications. This is what is called ‘correcting the systematic errors’.
From La Valeur de la Science (1904), 142, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 77. From the French, “La loi sort de l’expérience, mais elle n’en sort pas immédiatement. L’expérience est individuelle, la loi qu’on en tire est générale, l’expérience n’est qu’approchée, la loi est précise ou du moins prétend l’élre. L’expérience se fait dans des conditions toujours complexes, l’énoncé de la loi élimine ces complications. C’est ce qu’on appelle ‘corriger les erreurs systématiques’.”
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Let us not, in the pride of our superior knowledge, turn with contempt from the follies of our predecessors. The study of the errors into which great minds have fallen in the pursuit of truth can never be uninstructive.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 3, 3.
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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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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Looking back … over the long and labyrinthine path which finally led to the discovery [of the quantum theory], I am vividly reminded of Goethe’s saying that men will always be making mistakes as long as they are striving after something.
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Man is made for science; he reasons from effects to causes, and from causes to effects; but he does not always reason without error. In reasoning, therefore, from appearances which are particular, care must be taken how we generalize; we should be cautious not to attribute to nature, laws which may perhaps be only of our own invention.
'Theory of the Earth', Transactions of the Royal Society of Edinburgh, 1788, 1, 273.
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Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.
In 'Prop. 47: The human mind possesses an adequate knowledge of the eternal and infinite essence of God', Ethic, translated by William Hale White (1883), 93-94. Collected in The English and Foreign Philosophical Library, Vol. 21.
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Many from … an inconsiderate zeal unto truth, have too rashly charged the troops of error, and remain as trophies unto the enemies of truth.
In T. Chapman (ed.), Religio Medici (1643, 1831), part 1, sect. 6, 11.
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Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7. From the original French, “L’analyse mathématique est aussi étendue que la nature elle-même; elle définit tous les rapports sensibles, mesure les temps y les espaces, les forces, les températures; cette science difficile se forme avec lenteur, mais elle conserve tous les principes quelle a une fois acquis; elle s’accroît et s’affermit sans cesse au milieu de tant de variations et d’erreurs de l’esprit humain.”
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Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be backed up. It’s just that the reliability does not primarily come from mathematicians checking formal arguments; it come from mathematicians thinking carefully and critically about mathematical ideas.
Concerning revision of proofs. In 'On Proof and Progress in Mathematics', For the Learning of Mathematics (Feb 1995), 15, No. 1, 33. Reprinted from Bulletin of the American Mathematical Society (1994), 30, No. 2, 170.
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Mathematics is not a deductive science—that’s a cliché. When you try to prove a theorem, you don’t just list the hypotheses, and then start to reason. What you do is trial and error, experiment and guesswork.
In I Want to be a Mathematician: an Automathography in Three Parts (1985), 321.
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Mathematics, like dialectics, is an organ of the inner higher sense; in its execution it is an art like eloquence. Both alike care nothing for the content, to both nothing is of value but the form. It is immaterial to mathematics whether it computes pennies or guineas, to rhetoric whether it defends truth or error.
From Wilhelm Meislers Wanderjahre (1829), Zweites Buch. Collected in Goethe’s Werke (1830), Vol. 22, 252. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 36-37. The same book has another translation on p.202: “Mathematics, like dialectics, is an organ of the higher sense, in its execution it is an art like eloquence. To both nothing but the form is of value; neither cares anything for content. Whether mathematics considers pennies or guineas, whether rhetoric defends truth or error, is perfectly immaterial to either.” From the original German, “Die Mathematik ist, wie die Dialektik, ein Organ des inneren höheren Sinnes, in der Ausübung ist sie eine Kunst wie die Beredsamkeit. Für beide hat nichts Wert als die Form; der Gehalt ist ihnen gleichgültig. Ob die Mathematik Pfennige oder oder Guineen berechne, die Rhetorik Wahres oder Falsches verteidige, ist beiden vollkommen gleich.”
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Men today who have had an irreproachable training in the art are seen to abstain from the use of the hand as from the plague, and for this very reason, lest they should be slandered by the masters of the profession as barbers… . For it is indeed above all things the wide prevalence of this hateful error that prevents us even in our age from taking up the healing art as a whole, makes us confine ourselves merely to the treatment of internal complaints, and, if I may utter the blunt truth once for all, causes us, to the great detriment of mankind, to study to be healers only in a very limited degree.
As given in George I. Schwartz and ‎Philip W. Bishop, 'Andreas Vesalius', Moments of Discovery: The Development of Modern Science (1958), Vol. 1, 521.
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Mistakes are at the very base of human thought feeding the structure like root nodules. If we were not provided with the knack of being wrong, we could never get anything useful done.
In The Medusa and the Snail (1979), 37.
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Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you’ll never notice the flaws; if you doubt too much you won’t get started. It requires a lovely balance.
'You and Your Research', Bell Communications Research Colloquium Seminar, 7 Mar 1986.
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Much as I venerate the name of Newton, I am not therefore obliged to believe that he was infallible. I see … with regret that he was liable to err, and that his authority has, perhaps, sometimes even retarded the progress of science.
From 'Dr. Young’s Reply to the Animadversions of the Edinburgh Reviewers, on Some Papers Published in the Philosophical Transactions', collected in Thomas Young, ‎George Peacock (ed.), Miscellaneous Works of the Late Thomas Young (1855), Vol. 1, 201.
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My Lord said that he who knew men only in this way [from history] was like one who had got the theory of anatomy perfectly, but who in practice would find himself very awkward and liable to mistakes. That he again who knew men by observation was like one who picked up anatomy by practice, but who like all empirics would for a long time be liable to gross errors.
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Nature gropes and blunders and performs the crudest acts. There is no steady advance upward. There is no design.
As quoted in Bob Fenster, Duh!: The Stupid History of the Human Race (2000) , 208. [No other source was found by Webmaster. If you have information on a primary source, please contact Webmaster.]
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Nature is a source of truth. Experience does not ever err, it is only your judgment that errs in promising itself results which are not caused by your experiments.
The Notebook. As cited in Edward Schwartz, One Step Forward, Two Steps Backward (2003), 38, with caption “examining objects in all their diversity.” Also quoted in Daniel J. Boorstin, The Discoverers (1983), 350.
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Next to the promulgation of the truth, the best thing I can conceive that man can do is the public recantation of an error.
In Collected Papers of Joseph Baron Lister (1909), Vol. 1, 366. As quoted and cited in Sir Rickman John Godlee, Lord Lister (1918), 278.
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No idea should be suppressed. … And it applies to ideas that look like nonsense. We must not forget that some of the best ideas seemed like nonsense at first. The truth will prevail in the end. Nonsense will fall of its own weight, by a sort of intellectual law of gravitation. If we bat it about, we shall only keep an error in the air a little longer. And a new truth will go into orbit.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 233.
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No one wants to learn by mistakes, but we cannot learn enough from successes to go beyond the state of the art
To Engineer is Human: The Role of Failure in Successful Design (1992), 62.
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No science contains so many sophisms, errors, dreams, and lies as medicine.
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Of all the intellectual faculties, judgment is the last to arrive at maturity. The child should give its attention either to subjects where no error is possible at all, such as mathematics, or to those in which there is no particular danger in making a mistake, such as languages, natural science, history, and so on.
In Arthur Schopenhauer and T. Bailey (ed., trans.) Essays of Arthur Schopenhauer (1902), 67.
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Of all the offspring of Time, Error is the most ancient, and is so old and familiar an acquaintance, that Truth, when discovered, comes upon most of us like an intruder, and meets the intruder’s welcome.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 314.
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One of my surgical giant friends had in his operating room a sign “If the operation is difficult, you aren’t doing it right.” What he meant was, you have to plan every operation You cannot ever be casual You have to realize that any operation is a potential fatality.
From Cornelia Dean, 'A Conversation with Joseph E. Murray', New York Times (25 Sep 2001), F5.
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One way of dealing with errors is to have friends who are willing to spend the time necessary to carry out a critical examination of the experimental design beforehand and the results after the experiments have been completed. An even better way is to have an enemy. An enemy is willing to devote a vast amount of time and brain power to ferreting out errors both large and small, and this without any compensation. The trouble is that really capable enemies are scarce; most of them are only ordinary. Another trouble with enemies is that they sometimes develop into friends and lose a great deal of their zeal. It was in this way the writer lost his three best enemies. Everyone, not just scientists, needs a good few enemies.
Quoted in George A. Olah, A Life of Magic Chemistry (2001), 146.
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Orthodoxy can be as stubborn in science as in religion. I do not know how to shake it except by vigorous imagination that inspires unconventional work and contains within itself an elevated potential for inspired error. As the great Italian economist Vilfredo Pareto wrote: ‘Give me a fruitful error any time, full of seeds, bursting with its own corrections. You can keep your sterile truth for yourself.’ Not to mention a man named Thomas Henry Huxley who, when not in the throes of grief or the wars of parson hunting, argued that ‘irrationally held truths may be more harmful than reasoned errors.’
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Our science, so called, is always more barren and mixed with error than our sympathies.
In Early Spring in Massachusetts: From the Journal of Henry Thoreau (1881), 26.
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People see the wrongness in an idea much quicker that the rightness.
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Persons possessing great intellect and a capacity for excelling in the creative arts and also in the sciences are generally likely to have heavier brains than the ordinary individual. Arguing from this we might expect to find a corresponding lightness in the brain of the criminal, but this is not always the case ... Many criminals show not a single anomaly in their physical or mental make-up, while many persons with marked evidences of morphological aberration have never exhibited the criminal tendency.
Every attempt to prove crime to be due to a constitution peculiar only to criminals has failed signally. It is because most criminals are drawn from the ranks of the low, the degraded, the outcast, that investigators were ever deceived into attempting to set up a 'type' of criminal. The social conditions which foster the great majority of crimes are more needful of study and improvement.
From study of known normal brains we have learned that there is a certain range of variation. No two brains are exactly alike, and the greatest source of error in the assertions of Benedict and Lombroso has been the finding of this or that variation in a criminal’s brains, and maintaining such to be characteristic of the 'criminal constitution,' unmindful of the fact that like variations of structure may and do exist in the brains of normal, moral persons.
Address to the American Association for the Advancement of Science in Philadelphia (28 Dec 1904), as quoted in 'Americans of Future Will Have Best Brains', New York Times (29 Dec 1904), 6.
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Physical investigation, more than anything besides, helps to teach us the actual value and right use of the Imagination—of that wondrous faculty, which, left to ramble uncontrolled, leads us astray into a wilderness of perplexities and errors, a land of mists and shadows; but which, properly controlled by experience and reflection, becomes the noblest attribute of man; the source of poetic genius, the instrument of discovery in Science, without the aid of which Newton would never have invented fluxions, nor Davy have decomposed the earths and alkalies, nor would Columbus have found another Continent.
Presidential Address to Anniversary meeting of the Royal Society (30 Nov 1859), Proceedings of the Royal Society of London (1860), 10, 165.
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Prejudice for regularity and simplicity is a source of error that has only too often infected philosophy.
'De litteraria expeditione per pontificiam ditionem', Accademia della scienze, Bologna, Commentarii, 1757, 4, 353, 361. Trans. J. L. Heilbron, Weighing Imponderables and Other Quantitative Science around 1800 (1993), 227.
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Reason and free inquiry are the only effectual agents against error.
Thomas Jefferson and Albert Ellery Bergh (ed.), The Writings of Thomas Jefferson (1905), Vols 1, 221.
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George E.P. Box quote: Remember that all models are wrong; the practical question is how wrong do they have to be to not
[Co-author with Norman R. Draper] (source)
Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful. [Co-author with Norman R. Draper]
In George E.P. Box and Norman R. Draper, Empirical Model-Building and Response Surfaces (1987), 74.
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Remember that [scientific thought] is the guide of action; that the truth which it arrives at is not that which we can ideally contemplate without error, but that which we may act upon without fear; and you cannot fail to see that scientific thought is not an accompaniment or condition of human progress, but human progress itself.
'Aims and Instruments of Scientific Thought,' a lecture delivered to the British Association on 19 Aug 1872. In Leslie Stephen and Frederick Pollock (eds.), Lectures and Essays, by the Late William Kingdon Clifford (1886), 109.
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Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one microcentury as von Neumann used to say) everybody's attention will turn elsewhere.
In 'Ten Lessons I Wish I Had Been Taught', Indiscrete Thoughts (2008), 197.
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Scarcely any attempt is entirely a failure; scarcely any theory, the result of steady thought, is altogether false; no tempting form of Error is without some latent charm derived from Truth.
In 'Lecture 7', Lectures on the History of Moral Philosophy in England (1852), 101.
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Science can progress on the basis of error as long as it is not trivial.
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Science can purify religion from error and superstition. Religion can purify science from idolatry and false absolutes. Each can draw the other into a wider world, a world in which both can flourish.
In Letter (1 Jun 1988) to Father George V. Coyne, Director of the Vatican Observatory. On vatican.va website.
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Science differs from politics or religion, in precisely this one discipline: we agree in advance to simply reject our own findings when they have been shown to be in error.
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Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
Letter to G. F. Becker, 11 June 1893. Merrill Collection, Library of Congress. Quoted in Nathan Reingold, Science in Nineteenth-Century America: A Documentary History (1966), 231-2.
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Science in the modern world has many uses, its chief use, however, is to provide long words to cover the errors of the rich. The word “kleptomania” is a vulgar example of what I mean.
From 'Celts and Celtophiles', in Heretics (1905, 1909), 171.
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Sciences … voluntary relapse into errors. … The scientist is like a man who purposely marches many steps backward before he jumps a trench.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 2.
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Since the world is what it is, it is clear that valid reasoning from sound principles cannot lead to error; but a principle may be so nearly true as to deserve theoretical respect, and yet may lead to practical consequences which we feel to be absurd. There is therefore a justification for common sense in philosophy, but only as showing that our theoretical principles cannot be quite correct so long as their consequences are condemned by an appeal to common sense which we feel to be irresistible.
In A History of Western Philosophy, (1945, 1996), 553.
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So-called extraordinary events always split into two extremes naturalists who have not witnessed them: those who believe blindly and those who do not believe at all. The latter have always in mind the story of the golden goose; if the facts lie slightly beyond the limits of their knowledge, they relegate them immediately to fables. The former have a secret taste for marvels because they seem to expand Nature; they use their imagination with pleasure to find explanations. To remain doubtful is given to naturalists who keep a middle path between the two extremes. They calmly examine facts; they refer to logic for help; they discuss probabilities; they do not scoff at anything, not even errors, because they serve at least the history of the human mind; finally, they report rather than judge; they rarely decide unless they have good evidence.
Quoted in Albert V. Carozzi, Histoire des sciences de la terre entre 1790 et 1815 vue à travers les documents inédités de la Societé de Physique et d'Histoire Naturelle de Genève, trans. Albert V. and Marguerite Carozzi. (1990), 175.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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Surely it must be admitted that if the conceptions of Physics are presented to the beginner in erroneous language, there is a danger that in many instances these conceptions will never be properly acquired. And is not accurate language as cheap as inaccurate?
A paper read at the Association for the Improvement of Geometrical Teaching (19 Jan 1889), 'The Vices of our Scientific Education', in Nature (6 Jun 1889), 40, 128.
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The Mathematics are Friends to Religion, inasmuch as they charm the Passions, restrain the Impetuosity of the Imagination, and purge the Mind from Error and Prejudice. Vice is Error, Confusion, and false Reasoning; and all Truth is more or less opposite to it. Besides, Mathematical Studies may serve for a pleasant Entertainment for those Hours which young Men are apt to throw away upon their Vices; the Delightfulness of them being such as to make Solitude not only easy, but desirable.
In An Essay On the Usefulness of Mathematical Learning, (1701) 8-9.
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The advantage which science gained by Gauss’ long-lingering method of publication is this: What he put into print is as true and important today as when first published; his publications are statutes, superior to other human statutes in this, that nowhere and never has a single error been detected in them. This justifies and makes intelligible the pride with which Gauss said in the evening of his life of the first larger work of his youth: “The Disquisitiones arithmeticae belong to history.”
In Allgemeine Deutsche Biographie (1878, 8, 435. As cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 158.
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The aim of science is not to open the door to infinite wisdom, but to set a limit to infinite error.
Play, The Life of Galileo (1939, 1994), scene 9, 74.
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The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, Seek simplicity and distrust it.
In The Concept of Nature: Tarner Lectures Delivered in Trinity College, November 1919 (1920), 163.
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The belief that all things are created solely for the utility of man has stained with many errors that most noble part of physics which deals with the ends of things.
R.W. Home (ed.), Aepinus's Essay on the Theory of Electricity and Magnetism (1979), 399.
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The body of science is not, as it is sometimes thought, a huge coherent mass of facts, neatly arranged in sequence, each one attached to the next by a logical string. In truth, whenever we discover a new fact it involves the elimination of old ones. We are always, as it turns out, fundamentally in error.
In 'On Science and Certainty', Discover Magazine (Oct 1980)
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The capacity to blunder slightly is the real marvel of DNA. Without this special attribute, we would still be anaerobic bacteria and there would be no music.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1979), 28.
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The chief malady of man is restless curiosity about things which he cannot understand; and it is not so bad for him to be in error as to be curious to no purpose.
In Pensées. As translated by W.F. Trotter in Blaise Pascal: Thoughts, Letters, and Minor Works (1910), 13.
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The desire to economize time and mental effort in arithmetical computations, and to eliminate human liability to error is probably as old as the science of arithmetic itself.
Opening of proposal submitted to I.B.M., 'Proposed Automatic Calculating Machine' (1937). As quoted by I. Bernard Cohen, in Howard Aiken: Portrait of a Computer Pioneer (2000), 63.
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The difference between the amoeba and Einstein is that, although both make use of the method of trial and error elimination, the amoeba dislikes erring while Einstein is intrigued by it.
In Objective Knowledge: An Evolutionary Approach (1972), 70. As cited in Alexander Naraniecki, Returning to Karl Popper: A Reassessment of his Politics and Philosophy (2014), 89, footnote.
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The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.
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The errors of a wise man are literally more instructive than the truths of a fool. The wise man travels in lofty, far-seeing regions; the fool in low-lying, high-fenced lanes; retracing the footsteps of the former, to discover where he diviated, whole provinces of the universe are laid open to us; in the path of the latter, granting even that he has not deviated at all, little is laid open to us but two wheel-ruts and two hedges.
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 425:26.
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The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning.
In Thomas Hobbes and William Molesworth (ed.) Leviathan: Or the Matter, Form and Power of a Commonwealth Ecclesiastical and Civil (1839), Vol. 3, 24.
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The errors of great men are venerable because they are more fruitful than the truths of little men.
Friedrich Wilhelm Nietzsche and Walter Kaufmann (ed. & trans.), The Portable Nietzsche (1954), 30.
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The errors which arise from the absence of facts are far more numerous and more durable than those which result from unsound reasoning respecting true data.
In 'Of Price as Measured by Money', On the Economy of Machinery and Manufactures (1st ed., 1832), chap. 17, 112.
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The explorations of space end on a note of uncertainty. And necessarily so. … We know our immediate neighborhood rather intimately. With increasing distance our knowledge fades, and fades rapidly. Eventually, we reach the dim boundary—the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial. The search will continue. Not until the empirical resources are exhausted, need we pass on to the dreamy realms of speculation.
From conclusion of The Silliman Memorial Lectures Series delivered at Yale University (Fall 1935). Collected in The Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202.
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The first step in all physical investigations, even in those which admit of the application of mathematical reasoning and the deductive method afterwards, is the observation of natural phenomena; and the smallest error in such observation in the beginning is sufficient to vitiate the whole investigation afterwards. The necessity of strict and minute observation, then, is the first thing which the student of the physical sciences has to learn; and it is easy to see with what great advantage the habit thus acquired may be carried into everything else afterwards.
Presidential Address to Anniversary meeting of the Royal Society (30 Nov 1859), Proceedings of the Royal Society of London (1860), 10, 164-165.
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The frequent allegation that the selective processes in the human species are no longer 'natural' is due to persistence of the obsolete nineteenth-century concept of 'natural' selection. The error of this view is made clear when we ask its proponents such questions as, why should the 'surviving fittest' be able to withstand cold and inclement weather without the benefit of fire and clothing? Is it not ludicrous to expect selection to make us good at defending ourselves against wild beasts when wild beasts are getting to be so rare that it is a privilege to see one outside of a zoo? Is it necessary to eliminate everyone who has poor teeth when our dentists stand ready to provide us with artificial ones? Is it a great virtue to be able to endure pain when anaesthetics are available?
[Co-author with American statistician Gordon Allen]
Theodosius Dobzhansky and Gordon Allen, 'Does Natural Selection Continue to Operate in Modern Mankind?', American Anthropologist, 1956, 58, 595.
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The glory of science is not that it discovers “truth”; rather it advances inexorably by discovering and correcting error.
In Francis Bello, Lawrence Lessing and George A.W. Boehm, Great American Scientists (1960, 1961), 116.
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The great error of the 19th century, in morality as well as in science and art, has been to mingle and confound man and nature without pausing to consider that in art as in science and morality he is a man only in so far as he distinguishes himself from nature and makes himself an exception to it.
As quoted in Working and Thinking on the Waterfront: A Journal, June 1958-May 1959 (1969), 122.
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The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, “The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics.” It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoiter and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken.
In History of Mathematics (1897), 1-2.
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The history of science teaches only too plainly the lesson that no single method is absolutely to be relied upon, that sources of error lurk where they are least expected, and that they may escape the notice of the most experienced and conscientious worker.
Transactions of the Sections', Reports of the British Association for the Advancement of Science (1883), 438.
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The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error. But science is one of the very few human activities—perhaps the only one—in which errors are systematically criticized and fairly often, in time, corrected. This is why we can say that, in science, we often learn from our mistakes, and why we can speak clearly and sensibly about making progress there. In most other fields of human endeavour there is change, but rarely progress ... And in most fields we do not even know how to evaluate change.
From Conjectures and Refutations: The Growth of Scientific Knowledge (1963), 216. Reproduced in Karl Popper, Truth, Rationality and the Growth of Scientific Knowledge (1979), 9.
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The intricate edifice of verifiable fact and tested theory that has been patiently created in just a brief few hundred years is man’s most solid achievement on earth.
In Francis Bello, Lawrence Lessing and George A.W. Boehm, Great American Scientists (1960, 1961), 117.
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The law that entropy always increases—the Second Law of Thermodynamics—holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
Gifford Lectures (1927), The Nature of the Physical World (1928), 74.
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The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search for truth. So it does more harm than good.
From Novum Organum (1620), Book 1, Aphorism 12. 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, 48-49.
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The maladies that affect the clerks aforesaid arise from three causes. First, constant sitting, secondly, the incessant movement of the the hand and always in the same direction, thirdly, the strain on the mind from the effort not to disfigure the books by errors or cause loss to their employers when they add, subtract, or do other sums in arithmetic. The diseases brought about by sitting constantly are easily understood; they are obstructions of the viscera, e.g. the liver and spleen, indigestion in the stomach, numbness of the legs, a considerable hindrance in the circulation of the blood, and an unhealthy habit.
De Morbis Artificum (1713), supplement, ch. 2, translated by W.C. Wright (1964).
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The most erroneous stories are those we think we know best—and therefore never scrutinize or question.
Full House: The Spread of Excellence from Plato to Darwin (1997), 57.
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The old fashioned family physician and general practitioner ... was a splendid figure and useful person in his day; but he was badly trained, he was often ignorant, he made many mistakes, for one cannot by force of character and geniality of person make a diagnosis of appendicitis, or recognize streptococcus infection.
New York Medical Journal (1913), 97, 1.
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The one lesson that comes out of all our theorizing and experimenting is that there is only one really scientific progressive method; and that is the method of trial and error.
…...
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The only ethical principle which has made science possible is that the truth shall be told all the time. If we do not penalize false statements made in error, we open up the way for false statements by intention. And a false statement of fact, made deliberately, is the most serious crime a scientist can commit.
In The Search (1934, rev. ed. 1959). Also seen attributed to Dorothy L. Sayers, Gaudy Night (1935). Webmaster has not yet solved the mystery of which author wrote it first. If you have access to both books, and can identify the first to publish, please contact Webmaster.
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The only sure foundations of medicine are, an intimate knowledge of the human body, and observation on the effects of medicinal substances on that. The anatomical and clinical schools, therefore, are those in which the young physician should be formed. If he enters with innocence that of the theory of medicine, it is scarcely possible he should come out untainted with error. His mind must be strong indeed, if, rising above juvenile credulity, it can maintain a wise infidelity against the authority of his instructors, and the bewitching delusions of their theories.
In letter to Caspar Wistar (21 Jun 1807), collected in Thomas Jefferson Randolph (ed.), Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson (1829), Vol. 4, 93.
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The orbits of certainties touch one another; but in the interstices there is room enough for error to go forth and prevail.
In The Maxims and Reflections of Goethe (1906), 187.
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The present state of the earth and of the organisms now inhabiting it, is but the last stage of a long and uninterrupted series of changes which it has undergone, and consequently, that to endeavour to explain and account for its present condition without any reference to those changes (as has frequently been done) must lead to very imperfect and erroneous conclusions.
In 'On the Law which has regulated the Introduction of New Species', The Annals and Magazine of Natural History (1855), 16, No. 93, 184.
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The Principle of Uncertainty is a bad name. In science or outside of it we are not uncertain; our knowledge is merely confined, within a certain tolerance. We should call it the Principle of Tolerance. And I propose that name in two senses: First, in the engineering sense, science has progressed, step by step, the most successful enterprise in the ascent of man, because it has understood that the exchange of information between man and nature, and man and man, can only take place with a certain tolerance. But second, I also use the word, passionately, about the real world. All knowledge, all information between human beings, can only be exchanged within a play of tolerance. And that is true whether the exchange is in science, or in literature, or in religion, or in politics, or in any form of thought that aspires to dogma. It’s a major tragedy of my lifetime and yours that scientists were refining, to the most exquisite precision, the Principle of Tolerance, and turning their backs on the fact that all around them, tolerance was crashing to the ground beyond repair. The Principle of Uncertainty or, in my phrase, the Principle of Tolerance, fixed once for all the realization that all knowledge is limited. It is an irony of history that at the very time when this was being worked out there should rise, under Hitler in Germany and other tyrants elsewhere, a counter-conception: a principle of monstrous certainty. When the future looks back on the 1930s it will think of them as a crucial confrontation of culture as I have been expounding it, the ascent of man, against the throwback to the despots’ belief that they have absolute certainty. It is said that science will dehumanize people and turn them into numbers. That is false: tragically false. Look for yourself. This is the concentration camp and crematorium at Auschwitz. This is where people were turned into numbers. Into this pond were flushed the ashes of four million people. And that was not done by gas. It was done by arrogance. It was done by dogma. It was done by ignorance. When people believe that they have absolute knowledge, with no test in reality this is how they behave. This is what men do when they aspire to the knowledge of gods. Science is a very human form of knowledge. We are always at the brink of the known; we always feel forward for what is to be hoped. Every judgment in science stands on the edge of error, and is personal. Science is a tribute to what we can know although we are fallible. In the end, the words were said by Oliver Cromwell: “I beseech you, in the bowels of Christ: Think it possible you may be mistaken.” We have to cure ourselves of the itch for absolute knowledge and power. We have to close the distance between the push-button order and the human act. We have to touch people. [Referring to Heisenberg’s Uncertainty Principle.]
'Knowledge or Certainty,' episode 11, The Ascent of Man (1972), BBC TV series.
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The results of science are never quite true. By a healthy independence of thought perhaps we sometimes avoid adding other people’s errors to our own.
In 'Space, Time and Relativity', The Aims of Education and Other Essays (1929), 149.
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The role of hypothesis in research can be discussed more effectively if we consider first some examples of discoveries which originated from hypotheses. One of the best illustrations of such a discovery is provided by the story of Christopher Columbus’ voyage; it has many of the features of a classic discovery in science. (a) He was obsessed with an idea—that since the world is round he could reach the Orient by sailing West, (b) the idea was by no means original, but evidently he had obtained some additional evidence from a sailor blown off his course who claimed to have reached land in the west and returned, (c) he met great difficulties in getting someone to provide the money to enable him to test his idea as well as in the actual carrying out of the experimental voyage, (d) when finally he succeeded he did not find the expected new route, but instead found a whole new world, (e) despite all evidence to the contrary he clung to the bitter end to his hypothesis and believed that he had found the route to the Orient, (f) he got little credit or reward during his lifetime and neither he nor others realised the full implications of his discovery, (g) since his time evidence has been brought forward showing that he was by no means the first European to reach America.
The Art of Scientific Investigation (1950), 41.
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The scientific method is a potentiation of common sense, exercised with a specially firm determination not to persist in error if any exertion of hand or mind can deliver us from it. Like other exploratory processes, it can be resolved into a dialogue between fact and fancy, the actual and the possible; between what could be true and what is in fact the case. The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about nature. It begins as a story about a Possible World—a story which we invent and criticise and modify as we go along, so that it ends by being, as nearly as we can make it, a story about real life.
Induction and Intuition in Scientific Thought (1969), 59.
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