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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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'Normal science' means research firmly based upon one or more past scientific achievements, achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice.
The Structure of Scientific Revolutions (1962), 10.
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'Normal' science, in Kuhn's sense, exists. It is the activity of the non-revolutionary, or more precisely, the not-too-critical professional: of the science student who accepts the ruling dogma of the day... in my view the 'normal' scientist, as Kuhn describes him, is a person one ought to be sorry for... He has been taught in a dogmatic spirit: he is a victim of indoctrination... I can only say that I see a very great danger in it and in the possibility of its becoming normal... a danger to science and, indeed, to our civilization. And this shows why I regard Kuhn's emphasis on the existence of this kind of science as so important.
'Normal Science and its Dangers', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge (1970), 52-3.
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πολλὰ τὰ δεινὰ κοὐδὲν ἀνθρώπου δεινότερον πέλει.
Wonders are many, and none is more wonderful than man.
Sophocles
First line of a choral ode in Antigone, line 332, translated by R.C. Jebb (1891). This may not be the closest translation of ambiguous words. Walter Arnold Kaufmann suggests a closer meaning would be “Much is awesome, but nothing more awesome than man” in Tragedy and Philosophy (1992), 237. Alternate word translations could be terrors, danger, misfortune or distress. Hence the variation in other standard translations on this web page.
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(1) I have told you more than I know about osteoporosis. (2) What I have told you is subject to change without notice. (3) I hope I raised more questions than I have given answers. (4) In any case, as usual, a lot more work is necessary.
Conclusion of one of his papers.
In Barry G. Firkin, Judith A. Whitworth, Dictionary of Medical Eponyms (1996), 5.
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... an analysis that puts the final link in the chain, for here we see correlations between cytological evidence and genetic results that are so strong and obvious that their validity cannot be denied. This paper has been called a landmark in experimental genetics. It is more than that—it is a cornerstone.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931), demonstrating that the exchange of genetic information that occurs during the production of sex cells is accompanied by an exchange of chromosomal material.
Classic Papers in Genetics (1959), 156.
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... I should think that anyone who considered it more reasonable for the whole universe to move in order to let the Earth remain fixed would be more irrational than one who should climb to the top of your cupola just to get a view of the city and its environs, and then demand that the whole countryside should revolve around him so that he would not have to take the trouble to turn his head.
In Dialogue Concerning the Two Chief World Systems (1632).
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... in going over the history of all the inventions for which history could be obtained it became more and more clear that in addition to training and in addition to extensive knowledge, a natural quality of mind was also necessary.
Aphorism listed Frederick Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932) (1999), 54, being Transactions of the American Philosophical Society, Held at Philadelphia For Promoting Useful Knowledge, Vol. 86, Pt. 6.
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... in real life mistakes are likely to be irrevocable. Computer simulation, however, makes it economically practical to make mistakes on purpose. If you are astute, therefore, you can learn much more than they cost. Furthermore, if you are at all discreet, no one but you need ever know you made a mistake.
With co-author John Osborn, in Natural Automata and Useful Simulations edited by H. H. Pattee et al. (1966).
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... in time of war, soldiers, however sensible, care a great deal more on some occasions about slaking their thirst than about the danger of enteric fever.
[Better known as typhoid, the disease is often spread by drinking contaminated water.]
Parliamentaray Debate (21 Mar 1902). Quoted in Winston Churchill and Richard Langworth (ed.), Churchill by Himself: The Definitive Collection of Quotations (2008), 469.
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... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself … A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.
'Operational Definition and Analogy in Physical Theories', British Journal for the Philosophy of Science (Feb 1952), 2, No. 8, 291.
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... the cooperative forces are biologically the more important and vital. The balance between the cooperative and altruistic tendencies and those which are disoperative and egoistic is relatively close. Under many conditions the cooperative forces lose, In the long run, however, the group centered, more altruistic drives are slightly stronger. ... human altruistic drives are as firmly based on an animal ancestry as is man himself. Our tendencies toward goodness... are as innate as our tendencies toward intelligence; we could do well with more of both.
Where Angels Fear to Tread: A contribution from general sociology to human ethics, Science, vol 97, 1943, p.521
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...an idea is no more an even relatively constant thing than is a feeling or emotion or volitional process. There exist only changing and transient ideational processes; there are no permanent ideas that return again and disappear again.
An Introduction to Psychology (1912)
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...for our wisdom is better than the strength of men or of horses. ... nor is it right to prefer strength to excellent wisdom. For if there should be in the city [any athlete whose skill] is honoured more than strength ... the city would not on that account be any better governed.
Quoted in Arthur Fairbanks (ed. And trans.), The First Philosophers of Greece (1898), 73, fragment 19.
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...for the animals, which we resemble and which would be our equals if we did not have reason, do not reflect upon the actions or the passions of their external or internal senses, and do not know what is color, odor or sound, or if there is any differences between these objects, to which they are moved rather than moving themselves there. This comes about by the force of the impression that the different objects make on their organs and on their senses, for they cannot discern if it is more appropriate to go and drink or eat or do something else, and they do not eat or drink or do anything else except when the presence of objects or the animal imagination [l'imagination brutalle], necessitates them and transports them to their objects, without their knowing what they do, whether good or bad; which would happen to us just as to them if we were destitute of reason, for they have no enlightenment except what they must have to take their nourishment and to serve us for the uses to which God has destined them.
[Arguing the uniqueness of man by regarding animals to be merely automatons.].
Les Préludes de l'Harmonie Universelle (1634), 135-139. In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1974), Vol. 9, 318.
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...it would be a simple way of solving the goiter problem. And in addition to that it would be the biggest thing in a medical proposition to be carried out in the state of Michigan, and Michigan is a large place. And as I thought of the thing the more convinced I became that this oughtn't to be a personal thing, This ought to be something done by the Michigan State Medical Society as a body.
Recommending the addition of a trace of iodine to table salt.
Opening address to the Medical Department of the University of Michigan, Sep 1914. Quoted by Howard Markel in 'When it Rains it Pours' : Endemic Goiter, Iodized Salt, and David Murray Cowie, M.D. American Journal of Public Health, Feb 1987, vol.77, No.2, page 222.
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...neither is it possible to discover the more remote and deeper parts of any science, if you stand but upon the level of the same science, and ascend not to a higher science.
Francis Bacon, Basil Montagu (Ed.), The Works of Francis Bacon (1852), Vol. 1, 173.
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...reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge … as an attempt by our mind to return to union with things as they are in their ordered wholeness…. and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality … Its measure is the distance thought has travelled … toward that intelligible system … The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest.
The Nature of Thought (1939), Vol II, 264. Quoted in Erhard Scheibe and Brigitte Falkenburg (ed), Between Rationalism and Empiricism: Selected Papers in the Philosophy of Physics (2001), 233
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...the remark attributed to Mrs. [Agatha] Christie that 'the older you get, the more interesting you become to an archaeologist,' was the creation of some pundit whose neck Mrs. Christie would be glad to wring if he would care to identify himself—she neither made the remark nor does she consider it particularly complimentary or amusing.
Gordon Ramsey, Agatha Christie: Mistress of Mystery (1967), 23. In Russell H. Fitzgibbon, The Agatha Christie Companion 1980), 22.
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...those experiments be not only esteemed which have an immediate and present use, but those principally which are of most universal consequence for invention of other experiments, and those which give more light to the invention of causes; for the invention of the mariner's needle, which giveth the direction, is of no less benefit for navigation than the invention of the sails, which give the motion.
The Second 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), 200
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...travel is more than the seeing of sights; it is a change that goes on, deep and permanent, in the ideas of living.
…...
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...[T]he natural history of the rat is tragically similar to that of man ... some of the more obvious qualities in which rats resemble men — ferocity, omnivorousness, and adaptability to all climates ... the irresponsible fecundity with which both species breed at all seasons of the year with a heedlessness of consequences, which subjects them to wholesale disaster on the inevitable, occasional failure of the food supply.... [G]radually, these two have spread across the earth, keeping pace with each other and unable to destroy each other, though continually hostile. They have wandered from East to West, driven by their physical needs, and — unlike any other species of living things — have made war upon their own kind. The gradual, relentless, progressive extermination of the black rat by the brown has no parallel in nature so close as that of the similar extermination of one race of man by another...
Rats, Lice and History(1935)
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1839—The fermentation satire
THE MYSTERY OF ALCOHOLIC FERMENTATION RESOLVED
(Preliminary Report by Letter) Schwindler
I am about to develop a new theory of wine fermentation … Depending on the weight, these seeds carry fermentation to completion somewhat less than as in the beginning, which is understandable … I shall develop a new theory of wine fermentation [showing] what simple means Nature employs in creating the most amazing phenomena. I owe it to the use of an excellent microscope designed by Pistorius.
When brewer’s yeast is mixed with water the microscope reveals that the yeast dissolves into endless small balls, which are scarcely 1/800th of a line in diameter … If these small balls are placed in sugar water, it can be seen that they consist of the eggs of animals. As they expand, they burst, and from them develop small creatures that multiply with unbelievable rapidity in a most unheard of way. The form of these animals differs from all of the 600 types described up until now. They possess the shape of a Beinsdorff still (without the cooling apparatus). The head of the tube is a sort of proboscis, the inside of which is filled with fine bristles 1/2000th of a line long. Teeth and eyes are not discernible; however, a stomach, intestinal canal, anus (a rose red dot), and organs for secretion of urine are plainly discernible. From the moment they are released from the egg one can see these animals swallow the sugar from the solution and pass it to the stomach. It is digested immediately, a process recognized easily by the resultant evacuation of excrements. In a word, these infusors eat sugar, evacuate ethyl alcohol from the intestinal canal, and carbon dioxide from the urinary organs. The bladder, in the filled state, has the form of a champagne bottle; when empty, it is a small button … As soon as the animals find no more sugar present, they eat each other up, which occurs through a peculiar manipulation; everything is digested down to the eggs which pass unchanged through the intestinal canal. Finally, one again fermentable yeast, namely the seed of the animals, which remain over.
In 'Das entriithselle Geheimiss der geisligen Giihrung', Annalen der Pharmacie und Chemie (1839), 29, 100-104; adapted from English translalion by Ralph E. Oesper, The Human Side of Scientists (1975), 203-205.
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Ath. There still remain three studies suitable for freemen. Calculation in arithmetic is one of them; the measurement of length, surface, and depth is the second; and the third has to do with the revolutions of the stars in reference to one another … there is in them something that is necessary and cannot be set aside, … if I am not mistaken, [something of] divine necessity; for as to the human necessities of which men often speak when they talk in this manner, nothing can be more ridiculous than such an application of the words.
Cle. And what necessities of knowledge are there, Stranger, which are divine and not human?
Ath. I conceive them to be those of which he who has no use nor any knowledge at all cannot be a god, or demi-god, or hero to mankind, or able to take any serious thought or charge of them.
Plato
In Republic, Bk. 7, in Jowett, Dialogues of Plato (1897, 2010), Vol. 4, 331.
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Bernard: Oh, you’re going to zap me with penicillin and pesticides. Spare me that and I’ll spare you the bomb and aerosols. But don’t confuse progress with perfectibility. A great poet is always timely. A great philosopher is an urgent need. There’s no rush for Isaac Newton. We were quite happy with Aristotle’s cosmos. Personally, I preferred it. Fifty-five crystal spheres geared to God’s crankshaft is my idea of a satisfying universe. I can’t think of anything more trivial than the speed of light. Quarks, quasars—big bangs, black holes—who [cares]? How did you people con us out of all that status? All that money? And why are you so pleased with yourselves?
Chloe: Are you against penicillin, Bernard?
Bernard: Don’t feed the animals.
In the play, Acadia (1993), Act 2, Scene 5, 61.
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Between the frontiers of the three super-states Eurasia, Oceania, and Eastasia, and not permanently in possession of any of them, there lies a rough quadrilateral with its corners at Tangier, Brazzaville, Darwin, and Hongkong. These territories contain a bottomless reserve of cheap labour. Whichever power controls equatorial Africa, or the Middle East or Southern India or the Indonesian Archipelago, disposes also of the bodies of hundreds of millions of ill-paid and hardworking coolies, expended by their conquerors like so much coal or oil in the race to turn out more armaments, to capture more territory, to control more labour, to turn out more armaments, to capture more territory, to control…
Thus George Orwell—in his only reference to the less-developed world.
I wish I could disagree with him. Orwell may have erred in not anticipating the withering of direct colonial controls within the “quadrilateral” he speaks about; he may not quite have gauged the vehemence of urges to political self-assertion. Nor, dare I hope, was he right in the sombre picture of conscious and heartless exploitation he has painted. But he did not err in predicting persisting poverty and hunger and overcrowding in 1984 among the less privileged nations.
I would like to live to regret my words but twenty years from now, I am positive, the less-developed world will be as hungry, as relatively undeveloped, and as desperately poor, as today.
'The Less-Developed World: How Can We be Optimists?' (1964). Reprinted in Ideals and Realities (1984), xv-xvi. Referencing a misquote from George Orwell, Nineteen Eighty Four (1949), Ch. 9.
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Ce grand ouvrage, toujours plus merveilleux à mesure qu’il est plus connu, nous donne une si grande idée de son ouvrier, que nous en sentons notre esprit accablé d’admiration et de respect.
[The Universe] This great work, always more amazing in proportion as it is better known, raises in us so grand an idea of its Maker, that we find our mind overwhelmed with feelings of wonder and adoration.
Original French and translation in Craufurd Tait Ramage (ed.) Beautiful Thoughts from French and Italian Authors (1866), 119-120.
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Ces détails scientifiques qui effarouchent les fabricans d’un certain âge, ne seront qu’un jeu pour leurs enfans, quand ils auront apprit dans leurs collèges un peu plus de mathématiques et un peu moins de Latin; un peu plus de Chimie, et un peu moins de Grec!
The scientific details which now terrify the adult manufacturer will be mere trifles to his children when they shall be taught at school, a little more Mathematics and a little less Latin, a little more Chemistry, and a little less Greek.
As quoted in 'Sketches From Life of Some Eminent Foreign Scientific Lecturers: Dumas', Magazine of Popular Science, and Journal of the Useful Arts (1836). Vol. 1, 177.
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Changements arrivées dans le globe: Quand on a vu de ses yeux une montagne s’avancer dans une plaine, c’est-à-dire un immense rocher de cette montagne se détacher et couvrir des champs, un château tout entier enfoncé dans la terre, un fleuve englouti qui sort ensuite de son abîme, des marques indubitables qu’un vaste amas d’eau inondait autrefois un pays habité aujourd’hui, et cent vestiges d’autres révolutions, on est alors plus disposé à croire les grands changements qui ont altéré la face du monde, que ne l’est une dame de Paris qui sait seulement que la place où est bâtie sa maison était autrefois un champ labourable. Mais une dame de Naples, qui a vu sous terre les ruines d’Herculanum, est encore moins asservie au préjugé qui nous fait croire que tout a toujours été comme il est aujourd’hui.
Changes That Have Occurred in the Globe: When we have seen with our own eyes a mountain progressing into a plain; that is to say, an immense boulder separating from this mountain and covering the fields; an entire castle broken into pieces over the ground; a river swallowed up which then bursts out from its abyss; clear marks of a vast amount of water having once flooded regions now inhabited, and a hundred vestiges of other transformations, then we are much more willing to believe that great changes altered the face of the earth, than a Parisian lady who knows only that the place where her house was built was once a cultivated field. However, a lady from Naples who has seen the buried ruins of Herculaneum, is much less subject to the bias which leads us to believe that everything has always been as it is today.
From article 'Changements arrivées dans le globe', in Dictionnaire philosophique (1764), collected in Œuvres Complètes de Voltaire (1878), Vol. 2, 427-428. Translated by Ian Ellis.
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Chaos umpire sits
And by decision more embroils the fray
By which he reigns: next him high arbiterChance governs all.
In Richard Bentlet (ed.), Milton's Paradise Lost (1732), book 2, lines 907-910, 70.
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Die Wissenschaft ist ein Land, welches die Eigenschaft hat, um so mehr Menschen beherbergen zu können, je mehr Bewohner sich darin sammeln; sie ist ein Schatz, der um so grösser wird, je mehr man ihn teilt. Darum kann jeder von uns in seiner Art seine Arbeit tun, und die Gemeinsamkeit bedeutet nicht Gleichförmigkeit.
Science is one land, having the ability to accommodate even more people, as more residents gather in it; it is a treasure that is the greater the more it is shared. Because of that, each of us can do his work in his own way, and the common ground does not mean conformity.
Speaking (in German) at the Banquet to Past Presidents, the Chemical Society, as published in William Crookes (ed.) The Chemical News (16 Dec 1898), 78, 298. Also used as epigraph, in Paul Walden, Wilhelm Ostwald (1904), 1. Translation by Webmaster.
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Dilbert: And we know mass creates gravity because more dense planets have more gravity.
Dogbert: How do we know which planets are more dense?
Dilbert:They have more gravity.
Dogbert: That's circular reasoning.
Dilbert: I prefer to think of it as having no loose ends.
Dilbert cartoon strip (1 Mar 1999).
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Dilbert: It took weeks but I’ve calculated a new theory about the origin of the universe. According to my calculations it didn’t start with a “Big Bang” at all—it was more of “Phhbwt” sound. You may be wondering about the practical applications of the “Little Phhbwt” theory.
Dogbert: I was wondering when you’ll go away.
Dilbert comic strip (1 Jan 1993)
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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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Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. … Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
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Frustra fit per plura, quod fieri potest per pauciora.
It is vain to do with more what can be done with less.
Ockham’s Razor.Summa logicae (The Sum of All Logic)(prior to 1324), Part I, Chap. 12. [The village of Ockham is in Surrey. The saying (which was applied for diminishing the number of religious truths that can be proved by reason) is not Ockham's own. As given in Joseph Rickaby, Scholasticism (1908), 54, footnote, it is found a generation before Ockham in Petrus Aureolus, The Eloquent Doctor, 2 Sent. dist. 12, q.1.]
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Hominem ad deos nulla re propius accedunt quam salutem hominibus dando,
In nothing do men more nearly approach the gods, than in giving health to men.
Henry Thomas Riley, Dictionary of Latin Quotations, Proverbs, Maxims, and Mottos (1866), 152.
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If the Indians hadn’t spent the $24. In 1626 Peter Minuit, first governor of New Netherland, purchased Manhattan Island from the Indians for about $24. … Assume for simplicity a uniform rate of 7% from 1626 to the present, and suppose that the Indians had put their $24 at [compound] interest at that rate …. What would be the amount now, after 280 years? 24 x (1.07)280 = more than 4,042,000,000.
The latest tax assessment available at the time of writing gives the realty for the borough of Manhattan as $3,820,754,181. This is estimated to be 78% of the actual value, making the actual value a little more than $4,898,400,000.
The amount of the Indians’ money would therefore be more than the present assessed valuation but less than the actual valuation.
In A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays (1908), 47-48.
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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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Il y aura toujours une valeur (ou plusieurs) qui dépassera toutes les autres.
There will always be one (or more) value that will exceed all others.
Origin French in 'Les Valeurs Extrêmes des Distributions Statistiques', Annales de l'Institut Henri Poincaré (1935), 5, 115. English by Webmaster using Google Translate.
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La nature veut que dans certains temps les hommes se succèdent les uns aux autres par le moyen de la mort; il leur est permis de se défendre contr’elle jusqu’à un certain point; mais passé cela, on aura beau faire de nouvelles découvertes dans l’Anatomie, on aura beau pénétrer de plus en plus dans les secrets de la structure du corps humain, on ne prendra point la Nature pour dupe, on mourra comme à l’ordinaire.
Nature intends that at fixed periods men should succeed each other by the instrumentality of death. They are allowed to keep it at bay up to a certain point; but when that is passed, it will be of no use to make new discoveries in anatomy, or to penetrate more and more into the secrets of the structure of the human body; we shall never outwit nature, we shall die as usual.
In 'Dialogue 5: Dialogues De Morts Anciens', Nouveaux Dialogues des Morts (2nd Ed., 1683), Vol. 1, 154-155. As translated in Craufurd Tait Ramage, Beautiful Thoughts from French and Italian Authors (1866), 113.
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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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Le savant n’étudie pas la nature parce que cela est utile; il l’étudie parce qu’il y prend plaisir et il y prend plaisir parce qu’elle est belle. Si la nature n’était pas belle, elle ne vaudrait pas la peine d’être connue, la vie ne vaudrait pas la peine d’être vécue.
The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.
In Science et Méthode (1920), 48, as translated by Francis Maitland, in Science and Method (1908, 1952), 15.
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L’analyse mathématique … dans l’étude de tous les phénomènes; elle les interprète par le même langage, comme pour attester l’unité et la simplicité du plan de l’univers, et rendre encore plus manifeste cet ordre immuable qui préside à toutes les causes naturelles.
Mathematical analysis … in the study of all phenomena, interprets them by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), xv, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 8.
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Medicus enim nihil aliud est quam animi consolatio
A doctor is nothing more than consolation for the spirit.
Satyricon, Cap. 42. In Iain Bamforth, The Body in the Library (2003), 298.
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On se persuade mieux, pour l’ordinaire, par les raisons qu’on a soi-même trouvées, que par celles qui sont venues dans l’esprit des autres.
We are generally more effectually persuaded by reasons we have ourselves discovered than by those which have occurred to others.
Pensées (1670), Section 1, aphorism 18. In H. F. Stewart (ed.), Pascal's Pensées (1950), 11. Original French text in Pensées de Pascal: publiées dans leur texte authentique (1866), Vol. 1, 99.
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Prospero: Hast thou, spirit,
Performed, to point, the tempest that I bade thee?
Ariel: To every article.
I boarded the king’s ship. Now on the beak,
Now in the waist, the deck, in every cabin,
I flamed amazement.
Sometime I’d divide
And burn in many places; on the topmast,
The yards, and bowsprit would I flame distinctly,
Then meet and join. Jove’s lightnings, the precursors
O’ th’ dreadful thunderclaps, more momentary
And sight-outrunning were not. The fire and cracks
Of sulphurous roaring the most mighty Neptune
Seem to besiege, and make his bold waves tremble;
Yea, his dread trident shake.
In The Tempest (1611), Act 1, Scene 2, line 193-206.
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Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se colorer d'une teinte rose uniforme et à partir de ce moment on aura beau agiter le vase, le vin et l'eau ne partaîtront plus pouvoir se séparer. Tout cela, Maxwell et Boltzmann l'ont expliqué, mais celui qui l'a vu plus nettement, dans un livre trop peu lu parce qu'il est difficile à lire, c'est Gibbs dans ses principes de la Mécanique Statistique.
Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from th at moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 3.
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Question: If you walk on a dry path between two walls a few feet apart, you hear a musical note or “ring” at each footstep. Whence comes this?
Answer: This is similar to phosphorescent paint. Once any sound gets between two parallel reflectors or walls, it bounds from one to the other and never stops for a long time. Hence it is persistent, and when you walk between the walls you hear the sounds made by those who walked there before you. By following a muffin man down the passage within a short time you can hear most distinctly a musical note, or, as it is more properly termed in the question, a “ring” at every (other) step.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 175-6, Question 2. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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Ratbert (as lab rat, to scientist): Doc, we have to talk. Every day you feed me over a hundred pounds of macaroni and cheese. At first I thought you were just being a good host. But lately I’ve been thinking it could be something far more sinister.
Scientist (thinking): Macaroni and cheese causes paranoia.
Dilbert cartoon strip (24 Jul 1990).
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Se è vero che ci si abitua al dolore, come mai con l’andare degli anni si soffre sempre di píu?
If it is true that one gets used to suffering, how is it that, as the years go by, one always suffers more?
Diary entry for 21 Nov 1937, in Il mestiere di vivere (1947), 303. Translated as The Burning Brand: Diaries 1935-1950 (1961), 70.
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That the general characters of the big group to which the embryo belongs appear in development earlier than the special characters. In agreement with this is the fact that the vesicular form is the most general form of all; for what is common in a greater degree to all animals than the opposition of an internal and an external surface?
The less general structural relations are formed after the more general, and so on until the most special appear.
The embryo of any given form, instead of passing through the state of other definite forms, on the contrary separates itself from them.

Fundamentally the embryo of a higher animal form never resembles the adult of another animal form, but only its embryo.
Über Entwicklungsgeschichte der Thiere: Beobachtung und Reflexion (1828), 224. Trans. E. S. Russell, Form and Function: A Contribution to the History of Animal Morphology (1916), 125-6.
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That the Sun will not rise Tomorrow is no less intelligible a Proposition and implies no more contradiction than the Affirmation that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood.
An Enquiry Concerning Human Understanding (1748), 48.
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The Charms of Statistics.—It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence. Some people hate the very name of statistics, but I find them full of beauty and interest. Whenever they are not brutalised, but delicately handled by the higher methods, and are warily interpreted, their power of dealing with complicated phenomena is extraordinary. They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man.
Natural Inheritance (1889), 62-3.
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Tout le monde convient maintenant qu’une Physique d’où l'on banniroit tout ce qui peut avoir quelque rapport avec les mathématiques, pour se borner à un simple recueil d’observations & d’experiences, ne seroit qu’un amusement historique, plus propre à récréer un cercle de personnes oisives, qu’à occuper un esprit véritablement philosophique.
Everyone now agrees that a Physics where you banish all relationship with mathematics, to confine itself to a mere collection of experiences and observations, would be but an historical amusement, more fitting to entertain idle people, than to engage the mind of a true philosopher.
In Dictionnaire de Physique (1781), Vol. 8, 209. English version via Google Translate, tweaked by Webmaster. Also seen translated as—“Everyone now agrees that a physics lacking all connection with mathematics…would only be an historical amusement, fitter for entertaining the idle than for occupying the mind of a philosopher”—in John L. Heilbron, Electricity in the 17th and 18th centuries: A Study of Early Modern Physics (1979), 74. In the latter source, the subject quote immediately follows a different one by Franz Karl Achard. An editor misreading that paragraph is the likely reason the subject quote will be found in Oxford Dictionary of Science Quotations attributed to Achard. Webmaster checked the original footnoted source, and corrected the author of this entry to Paulian (16 May 2014).
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Ut ager quamvis fertilis sine cultura fructuosus esse non potest, sic sine doctrina animus.
A mind without instruction can no more bear fruit than can a field, however fertile, without cultivation.
In Hannis Taylor and Mary Lillie Taylor Hunt, Cicero: a Sketch of His Life and Works (2nd Ed., 1918), 597.
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[About gorillas] You take these fine, regal animals. How many (human) fathers have the same sense of paternity? How many human mothers are more caring? The family structure is unbelievably strong.
As quoted in article from Times Wire Services, 'Naturalist Dian Fossey Slain at Camp in Rwanda: American Was Expert on Mountain Gorillas; Assailants Hunted', Los Angeles Times (29 Dec 1985).
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[Almost certainly not by Einstein.] The more I study science, the more I believe in God.
No cited primary source has been found, so it is almost certainly falsely linked with Einstein. Also, it is not compatible with Einstein’s documented statements on his religious views. See, for example, the quote beginning “It was, of course, a lie what you read about my religious convictions….” The subject quote is included here so readers may find this disclaimer.
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[Describing the effects of over-indulgence in wine:]
But most too passive, when the blood runs low
Too weakly indolent to strive with pain,
And bravely by resisting conquer fate,
Try Circe's arts; and in the tempting bowl
Of poisoned nectar sweet oblivion swill.
Struck by the powerful charm, the gloom dissolves
In empty air; Elysium opens round,
A pleasing frenzy buoys the lightened soul,
And sanguine hopes dispel your fleeting care;
And what was difficult, and what was dire,
Yields to your prowess and superior stars:
The happiest you of all that e'er were mad,
Or are, or shall be, could this folly last.
But soon your heaven is gone: a heavier gloom
Shuts o'er your head; and, as the thundering stream,
Swollen o'er its banks with sudden mountain rain,
Sinks from its tumult to a silent brook,
So, when the frantic raptures in your breast
Subside, you languish into mortal man;
You sleep, and waking find yourself undone,
For, prodigal of life, in one rash night
You lavished more than might support three days.
A heavy morning comes; your cares return
With tenfold rage. An anxious stomach well
May be endured; so may the throbbing head;
But such a dim delirium, such a dream,
Involves you; such a dastardly despair
Unmans your soul, as maddening Pentheus felt,
When, baited round Citheron's cruel sides,
He saw two suns, and double Thebes ascend.
The Art of Preserving Health: a Poem in Four Books (2nd. ed., 1745), Book IV, 108-110.
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[Instead of collecting stamps, he collected dictionaries and encyclopaedias:] Because you can learn more from them.
'Dr Linus Pauling, Atomic Architect', Science Illustrated (1948), 3, 40.
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[Pechblende] einer eigenthümlichen, selbstständigen metallischen Substanz bestehe. Es fallen folglich auch deren bisherige Benennungen, als: Ресhblende Eisenpecherz, hinweg, welche nun durch einen neuen ausschliessend bezeichnenden Namen zu ersetzen sind. Ich habe dazu den Namen: Uranerz (Uranium) erwählt; zu einigem Andenken, dass die chemische Ausfindung dieses neuen Metallkörpers in die Epoche der astronomischen. Entdeckung des Planeten Uranus gefallen sei.
[Pitchblende] consists of a peculiar, distinct, metallic substance. Therefore its former denominations, pitch-blende, pitch-iron-ore, &c. are no longer applicable, and must be supplied by another more appropriate name.—I have chosen that of uranite, (Uranium), as a kind of memorial, that the chemical discovery of this new metal happened in the period of the astronomical discovery of the new planet Uranus.
In original German edition, Beiträge Zur Chemischen Kenntniss Der Mineralkörper (1797), Vol. 2, 215. English edition, translator not named, Analytical Essays Towards Promoting the Chemical Knowledge of Mineral Substances (1801), 491. The new planet was discovered on 13 Mar 1781 by William Herschel, who originally named it Georgium Sidus (George's Star) to honour King George III.
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[Question: Do you feel that scientists correct themselves as often as they should?]
More often than politicians, but not as often as they should.
Interview with Deborah Solomon, 'The Science of Second-Guessing', in New York Times Magazine (12 Dec 2004), 37.
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[When asked “Dr. Einstein, why is it that when the mind of man has stretched so far as to discover the structure of the atom we have been unable to devise the political means to keep the atom from destroying us?”] That is simple, my friend. It is because politics is more difficult than physics.
Einstein’s answer to a conferee at a meeting at Princeton, N.J. (Jan 1946), as recalled by Greenville Clark in 'Letters to the Times', in New York Times (22 Apr 1955), 24.
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SCIENCE: a way of finding things out and then making them work. Science explains what is happening around us the whole time. So does RELIGION, but science is better because it comes up with more understandable excuses when it's wrong.
Wings (1990, 2007), 147.
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A basis of physical science no more justifies dogmatism than a metaphysical basis does.
Letter to E.C. Chapman (29 Jul 1891), Dan H. Laurence (ed.), Collected Letters (1965), Vol. 1, 303.
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A biologist, if he wishes to know how many toes a cat has, does not "frame the hypothesis that the number of feline digital extremities is 4, or 5, or 6," he simply looks at a cat and counts. A social scientist prefers the more long-winded expression every time, because it gives an entirely spurious impression of scientificness to what he is doing.
In Science is a Sacred Cow (1950), 151.
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A box is more a coffin for the human spirit than an inspiration.
Quoted in Aline B. Louchheim, 'Wright Analyzes Architect's Need', New York Times (26 May 1953), 23. Wright was interviewed at age 83 for the opening of a small exhibition of his work at the gallery of the National Institute and the American Academy of Arts and Letters, New York.
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A chemical name should not be a phrase, it ought not to require circumlocutions to become definite; it should not be of the type “Glauber’s salt”, which conveys nothing about the composition of the substance; it should recall the constituents of a compound; it should be non-committal if nothing is known about the substance; the names should preferably be coined from Latin or Greek, so that their meaning can be more widely and easily understood; the form of the words should be such that they fit easily into the language into which they are to be incorporated.
(1782) As quoted in Archibald Clow, Chemical Revolution: A Contribution to Social Technology (1952, 1992), 618.
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A circumstance which influenced my whole career more than any other … was my friendship with Professor Henslow … a man who knew every branch of science…. During the latter half of my time at Cambridge [I] took long walks with him on most days; so that I was called by some of the dons “the man who walks with Henslow.”
In Charles Darwin and Francis Darwin (ed.), 'Autobiography', The Life and Letters of Charles Darwin (1887, 1896), Vol. 1, 44.
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A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.
In 'On the Development of the Methods of Theoretical Physics in Recent Times', Populäre Schriften, Essay 14. Address (22 Sep 1899) to the Meeting of Natural Scientists at Munich. Collected in Brian McGuinness (ed.), Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, Selected Writings (1974), 79.
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A common fallacy in much of the adverse criticism to which science is subjected today is that it claims certainty, infallibility and complete emotional objectivity. It would be more nearly true to say that it is based upon wonder, adventure and hope.
Quoted in E. J. Bowen's obituary of Hinshelwood, Chemistry in Britain (1967), Vol. 3, 536.
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A comparatively small variety of species is found in the older rocks, although of some particular ones the remains are very abundant; ... Ascending to the next group of rocks, we find the traces of life become more abundant, the number of species extended.
Vestiges of the Natural History of Creation (1844), 60-1.
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A computer lets you make more mistakes faster than any invention in human history—with the possible exceptions of handguns and tequila.
…...
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A cosmic mystery of immense proportions, once seemingly on the verge of solution, has deepened and left astronomers and astrophysicists more baffled than ever. The crux ... is that the vast majority of the mass of the universe seems to be missing.
[Reporting a Nature article discrediting explanation of invisible mass being due to neutrinos]
In 'If Theory is Right, Most of Universe is Still “Missing”', New York Times (11 Sep 1984).
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A day of worry is more exhausting than a week of work.
The Use of Life (1895), 212.
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A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.
Science and the Common Understanding (1954), 53-4.
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A discovery is like falling in love and reaching the top of a mountain after a hard climb all in one, an ecstasy not induced by drugs but by the revelation of a face of nature that no one has seen before and that often turns out to be more subtle and wonderful than anyone had imagined.
'True Science', review of Peter Medawar, Advice to a Young Scientist (1980). In The London Review of Books (Mar 1981), 6.
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A few generations ago the clergy, or to speak more accurately, large sections of the clergy were the standing examples of obscurantism. Today their place has been taken by scientists.
In The Function of Reason (1929), 34-35.
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A few of the results of my activities as a scientist have become embedded in the very texture of the science I tried to serve—this is the immortality that every scientist hopes for. I have enjoyed the privilege, as a university teacher, of being in a position to influence the thought of many hundreds of young people and in them and in their lives I shall continue to live vicariously for a while. All the things I care for will continue for they will be served by those who come after me. I find great pleasure in the thought that those who stand on my shoulders will see much farther than I did in my time. What more could any man want?
In 'The Meaning of Death,' in The Humanist Outlook edited by A. J. Ayer (1968) [See Gerald Holton and Sir Isaac Newton].
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A formative influence on my undergraduate self was the response of a respected elder statesmen of the Oxford Zoology Department when an American visitor had just publicly disproved his favourite theory. The old man strode to the front of the lecture hall, shook the American warmly by the hand and declared in ringing, emotional tones: ‘My dear fellow, I wish to thank you. I have been wrong these fifteen years.’ And we clapped our hands red. Can you imagine a Government Minister being cheered in the House of Commons for a similar admission? “Resign, Resign” is a much more likely response!
…...
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A fossil hunter needs sharp eyes and a keen search image, a mental template that subconsciously evaluates everything he sees in his search for telltale clues. A kind of mental radar works even if he isn’t concentrating hard. A fossil mollusk expert has a mollusk search image. A fossil antelope expert has an antelope search image. … Yet even when one has a good internal radar, the search is incredibly more difficult than it sounds. Not only are fossils often the same color as the rocks among which they are found, so they blend in with the background; they are also usually broken into odd-shaped fragments. … In our business, we don’t expect to find a whole skull lying on the surface staring up at us. The typical find is a small piece of petrified bone. The fossil hunter’s search therefore has to have an infinite number of dimensions, matching every conceivable angle of every shape of fragment of every bone on the human body.
Describing the skill of his co-worker, Kamoya Kimeu, who discovered the Turkana Boy, the most complete specimen of Homo erectus, on a slope covered with black lava pebbles.
Richard Leakey and Roger Lewin, Origins Reconsidered: In Search of What Makes Us Human (1992), 26.
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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 good farmer is nothing more nor less than a handy man with a sense of humus.
In 'The Practical Farmer' (Oct 1940), collected in One Man’s Meat (1942), 218.
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A good scare is worth more to a man than advice.
Seen, for example, in Edgar Watson Howe, Country Town Sayings: A Collection of Paragraphs From the Atchison Globe (1911), 141. It is not made clear in the book, whether Howe originated this, or collected it as a saying.
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A government, at bottom, is nothing more than a gang of men, and as a practical matter most of them are inferior men ... Government is actually the worst failure of civilized man. There has never been a really good one, and even those that are most tolerable are arbitrary, cruel, grasping and unintelligent. Indeed, it would not be far wrong to describe the best as the common enemy of all decent citizens.
…...
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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 137-138. (Note that Bernard overlooks how the statistical method can be useful: a surgeon announcing a mortality rate of 40% invites comparison. A surgeon with worse outcomes should adopt this method. If a surgeon has a better results, that method should be adopted.)
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A harmless and a buoyant cheerfulness are not infrequent concomitants of genius; and we are never more deceived than when we mistake gravity for greatness, solemnity for science, and pomposity for erudition.
Lacon: Or, Many Things in Few Words (1865), 57.
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A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
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A learned man is an idler who kills time with study. Beware of his false knowledge: it is more dangerous than ignorance.
In 'Maxims for Revolutionists: Education', in Man and Superman (1905), 230.
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A lecture is much more of a dialogue than many of you probably realize.
From speech given at an anti-war teach-in at the Massachusetts Institute of Technology, (4 Mar 1969) 'A Generation in Search of a Future', as edited by Ron Dorfman for Chicago Journalism Review, (May 1969).
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A life spent in making mistakes is not only more honorable but more useful than a life spent doing nothing.
In 'Preface on Doctors', The Doctor's Dilemma (1909, 1911), lxxxv.
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A living speck—the merest dab of life—capable of pleasure and pain, is far more interesting to me than all the immensities of mere matter.
In Jean-Henri Fabre and Alexander Teixeira de Mattos (trans.), Fabre’s Book of Insects (1921, 1998), 120.
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A lot of scientific papers do deal with matters of atheoretical fact ... for example, whenever somebody finds a new “world's largest dinosaur,” which has only slightly more scientific relevance than shooting the record moose. In short, not everything that gets published in scientific journals bears the distinctive hallmarks of science.
In 'Paleoanthropology: Science or Mythical Charter?', Journal of Anthropological Research (Summer 2002), 58, No. 2, 186.
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A machine has value only as it produces more than it consumes—so check your value to the community.
As given in M. P. Singh, Quote Unquote: A Handbook of Quotations (2005), 86. Webmaster has not yet found a more reliable source.
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A map of the moon... should be in every geological lecture room; for no where can we have a more complete or more magnificent illustration of volcanic operations. Our sublimest volcanoes would rank among the smaller lunar eminences; and our Etnas are but spitting furnaces.
'On the Volcanoes of the Moon', American Journal of Science, 1846, 2 (2nd Series), 347.
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A mathematician thinks that two points are enough to define a straight line, while a physicist wants more data.
Anonymous
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A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 84.
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A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks.
In Rota's 'Introduction' written (1980) to preface Philip J. Davis and Reuben Hersh, The Mathematical Experience (1981, 2012), xxii.
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A mile and a half from town, I came to a grove of tall cocoanut trees, with clean, branchless stems reaching straight up sixty or seventy feet and topped with a spray of green foliage sheltering clusters of cocoanuts—not more picturesque than a forest of colossal ragged parasols, with bunches of magnified grapes under them, would be. I once heard a grouty northern invalid say that a cocoanut tree might be poetical, possibly it was; but it looked like a feather-duster struck by lightning. I think that describes it better than a picture—and yet, without any question, there is something fascinating about a cocoanut tree—and graceful, too.
In Roughing It (1913), 184-85.
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A Miracle is a Violation of the Laws of Nature; and as a firm and unalterable Experience has established these Laws, the Proof against a Miracle, from the very Nature of the Fact, is as entire as any Argument from Experience can possibly be imagined. Why is it more than probable, that all Men must die; that Lead cannot, of itself, remain suspended in the Air; that Fire consumes Wood, and is extinguished by Water; unless it be, that these Events are found agreeable to the Laws of Nature, and there is required a Violation of these Laws, or in other Words, a Miracle to prevent them? Nothing is esteem'd a Miracle, if it ever happen in the common Course of Nature... There must, therefore, be a uniform Experience against every miraculous Event, otherwise the Event would not merit that Appellation. And as a uniform Experience amounts to a Proof, there is here a direct and full Proof, from the Nature of the Fact, against the Existence of any Miracle; nor can such a Proof be destroy'd, or the Miracle render'd credible, but by an opposite Proof, which is superior.
An Enquiry Concerning Human Understanding (1748), 180-181.
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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 newspaper is a device for making the ignorant more ignorant and the crazy crazier.
In A Mencken Chrestomathy (1949, 1956), 625.
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A noteworthy and often-remarked similarity exists between the facts and methods of geology and those of linguistic study. The science of language is, as it were, the geology of the most modern period, the Age of the Man, having for its task to construct the history of development of the earth and its inhabitants from the time when the proper geological record remains silent … The remains of ancient speech are like strata deposited in bygone ages, telling of the forms of life then existing, and of the circumstances which determined or affected them; while words are as rolled pebbles, relics of yet more ancient formations, or as fossils, whose grade indicates the progress of organic life, and whose resemblances and relations show the correspondence or sequence of the different strata; while, everywhere, extensive denudation has marred the completeness of the record, and rendered impossible a detailed exhibition of the whole course of development.
In Language and the Study of Language (1867), 47.
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A number of years ago, when I was a freshly-appointed instructor, I met, for the first time, a certain eminent historian of science. At the time I could only regard him with tolerant condescension.
I was sorry of the man who, it seemed to me, was forced to hover about the edges of science. He was compelled to shiver endlessly in the outskirts, getting only feeble warmth from the distant sun of science- in-progress; while I, just beginning my research, was bathed in the heady liquid heat up at the very center of the glow.
In a lifetime of being wrong at many a point, I was never more wrong. It was I, not he, who was wandering in the periphery. It was he, not I, who lived in the blaze.
I had fallen victim to the fallacy of the “growing edge;” the belief that only the very frontier of scientific advance counted; that everything that had been left behind by that advance was faded and dead.
But is that true? Because a tree in spring buds and comes greenly into leaf, are those leaves therefore the tree? If the newborn twigs and their leaves were all that existed, they would form a vague halo of green suspended in mid-air, but surely that is not the tree. The leaves, by themselves, are no more than trivial fluttering decoration. It is the trunk and limbs that give the tree its grandeur and the leaves themselves their meaning.
There is not a discovery in science, however revolutionary, however sparkling with insight, that does not arise out of what went before. “If I have seen further than other men,” said Isaac Newton, “it is because I have stood on the shoulders of giants.”
Adding A Dimension: Seventeen Essays on the History of Science (1964), Introduction.
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A painter makes patterns with shapes and colours, a poet with words. A painting may embody an “idea,” but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, as Housman insisted, the importance of ideas in poetry is habitually exaggerated. … The poverty of ideas seems hardly to affect the beauty of the verbal pattern. A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.
In A Mathematician’s Apology (1940, 2012), 84-85.
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A physician is obligated to consider more than a diseased organ, more than even the whole man—he must view the man in his world.
Attributed by Rene Dubos, Man Adapting (1965, 1980), Chap. 12, 342. Dubos introduces the quote with “is reported to have taught” and no other citation.
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A physicist learns more and more about less and less, until he knows everything about nothing; whereas a philosopher learns less and less about more and more, until he knows nothing about everything.
Anonymous
Saying.
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A poet is, after all, a sort of scientist, but engaged in a qualitative science in which nothing is measurable. He lives with data that cannot be numbered, and his experiments can be done only once. The information in a poem is, by definition, not reproducible. ... He becomes an equivalent of scientist, in the act of examining and sorting the things popping in [to his head], finding the marks of remote similarity, points of distant relationship, tiny irregularities that indicate that this one is really the same as that one over there only more important. Gauging the fit, he can meticulously place pieces of the universe together, in geometric configurations that are as beautiful and balanced as crystals.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1995), 107.
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A powerful telescope superior to and more powerful than any telescope ever yet made … and also, a suitable Observatory connected therewith … and shall be made useful in promoting science.
From Third Deed of Trust (1874). Excepted in 'Formal Recognition of the Transfer of the Lick Observatory to the Board of Regents of the University', Annual Report of the Secretary to the Board of Regents of the University of California For the Year Ending June 30, 1888, 125.
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A reference to the two sorts of doctors is also found in the Republic: “Now you know that when patients do not require medicine, but have only to be put under a regimen, the inferior sort of practitioner is deemed to be good enough; but when medicine has to be given, then the doctor should be more of a man.”
Osler is referring to Plato’s Dialogues, iii, 153. In Address (1893) to the Johns Hopkins Hospital Historical Club, 'Physic and Physicians as Depicted in Plato', collected in Aequanimitas: With Other Addresses to Medical Students, Nurses and Practitioners of Medicine (1904), 70.
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A research laboratory jealous of its reputation has to develop less formal, more intimate ways of forming a corporate judgment of the work its people do. The best laboratories in university departments are well known for their searching, mutual questioning.
In Editorial, 'Is Science Really a Pack of Lies', Nature (1983), 303, 1257. As quoted and cited in Bradley P. Fuhrman, Jerry J. Zimmerman, Pediatric Critical Care (2011).
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A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 113. Note that Hardy wrote these words while World War II was raging.
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A scientific writer can scarcely encounter anything more undesirable than, after completing a work, to have one of the foundations shaken. I became aware of this situation through a letter from Mr. Bertrand Russell as the printing of this volume neared completion.
In Epilog, Grundgestze der Arithmetic (1903), Vol. 2, 253. Russell wrote in 1901, just as Frege was about to publish Volume 2 of his last major work. English translation by Webmaster using Google translate and online dictionaries, from the original German: “Einem wissenschaftlichen Schriftsteller kann kaum etwas Unerwünschteres begegnen, als dass ihm nach Vollendung einer Arbeit eine der Grundlagen seines Baues erschüttert wird. In diese Lage wurde ich durch einen Brief des Herrn Bertrand Russell versetzt, als der Druck dieses Bandes sich seinem Ende näherte.” The translation in John E. Hopcroft, 'Turing Machines', Scientific American (May 1984), 250, No. 5, 95, gives: “A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.”
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A scientist has to be neutral in his search for the truth, but he cannot be neutral as to the use of that truth when found. If you know more than other people, you have more responsibility, rather than less.
Attributed as a quote, without citation, in J. Robert Moskin, Morality in America (1966), 61. Please contact webmaster if you know a primary print source.
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A scientist who would know the laws of nature must sit passively before nature. He may not dictate to nature its laws, nor may he impose his own intelligence upon nature; rather, the more passive he is before nature, the more nature will reveal its secrets.
In The World's First Love (1952, 2010), 107.
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A sign of a celebrity is often that his name is worth more than his services.
In The Image: A Guide to Pseudo-Events in America (1961), 220.
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A small bubble of air remained unabsorbed... if there is any part of the phlogisticated air [nitrogen] of our atmosphere which differs from the rest, and cannot be reduced to nitrous acid, we may safely conclude that it is not more than 1/120 part of the whole.
Cavendish did not realize the significance of the remaining small bubble. Not until a century later were the air’s Noble Gases appreciated.
'Experiments on Air', read 2 June 1785, Philosophical Transactions of the Royal Society, 1785, 75, 382.
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A species consists of a group of populations which replace each other geographically or ecologically and of which the neighboring ones integrate or hybridise wherever they are in contact or which are potentially capable of doing so (with one or more of the populations) in those cases where contact is prevented by geographical or ecological barriers.
'Speciation Phenomena in Birds', The American Naturalist (1940), 74, 256.
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A study of Disease—of Pestilences methodically prepared and deliberately launched upon man and beast—is certainly being pursue in the laboratories of more than one great country. Blight to destroy crops, Anthrax to slay horses and cattle, Plague to poison not armies but whole districts—such are the lines along which military science is remorselessly advancing.
'Shall We All Commit Suicide?'. Pall Mall (Sep 1924). Reprinted in Thoughts and Adventures (1932), 250.
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A terrible wilderness of mountainous country constitutes the immediate environment of St. Paul's. It is a precipitous cliff into the abyss, a gate of hell, more horrible than the fantasy of Dante could express it.
St. Paul's Monastery is located 300-km southeast of Cairo, on the southern edge of a desert mountain range, adjacent to the Gulf of Suez
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A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown.
Autobiographical Notes (1946), 33. Quoted in Gerald Holton and Yehuda Elkana, Albert Einstein: Historical and Cultural Perspectives (1997), 227.
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A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.
In Scientific American (May 1963). As quoted and cited in The Hutchinson Encyclopedia of Science (1998), 468.
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A tree is beautiful, but what’s more, it has a right to life; like water, the sun and the stars, it is essential. Life on earth is inconceivable without trees. Forests create climate, climate influences peoples’ character, and so on and so forth. There can be neither civilization nor happiness if forests crash down under the axe, if the climate is harsh and severe, if people are also harsh and severe. ... What a terrible future!
In letter to A.S. Suvorin (18 Oct 1888).
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A vision of the whole of life!. Could any human undertaking be ... more grandiose? This attempt stands without rival as the most audacious enterprise in which the mind of man has ever engaged ... Here is man, surrounded by the vastness of a universe in which he is only a tiny and perhaps insignificant part—and he wants to understand it.
…...
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A weird happening has occurred in the case of a lansquenet named Daniel Burghammer, of the squadron of Captain Burkhard Laymann Zu Liebenau, of the honorable Madrucci Regiment in Piadena, in Italy. When the same was on the point of going to bed one night he complained to his wife, to whom he had been married by the Church seven years ago, that he had great pains in his belly and felt something stirring therein. An hour thereafter he gave birth to a child, a girl. When his wife was made aware of this, she notified the occurrence at once. Thereupon he was examined and questioned. … He confessed on the spot that he was half man and half woman and that for more than seven years he had served as a soldier in Hungary and the Netherlands… . When he was born he was christened as a boy and given in baptism the name of Daniel… . He also stated that while in the Netherlands he only slept once with a Spaniard, and he became pregnant therefrom. This, however, he kept a secret unto himself and also from his wife, with whom he had for seven years lived in wedlock, but he had never been able to get her with child… . The aforesaid soldier is able to suckle the child with his right breast only and not at all on the left side, where he is a man. He has also the natural organs of a man for passing water. Both are well, the child is beautiful, and many towns have already wished to adopt it, which, however, has not as yet been arranged. All this has been set down and described by notaries. It is considered in Italy to be a great miracle, and is to be recorded in the chronicles. The couple, however, are to be divorced by the clergy.
Anonymous
'From Piadena in Italy, the 26th day of May 1601'. As quoted in George Tennyson Matthews (ed.) The Fugger Newsletter (1970), 247-248. A handwritten collection of news reports (1568-1604) by the powerful banking and merchant house of Fugger in Ausburg. This was footnoted in The Story of the Secret Service (1937), 698. https://books.google.com/books?id=YfssAAAAMAAJ Richard Wilmer Rowan - 1937
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A well-chosen anthology is a complete dispensary of medicine for the more common mental disorders, and may be used as much for prevention as cure.
'The Use of Poetry', On English Poetry (1922), 85.
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A wise physician, skill’d our wounds to heal, is more than armies to the public weal.
Homer and Alexander Pope (trans.), The Iliad of Homer (1809), Vol. 2, 144.
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A work of morality, politics, criticism will be more elegant, other things being equal, if it is shaped by the hand of geometry.
From Préface sur l'Utilité des Mathématiques et de la Physique (1729), as translated in Florian Cajori, Mathematics in Liberal Education (1928), 61.
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A zygote is a gamete’s way of producing more gametes. This may be the purpose of the universe.
In Time Enough for Love: The Lives of Lazarus Long (1973), 262.
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About 6 or 8 years ago My Ingenious friend Mr John Robinson having [contrived] conceived that a fire engine might be made without a Lever—by Inverting the Cylinder & placing it above the mouth of the pit proposed to me to make a model of it which was set about by having never Compleated & I [being] having at that time Ignorant little knoledge of the machine however I always thought the Machine Might be applied to [more] other as valuable purposes [than] as drawing Water.
Entry in notebook (1765). The bracketed words in square brackets were crossed out by Watt. in Eric Robinson and Douglas McKie (eds.), Partners in Science: Letters of James Watt and Joseph Black (1970), 434.
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About 85 per cent of my “thinking” time was spent getting into a position to think, to make a decision, to learn something I needed to know. Much more time went into finding or obtaining information than into digesting it. Hours went into the plotting of graphs... When the graphs were finished, the relations were obvious at once, but the plotting had to be done in order to make them so.
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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About medications that are drunk or applied to wounds it is worth learning from everyone; for people do not discover these by reasoning but by chance, and experts not more than laymen.
Affections, in Hippocrates, trans. P. Potter (1988), Vol. 5, 69. Littré VI, 254.
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Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence…. The two propositions: “The earth turns round” and “it is more convenient to suppose the earth turns round” have the same meaning; there is nothing more in the one than in the other.
From La Science et l’Hypothèse (1908), 141, as translated by George Bruce Halsted in Science and Hypothesis (1905), 85-86. From the original French, “L’espace absolu, c’est-à-dire le repère auquel il faudrait rapporter la terre pour savoir si réellement elle tourne, n’a aucune existence objective. … Ces deux propositions: ‘la terre tourne’, et: ‘il est plus commode de supposer que la terre tourne’, ont un seul et même sens; il n’y a rien de plus dans l’une que dans l’autre.”
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Absorbed in the special investigation, I paid no heed to the edifice which was meanwhile unconsciously building itself up. Having however completed the comparison of the fossil species in Paris, I wanted, for the sake of an easy revision of the same, to make a list according to their succession in geological formations, with a view of determining the characteristics more exactly and bringing them by their enumeration into bolder relief. What was my joy and surprise to find that the simplest enumeration of the fossil fishes according to their geological succession was also a complete statement of the natural relations of the families among themselves; that one might therefore read the genetic development of the whole class in the history of creation, the representation of the genera and species in the several families being therein determined; in one word, that the genetic succession of the fishes corresponds perfectly with their zoological classification, and with just that classification proposed by me.
Quoted in Elizabeth Cary Agassiz (ed.), Louis Agassiz: His Life and Correspondence (1885), Vol. I, 203-4.
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Access to more information isn’t enough—the information needs to be correct, timely, and presented in a manner that enables the reader to learn from it. The current network is full of inaccurate, misleading, and biased information that often crowds out the valid information. People have not learned that “popular” or “available” information is not necessarily valid.
Response to the Pew Research Center survey question, “Is Google making us stupid?” Posted 19 Feb 2010 on page 'Future of the Internet IV' at pewinternet.org website.
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Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life.
The Expanding Universe (1933), 56-57.
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Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.
J. C. Maxwell on Louis Poinsôt (1777-1859) in 'On a Dynamical Top' (1857). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 248.
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Accountants and second-rate business school jargon are in the ascendant. Costs, which rise rapidly, and are easily ascertained and comprehensible, now weigh more heavily in the scales than the unquantifiable and unpredictable values and future material progress. Perhaps science will only regain its lost primacy as peoples and government begin to recognize that sound scientific work is the only secure basis for the construction of policies to ensure the survival of Mankind without irreversible damage to Planet Earth.
In New Scientist, March 3, 1990.
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Adam, the first man, didn’t know anything about the nucleus but Dr. George Gamow, visiting professor from George Washington University, pretends he does. He says for example that the nucleus is 0.00000000000003 feet in diameter. Nobody believes it, but that doesn't make any difference to him.
He also says that the nuclear energy contained in a pound of lithium is enough to run the United States Navy for a period of three years. But to get this energy you would have to heat a mixture of lithium and hydrogen up to 50,000,000 degrees Fahrenheit. If one has a little stove of this temperature installed at Stanford, it would burn everything alive within a radius of 10,000 miles and broil all the fish in the Pacific Ocean.
If you could go as fast as nuclear particles generally do, it wouldn’t take you more than one ten-thousandth of a second to go to Miller's where you could meet Gamow and get more details.
'Gamow interviews Gamow' Stanford Daily, 25 Jun 1936. In Helge Kragh, Cosmology and Controversy: The Historica1 Development of Two Theories of the Universe (1996), 90.
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Carl Sagan quote Advances in medicine and agriculture
A bean farmer checks her crop in Congo. Photo by Neil Palmer (CIAT). CC2.0 (source)
Advances in medicine and agriculture have saved vastly more lives than have been lost in all the wars in history.
The Demon-Haunted World: Science as a Candle in the Dark (1996), 11.
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Advocacy of leaf protein as a human food is based on the undisputed fact that forage crops (such as lucerne) give a greater yield of protein than other types of crops. Even with connventional food crops there is more protein in the leafy parts than in the seeds or tubs that are usually harvested.
Quoted in 'India Children to Eat Leaf Protein in a Diet Test', New York Times (16 Dec 1973), 46.
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After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formerly used, if some assumptions (which are called axioms) were granted me. They follow in this order.
There is no one center of all the celestial circles or spheres.
The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere.
All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe.
The ratio of the earth's distance from the sun to the height of the firmament is so much smaller than the ratio of the earth's radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.
Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth's motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.
What appears to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve about the sun like any other planet. The earth has, then, more than one motion.
The apparent retrograde and direct motion of the planets arises not from their motion but from the earth's. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.
'The Commentariolus', in Three Copernican Treatises (c.1510), trans. E. Rosen (1939), 58-9.
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After some experiments made one day at my house upon the phosphorus, a little piece of it being left negligently upon the table in my chamber, the maid making the bed took it up in the bedclothes she had put on the table, not seeing the little piece. The person who lay afterwards in the bed, waking at night and feeling more than ordinary heat, perceived that the coverlet was on fire.
Quoted in John Emsley, The 13th Element: The Sordid Tale of Murder, Fire, and Phosphorus (2000), 11.
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After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Atombau und Spektrallinien (1919), viii, Atomic Structure and Spectral Lines, trans. Henry L. Brose (1923), viii.
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Aging is an inevitable process. I surely wouldn't want to grow younger. The older you become, the more you know; your bank account of knowledge is much richer.
Found in several quote books, but without citation, for example, in Tom Crisp, The Book of Bill: Choice Words Memorable Men (2009), 220. If you know the primary source, please contact Webmaster.
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Alcoholism, the opium habit and tobaccoism are a trio of poison habits which have been weighty handicaps to human progress during the last three centuries. In the United States, the subtle spell of opium has been broken by restrictive legislation; the grip of the rum demon has been loosened by the Prohibition Amendment to the Constitution, but the tobacco habit still maintains its strangle-hold and more than one hundred million victims of tobaccoism daily burn incense to the smoke god.
In Tobaccoism: or, How Tobacco Kills (1922), Preface, 7.
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Alexander the king of the Macedonians, began like a wretch to learn geometry, that he might know how little the earth was, whereof he had possessed very little. Thus, I say, like a wretch for this, because he was to understand that he did bear a false surname. For who can be great in so small a thing? Those things that were delivered were subtile, and to be learned by diligent attention: not which that mad man could perceive, who sent his thoughts beyond the ocean sea. Teach me, saith he, easy things. To whom his master said: These things be the same, and alike difficult unto all. Think thou that the nature of things saith this. These things whereof thou complainest, they are the same unto all: more easy things can be given unto none; but whosoever will, shall make those things more easy unto himself. How? With uprightness of mind.
In Thomas Lodge (trans.), 'Epistle 91', The Workes of Lucius Annaeus Seneca: Both Morrall and Naturall (1614), 383. Also in Robert Édouard Moritz, Memorabilia Mathematica (1914), 135.
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Algebra is generous; she often gives more than is asked of her.
Quoted in Bulletin American Mathematical Society (1905), 2, 285. As cited in Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 275.
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All admit that the mountains of the globe are situated mostly along the border regions of the continents (taking these regions as 300 to 1000 miles or more in width), and that over these same areas the sedimentary deposits have, as a general thing, their greatest thickness. At first thought, it would seem almost incredible that the upliftings of mountains, whatever their mode of origin, should have taken place just where the earth’s crust, through these sedimentary accumulations, was the thickest, and where, therefore, there was the greatest weight to be lifted. … Earthquakes show that even now, in this last of the geological ages, the same border regions of the continents, although daily thickening from the sediments borne to the ocean by rivers, are the areas of the greatest and most frequent movements of the earth’s crust. (1866)
[Thus, the facts were known long ago; the explanation by tectonic activity came many decades later.]
In 'Observations on the Origin of Some of the Earth's Features', The American Journal of Science (Sep 1866), Second Series, 42, No. 125, 210-211.
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All disease, at some period or other of its course, is more or less a reparative process, not necessarily accompanied with suffering: an effort of nature to remedy a process of poisoning or of decay, which has taken place weeks, months, sometimes years beforehand, unnoticed.
In Notes on Nursing: What It Is and What It Is Not (1859), 5.
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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 human discoveries seem to be made only for the purpose of confirming more strongly the truths come from on high, and contained in the sacred writings.
Quoted in Marcel de Serres, 'On the Physical Facts in the Bible Compared with the Discoveries of the Modern Sciences', The Edinburgh New Philosophical Journal (1845), Vol. 38, 260.
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All knowledge and understanding of the Universe was no more than playing with stones and shells on the seashore of the vast imponderable ocean of truth.
…...
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All Modern Men are descended from a Wormlike creature but it shows more on some people.
The Great Bustard and Other People (1944), 30.
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All of the books in the world contain no more information than is broadcast as video in a single large American city in a single year. Not all bits have equal value.
…...
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All of us are interested in our roots. Generally this interest is latent in youth, and grows with age. Until I reached fifty I thought that history of science was a refuge for old scientists whose creative juices had dried up. Now of course I know that I was wrong! As we grow older, we become more interested in the past, in family history, local history, etc. Astronomy is, or was when I started in it, almost a family.
In Organizations and Strategies in Astronomy (2002), Vol. 3, 206.
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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 science is full of statements where you put your best face on your ignorance, where you say: … we know awfully little about this, but more or less irrespective of the stuff we don’t know about, we can make certain useful deductions.
From Assumption and Myth in Physical Theory (1967), 11.
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All scientists must focus closely on limited targets. Whether or not one’s findings on a limited subject will have wide applicability depends to some extent on chance, but biologists of superior ability repeatedly focus on questions the answers to which either have wide ramifications or lead to new areas of investigation. One procedure that can be effective is to attempt both reduction and synthesis; that is, direct a question at a phenomenon on one integrative level, identify its mechanism at a simpler level, then extrapolate its consequences to a more complex level of integration.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230-231,
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All that Anatomie can doe is only to shew us the gross and sensible parts of the body, or the vapid and dead juices all which, after the most diligent search, will be noe more able to direct a physician how to cure a disease than how to make a man; for to remedy the defects of a part whose organicall constitution and that texture whereby it operates, he cannot possibly know, is alike hard, as to make a part which he knows not how is made. Now it is certaine and beyond controversy that nature performs all her operations on the body by parts so minute and insensible that I thinke noe body will ever hope or pretend, even by the assistance of glasses or any other intervention, to come to a sight of them, and to tell us what organicall texture or what kinde offerment (for whether it be done by one or both of these ways is yet a question and like to be soe always notwithstanding all the endeavours of the most accurate dissections) separate any part of the juices in any of the viscera, or tell us of what liquors the particles of these juices are, or if this could be donne (which it is never like to be) would it at all contribute to the cure of the diseases of those very parts which we so perfectly knew.
'Anatomie' (1668). Quoted in Kenneth Dewhurst (ed.), Dr. Thomas Sydenham (1624-1689): His Life and Original Writings (1966), 85-6.
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All the inventions and devices ever constructed by the human hand or conceived by the human mind, no matter how delicate, how intricate and complicated, are simple, childish toys compared with that most marvelously wrought mechanism, the human body. Its parts are far more delicate, and their mutual adjustments infinitely more accurate, than are those of the most perfect chronometer ever made.
In Plain Facts For Old and Young: Embracing the Natural History and Hygiene of Organic Life (1879, 1887), Revised Ed., 332.
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All the more recent work on alkaptonuria has... strengthened the belief that the homogentisic acid excreted is derived from tyrosin, but why alkaptonuric individuals pass the benzene ring of their tyrosin unbroken and how and where the peculiar chemical change from tyrosin to homogentisic acid is brought about, remain unsolved problems.
'The Incidence of Alkaptonuria: A Study in Chemical Individuality', The Lancet, 1902, 2, 1616.
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All you really need to know for the moment is that the universe is a lot more complicated than you might think, even if you start from a position of thinking it’s pretty damn complicated in the first place.
In Mostly Harmless (1992), 195.
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Almost all the world is natural chemicals, so it really makes you re-think everything. A cup of coffee is filled with chemicals. They've identified a thousand chemicals in a cup of coffee. But we only found 22 that have been tested in animal cancer tests out of this thousand. And of those, 17 are carcinogens. There are ten milligrams of known carcinogens in a cup of coffee and thats more carcinogens than youre likely to get from pesticide residues for a year!
Paper to the American Chemical Society, 'Pollution, Pesticides and Cancer Misconceptions.' As cited by Art Drysdale, 'Latest Insider News: Natural vs. Synthetic Chemical Pesticides' (14 Feb 1999), on the mitosyfraudes.org website. Bruce Ames has delivered a similar statistic in various other publications.
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Almost daily we shudder as prophets of doom announce the impending end of civilization and universe. We are being asphyxiated, they say, by the smoke of the industry; we are suffocating in the ever growing mountain of rubbish. Every new project depicts its measureable effects and is denounced by protesters screaming about catastrophe, the upsetting of the land, the assault on nature. If we accepted this new mythology we would have to stop pushing roads through the forest, harnessing rivers to produce the electricity, breaking grounds to extract metals, enriching the soil with chemicals, killing insects, combating viruses … But progress—basically, an effort to organise a corner of land and make it more favourable for human life—cannot be baited. Without the science of pomiculture, for example, trees will bear fruits that are small, bitter, hard, indigestible, and sour. Progress is desirable.
Anonymous
Uncredited. In Lachman Mehta, Stolen Treasure (2012), 117.
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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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Alphonse of Castile is reported to have said that if he had had the making of the universe he would have done it much better. And I think so too. Instead of making a man go through the degradation of faculties and death, he should continually improve with age, and then be translated from this world to a superior planet, where he should begin life with the knowledge gained here, and so on. That would be to my mind, as an old man, a more satisfactory way of conducting affairs
Address, in 'Report to the Chemical Society's Jubilee', Nature (26 Mar 1891), 43, 493.
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Also the earth is not spherical, as some have said, although it tends toward sphericity, for the shape of the universe is limited in its parts as well as its movement… . The movement which is more perfect than others is, therefore, circular, and the corporeal form which is the most perfect is the sphere.
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Although few expressions are more commonly used in writing about science than “science revolution,” there is a continuing debate as to the propriety of applying the concept and term “revolution” to scientific change. There is, furthermore, a wide difference of opinion as to what may constitute a revolution. And although almost all historians would agree that a genuine alteration of an exceptionally radical nature (the Scientific Revolution) occurred in the sciences at some time between the late fifteenth (or early sixteenth) century and the end of the seventeenth century, the question of exactly when this revolution occurred arouses as much scholarly disagreement as the cognate question of precisely what it was.
The Newtonian Revolution (1980), 3.
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Alvarez seemed to care less about the way the picture in the puzzle would look, when everything fit together, than about the fun of looking for pieces that fit. He loved nothing more than doing something that everybody else thought impossible. His designs were clever, and usually exploited some little-known principle that everyone else had forgotten.
As quoted in Walter Sullivan, 'Luis W. Alvarez, Nobel Physicist Who Explored Atom, Dies at 77: Obituary', New York Times (2 Sep 1988).
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America has never been united by blood or birth or soil. We are bound by ideals that move us beyond our backgrounds, lift us above our interests and teach us what it means to be citizens. Every child must be taught these principles. Every citizen must uphold them. And every immigrant, by embracing these ideals, makes our country more, not less, American.
…...
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Among the authorities it is generally agreed that the Earth is at rest in the middle of the universe, and they regard it as inconceivable and even ridiculous to hold the opposite opinion. However, if we consider it more closely the question will be seen to be still unsettled, and so decidedly not to be despised. For every apparent change in respect of position is due to motion of the object observed, or of the observer, or indeed to an unequal change of both.
'Book One. Chapter V. Whether Circular Motion is Proper to the Earth, and of its Place', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 40.
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Among the multitude of animals which scamper, fly, burrow and swim around us, man is the only one who is not locked into his environment. His imagination, his reason, his emotional subtlety and toughness, make it possible for him not to accept the environment, but to change it. And that series of inventions, by which man from age to age has remade his environment, is a different kind of evolution—not biological, but cultural evolution. I call that brilliant sequence of cultural peaks The Ascent of Man. I use the word ascent with a precise meaning. Man is distinguished from other animals by his imaginative gifts. He makes plans, inventions, new discoveries, by putting different talents together; and his discoveries become more subtle and penetrating, as he learns to combine his talents in more complex and intimate ways. So the great discoveries of different ages and different cultures, in technique, in science, in the arts, express in their progression a richer and more intricate conjunction of human faculties, an ascending trellis of his gifts.
The Ascent of Man (1973), 19-20.
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Among the older records, we find chapter after chapter of which we can read the characters, and make out their meaning: and as we approach the period of man’s creation, our book becomes more clear, and nature seems to speak to us in language so like our own, that we easily comprehend it. But just as we begin to enter on the history of physical changes going on before our eyes, and in which we ourselves bear a part, our chronicle seems to fail us—a leaf has been torn out from nature's record, and the succession of events is almost hidden from our eyes.
Letter 1 to William Wordsworth. Quoted in the appendix to W. Wordsworth, A Complete Guide to the Lakes, Comprising Minute Direction for the Tourist, with Mr Wordsworth's Description of the Scenery of the County and Three Letters upon the Geology of the Lake District (1842), 14.
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Among the scenes which are deeply impressed on my mind, none exceed in sublimity the primeval forests undefaced by the hand of man; whether those of Brazil, where the powers of Life are predominant, or those of Tierra del Fuego, where Death and Decay prevail. Both are temples filled with the varied productions of the God of Nature: no one can stand in these solitudes unmoved, and not feel that there is more in man than the mere breath of his body.
Journal of Researches: into the Natural History and Geology of the Countries Visited During the Voyage of H.M.S. Beagle Round the World (1839), ch. XXIII, 604-5.
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Among the scenes which are deeply impressed on my mind, none exceed in sublimity the primeval [tropical] forests, ... temples filled with the varied productions of the God of Nature. No one can stand in these solitudes unmoved, and not feel that there is more in man than the mere breath of his body.
In What Mr. Darwin Saw in His Voyage Round the World in the Ship “Beagle” 1879, 170.
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Among the studies to which the [Rockefeller] Foundation is giving support is a series in a relatively new field, which may be called molecular biology, in which delicate modern techniques are being used to investigate ever more minute details of certain life processes.
In 'Molecular Biology', Annual Report of the Rockefeller Foundation (1938), 203-4. Reprinted in a letter to Science (6 Nov 1970), 170, 582.
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Among those whom I could never pursuade to rank themselves with idlers, and who speak with indignation of my morning sleeps and nocturnal rambles, one passes the day in catching spiders, that he may count their eyes with a microscope; another exhibits the dust of a marigold separated from the flower with a dexterity worthy of Leuwenhoweck himself. Some turn the wheel of electricity; some suspend rings to a lodestone, and find that what they did yesterday, they can do again to-day.—Some register the changes of the wind, and die fully convinced that the wind is changeable.—There are men yet more profound, who have heard that two colorless liquors may produce a color by union, and that two cold bodies will grow hot of they are mingled: they mingle them, and produce the effect expected, say it is strange, and mingle them again.
In Tryon Edwards, A Dictionary of Thoughts (1908), 243.
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Among your pupils, sooner or later, there must be one. who has a genius for geometry. He will be Sylvester’s special pupil—the one pupil who will derive from his master, knowledge and enthusiasm—and that one pupil will give more reputation to your institution than the ten thousand, who will complain of the obscurity of Sylvester, and for whom you will provide another class of teachers.
Letter (18 Sep 1875) recommending the appointment of J.J. Sylvester to Daniel C. Gilman. In Daniel C. Gilman Papers, Ms. 1, Special Collections Division, Milton S. Eisenhower Library, Johns Hopkins University. As quoted in Karen Hunger Parshall, 'America’s First School of Mathematical Research: James Joseph Sylvester at The Johns Hopkins University 1876—1883', Archive for History of Exact Sciences (1988), 38, No. 2, 167.
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An alcoholic has been lightly defined as a man who drinks more than his own doctor.
Journal of the American Medical Association (1962), 181, 393.
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Arthur Stanley Eddington quote: An electron is no more (and no less) hypothetical than a star. Nowadays we count electrons one b
An electron is no more (and no less) hypothetical than a star. Nowadays we count electrons one by one in a Geiger counter, as we count the stars one by one on a photographic plate.
Messenger Lectures (1934), New Pathways in Science (1935), 21.
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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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An experiment is an observation that can be repeated, isolated and varied. The more frequently you can repeat an observation, the more likely are you to see clearly what is there and to describe accurately what you have seen. The more strictly you can isolate an observation, the easier does your task of observation become, and the less danger is there of your being led astray by irrelevant circumstances, or of placing emphasis on the wrong point. The more widely you can vary an observation, the more clearly will the uniformity of experience stand out, and the better is your chance of discovering laws.
In A Text-Book of Psychology (1909), 20.
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An immune system of enormous complexity is present in all vertebrate animals. When we place a population of lymphocytes from such an animal in appropriate tissue culture fluid, and when we add an antigen, the lymphocytes will produce specific antibody molecules, in the absence of any nerve cells. I find it astonishing that the immune system embodies a degree of complexity which suggests some more or less superficial though striking analogies with human language, and that this cognitive system has evolved and functions without assistance of the brain.
'The Generative Grammar of the Immune System', Nobel Lecture, 8 Dec 1984. In Nobel Lectures: Physiology or Medicine 1981-1990 (1993), 223.
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An infallible Remedy for the Tooth-ach, viz Wash the Root of an aching Tooth, in Elder Vinegar, and let it dry half an hour in the Sun; after which it will never ach more; Probatum est.
In Poor Richard's Almanack (1739).
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An irrefutable proof that such single-celled primaeval animals really existed as the direct ancestors of Man, is furnished according to the fundamental law of biogeny by the fact that the human egg is nothing more than a simple cell.
Natürlche Schöpfungsgeschichte, trans. E. R. Lankester, The History of Creation (1892), Vol. 2, 381.
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An ocean traveller has even more vividly the impression that the ocean is made of waves than that it is made of water.
Gifford Lecture at the University of Edinburgh (Mar 1927). In The Nature of the Physical World (1929, reprint 2005), 242.
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An unelectrified atom is so elusive that unless more than a million million are present we have no means sufficiently sensitive to detect them, or, to put it another way, unless we had a better test for a man than for an unelectrified molecule, we should be unable to find out that the earth was inhabited. … A billion unelectrified atoms may escape our observation, whereas a dozen or so electrified ones are detected without difficulty.
From the Romanes Lecture (10 Jun 1914) delivered in the Sheldonian Theatre, published as The Atomic Theory (1914), 9.
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Sigmund Freud quote: Analogies, it is true, decide nothing but they can make one feel more at home
Analogies, it is true, decide nothing but they can make one feel more at home.
New Introductory Lectures on Psycho-Analysis (1933), in James Strachey (ed.), The Standard Edition of the Complete Psychological Works of Sigmund Freud (1964), Vol. 22, 72.
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Anaximander the Milesian, a disciple of Thales, first dared to draw the inhabited world on a tablet; after him Hecataeus the Milesian, a much-travelled man, made the map more accurate, so that it became a source of wonder.
Agathemerus 1.1. In G. S. Kirk, J. E. Raven and M. Schofield (eds.), The Presocratic Philosophers: A Critical History with a Selection of Texts (1983), p. 104.
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Anaximenes ... also says that the underlying nature is one and infinite ... but not undefined as Anaximander said but definite, for he identifies it as air; and it differs in its substantial nature by rarity and density. Being made finer it becomes fire; being made thicker it becomes wind, then cloud, then (when thickened still more) water, then earth, then stones; and the rest come into being from these.
Simplicius, Commentary on Aristotle’s Physics, 24, 26-31, quoting Theophrastus on Anaximenes. In G. S. Kirk, J. E. Raven and M.Schofield (eds), The Presocratic Philosophers: A Critical History with a Selection of Texts (1983), p. 145.
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Anaximenes ... said that infinite air was the principle, from which the things that are becoming, and that are, and that shall be, and gods and things divine, all come into being, and the rest from its products. The form of air is of this kind: whenever it is most equable it is invisible to sight, but is revealed by the cold and the hot and the damp and by movement. It is always in motion; for things that change do not change unless there be movement. Through becoming denser or finer it has different appearances; for when it is dissolved into what is finer it becomes fire, while winds, again, are air that is becoming condensed, and cloud is produced from air by felting. When it is condensed still more, water is produced; with a further degree of condensation earth is produced, and when condensed as far as possible, stones. The result is that the most influential components of the generation are opposites, hot and cold.
Hippolytus, Refutation, 1.7.1. In G. S. Kirk, J. E. Raven and M. Schofield (eds.), The Presocratic Philosophers: A Critical History with a Selection of Texts (1983), p. 145.
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And as for Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.
In Advancement of Learning (1605), Book 2. Collected in The Works of Francis Bacon (1765), Vol. 1, 61.
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And I believe that the Binomial Theorem and a Bach Fugue are, in the long run, more important than all the battles of history.
This Week Magazine (1937).
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And I do not take my medicines from the apothecaries; their shops are but foul sculleries, from which comes nothing but foul broths. As for you, you defend your kingdom with belly-crawling and flattery. How long do you think this will last? ... let me tell you this: every little hair on my neck knows more than you and all your scribes, and my shoebuckles are more learned than your Galen and Avicenna, and my beard has more experience than all your high colleges.
'Credo', in J. Jacobi (ed.), Paracelsus: Selected Writings (1951), 80.
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And if one look through a Prism upon a white Object encompassed with blackness or darkness, the reason of the Colours arising on the edges is much the same, as will appear to one that shall a little consider it. If a black Object be encompassed with a white one, the Colours which appear through the Prism are to be derived from the Light of the white one, spreading into the Regions of the black, and therefore they appear in a contrary order to that, when a white Object is surrounded with black. And the same is to be understood when an Object is viewed, whose parts are some of them less luminous than others. For in the borders of the more and less luminous Parts, Colours ought always by the same Principles to arise from the Excess of the Light of the more luminous, and to be of the same kind as if the darker parts were black, but yet to be more faint and dilute.
Opticks (1704), Book I, Part 2, Prop. VIII, Prob. III, 123.
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And it has been sarcastically said, that there is a wide difference between a good physician and a bad one, but a small difference between a good physician and no physician at all; by which it is meant to insinuate, that the mischievous officiousness of art does commonly more than counterbalance any benefit derivable from it.
Elements of Medical Logic (1819), 8-9.
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And so I conclude that blood lives and is nourished of itself and in no way depends on any other part of the body as being prior to it or more excellent... So that from this we may perceive the causes not only of life in general... but also of longer or shorter life, of sleeping and waking, of skill, of strength and so forth.
Disputations Touching the Generation of Animals (1651), trans. Gweneth Whitteridge (1981), Chapter 52, 247. Alternate translation: “We conclude that blood lives of itself and that it depends in no ways upon any parts of the body. Blood is the cause not only of life in general, but also of longer or shorter life, of sleep and waking, of genius, aptitude, and strength. It is the first to live and the last to die.”
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And so the great truth, now a paradox, may become a commonplace, that man is greater than his surroundings, and that the production of a breed of men and women, even in our great cities, less prone to disease, and pain, more noble in aspect, more rational in habits, more exultant in the pure joy of living, is not only scientifically possible, but that even the partial fulfillment of this dream, if dream it be, is the most worthy object towards which the lover of his kind can devote the best energies of his life.
In 'The Breed of Man', The Nineteenth Century, (Oct 1900), 669, as collected in Martin Polley (ed.), The History of Sport in Britain, 1880-1914: Sport, Education, and Improvement (2004), Vol. 2, 181.
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And we daily in our experiments electrise bodies plus or minus, as we think proper. [These terms we may use till your Philosophers give us better.] To electrise plus or minus, no more needs to be known than this, that the parts of the Tube or Sphere, that are rubb’d, do, in the Instant of Friction, attract the Electrical Fire, and therefore take it from the Thin rubbing; the same parts immediately, as the Friction upon them ceases, are disposed to give the fire they have received, to any Body that has less.
Letter 25 May 1747. Quoted in I. Bernard Cohen, Franklin and Newton: An Enquiry into Speculative Newtonian Experimental Science and Franklin’s Work in Electricity as an Example Thereof (1956), 439.
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And ye who wish to represent by words the form of man and all the aspects of his membrification, get away from that idea. For the more minutely you describe, the more you will confuse the mind of the reader and the more you will prevent him from a knowledge of the thing described. And so it is necessary to draw and describe.
From Notebooks (AnA, 14v; Cf. QII, 1), as translated by J. Playfair McMurrich, in Leonardo da Vinci the Anatomist (1930), 76, (Institution Publication 411, Carnegie Institution of Washington).
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And yet in a funny way our lack of success led to our breakthrough; because, since we could not get a cell line off the shelf doing what we wanted, we were forced to construct it. And the original experiment ... developed into a method for the production of hybridomas ... [which] was of more importance than our original purpose.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 256-257.
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Angling may be said to be so like the Mathematics that it can never be fully learnt; at least not so fully but that there will still be more new experiments left for the trial of other men that succeed us.
In The Complete Angler (1653, 1915), 7.
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Animals generally seem naturally disposed to … intercourse at about the same period of the year, and that is when winter is changing into summer…. In the human species, the male experiences more under sexual excitement in winter, and the female in summer.
Aristotle
In The Works of Aristotle: Historia Animalium (350 BC), (The History of Animals), Book V, Part 8, 542a20 translated in William David Ross and John Alexander Smith (eds.), D’Arcy Wentworth Thompson (trans.), (1910), Vol. 4, 27-28
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Anthropology has reached that point of development where the careful investigation of facts shakes our firm belief in the far-reaching theories that have been built up. The complexity of each phenomenon dawns on our minds, and makes us desirous of proceeding more cautiously. Heretofore we have seen the features common to all human thought. Now we begin to see their differences. We recognize that these are no less important than their similarities, and the value of detailed studies becomes apparent. Our aim has not changed, but our method must change. We are still searching for the laws that govern the growth of human culture, of human thought; but we recognize the fact that before we seek for what is common to all culture, we must analyze each culture by careful and exact methods, as the geologist analyzes the succession and order of deposits, as the biologist examines the forms of living matter. We see that the growth of human culture manifests itself in the growth of each special culture. Thus we have come to understand that before we can build up the theory of the growth of all human culture, we must know the growth of cultures that we find here and there among the most primitive tribes of the Arctic, of the deserts of Australia, and of the impenetrable forests of South America; and the progress of the civilization of antiquity and of our own times. We must, so far as we can, reconstruct the actual history of mankind, before we can hope to discover the laws underlying that history.
The Jesup North Pacific Expedition: Memoir of the American Museum of Natural History (1898), Vol. 1, 4.
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Anton Chekhov wrote that ‘one must not put a loaded rifle on stage if no one is thinking of firing it.’ Good drama requires spare and purposive action, sensible linking of potential causes with realized effects. Life is much messier; nothing happens most of the time. Millions of Americans (many hotheaded) own rifles (many loaded), but the great majority, thank God, do not go off most of the time. We spend most of real life waiting for Godot, not charging once more unto the breach.
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Ants are more like the parts of an animal than entities on their own. They are mobile cells, circulating through a dense connective tissue of other ants in a matrix of twigs. The circuits are so intimately interwoven that the anthill meets all the essential criteria of an organism.
In 'Antaeus in Manhattan', The Lives of a Cell: Notes of a Biology Watcher (1974), 63.
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Any child born into the hugely consumptionist way of life so common in the industrial world will have an impact that is, on average, many times more destructive than that of a child born in the developing world.
Al Gore
Earth in the Balance: Ecology and the Human Spirit (2006), 308.
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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 intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius - and a lot of courage - to move in the opposite direction.
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Any man who says he doesn’t like applause and recognition is either a fool or a liar. You learn from mistakes, but success gives you the courage to go on and do even more.
As quoted in Lawrence K. Altman, 'Christiaan Barnard, 78, Surgeon For First Heart Transplant, Dies', New York Times (3 Sep 2001)
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Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of facts will certainly reject my theory.
The Origin of Species (1859), 482.
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Anyone who thinks science is trying to make human life easier or more pleasant is utterly mistaken.
In 'Quotation Marks', New York Times (11 Oct 1931), XX2.
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Anything at all that can be the object of scientific thought becomes dependent on the axiomatic method, and thereby indirectly on mathematics, as soon as it is ripe for the formation of a theory. By pushing ahead to ever deeper layers of axioms … we become ever more conscious of the unity of our knowledge. In the sign of the axiomatic method, mathematics is summoned to a leading role in science.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zürich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1115.
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Apprehension, uncertainty, waiting, expectation, fear of surprise, do a patient more harm than any exertion. Remember he is face to face with his enemy all the time.
In Notes on Nursing: What it is, and What it is Not (1860), 53.
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Archimedes possessed so high a spirit, so profound a soul, and such treasures of highly scientific knowledge, that though these inventions [used to defend Syracuse against the Romans] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians.
The Principles of Mathematics (1903), 451.
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Art gallery? Who needs it? Look up at the swirling silver-lined clouds in the magnificent blue sky or at the silently blazing stars at midnight. How could indoor art be any more masterfully created than God’s museum of nature?
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Art is more godlike than science. Science discovers; art creates.
John Opie
As given, without citation, in Maturin Murray Ballo, Edge-Tools of Speech (1851), 25. Also in a fictional conversation in novel by Baron Edward Bulwer Lytton, Zanoni (1842), 89.
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As a different, but perhaps more common, strategy for the suppression of novelty, we may admit the threatening object to our midst, but provide an enveloping mantle of ordinary garb… . This kind of cover-up, so often amusing in our daily lives, can be quite dangerous in science, for nothing can stifle originality more effectively than an ordinary mantle placed fully and securely over an extraordinary thing.
In 'A Short Way to Big Ends', Natural History (Jan 1986), 95, No. 1, 18.
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As a graduate student at Columbia University, I remember the a priori derision of my distinguished stratigraphy professor toward a visiting Australian drifter ... Today my own students would dismiss with even more derision anyone who denied the evident truth of continental drift–a prophetic madman is at least amusing; a superannuated fuddy-duddy is merely pitiful.
…...
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As advertising always convinces the sponsor even more than the public, the scientists have become sold, and remain sold, on the idea that they have the key to the Absolute, and that nothing will do for Mr. Average Citizen but to stuff himself full of electrons.
In Science is a Sacred Cow (1950), 26.
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As an Art, Mathematics has its own standard of beauty and elegance which can vie with the more decorative arts. In this it is diametrically opposed to a Baroque art which relies on a wealth of ornamental additions. Bereft of superfluous addenda, Mathematics may appear, on first acquaintance, austere and severe. But longer contemplation reveals the classic attributes of simplicity relative to its significance and depth of meaning.
In The Skeleton Key of Mathematics (1949), 12.
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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 an organ is exercised, circulation is more particularly directed to it and is more readily performed in it. Consequently, all its secretions and excretions increase. The more an organ is exercised, the more it is nourished.
'Réflexions sur les corps organisés et les sciences dont ils sont l'objet', Magasin Encyclopedique, III (1799), 471. Trans. Jonathan Mandelbaum in Pietro Corsi, The Age of Lamarck (1988), 75.
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As belief shrinks from this world, it is more necessary than ever that someone believe. Wild-eyed men in caves. Nuns in black. Monks who do not speak. We are left to believe... Hell is when no one believes.
White Noise. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 24
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As few subjects are more interesting to society, so few have been more frequently written upon than the education of youth.
Essay No. VI, 'On Education', first published in The Bee (10 Nov 1759), collected in The Works of Oliver Goldsmith (1900), Vol. 5, 95. Reprinted as Essay VII under the title 'On the Education of Youth', (1765). The Bee was a weekly paper wholly the work of Goldsmith.
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As for what I have done as a poet, I take no pride in whatever. Excellent poets have lived at the same time with me, poets more excellent lived before me, and others will come after me. But that in my country I am the only person who knows the truth in the difficult science of colors—of that, I say, I am not a little proud, and here have a consciousness of superiority to many.
Wed 18 Feb 1829. Johann Peter Eckermann, Conversations with Goethe, ed. J. K. Moorhead and trans. J. Oxenford, (1971), 302.
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As I look back over my efforts, I would characterize my contributions as being largely in the realm of model building. ... I perceive myself as rather uninhibited, with a certain mathematical facility and more interest in the broad aspect of a problem than the delicate nuances. I am more interested in discovering what is over the next rise than in assiduously cultivating the beautiful garden close at hand.
'Men, Mines and Molecules', Annual Review of Physical Chemistry, 1977, 28, 13.
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As I strayed into the study of an eminent physicist, I observed hanging against the wall, framed like a choice engraving, several dingy, ribbon-like strips of, I knew not what... My curiosity was at once aroused. What were they? ... They might be shreds of mummy-wraps or bits of friable bark-cloth from the Pacific, ... [or] remnants from a grandmother’s wedding dress... They were none of these... He explained that they were carefully-prepared photographs of portions of the Solar Spectrum. I stood and mused, absorbed in the varying yet significant intensities of light and shade, bordered by mystic letters and symbolic numbers. As I mused, the pale legend began to glow with life. Every line became luminous with meaning. Every shadow was suffused with light shining from behind, suggesting some mighty achievement of knowledge; of knowledge growing more daring in proportion to the remoteness of the object known; of knowledge becoming more positive in its answers, as the questions which were asked seemed unanswerable. No Runic legend, no Babylonish arrowhead, no Egyptian hieroglyph, no Moabite stone, could present a history like this, or suggest thoughts of such weighty import or so stimulate and exalt the imagination.
The Sciences of Nature Versus the Science of Man: A Plea for the Science of Man (1871), 7-9.
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As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.
Collected Works (1877), Vol. 5, 25-26. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 412.
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As never before, the work of the engineer is basic to the kind of society to which our best efforts are committed. Whether it be city planning, improved health care in modern facilities, safer and more efficient transportation, new techniques of communication, or better ways to control pollution and dispose of wastes, the role of the engineer—his initiative, creative ability, and hard work—is at the root of social progress.
Remarks for National Engineers Week (1971). As quoted in Consulting Engineer (1971), 36, 18.
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As new areas of the world came into view through exploration, the number of identified species of animals and plants grew astronomically. By 1800 it had reached 70,000. Today more than 1.25 million different species, two-thirds animal and one-third plant, are known, and no biologist supposes that the count is complete.
In The Intelligent Man's Guide to Science: The Biological Sciences (1960), 654. Also in Isaac Asimov’s Book of Science and Nature Quotations (1988), 320.
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As one of the elder members of the community of integrative biologists, I am overwhelmingly aware that during this continuing intellectual revolution, seniority is more likely to be correlated with obsolescence than with wisdom.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 330.
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As pilgrimages to the shrines of saints draw thousands of English Catholics to the Continent, there may be some persons in the British Islands sufficiently in love with science, not only to revere the memory of its founders, but to wish for a description of the locality and birth-place of a great master of knowledge—John Dalton—who did more for the world’s civilisation than all the reputed saints in Christendom.
In The Worthies of Cumberland (1874), 25.
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As pure truth is the polar star of our science [mathematics], so it is the great advantage of our science over others that it awakens more easily the love of truth in our pupils. … If Hegel justly said, “Whoever does not know the works of the ancients, has lived without knowing beauty,” Schellbach responds with equal right, “Who does not know mathematics, and the results of recent scientific investigation, dies without knowing truth.”
Max Simon
From Didaktik und Methodik des Rechnens und der Mathematik (1908), 37. As quoted and translated in J.W.A. Young, Teaching of Mathematics in the Elementary and the Secondary School (1907), 44. From the original German, “Wenn Hegel mit Recht sagt: ‘Wer die Werke der Alten nicht kennt, der hat gelebt, ohne die Schönheit gekannt zu haben’, so erwidert Schellbach mit nicht minderem Recht: ‘Wer die Math. und die Resultate der neueren Naturforschung nicht gekannt hat, der stirbt, ohne die Wahrheit zu kennen.’”
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As regards railways, it is certain that nothing is so profitable, because nothing is so cheaply transported, as passenger traffic. Goods traffic, of whatsoever description, must be more or less costly. Every article conveyed by railway requires handling and conveyance beyond the limit of the railway stations; but passengers take care of themselves, and find their own way.
From 'Railway System and its Results' (Jan 1856) read to the Institution of Civil Engineers, reprinted in Samuel Smiles, Life of George Stephenson (1857), 520.
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As science has supplanted its predecessors, so it may hereafter be superseded by some more perfect hypothesis, perhaps by some totally different way of looking at the phenomena—of registering the shadows on the screen—of which we in this generation can form no idea. The advance of knowledge is an infinite progression towards a goal that for ever recedes.
In The Golden Bough: A Study in Magic and Religion (1890, 1900), Vol. 3, 460.
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As science is more and more subject to grave misuse as well as to use for human benefit it has also become the scientist's responsibility to become aware of the social relations and applications of his subject, and to exert his influence in such a direction as will result in the best applications of the findings in his own and related fields. Thus he must help in educating the public, in the broad sense, and this means first educating himself, not only in science but in regard to the great issues confronting mankind today.
Message to University Students Studying Science', Kagaku Asahi 11, no. 6 (1951), 28-29. Quoted in Elof Axel Carlson, Genes, Radiation, and Society: The Life and Work of H. J. Muller (1981), 371.
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As science, of necessity, becomes more involved with itself, so also, of necessity, it becomes more international. I am impressed to know that of the 670 members of this Academy [National Academy of Sciences], 163 were born in other lands.
From Address to the Centennial Convocation of the National Academy of Sciences (22 Oct 1963), 'A Century of Scientific Conquest.' Online at The American Presidency Project.
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As scientific men we have all, no doubt, felt that our fellow men have become more and more satisfying as fish have taken up their work which has been put often to base uses, which must lead to disaster. But what sin is to the moralist and crime to the jurist so to the scientific man is ignorance. On our plane, knowledge and ignorance are the immemorial adversaries. Scientific men can hardly escape the charge of ignorance with regard to the precise effect of the impact of modern science upon the mode of living of the people and upon their civilisation. For them, such a charge is worse than that of crime.
From Banquet Speech (10 Dec 1922), Nobel Prize in Chemistry, collected in Carl Gustaf Santesson (ed.), Les Prix Nobel en 1921-1922 (1923).
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As soon as he ceased to be mad he became merely stupid. There are maladies we must not seek to cure because they alone protect us from others that are more serious.
'Le Côté de Guermantes', À la recherche du temps perdu (1913-27).
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As soon as we got rid of the backroom attitude and brought our apparatus fully into the Department with an inexhaustible supply of living patients with fascinating clinical problems, we were able to get ahead really fast. Any new technique becomes more attractive if its clinical usefulness can be demonstrated without harm, indignity or discomfort to the patient... Anyone who is satisfied with his diagnostic ability and with his surgical results is unlikely to contribute much to the launching of a new medical science. He should first be consumed with a divine discontent with things as they are. It greatly helps, of course, to have the right idea at the right time, and quite good ideas may come, Archimedes fashion, in one's bath..
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As the Director of the Theoretical Division of Los Alamos, I participated at the most senior level in the World War II Manhattan Project that produced the first atomic weapons.
Now, at age 88, I am one of the few remaining such senior persons alive. Looking back at the half century since that time, I feel the most intense relief that these weapons have not been used since World War II, mixed with the horror that tens of thousands of such weapons have been built since that time—one hundred times more than any of us at Los Alamos could ever have imagined.
Today we are rightly in an era of disarmament and dismantlement of nuclear weapons. But in some countries nuclear weapons development still continues. Whether and when the various Nations of the World can agree to stop this is uncertain. But individual scientists can still influence this process by withholding their skills.
Accordingly, I call on all scientists in all countries to cease and desist from work creating, developing, improving and manufacturing further nuclear weapons - and, for that matter, other weapons of potential mass destruction such as chemical and biological weapons.
[On the occasion of the 50th Anniversary of Hiroshima.]
Letter, Bulletin of the Atomic Scientists (Nov 1995), 51:6, 3.
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As the issues are greater than men ever sought to realize before, the recriminations will be fiercer and pride more desperately hurt. It may help to recall that many recognized before the bomb ever feel that the time had already come when we must learn to live in One World.
…...
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As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them.
In Florian Cajori, History of Mathematics (1893), 92.
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As the world has seen its age of stone, its age of bronze, and its age of iron, so it may before long have embarked on a new and even more prosperous era—the age of aluminium.
Magazine
Concluding remark in uncredited 'Topics of the Day' article, 'The Future of Aluminium', The Spectator (15 Jul 1893), 77.
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As to giving credit to whom credit is due, rest assured the best way to do good to one’s-self is to do justice to others. There is plenty for everybody in science, and more than can be consumed in our time. One may get a fair name by suppressing references, but the Jewish maxim is true, “He who seeks a name loses fame.”
Postscript to a note to George Wilson (1844). As quoted in George Wilson and Archibald Geikie, Memoir of Edward Forbes F.R.S. (1861), 366.
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As to the position of the earth, then, this is the view which some advance, and the views advanced concerning its rest or motion are similar. For here too there is no general agreement. All who deny that the earth lies at the centre think that it revolves about the centre, and not the earth only but, as we said before, the counter-earth as well. Some of them even consider it possible that there are several bodies so moving, which are invisible to us owing to the interposition of the earth. This, they say, accounts for the fact that eclipses of the moon are more frequent than eclipses of the sun; for in addition to the earth each of these moving bodies can obstruct it.
Aristotle
On the Heavens, 293b, 15-25. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 1, 483.
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As we descend deeper and deeper into this region, the inhabitants become more and more modified, and fewer and fewer, indicating our approach to an abyss where life is either extinguished, or exhibits but a few sparks to mark its lingering presence.
In The Natural History of the European Seas (1859), 26-27. (In the 19th century, knowledge was gained from deep sea life hauled in with nets.)
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As we push ever more deeply into the universe, probing its secrets, discovering its way, we must also constantly try to learn to cooperate across the frontiers that really divide earth’s surface.
In 'The President’s News Conference at the LBJ Ranch' (29 Aug 1965). Collected in Public Papers of the Presidents of the United States: Lyndon B. Johnson: 1965 (1966), 945.
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Astronomers = Moon Starers = No More Stars
Anagram
From 'The Anagram Hall of Fame' on the wordsmith.org website.
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Astronomy is a cold, desert science, with all its pompous figures,—depends a little too much on the glass-grinder, too little on the mind. ’Tis of no use to show us more planets and systems. We know already what matter is, and more or less of it does not signify.
In 'Country Life', collected in The Complete Works of Ralph Waldo Emerson (1904), Vol. 12, 166.
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Astronomy may be revolutionized more than any other field of science by observations from above the atmosphere. Study of the planets, the Sun, the stars, and the rarified matter in space should all be profoundly influenced by measurements from balloons, rockets, probes and satellites. ... In a new adventure of discovery no one can foretell what will be found, and it is probably safe to predict that the most important new discovery that will be made with flying telescopes will be quite unexpected and unforeseen. (1961)
Opening and closing of 'Flying Telescopes', Bulletin of the Atomic Scientists (May 1961), Vol. 17, No. 5, 191 and 194.
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At first he who invented any art that went beyond the common perceptions of man was naturally admired by men, not only because there was something useful in the inventions, but because he was thought wise and superior to the rest. But as more arts were invented, and some were directed to the necessities of life, others to its recreation, the inventors of the latter were always regarded as wiser than the inventors of the former, because their branches of knowledge did not aim at utility.
Aristotle
Metaphysics, 981b, 13-20. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1553.
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At first it seems obvious, but the more you think about it the stranger the deductions from this axiom seem to become; in the end you cease to understand what is meant by it.
As quoted, without citation, in Stories about Sets (1968), 84.
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At first sight nothing seems more obvious than that everything has a beginning and an end, and that everything can be subdivided into smaller parts. Nevertheless, for entirely speculative reasons the philosophers of Antiquity, especially the Stoics, concluded this concept to be quite unnecessary. The prodigious development of physics has now reached the same conclusion as those philosophers, Empedocles and Democritus in particular, who lived around 500 B.C. and for whom even ancient man had a lively admiration.
'Development of the Theory of Electrolytic Dissociation', Nobel Lecture, 11 December 1903. In Nobel Lectures: Chemistry 1901-1921 (1966), 45.
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At first, the sea, the earth, and the heaven, which covers all things, were the only face of nature throughout the whole universe, which men have named Chaos; a rude and undigested mass, and nothing more than an inert weight, and the discordant atoms of things not harmonizing, heaped together in the same spot.
Describing the creation of the universe from chaos, at the beginning of Book I of Metamorphoses, lines 5-9. As translated by Henry T. Riley, The Metamorphoses of Ovid, Vol I: Books I-VII (1858), 1-2. Riley footnoted: “A rude and undigested mass.—Ver. 7. This is very similar to the words of the Scriptures, ‘And the earth was without form and void,’ Genesis, ch. i. ver. 2.”
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At least once per year, some group of scientists will become very excited and announce that:
•The universe is even bigger than they thought!
•There are even more subatomic particles than they thought!
•Whatever they announced last year about global warming is wrong.
From newspaper column '25 Things I Have Learned in 50 Years' (Oct 1998), collected in Dave Barry Turns Fifty (2010), 183.
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At length being at Clapham where there is, on the common, a large pond which, I observed to be one day very rough with the wind, I fetched out a cruet of oil and dropt a little of it on the water. I saw it spread itself with surprising swiftness upon the surface; but the effect of smoothing the waves was not produced; for I had applied it first on the leeward side of the pond, where the waves were largest, and the wind drove my oil back upon the shore. I then went to the windward side, where they began to form; and there the oil, though not more than a tea-spoonful, produced an instant calm over a space several yards square, which spread amazingly, and extended itself gradually till it reached the leeside, making all that quarter of the pond, perhaps half an acre, as smooth as a looking-glass.
[Experiment to test an observation made at sea in 1757, when he had seen the wake of a ship smoothed, explained by the captain as presumably due to cooks emptying greasy water in to the sea through the scuppers.]
Letter, extract in 'Of the still of Waves by Means of Oil The Gentleman's Magazine (1775), Vol. 45, 82.
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At the beginning of its existence as a science, biology was forced to take cognizance of the seemingly boundless variety of living things, for no exact study of life phenomena was possible until the apparent chaos of the distinct kinds of organisms had been reduced to a rational system. Systematics and morphology, two predominantly descriptive and observational disciplines, took precedence among biological sciences during the eighteenth and nineteenth centuries. More recently physiology has come to the foreground, accompanied by the introduction of quantitative methods and by a shift from the observationalism of the past to a predominance of experimentation.
In Genetics and the Origin of Species (1937, 1982), 6.
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At the end of 1854 … the aggregate length of railways opened in Great Britain and Ireland at that time measured about 8,054 miles,—about the diameter of the globe, and nearly 500 miles more than the united lengths of the Thames, the Seine, the Rhone, the Ebro, the Tagus, the Rhine, the Elbe, the Vistula, the Dnieper, and the Danube, or the ten chief rivers of Europe. … the work of only twenty-five years.
From 'Railway System and its Results' (Jan 1856) read to the Institution of Civil Engineers, reprinted in Samuel Smiles, Life of George Stephenson (1857), 511-512.
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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