Both Quotes (494 quotes)
... there is an external world which can in principle be exhaustively described in scientific language. The scientist, as both observer and language-user, can capture the external facts of the world in prepositions that are true if they correspond to the facts and false if they do not. Science is ideally a linguistic system in which true propositions are in one-to-one relation to facts, including facts that are not directly observed because they involve hidden entities or properties, or past events or far distant events. These hidden events are described in theories, and theories can be inferred from observation, that is the hidden explanatory mechnism of the world can be discovered from what is open to observation. Man as scientist is regarded as standing apart from the world and able to experiment and theorize about it objectively and dispassionately.
'Introduction', Revolutions and Reconstructions in the Philosophy of Science (1981), xii. In John Templeton and Robert L. Herrmann, Is God the Only Reality (1994), 11-12.
... [I]nfectious disease is merely a disagreeable instance of a widely prevalent tendency of all living creatures to save themselves the bother of building, by their own efforts, the things they require. Whenever they find it possible to take advantage of the constructive labors of others, this is the path of least resistance. The plant does the work with its roots and its green leaves. The cow eats the plant. Man eats both of them; and bacteria (or investment bankers) eat the man. ...
Rats, Lice and History (1935).
...after my first feeling of revulsion had passed, I spent three of the most entertaining and instructive weeks of my life studying the fascinating molds which appeared one by one on the slowly disintegrating mass of horse-dung. Microscopic molds are both very beautiful and absorbingly interesting. The rapid growth of their spores, the way they live on each other, the manner in which the different forms come and go, is so amazing and varied that I believe a man could spend his life and not exhaust the forms or problems contained in one plate of manure.
The World Was My Garden (1938, 1941), 55.
...[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)
Ac kynde wit cometh
Of alle kynnes syghtes,
Of briddes and of beestes,
Of tastes of truthe and of deceites.
Mother-Wit comes from all kinds of experiences,
Of birds and beasts and of tests both true and false.
Of alle kynnes syghtes,
Of briddes and of beestes,
Of tastes of truthe and of deceites.
Mother-Wit comes from all kinds of experiences,
Of birds and beasts and of tests both true and false.
In William Langland and B. Thomas Wright (ed.) The Vision and Creed of Piers Ploughman (1842), 235. Modern translation by Terrence Tiller in Piers Plowman (1981, 1999), 123.
Dass die bis jetzt unzerlegten chemischen Elemente absolut unzerlegbare Stoffe seien, ist gegenwärtig mindestens sehr unwahrscheinlich. Vielmehr scheint es, dass die Atome der Elemente nicht die letzten, sondern nur die näheren Bestandtheile der Molekeln sowohl der Elemente wie der Verbindungen bilden, die Molekeln oder Molecule als Massentheile erster, die Atome als solche zweiter Ordnung anzusehen sind, die ihrerseits wiederum aus Massentheilchen einer dritten höheren Ordnung bestehen werden.
That the as yet undivided chemical elements are absolutely irreducible substances, is currently at least very unlikely. Rather it seems, that the atoms of elements are not the final, but only the immediate constituents of the molecules of both the elements and the compounds—the Molekeln or molecule as foremost division of matter, the atoms being considered as second order, in turn consisting of matter particles of a third higher order.
[Speculating in 1870, on the existence of subatomic particles, in opening remark of the paper by which he became established as co-discoverer of the Periodic Law.]
That the as yet undivided chemical elements are absolutely irreducible substances, is currently at least very unlikely. Rather it seems, that the atoms of elements are not the final, but only the immediate constituents of the molecules of both the elements and the compounds—the Molekeln or molecule as foremost division of matter, the atoms being considered as second order, in turn consisting of matter particles of a third higher order.
[Speculating in 1870, on the existence of subatomic particles, in opening remark of the paper by which he became established as co-discoverer of the Periodic Law.]
'Die Natur der chemischen Elemente als Function ihrer Atomgewichte' ('The Nature of the Chemical Elements as a Function of their Atomic Weight'), Annalen der Chemie (1870), supp. b, 354. Original German paper reprinted in Lothar Meyer and Dmitry Ivanovich Mendeleyev, Das natürliche System der chemischen Elemente: Abhandlungen (1895), 9. Translation by Webmaster, with punctuation faithful to the original, except a comma was changed to a dash to improve readability.
Ron Hutcheson, a Knight-Ridder reporter: [Mr. President, what are your] personal views [about the theory of] intelligent design?
President George W. Bush: [Laughing. You're] doing a fine job of dragging me back to the past [days as governor of Texas]. ... Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught...”
Hutcheson: Both sides ought to be properly taught?
President: Yes ... so people can understand what the debate is about.
Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?
President: I think that part of education is to expose people to different schools of thought, and I'm not suggesting—you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.
Hutcheson: So we've got to give these groups—...
President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]
President George W. Bush: [Laughing. You're] doing a fine job of dragging me back to the past [days as governor of Texas]. ... Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught...”
Hutcheson: Both sides ought to be properly taught?
President: Yes ... so people can understand what the debate is about.
Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?
President: I think that part of education is to expose people to different schools of thought, and I'm not suggesting—you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.
Hutcheson: So we've got to give these groups—...
President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]
From conversation with reporters at the White House (1 Aug 2005), as quoted by Matthew Cooper in 'Fanning the Controversy Over “Intelligent Design”', Time (3 Aug 2005). The Time writer stated, “The president has gone farther in questioning the widely-taught theories of evolution and natural selection than any president since Ronald Reagan, who advocated teaching creationism in public schools alongside evolution.” Just a few months later, in the nation's first case on that point, on 20 Dec 2005, “a federal judge [John E. Jones] ruled it was unconstitutional for a Pennsylvania school district to present intelligent design as an alternative in high school biology courses, because it is a religious viewpoint,” as reported by Laurie Goodstein in 'Judge Rejects Teaching Intelligent Design', New York Times (21 Dec 2005). Goodstein also wrote “Judge Jones, a Republican appointed by President Bush, concluded that intelligent design was not science,” and that “the evidence in the trial proved that intelligent design was 'creationism relabeled.' The Supreme Court has already ruled that creationism ... cannot be taught as science in a public school.”
Where faith commences, science ends. Both these arts of the human mind must be strictly kept apart from each other. Faith has its origin in the poetic imagination; knowledge, on the other hand, originates in the reasoning intelligence of man. Science has to pluck the blessed fruits from the tree of knowledge, unconcerned whether these conquests trench upon the poetical imaginings of faith or not.
In Ernst Haeckel and E. Ray Lankester (trans.), The History of Creation (1880), Vol. 1, 9.
[About John Evershed] There is much in our medallist’s career which is a reminder of the scientific life of Sir William Huggins. They come from the same English neighbourhood and began as amateurs of the best kind. They both possess the same kind of scientific aptitude.
Address, presenting the Gold medal of the Royal Astronomical Society to Evershed, as quoted in F.J.M. Stratton, 'John Evershed', Biographical Memoirs of Fellows of the Royal Society (Nov 1957), 3, 40.
[Students or readers about teachers or authors.] They will listen with both ears to what is said by the men just a step or two ahead of them, who stand nearest to them, and within arm’s reach. A guide ceases to be of any use when he strides so far ahead as to be hidden by the curvature of the earth.
From Lecture (5 Apr 1917) at Hackley School, Tarrytown, N.Y., 'Choosing Books', collected in Canadian Stories (1918), 150.
A book should have either intelligibility or correctness; to combine the two is impossible, but to lack both is to be unworthy of a place as Euclid has occupied in education.
In essay, 'Mathematics and the Metaphysicians' (1901), collected in Mysticism and Logic: And Other Essays (1917), 73. The essay was also published as 'Recent Work in the Philosophy of Mathematics', in the American magazine, International Monthly.
A century ago, Darwin and his friends were thought to be dangerous atheists, but their heresy simply replaced a benevolent personal deity called God by a benevolent impersonal deity called Evolution. In their different ways Bishop Wilberforce and T.H. Huxley both believed in Fate.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
A crystal is like a class of children arranged for drill, but standing at ease, so that while the class as a whole has regularity both in time and space, each individual child is a little fidgety!
In Crystals and X-Rays (1948), 22.
A demonstrative and convincing proof that an acid does consist of pointed parts is, that not only all acid salts do Crystallize into edges, but all Dissolutions of different things, caused by acid liquors, do assume this figure in their Crystallization; these Crystalls consist of points differing both in length and bigness from one another, and this diversity must be attributed to the keener or blunter edges of the different sorts of acids
A Course of Chymistry (1675), trans. W. Harris (1686), 24.
A discovery must be, by definition, at variance with existing knowledge. During my lifetime, I made two. Both were rejected offhand by the popes of the field. Had I predicted these discoveries in my applications, and had those authorities been my judges, it is evident what their decisions would have been.
In 'Dionysians and Apollonians', Science (2 Jun 1972), 176, 966. Reprinted in Mary Ritchie Key, The Relationship of Verbal and Nonverbal Communication (1980), 318.
A huge net is being dragged across the sea floor, destroying everything in its path. Ahead of it bloom undersea forests and their hundreds and thousands of living creatures, both plant and animal; behind it is a desert. The net is pulled to the surface and most of the dead and dying life forms in it are thrown out. A few marketable species are retained. [Trawling] is like taking a front-end loader and scraping up your entire front garden and shredding it, keeping a few pebbles, and dumping the rest of it down the drain.
In Payback: Debt and the Shadow Side of Wealth (2008), 191.

A man cannot be professor of zoölogy on one day and of chemistry on the next, and do good work in both. As in a concert all are musicians,—one plays one instrument, and one another, but none all in perfection.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 146.
A moment’s consideration of this case shows what a really great advance in the theory and practise of breeding has been obtained through the discovery of Mendel’s law. What a puzzle this case would have presented to the biologist ten years ago! Agouti crossed with chocolate gives in the second filial generation (not in the first) four varieties, viz., agouti, chocolate, black and cinnamon. We could only have shaken our heads and looked wise (or skeptical).
Then we had no explanation to offer for such occurrences other than the “instability of color characters under domestication,” the “effects of inbreeding,” “maternal impressions.” Serious consideration would have been given to the proximity of cages containing both black and cinnamon-agouti mice.
Now we have a simple, rational explanation, which anyone can put to the test. We are able to predict the production of new varieties, and to produce them.
We must not, of course, in our exuberance, conclude that the powers of the hybridizer know no limits. The result under consideration consists, after all, only in the making of new combinations of unit characters, but it is much to know that these units exist and that all conceivable combinations of them are ordinarily capable of production. This valuable knowledge we owe to the discoverer and to the rediscoverers of Mendel’s law.
Then we had no explanation to offer for such occurrences other than the “instability of color characters under domestication,” the “effects of inbreeding,” “maternal impressions.” Serious consideration would have been given to the proximity of cages containing both black and cinnamon-agouti mice.
Now we have a simple, rational explanation, which anyone can put to the test. We are able to predict the production of new varieties, and to produce them.
We must not, of course, in our exuberance, conclude that the powers of the hybridizer know no limits. The result under consideration consists, after all, only in the making of new combinations of unit characters, but it is much to know that these units exist and that all conceivable combinations of them are ordinarily capable of production. This valuable knowledge we owe to the discoverer and to the rediscoverers of Mendel’s law.
'New Colour Variety of the Guinea Pig', Science, 1908, 28, 250-252.
A most vile face! and yet she spends me forty pound a year in Mercury and Hogs Bones. All her teeth were made in the Black-Fryars, both her Eyebrows i’ the Strand, and her Hair in Silver-street. Every part of Town owns a Piece of her.
A reference to artificial teeth by character Otter, speaking of his wife, in Epicoene: or, The Silent Woman (1609), Act IV, Sc. 2, 64. Also, True-wit makes a specific reference to “false Teeth” in Act I, Sc. 1, 10.
A page from a journal of modern experimental physics will be as mysterious to the uninitiated as a Tibetan mandala. Both are records of enquiries into the nature of the universe.
In The Tao of Physics (1975), 36.
A statistician is one who has learned how to get valid evidence from statistics and how (usually) to avoid being misled by irrelevant facts. It’s too bad that we apply the same name to this kind of person that we use for those who only tabulate. It’s as if we had the same name for barbers and brain surgeons because they both work on the head.
In How to Tell the Liars from the Statisticians (1983), 1.
A thorough advocate in a just cause, a penetrating mathematician facing the starry heavens, both alike bear the semblance of divinity
In Wilhelm Meister, Wanderjahre, Zweites Buch, in 'Sprüche in Prosa' Natur, VI, 947.
A very sincere and serious freshman student came to my office with a question that had clearly been troubling him deeply. He said to me, ‘I am a devout Christian and have never had any reason to doubt evolution, an idea that seems both exciting and well documented. But my roommate, a proselytizing evangelical, has been insisting with enormous vigor that I cannot be both a real Christian and an evolutionist. So tell me, can a person believe both in God and in evolution?’ Again, I gulped hard, did my intellectual duty, a nd reassured him that evolution was both true and entirely compatible with Christian belief –a position that I hold sincerely, but still an odd situation for a Jewish agnostic.
…...
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.
'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
A … difference between most system-building in the social sciences and systems of thought and classification of the natural sciences is to be seen in their evolution. In the natural sciences both theories and descriptive systems grow by adaptation to the increasing knowledge and experience of the scientists. In the social sciences, systems often issue fully formed from the mind of one man. Then they may be much discussed if they attract attention, but progressive adaptive modification as a result of the concerted efforts of great numbers of men is rare.
The Study of Man (1941), 19-20.
About ten months ago [1609] a report reached my ears that a certain Fleming [Hans Lippershey] had constructed a spyglass, by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby... Of this truly remarkable effect several experiences were related, to which some persons gave credence while others denied them. A few days later the report was confirmed to me in a letter from a noble Frenchman at Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to enquire into the means by which I might arrive at the invention of a similar instrument. This I did shortly afterwards, my basis being the theory of refraction. First I prepared a tube of lead, at the ends of which I fitted two glass lenses, both plane on one side while on the other side one was spherically convex and the other concave.
The Starry Messenger (1610), trans. Stillman Drake, Discoveries and Opinions of Galileo (1957), 28-9.
Adam is fading out. It is on account of Darwin and that crowd. I can see that he is not going to last much longer. There's a plenty of signs. He is getting belittled to a germ—a little bit of a speck that you can't see without a microscope powerful enough to raise a gnat to the size of a church. They take that speck and breed from it: first a flea; then a fly, then a bug, then cross these and get a fish, then a raft of fishes, all kinds, then cross the whole lot and get a reptile, then work up the reptiles till you've got a supply of lizards and spiders and toads and alligators and Congressmen and so on, then cross the entire lot again and get a plant of amphibiums, which are half-breeds and do business both wet and dry, such as turtles and frogs and ornithorhyncuses and so on, and cross-up again and get a mongrel bird, sired by a snake and dam'd by a bat, resulting in a pterodactyl, then they develop him, and water his stock till they've got the air filled with a million things that wear feathers, then they cross-up all the accumulated animal life to date and fetch out a mammal, and start-in diluting again till there's cows and tigers and rats and elephants and monkeys and everything you want down to the Missing Link, and out of him and a mermaid they propagate Man, and there you are! Everything ship-shape and finished-up, and nothing to do but lay low and wait and see if it was worth the time and expense.
'The Refuge of the Derelicts' collected in Mark Twain and John Sutton Tuckey, The Devil's Race-Track: Mark Twain's Great Dark Writings (1980), 340-41.
- 1980
Adrenalin does not excite sympathetic ganglia when applied to them directly, as does nicotine. Its effective action is localised at the periphery. The existence upon plain muscle of a peripheral nervous network, that degenerates only after section of both the constrictor and inhibitory nerves entering it, and not after section of either alone, has been described. I find that even after such complete denervation, whether of three days' or ten months' duration, the plain muscle of the dilatator pupillae will respond to adrenalin, and that with greater rapidity and longer persistence than does the iris whose nervous relations are uninjured. Therefore it cannot be that adrenalin excites any structure derived from, and dependent for its persistence on, the peripheral neurone. But since adrenalin does not evoke any reaction from muscle that has at no time of its life been innervated by the sympathetic, the point at which the stimulus of the chemical excitant is received, and transformed into what may cause the change of tension of the muscle fibre, is perhaps a mechanism developed out of the muscle cell in response to its union with the synapsing sympathetic fibre, the function of which is to receive and transform the nervous impulse. Adrenalin might then be the chemical stimulant liberated on each occasion when the impulse arrives at the periphery.
'On the Action of Adrenalin', Proceedings of the Physiological Society, 21 May 1904, in The Journal of Physiology 1904, 31, xxi.
All fossil anthropoids found hitherto have been known only from mandibular or maxillary fragments, so far as crania are concerned, and so the general appearance of the types they represented had been unknown; consequently, a condition of affairs where virtually the whole face and lower jaw, replete with teeth, together with the major portion of the brain pattern, have been preserved, constitutes a specimen of unusual value in fossil anthropoid discovery. Here, as in Homo rhodesiensis, Southern Africa has provided documents of higher primate evolution that are amongst the most complete extant. Apart from this evidential completeness, the specimen is of importance because it exhibits an extinct race of apes intermediate between living anthropoids and man ... Whether our present fossil is to be correlated with the discoveries made in India is not yet apparent; that question can only be solved by a careful comparison of the permanent molar teeth from both localities. It is obvious, meanwhile, that it represents a fossil group distinctly advanced beyond living anthropoids in those two dominantly human characters of facial and dental recession on one hand, and improved quality of the brain on the other. Unlike Pithecanthropus, it does not represent an ape-like man, a caricature of precocious hominid failure, but a creature well advanced beyond modern anthropoids in just those characters, facial and cerebral, which are to be anticipated in an extinct link between man and his simian ancestor. At the same time, it is equally evident that a creature with anthropoid brain capacity and lacking the distinctive, localised temporal expansions which appear to be concomitant with and necessary to articulate man, is no true man. It is therefore logically regarded as a man-like ape. I propose tentatively, then, that a new family of Homo-simidæ be created for the reception of the group of individuals which it represents, and that the first known species of the group be designated Australopithecus africanus, in commemoration, first, of the extreme southern and unexpected horizon of its discovery, and secondly, of the continent in which so many new and important discoveries connected with the early history of man have recently been made, thus vindicating the Darwinian claim that Africa would prove to be the cradle of mankind.
'Australopithicus africanus: The Man-Ape of South Africa', Nature, 1925, 115, 195.
All of my knowledge, of both science and religion, I incorporate into the classical tradition of my painting.
In G. Barry Golson (ed.), The Playboy Interview II (1983), 35.
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,
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.
Almighty God, to whose efficacious Word all things owe their original, abounding in his own glorious Essence with infinite goodness and fecundity, did in the beginning Create Man after his own likeness, Male and Female, created he them; the true distinction of which Sexes, consists merely in the different site of those parts of the body, wherein Generation necessarily requires a Diversity: for both Male and Female he impartially endued with the same, and altogether indifferent form of Soul, the Woman being possess’d of no less excellent Faculties of Mind, Reason, and Speech, than the Man, and equally with him aspiring to those Regions of Bliss and Glory, where there shall be no exception of Sex.
In Female Pre-eminence: Or, The Dignity and Excellency of that Sex above the Male, translation (1670).
Almost everyone... seems to be quite sure that the differences between the methodologies of history and of the natural sciences are vast. For, we are assured, it is well known that in the natural sciences we start from observation and proceed by induction to theory. And is it not obvious that in history we proceed very differently? Yes, I agree that we proceed very differently. But we do so in the natural sciences as well.
In both we start from myths—from traditional prejudices, beset with error—and from these we proceed by criticism: by the critical elimination of errors. In both the role of evidence is, in the main, to correct our mistakes, our prejudices, our tentative theories—that is, to play a part in the critical discussion, in the elimination of error. By correcting our mistakes, we raise new problems. And in order to solve these problems, we invent conjectures, that is, tentative theories, which we submit to critical discussion, directed towards the elimination of error.
In both we start from myths—from traditional prejudices, beset with error—and from these we proceed by criticism: by the critical elimination of errors. In both the role of evidence is, in the main, to correct our mistakes, our prejudices, our tentative theories—that is, to play a part in the critical discussion, in the elimination of error. By correcting our mistakes, we raise new problems. And in order to solve these problems, we invent conjectures, that is, tentative theories, which we submit to critical discussion, directed towards the elimination of error.
The Myth of the Framework: In Defence of Science and Rationality (1993), 140.
Although the cooking of food presents some unsolved problems, the quick warming of cooked food and the thawing of frozen food both open up some attractive uses. ... There is no important reason why the the housewife of the future should not purchase completely frozen meals at the grocery store just as she buys quick frozen vegetables. With a quick heating, high-frequency unit in her kitchen, food preparation from a pre-cooked, frozen meal becomes a simple matter.
[Predicting home kitchen appliances could be developed from the radionic tube employed to jam enemy radar in World War II.]
[Predicting home kitchen appliances could be developed from the radionic tube employed to jam enemy radar in World War II.]
In 'Physics of Today Become the Engineering of Tomorrow', Proceedings of the National Electronics Conference (1947), Vols. 1-2, 24-25. Note: by 1947 Ratheon was able to demonstrate a refrigerator-sized commercial microwave oven.
Among both the Northern and Eastern Hamites are to be found some of the most beautiful types of humanity.
In An Introduction to Physical Anthropology (1960), 456.
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.
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.
An astronomer must be the wisest of men; his mind must be duly disciplined in youth; especially is mathematical study necessary; both an acquaintance with the doctrine of number, and also with that other branch of mathematics, which, closely connected as it is with the science of the heavens, we very absurdly call geometry, the measurement of the earth.
— Plato
From the 'Epilogue to the Laws' (Epinomis), 988-990. As quoted in William Whewell, History of the Inductive Sciences from the Earliest to the Present Time (1837), Vol. 1, 161. (Although referenced to Plato’s Laws, the Epinomis is regarded as a later addition, not by Plato himself.)
An atom-blaster is a good weapon, but it can point both ways.
In The FoundationTrilogy (1951), Vol. 2, 207.
And from this such small difference of eight minutes [of arc] it is clear why Ptolemy, since he was working with bisection [of the linear eccentricity], accepted a fixed equant point… . For Ptolemy set out that he actually did not get below ten minutes [of arc], that is a sixth of a degree, in making observations. To us, on whom Divine benevolence has bestowed the most diligent of observers, Tycho Brahe, from whose observations this eight-minute error of Ptolemy’s in regard to Mars is deduced, it is fitting that we accept with grateful minds this gift from God, and both acknowledge and build upon it. So let us work upon it so as to at last track down the real form of celestial motions (these arguments giving support to our belief that the assumptions are incorrect). This is the path I shall, in my own way, strike out in what follows. For if I thought the eight minutes in [ecliptic] longitude were unimportant, I could make a sufficient correction (by bisecting the [linear] eccentricity) to the hypothesis found in Chapter 16. Now, because they could not be disregarded, these eight minutes alone will lead us along a path to the reform of the whole of Astronomy, and they are the matter for a great part of this work.
Astronomia Nova, New Astronomy (1609), ch. 19, 113-4, Johannes Kepler Gesammelte Werke (1937-), Vol. 3, 177-8.
André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That’s one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity.
In I Want to be a Mathematician: an Automathography (1985), 123.
Any demanding high technology tends to develop influential and dedicated constituencies of those who link its commercial success with both the public welfare and their own. Such sincerely held beliefs, peer pressures, and the harsh demands that the work i
Foreign Affairs (Oct 1976).
Apart from the hostile influence of man, the organic and the inorganic world are … bound together by such mutual relations and adaptations as secure, if not the absolute permanence and equilibrium of both … at least a very slow and gradual succession of changes in those conditions. But man is everywhere a disturbing agent. Wherever he plants his foot, the harmonies of nature are turned to discords.
In Man and Nature, (1864), 35-36.
Architects who have aimed at acquiring manual skill without scholarship have never been able to reach a position of authority to correspond to their pains, while those who relied only upon theories and scholarship were obviously hunting the shadow, not the substance. But those who have a thorough knowledge of both, like men armed at all points, have the sooner attained their object and carried authority with them.
In De Architectura, Book 1, Chap 1, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 3.
Arithmetic, as we shall see by and by, is overdone, in a certain sense, in our schools; just so far as the teaching is based upon the concrete, so far is it profitable; but when the book-makers begin to make it too abstract, as they very often do, it becomes a torture to both teacher and learners, or, at best, a branch of imaginary knowledge unconnected with real life.
From 'Introduction', Mathematical Teaching and its Modern Methods (1886), 10.
Art and science coincide insofar as both aim to improve the lives of men and women. The latter normally concerns itself with profit, the former with pleasure. In the coming age, art will fashion our entertainment out of new means of productivity in ways that will simultaneously enhance our profit and maximize our pleasure.
Brecht’s positive vision of theater in the coming age of technology, expressed in Little Organon for the Theater (1949). In The Columbia World of Quotations (1996).
As a boy I had liked both drawing and physics, and I always abhorred the role of being a spectator. In 1908, when I was 15, I designed, built and flew a toy model airplane which won the then-famous James Gordon Bennett Cup. By 16 I had discovered that design could be fun and profitable, and this lesson has never been lost on me.
On the official Raymond Loewry website.
As a child, I received instruction both in the Bible and in the Talmud. I am a Jew, but I am enthralled by the luminous figure of the Nazarene.
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As a nation, we are too young to have true mythic heroes, and we must press real human beings into service. Honest Abe Lincoln the legend is quite a different character from Abraham Lincoln the man. And so should they be. And so should both be treasured, as long as they are distinguished. In a complex and confusing world, the perfect clarity of sports provides a focus for legitimate, utterly unambiguous support or disdain. The Dodgers are evil, the Yankees good. They really are, and have been for as long as anyone in my family can remember.
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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]
As the ostensible effect of the heat … consists not in warming the surrounding bodies but in rendering the ice fluid, so, in the case of boiling, the heat absorbed does not warm surrounding bodies but converts the water into vapor. In both cases, considered as the cause of warmth, we do not perceive its presence: it is concealed, or latent, and I gave it the name of “latent heat.”
As was the case for Nobel's own invention of dynamite, the uses that are made of increased knowledge can serve both beneficial and potentially harmful ends. Increased knowledge clearly implies increased responsibility. We reject the notion advocated in some quarters that man should stop eating from the tree of knowledge, as if that were humanly possible.
From Nobel Banquet Speech (10 Dec 1981), in Wilhelm Odelberg (ed.), Les Prix Nobel 1981 (1981), 44.
Astronomy concerns itself with the whole of the visible universe, of which our earth forms but a relatively insignificant part; while Geology deals with that earth regarded as an individual. Astronomy is the oldest of the sciences, while Geology is one of the newest. But the two sciences have this in common, that to both are granted a magnificence of outlook, and an immensity of grasp denied to all the rest.
Proceedings of the Geological Society of London (1903), 59, lxviii.
At bottom each “exact” science is, and must be speculative, and its chief tool of research, too rarely used with both courage and judgement, is the regulated imagination.
In Igneous Rocks and their Origin (1914), Introduction, xxi.
At fertilization, these two “haploid” nuclei are added together to make a “diploid” nucleus that now contains 2a, 2b and so on; and, by the splitting of each chromosome and the regulated karyokinetic separation of the daughter chromosomes, this double series is inherited by both of the primary blastomeres. In the resulting resting nuclei the individual chromosomes are apparently destroyed. But we have the strongest of indications that, in the stroma of the resting nucleus, every one of the chromosomes that enters the nucleus survives as a well-defined region; and as the cell prepares for its next division this region again gives rise to the same chromosome (Theory of the Individuality of the Chromosomes). In this way the two sets of chromosomes brought together at fertilization are inherited by all the cells of the new individual. It is only in the germinal cells that the so called reduction division converts the double series into a single one. Out of the diploid state, the haploid is once again generated.
In Arch. Zellforsch, 1909, 3, 181, trans. Henry Harris, The Birth of the Cell (1999), 171-2.
At the entrance to the observatory Stjerneborg located underground, Tycho Brahe built a Ionic portal. On top of this were three sculptured lions. On both sides were inscriptions and on the backside was a longer inscription in gold letters on a porfyr stone: Consecrated to the all-good, great God and Posterity. Tycho Brahe, Son of Otto, who realized that Astronomy, the oldest and most distinguished of all sciences, had indeed been studied for a long time and to a great extent, but still had not obtained sufficient firmness or had been purified of errors, in order to reform it and raise it to perfection, invented and with incredible labour, industry, and expenditure constructed various exact instruments suitable for all kinds of observations of the celestial bodies, and placed them partly in the neighbouring castle of Uraniborg, which was built for the same purpose, partly in these subterranean rooms for a more constant and useful application, and recommending, hallowing, and consecrating this very rare and costly treasure to you, you glorious Posterity, who will live for ever and ever, he, who has both begun and finished everything on this island, after erecting this monument, beseeches and adjures you that in honour of the eternal God, creator of the wonderful clockwork of the heavens, and for the propagation of the divine science and for the celebrity of the fatherland, you will constantly preserve it and not let it decay with old age or any other injury or be removed to any other place or in any way be molested, if for no other reason, at any rate out of reverence to the creator’s eye, which watches over the universe. Greetings to you who read this and act accordingly. Farewell!
(Translated from the original in Latin)
At the moment I am occupied by an investigation with Kirchoff which does not allow us to sleep. Kirchoff has made a totally unexpected discovery, inasmuch as he has found out the cause for the dark lines in the solar spectrum and can produce these lines artificially intensified both in the solar spectrum and in the continuous spectrum of a flame, their position being identical with that of Fraunhofer’s lines. Hence the path is opened for the determination of the chemical composition of the Sun and the fixed stars.
Letter to H.E. Roscoe (Nov 1859). In The Life and Experiences of Sir Henry Enfield Roscoe (1906), 71.
At the moment I am occupied by an investigation with Kirchoff which does not allow us to sleep. Kirchoff has made a totally unexpected discovery, inasmuch as he has found out the cause for the dark lines in the solar spectrum and can produce these lines artificially intensified both in the solar spectrum and in the continuous spectrum of a flame, their position being identical with that of Fraunhofer’s lines. Hence the path is opened for the determination of the chemical composition of the Sun and the fixed stars.
Letter to H.E. Roscoe (Nov 1859). In The Life and Experiences of Sir Henry Enfield Roscoe (1906), 81.
Bacteria are highly adaptable. They frequently change both morphologically and functionally. Their virulence is also an essentially fluctuating property, that increases or diminishes according to the conditions to which the pathogenic organism is subjected.
In Studies in Immunity (1909), 1.
Basic research at universities comes in two varieties: research that requires big bucks and research that requires small bucks. Big bucks research is much like government research and in fact usually is government research but done for the government under contract. Like other government research, big bucks academic research is done to understand the nature and structure of the universe or to understand life, which really means that it is either for blowing up the world or extending life, whichever comes first. Again, that's the government's motivation. The universities' motivation for conducting big bucks research is to bring money in to support professors and graduate students and to wax the floors of ivy-covered buildings. While we think they are busy teaching and learning, these folks are mainly doing big bucks basic research for a living, all the while priding themselves on their terrific summer vacations and lack of a dress code.
Smalls bucks research is the sort of thing that requires paper and pencil, and maybe a blackboard, and is aimed primarily at increasing knowledge in areas of study that don't usually attract big bucks - that is, areas that don't extend life or end it, or both. History, political science, and romance languages are typically small bucks areas of basic research. The real purpose of small bucks research to the universities is to provide a means of deciding, by the quality of their small bucks research, which professors in these areas should get tenure.
Smalls bucks research is the sort of thing that requires paper and pencil, and maybe a blackboard, and is aimed primarily at increasing knowledge in areas of study that don't usually attract big bucks - that is, areas that don't extend life or end it, or both. History, political science, and romance languages are typically small bucks areas of basic research. The real purpose of small bucks research to the universities is to provide a means of deciding, by the quality of their small bucks research, which professors in these areas should get tenure.
Accidental Empires (1992), 78.
Be temperate in wine, in eating, girls, & sloth;
Or the Gout will seize you and plague you both.
Or the Gout will seize you and plague you both.
In Poor Richard's Almanack (1734).
Because intelligence is our own most distinctive feature, we may incline to ascribe superior intelligence to the basic primate plan, or to the basic plan of the mammals in general, but this point requires some careful consideration. There is no question at all that most mammals of today are more intelligent than most reptiles of today. I am not going to try to define intelligence or to argue with those who deny thought or consciousness to any animal except man. It seems both common and scientific sense to admit that ability to learn, modification of action according to the situation, and other observable elements of behavior in animals reflect their degrees of intelligence and permit us, if only roughly, to compare these degrees. In spite of all difficulties and all the qualifications with which the expert (quite properly) hedges his conclusions, it also seems sensible to conclude that by and large an animal is likely to be more intelligent if it has a larger brain at a given body size and especially if its brain shows greater development of those areas and structures best developed in our own brains. After all, we know we are intelligent, even though we wish we were more so.
In The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 78.
Behold the mighty dinosaur,
Famous in prehistoric lore,
Not only for his power and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains—
One in his head (the usual place),
The other at his spinal base.
Thus he could reason 'A priori'
As well as 'A posteriori'.
No problem bothered him a bit
He made both head and tail of it.
So wise was he, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along.
If something slipped his forward mind
'Twas rescued by the one behind.
And if in error he was caught
He had a saving afterthought.
As he thought twice before he spoke
He had no judgment to revoke.
Thus he could think without congestion
Upon both sides of every question.
Oh, gaze upon this model beast
Defunct ten million years at least.
Famous in prehistoric lore,
Not only for his power and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains—
One in his head (the usual place),
The other at his spinal base.
Thus he could reason 'A priori'
As well as 'A posteriori'.
No problem bothered him a bit
He made both head and tail of it.
So wise was he, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along.
If something slipped his forward mind
'Twas rescued by the one behind.
And if in error he was caught
He had a saving afterthought.
As he thought twice before he spoke
He had no judgment to revoke.
Thus he could think without congestion
Upon both sides of every question.
Oh, gaze upon this model beast
Defunct ten million years at least.
'The Dinosaur: A Poem' (1912). In E. H. Colbert (ed.), The Dinosaur Book (1951), 78.
Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611. [The French phrase, à peu près means “approximately”. —Webmaster]
Biological diversity is unique in its importance to both developed and developing countries.
In 'Edward O. Wilson: The Biological Diversity Crisis: A Challenge to Science', Issues in Science and Technology (Fall 1985), 2, No. 1, 28.
Biology is a science of three dimensions. The first is the study of each species across all levels of biological organization, molecule to cell to organism to population to ecosystem. The second dimension is the diversity of all species in the biosphere. The third dimension is the history of each species in turn, comprising both its genetic evolution and the environmental change that drove the evolution. Biology, by growing in all three dimensions, is progressing toward unification and will continue to do so.
In 'Systematics and the Future of Biology', Systematics and the Origin of Species: on Ernst Mayr's 100th anniversary, Volume 102, Issues 22-26 (2005), 1.
Biology occupies a position among the sciences both marginal and central. Marginal because, the living world, constituting only a tiny and very “special” part of the universe, it does not seem likely that the study of living beings will ever uncover general laws applicable outside the biosphere. But if the ultimate aim of the whole of science is indeed, as I believe, to clarify man's relationship to the universe, then biology must be accorded a central position, since of all the disciplines it is the one that endeavours to go most directly to the heart of the problems that must be resolved before that of “human nature” can even be framed in other than metaphysical terms.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), xi.
Boltzmann was both a wizard of a mathematician and a physicist of international renown. The magnitude of his output of scientific papers was positively unnerving. He would publish two, three, sometimes four monographs a year; each one was forbiddingly dense, festooned with mathematics, and as much as a hundred pages in length.
In 'The Bulldog: A Profile of Ludwig Boltzmann', The American Scholar (1 Jan 1999), 99.
Both biological and cultural diversity are now severely threatened and working for their preservation is a critical task.
The Quark and the Jaguar: Adventure in the Simple and Compex (1994), 374-375.
Both died, ignored by most; they neither sought nor found public favour, for high roads never lead there. Laurent and Gerhardt never left such roads, were never tempted to peruse those easy successes which, for strongly marked characters, offer neither allure nor gain. Their passion was for the search for truth; and, preferring their independence to their advancement, their convictions to their interests, they placed their love for science above that of their worldly goods; indeed above that for life itself, for death was the reward for their pains. Rare example of abnegation, sublime poverty that deserves the name nobility, glorious death that France must not forget!
'Éloge de Laurent et Gerhardt', Moniteur Scientifique (1862), 4, 473-83, trans. Alan J. Rocke.
Both history of nature and history of humanity are 'historical' and yet cannot dispense with uniformity. In both there is 'uniformity' ('science') as well as non-uniformity ('history'); in both 'history respects itself and 'history does not repeat itself. But, as even the history of humanity has its uniformitarian features, uniformity can still less be dispensed with in 'history' of nature, which, being one of the natural sciences, is less historical and, consequently, more uniformitarian.
Natural Law and Divine Miracle: The Principle of Uniformity in Geology, Biology and Theology (1963), 151.
Both religion and natural science require a belief in God for their activities, to the former He is the starting point, and to the latter the goal of every thought process. To the former He is the foundation, to the latter, the crown of the edifice of every generalized world view.
Lecture, 'Religion and Natural Science' (1937) In Max Planck and Frank Gaynor (trans.), Scientific Autobiography and Other Papers (1949), 184.
Both religion and science must preserve their autonomy and their distinctiveness. Religion is not founded on science nor is science an extension of religion. Each should possess its own principles, its pattern of procedures, its diversities of interpretation and its own conclusions.
In Letter (1 Jun 1988) to Father George V. Coyne, Director of the Vatican Observatory. On vatican.va website.
Both Religion and science require faith in God. For believers, God is in the beginning, and for physicists He is at the end of all considerations.
Sometimes seen attributed (doubtfully?) to Max Planck. Widely seen on the web, but always without citation. Webmaster has not yet found any evidence in print that this is a valid Planck quote, and must be skeptical that it is. Contact Webmaster if you know a primary source.
Both science and art have to do with ordered complexity.
In The Griffin (1957), 6, No 10.
Both social and biosocial factors are necessary to interpret crosscultural studies, with the general proviso that one’s research interest determines which elements, in what combinations, are significant for the provision of understanding.
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Both the man of science and the man of art live always at the edge of mystery, surrounded by it; both always, as to the measure of their creation, have had to do with the harmonization of what is new with what is familiar, with the balance between novelty and synthesis, with the struggle to make partial order in total chaos.
Address at the close of the year-long Bicentennial Celebration of Columbia University (26 Dec 54). Printed in 'Prospects in the Arts and Sciences', Bulletin of the Atomic Scientists (Feb 1955), 52.
Both the physicist and the mystic want to communicate their knowledge, and when they do so with words their statements are paradoxical and full of logical contradictions.
In The Tao of Physics (1975), 46.
But medicine has long had all its means to hand, and has discovered both a principle and a method, through which the discoveries made during a long period are many and excellent, while full discovery will be made, if the inquirer be competent, conduct his researches with knowledge of the discoveries already made, and make them his starting-point. But anyone who, casting aside and rejecting all these means, attempts to conduct research in any other way or after another fashion, and asserts that he has found out anything, is and has been victim of deception.
Ancient Medicine, in Hippocrates, trans. W. H. S. Jones (1923), Vol. I, 15.
By the act of generation nothing more is done than to ferment the sperm of ye female by the sperm of ye male that it may thereby become fit nourishment for ye Embryo: ffor ye nourishment of all animals is prepared by ferment & the ferment is taken from animals of the same kind, & makes the nourishment subtile & spiritual. In adult animals the nourishmt is fermented by the choler and pancreatic juice both wch come from the blood. The Embryo not being able to ferment its own nourishment wch comes from the mothers blood has it fermented by the sperm wch comes from ye fathers blood, & by this nourishment it swells, drops off from ye Ovarium & begins to grow with a life distinct from that of ye mother.
From 'Quæst 25' in Draft version of The Queries manuscript, Add. MS. 3970, folio 235 held by the University of Cambridge Library. As quoted and cited in R.W. Home, 'Force, Electricity, and Living Matter', from Margaret J. Osler and Paul Lawrence Farber (eds.), Religion, Science, and Worldview: Essays in Honor of Richard S. Westfall (2002), 113.
By the worldly standards of public life, all scholars in their work are of course oddly virtuous. They do not make wild claims, they do not cheat, they do not try to persuade at any cost, they appeal neither to prejudice nor to authority, they are often frank about their ignorance, their disputes are fairly decorous, they do not confuse what is being argued with race, politics, sex or age, they listen patiently to the young and to the old who both know everything. These are the general virtues of scholarship, and they are peculiarly the virtues of science.
In Science and Human Values (1956).
Can I pay any higher tribute to a man [George Gaylord Simpson] than to state that his work both established a profession and sowed the seeds for its own revision? If Simpson had reached final truth, he either would have been a priest or would have chosen a dull profession. The history of life cannot be a dull profession.
From 'G.G. Simpson, Paleontology, and the Modern Synthesis', collected in Ernst Mayr, William B. Provine (eds.), The Evolutionary Synthesis: Perspectives on the Unification of Biology (1998), 171.
Casting off the dark fog of verbal philosophy and vulgar medicine, which inculcate names alone ... I tried a series of experiments to explain more clearly many phenomena, particularly those of physiology. In order that I might subject as far as possible the reasonings of the Galenists and Peripatetics to sensory criteria, I began, after trying experiments, to write dialogues in which a Galenist adduced the better-known and stronger reasons and arguments; these a mechanist surgeon refuted by citing to the contrary the experiments I had tried, and a third, neutral interlocutor weighed the reasons advanced by both and provided an opportunity for further progress.
'Malpighi at Pisa 1656-1659', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 1, 155-6.
Certainlie these things agree,
The Priest, the Lawyer, & Death all three:
Death takes both the weak and the strong.
The lawyer takes from both right and wrong,
And the priest from living and dead has his Fee.
The Priest, the Lawyer, & Death all three:
Death takes both the weak and the strong.
The lawyer takes from both right and wrong,
And the priest from living and dead has his Fee.
In Poor Richard's Almanack (1737).
Chemistry affords two general methods of determining the constituent principles of bodies, the method of analysis, and that of synthesis. When, for instance, by combining water with alkohol, we form the species of liquor called, in commercial language, brandy or spirit of wine, we certainly have a right to conclude, that brandy, or spirit of wine, is composed of alkohol combined with water. We can produce the same result by the analytical method; and in general it ought to be considered as a principle in chemical science, never to rest satisfied without both these species of proofs. We have this advantage in the analysis of atmospherical air, being able both to decompound it, and to form it a new in the most satisfactory manner.
Elements of Chemistry (1790), trans. R. Kerr, 33.
Chemists have made of phlogiston a vague principle which is not at all rigorously defined, and which, in consequence, adapts itself to all explanations in which it is wished it shall enter; sometimes it is free fire, sometimes it is fire combined with the earthy element; sometimes it passes through the pores of vessels, sometimes they are impenetrable to it; it explains both the causticity and non-causticity, transparency and opacity, colours and absence of colours. It is a veritable Proteus which changes its form every instant. It is time to conduct chemistry to a more rigorous mode of reasoning ... to distinguish fact and observation from what is systematic and hypothetical.
'Réflexions sur le phlogistique', Mémoires de l'Académie des Sciences, 1783, 505-38. Reprinted in Oeuvres de Lavoisier (1864), Vol. 2, 640, trans. M. P. Crosland.
Christian Science … is the direct denial both of science and of Christianity, for Science rests wholly on the recognition of truth and Christianity on the recognition of pain.
From The Illustrated London News (1 Nov 1930), 177, Part 2, 750. In 'More on American Optimism', Collected Works (1990), Vol. 35, 406-407.
Complex organisms cannot be construed as the sum of their genes, nor do genes alone build particular items of anatomy or behavior by them selves. Most genes influence several aspects of anatomy and behavior–as they operate through complex interactions with other genes and their products, and with environmental factors both within and outside the developing organism. We fall into a deep error, not just a harmful oversimplification, when we speak of genes ‘for’ particular items of anatomy or behavior.
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Courtship, properly understood, is the process whereby both the male and the female are brought into that state of sexual tumescence which is a more or less necessary condition for sexual intercourse. The play of courtship cannot, therefore, be considered to be definitely brought to an end by the ceremony of marriage; it may more properly be regarded as the natural preliminary to every act of coitus.
Studies in the Psychology of Sex (1921), Vol. 3, 239.
Culture is activity of thought, and receptiveness to beauty and humane feeling. Scraps of information have nothing to do with it. A merely well informed man is the most useless bore on God’s earth. What we should aim at producing is men who possess both culture and expert knowledge in some special direction.
Opening sentences of Chapter 1,'The Aims of Education', in Aims of Education and Other Essays (1917), 1.
Cyberspace consists of transactions, relationships, and thought itself, arrayed like a standing wave in the web of our communications. Ours is a world that is both everywhere and nowhere, but it is not where bodies live. We are creating a world that all may enter without privilege or prejudice accorded by race, economic power, military force, or station of birth. We are creating a world where anyone, anywhere may express his or her beliefs, no matter how singular, without fear of being coerced into silence or conformity.
In 'A Declaration of the Independence of Cyberspace' (8 Feb 1996). Published on Electronic Frontier Foundation website. Reproduced in Lawrence Lessig, Code: Version 2.0) (2008), 303.
Dangerous, therefore, is it to take shelter under a tree, during a thunder-gust. It has been fatal to many, both men and beasts.
'Letter IV. Containing Observations and Suppositions towards forming a new Hypothesis, for explaining the several Phænomena of Thunder-Gusts', in Experiments and Observations on Electricity, Made at Philadelphia in America by Mr. Benjamin Franklin, and Commnicated in Several Letters to Mr. P. Collinson, of London, F.R.S. (1751), 47. In the book, the letter is undated, but it is printed after a footnote dated 29 Apr 1749, and is followed by one dated 29 Jul 1750. Therefore, it is assumed by later authors to have been written in summer 1749. When I. Bernard Cohen editted Benjamin Franklin's Experiments (1941), 209, he wrote that the letter was wrtten during summer or autumn of 1749 and “was dispatched, not to Collinson, but to Dr John Mitchel F.R.S." In his later books, Cohen dates it as 29 Apr 1749.
Darwin's characteristic perspicacity is nowhere better illustrated than in his prophecy of the reaction of the world of science. He admitted at once that it would be impossible to convince those older men '...whose minds are stocked with a multitude of facts, all viewed ... from a point of view directly opposite to mine ... A few naturalists endowed with much flexibility of mind and who have already begun to doubt the immutability of species, may be influenced by this volume; but I look with confidence to the young and rising naturalists, who will be able to view both sides with equal impartiality.
'The Reaction of American scientists to Darwinism', American Historical Review 1932), 38, 687. Quoted in David L. Hull, Science as Process (), 379.
Discovery follows discovery, each both raising and answering questions, each ending a long search, and each providing the new instruments for a new search.
In 'Prospects in the Arts and Sciences,' in Fifty Famous Essays (1964).
Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion.’
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Doubtless it is true that while consciousness is occupied in the scientific interpretation of a thing, which is now and again “a thing of beauty,” it is not occupied in the aesthetic appreciation of it. But it is no less true that the same consciousness may at another time be so wholly possessed by the aesthetic appreciation as to exclude all thought of the scientific interpretation. The inability of a man of science to take the poetic view simply shows his mental limitation; as the mental limitation of a poet is shown by his inability to take the scientific view. The broader mind can take both.
In An Autobiography (1904), Vol. 1, 485.
During my pre-college years I went on many trips with my father into the oil fields to visit their operations. … I puttered around the machine, electronics, and automobile shops while he carried on his business. Both of my parents are inveterate do-it-yourselfers, almost no task being beneath their dignity or beyond their ingenuity. Having picked up a keen interest in electronics from my father, I used to fix radios and later television sets for fun and spending money. I built my own hi-fi set and enjoyed helping friends with their amateur radio transmitters, but lost interest as soon as they worked.
Remarks on how his high school interests foreshadowed his career as a radio astronomer. From autobiography in Stig Lundqvist (ed.) Nobel Lectures, Physics 1971-1980 (1992).
Engineers apply the theories and principles of science and mathematics to research and develop economical solutions to practical technical problems. Their work is the link between scientific discoveries and commercial applications. Engineers design products, the machinery to build those products, the factories in which those products are made, and the systems that ensure the quality of the product and efficiency of the workforce and manufacturing process. They design, plan, and supervise the construction of buildings, highways, and transit systems. They develop and implement improved ways to extract, process, and use raw materials, such as petroleum and natural gas. They develop new materials that both improve the performance of products, and make implementing advances in technology possible. They harness the power of the sun, the earth, atoms, and electricity for use in supplying the Nation’s power needs, and create millions of products using power. Their knowledge is applied to improving many things, including the
quality of health care, the safety of food products, and the efficient operation of financial systems.
Bureau of Labor Statistics, Occupational Outlook Handbook (2000) as quoted in Charles R. Lord. Guide to Information Sources in Engineering (2000), 5. This definition has been revised and expanded over time in different issues of the Handbook.
Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
Euclid always contemplates a straight line as drawn between two definite points, and is very careful to mention when it is to be produced beyond this segment. He never thinks of the line as an entity given once for all as a whole. This careful definition and limitation, so as to exclude an infinity not immediately apparent to the senses, was very characteristic of the Greeks in all their many activities. It is enshrined in the difference between Greek architecture and Gothic architecture, and between Greek religion and modern religion. The spire of a Gothic cathedral and the importance of the unbounded straight line in modern Geometry are both emblematic of the transformation of the modern world.
In Introduction to Mathematics (1911), 119.
Every creature has its own food, and an appropriate alchemist with the task of dividing it ... The alchemist takes the food and changes it into a tincture which he sends through the body to become blood and flesh. This alchemist dwells in the stomach where he cooks and works. The man eats a piece of meat, in which is both bad and good. When the meat reaches the stomach, there is the alchemist who divides it. What does not belong to health he casts away to a special place, and sends the good wherever it is needed. That is the Creator's decree... That is the virtue and power of the alchemist in man.
Volumen Medicinae Paramirum (c. 1520), in Paracelsus: Essential Readings, edited by Nicholas Goodrick-Clarke (1990), 50-1.
Every discipline must be honored for reason other than its utility, otherwise it yields no enthusiasm for industry.
For both reasons, I consider mathematics the chief subject for the common school. No more highly honored exercise for the mind can be found; the buoyancy [Spannkraft] which it produces is even greater than that produced by the ancient languages, while its utility is unquestioned.
For both reasons, I consider mathematics the chief subject for the common school. No more highly honored exercise for the mind can be found; the buoyancy [Spannkraft] which it produces is even greater than that produced by the ancient languages, while its utility is unquestioned.
In 'Mathematischer Lehrplan für Realschulen' Werke [Kehrbach] (1890), Bd. 5, 167. (Mathematics Curriculum for Secondary Schools). As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 61.
Every species has come into existence coincident both in time and space with a pre-existing closely allied species.
In 'On the Law Which has Regulated the Introduction of New Species', The Annals and Magazine of Natural History, Including Zoology, Botany and Geology (1855), 16, 186.
Everyone admits that the male is the primary efficient cause in generation, as being that in whom the species or form resides, and they further assert that his genitures emitted in coitus causes the egg both to exist and to be fertile. But how the semen of the cock produces the chick from the egg, neither the philosophers nor the physicians of yesterday or today have satisfactorily explained, or solved the problem formulated by Aristotle.
Disputations Touching the Generation of Animals (1651), trans. Gweneth Whitteridge (1981), Chapter 47, 214.
Exper. I. I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation I placed a small looking-glass without the window-shutter, in such a position as to reflect the sun's light, in a direction nearly horizontal, upon the opposite wall, and to cause the cone of diverging light to pass over a table on which were several little screens of card-paper. I brought into the sunbeam a slip of card, about one-thirtieth of an inch in breadth, and observed its shadow, either on the wall or on other cards held at different distances. Besides the fringes of colour on each side of the shadow, the shadow itself was divided by similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the shadow was observed, but leaving the middle of the shadow always white. Now these fringes were the joint effects of the portions of light passing on each side of the slip of card and inflected, or rather diffracted, into the shadow. For, a little screen being placed a few inches from the card, so as to receive either edge of the shadow on its margin, all the fringes which had before been observed in the shadow on the wall, immediately disappeared, although the light inflected on the other side was allowed to retain its course, and although this light must have undergone any modification that the proximity of the other edge of the slip of card might have been capable of occasioning... Nor was it for want of a sufficient intensity of light that one of the two portions was incapable of producing the fringes alone; for when they were both uninterrupted, the lines appeared, even if the intensity was reduced to one-tenth or one-twentieth.
'Experiments and Calculations Relative to Physical Optics' (read in 1803), Philosophical Transactions (1804), 94, 2-3.
False interpretation of the Bible has often clashed with science, as false science has with true interpretation; but true science is the natural ally of religion, for both are from God.
…...
Fiction is, indeed, an indispensable supplement to logic, or even a part of it; whether we are working inductively or deductively, both ways hang closely together with fiction: and axioms, though they seek to be primary verities, are more akin to fiction. If we had realized the nature of axioms, the doctrine of Einstein, which sweeps away axioms so familiar to us that they seem obvious truths, and substitutes others which seem absurd because they are unfamiliar, might not have been so bewildering.
In The Dance of Life (1923), 86.
Food may be defined as material which, when taken into the body, serves to either form tissue or yield energy, or both. This definition includes all the ordinary food materials, since they both build tissue and yield energy. It includes sugar and starch, because they yield energy and form fatty tissue. It includes alcohol, because the latter is burned to yield energy, though it does not build tissue. It excludes creatin, creatininin, and other so-called nitrogeneous extractives of meat, and likewise thein or caffein of tea and coffee, because they neither build tissue nor yield energy, although they may, at times, be useful aids to nutrition.
Methods and Results of Investigations on the Chemistry and Economy of Food, Bulletin 21, US Department of Agriculture (1895). Quoted in Ira Wolinsky, Nutrition in Exercise and Sport (1998), 36.
For it is owing to their wonder that men now both begin and at first began to philosophize; they wondered originally at the obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e.g. about the phenomena of the moon and those of the sun and the stars, and about the genesis of the universe. And a man who is puzzled and wonders thinks himself ignorant (whence even the lover of myth is in a sense a lover of wisdom, for myth is composed of wonders); therefore since they philosophized in order to escape from ignorance, evidently they were pursuing science in order to know, and not for any utilitarian end. And this is confirmed by the facts; for it was when almost all the necessities of life and the things that make for comfort and recreation were present, that such knowledge began to be sought. Evidently then we do not seek it for the sake of any advantage; but as the man is free, we say, who exists for himself and not for another, so we pursue this as the only free science, for it alone exists for itself.
Metaphysics, 982b, 12-27. In Jonathan Baines (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1554.
For it is the same whether you take it that the Earth is in motion or the Sky. For, in both the cases, it does not affect the Astronomical Science. It is just for the Physicist to see if it is possible to refute it.
In Syed Hasan Barani, 'Al-Biruni's Scientific Achievements', Indo-Iranica, 1952, S (4), 47.
For Linnaeus, Homo sapiens was both special and not special ... Special and not special have come to mean nonbiological and biological, or nurture and nature. These later polarizations are nonsensical. Humans are animals and everything we do lies within our biological potential ... the statement that humans are animals does not imply that our specific patterns of behavior and social arrangements are in any way directly determined by our genes. Potentiality and determination are different concepts.
…...
For the philosopher, order is the entirety of repetitions manifested, in the form of types or of laws, by perceived objects. Order is an intelligible relation. For the biologist, order is a sequence in space and time. However, according to Plato, all things arise out of their opposites. Order was born of the original disorder, and the long evolution responsible for the present biological order necessarily had to engender disorder.
An organism is a molecular society, and biological order is a kind of social order. Social order is opposed to revolution, which is an abrupt change of order, and to anarchy, which is the absence of order.
I am presenting here today both revolution and anarchy, for which I am fortunately not the only one responsible. However, anarchy cannot survive and prosper except in an ordered society, and revolution becomes sooner or later the new order. Viruses have not failed to follow the general law. They are strict parasites which, born of disorder, have created a very remarkable new order to ensure their own perpetuation.
An organism is a molecular society, and biological order is a kind of social order. Social order is opposed to revolution, which is an abrupt change of order, and to anarchy, which is the absence of order.
I am presenting here today both revolution and anarchy, for which I am fortunately not the only one responsible. However, anarchy cannot survive and prosper except in an ordered society, and revolution becomes sooner or later the new order. Viruses have not failed to follow the general law. They are strict parasites which, born of disorder, have created a very remarkable new order to ensure their own perpetuation.
'Interaction Among Virus, Cell, and Organism', Nobel Lecture (11 Dec 1965). In Nobel Lectures: Physiology or Medicine 1963-1970 (1972), 174.
Force, then, is Force, but mark you! Not a thing,
Only a Vector;
Thy barbèd arrows now have lost their sting,
Impotent spectre!
Thy reign, O force! is over. Now no more
Heed we thine action;
Repulsion leaves us where we were before,
So does attraction.
Both Action and Reaction now are gone.
Just ere they vanished,
Stress joined their hands in peace, and made them one;
Then they were banished....
Only a Vector;
Thy barbèd arrows now have lost their sting,
Impotent spectre!
Thy reign, O force! is over. Now no more
Heed we thine action;
Repulsion leaves us where we were before,
So does attraction.
Both Action and Reaction now are gone.
Just ere they vanished,
Stress joined their hands in peace, and made them one;
Then they were banished....
Reproduced in Bruce Clarke, Energy Forms: Allegory and Science in the Era of Classical Thermodynamics (2001), 20-21. In his parody of Shelley's Prometheus Unbound, Maxwell presents Newton's laws of motion updated into axioms of energy.
Frogs will eat red-flannel worms fed to them by biologists; this proves a great deal about both parties concerned.
Quoted in Joseph Wood Krutch, The Best of Two Worlds (1953), 105.
From common salt are obtained chemically as primary derivatives chlorine—both a war gas and a means of purifying water; and 'caustic soda.' … [O]n the chlorine side there is obtained chloride of lime, (a bleaching powder and a disinfectant), chloroform (an anesthetic), phosgene (a frightful ware gas), chloroacetophenone (another war gas), and an indigo and a yellow dye. [O]n the soda side we get metallic sodium, from which are derived sodium cyanide (a disinfectant), two medicines with [long] names, another war gas, and a beautiful violet dye. Thus, from a healthful, preservative condiment come things useful and hurtful—according to the intent or purpose.
The Homiletic Review, Vol. 83-84 (1922), Vol. 83, 209.
From my father I learned to build things, to take them apart, and to fix mechanical and electrical equipment in general. I spent vast hours in a woodworking shop he maintained in the basement of our house, building gadgets, working both with my father and alone, often late into the night. … This play with building, fixing, and designing was my favorite activity throughout my childhood, and was a wonderful preparation for my later career as an experimentalist working on the frontiers of chemistry and physics.
From 'Richard E. Smalley: Biographical', collected in Tore Frängsmyr (ed.), Les Prix Nobel: The Nobel Prizes 1996 (1997).
From that night on, the electron—up to that time largely the plaything of the scientist—had clearly entered the field as a potent agent in the supplying of man's commercial and industrial needs… The electronic amplifier tube now underlies the whole art of communications, and this in turn is at least in part what has made possible its application to a dozen other arts. It was a great day for both science and industry when they became wedded through the development of the electronic amplifier tube.
The Autobiography of Robert A. Millikan (1951), 136.
From the time of Aristotle it had been said that man is a social animal: that human beings naturally form communities. I couldn’t accept it. The whole of history and pre-history is against it. The two dreadful world wars we have recently been through, and the gearing of our entire economy today for defensive war belie it. Man's loathsome cruelty to man is his most outstanding characteristic; it is explicable only in terms of his carnivorous and cannibalistic origin. Robert Hartmann pointed out that both rude and civilised peoples show unspeakable cruelty to one another. We call it inhuman cruelty; but these dreadful things are unhappily truly human, because there is nothing like them in the animal world. A lion or tiger kills to eat, but the indiscriminate slaughter and calculated cruelty of human beings is quite unexampled in nature, especially among the apes. They display no hostility to man or other animals unless attacked. Even then their first reaction is to run away.
In Africa's Place In the Emergence of Civilisation (1959), 41.
From thus meditating on the great similarity of the structure of the warm-blooded animals, and at the same time of the great changes they undergo both before and after their nativity; and by considering in how minute a portion of time many of the changes of animals above described have been produced; would it be too bold to imagine that, in the great length of time since the earth began to exist, perhaps millions of ages before the commencement of the history of mankind would it be too bold to imagine that all warm-blooded animals have arisen from one living filament, which THE GREAT FIRST CAUSE endued with animality, with the power of acquiring new parts, attended with new propensities, directed by irritations, sensations, volitions and associations, and thus possessing the faculty of continuing to improve by its own inherent activity, and of delivering down these improvements by generation to its posterity, world without end!
Zoonomia, Or, The Laws of Organic Life, in three parts (1803), Vol. 1, 397.
Fundamentally, as is readily seen, there exists neither force nor matter. Both are abstractions of things, such as they are, looked at from different standpoints. They complete and presuppose each other. Isolated they are meaningless. … Matter is not a go-cart, to and from which force, like a horse, can be now harnessed, now loosed. A particle of iron is and remains exactly the same thing, whether it shoot through space as a meteoric stone, dash along on the tire of an engine-wheel, or roll in a blood-corpuscle through the veins of a poet. … Its properties are eternal, unchangeable, untransferable.
From the original German text in 'Über die Lebenskraft', Preface to Untersuchungen über tierische Elektrizität (1848), xliii. As translated in Ludwig Büchner, Force and Matter: Or, Principles of the Natural Order of the Universe (1891), 1.
Further, it will not be amiss to distinguish the three kinds and, as it were, grades of ambition in mankind. The first is of those who desire to extend their own power in their native country, a vulgar and degenerate kind. The second is of those who labor to extend the power and dominion of their country among men. This certainly has more dignity, though not less covetousness. But if a man endeavor to establish and extend the power and dominion of the human race itself over the universe, his ambition (if ambition it can be called) is without doubt both a more wholesome and a more noble thing than the other two. Now the empire of man over things depends wholly on the arts and sciences. For we cannot command nature except by obeying her.
From Novum Organum (1620), Book 1, Aphorism 129. Translated as The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 114.
Generality of points of view and of methods, precision and elegance in presentation, have become, since Lagrange, the common property of all who would lay claim to the rank of scientific mathematicians. And, even if this generality leads at times to abstruseness at the expense of intuition and applicability, so that general theorems are formulated which fail to apply to a single special case, if furthermore precision at times degenerates into a studied brevity which makes it more difficult to read an article than it was to write it; if, finally, elegance of form has well-nigh become in our day the criterion of the worth or worthlessness of a proposition,—yet are these conditions of the highest importance to a wholesome development, in that they keep the scientific material within the limits which are necessary both intrinsically and extrinsically if mathematics is not to spend itself in trivialities or smother in profusion.
In Die Entwickdung der Mathematik in den letzten Jahrhunderten (1884), 14-15.
Geometrical reasoning, and arithmetical process, have each its own office: to mix the two in elementary instruction, is injurious to the proper acquisition of both.
In Trigonometry and Double Algebra (1849), 92.
God and the Doctor we alike adore
But only when in danger, not before;
The danger o’er, both are alike requited,
God is forgotten, and the Doctor slighted.
But only when in danger, not before;
The danger o’er, both are alike requited,
God is forgotten, and the Doctor slighted.
…...
Good work is no done by “humble” men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking “Is what I do worth while?” and “Am I the right person to do it?” will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.
In A Mathematician’s Apology (1940, 1967), 66.
Gyroscope, n.: A wheel or disk mounted to spin rapidly about an axis and also free to rotate about one or both of two axes perpendicular to each other and the axis of spin so that a rotation of one of the two mutually perpendicular axes results from application of torque to the other when the wheel is spinning and so that the entire apparatus offers considerable opposition depending on the angular momentum to any torque that would change the direction of the axis of spin.
Webster's New Collegiate Dictionary (8th Ed., 1973), 513. (Webmaster comments: A definition which is perfectly easy to understand. Right?)
Half a century ago Oswald (1910) distinguished classicists and romanticists among the scientific investigators: the former being inclined to design schemes and to use consistently the deductions from working hypotheses; the latter being more fit for intuitive discoveries of functional relations between phenomena and therefore more able to open up new fields of study. Examples of both character types are Werner and Hutton. Werner was a real classicist. At the end of the eighteenth century he postulated the theory of “neptunism,” according to which all rocks including granites, were deposited in primeval seas. It was an artificial scheme, but, as a classification system, it worked quite satisfactorily at the time. Hutton, his contemporary and opponent, was more a romanticist. His concept of “plutonism” supposed continually recurrent circuits of matter, which like gigantic paddle wheels raise material from various depths of the earth and carry it off again. This is a very flexible system which opens the mind to accept the possible occurrence in the course of time of a great variety of interrelated plutonic and tectonic processes.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 456-7.
Hardly a pure science, history is closer to animal husbandry than it is to mathematics, in that it involves selective breeding. The principal difference between the husbandryman and the historian is that the former breeds sheep or cows or such, and the latter breeds (assumed) facts. The husbandryman uses his skills to enrich the future; the historian uses his to enrich the past. Both are usually up to their ankles in bullshit.
Another Roadside Attraction (1990), 127.
HOMŒOPATHY, n. A school of medicine midway between Allopathy and Christian Science. To the last both the others are distinctly inferior, for Christian Science will cure imaginary diseases, and they can
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary, 139.
How twins are born my discourse will explain thus. The cause is chiefly the nature of the womb in woman. For if it has grown equally on either side of its mouth, and if it opens equally, and also dries equally after menstruation, it can give nourishment, if it conceive the secretion of the man so that it immediately divides into both parts of the womb equally. Now if the seed secreted from both parents be abundant and strong, it can grow in both places, as it masters the nourishment that reaches it. In all other cases twins are not formed. Now when the secretion from both parents is male, of necessity boys are begotten in both places; but when from both it is female, girls are begotten. But when one secretion is female and the other male, whichever masters the other gives the embryo its sex. Twins are like one another for the following reasons. First, the places are alike in which they grow; then they were secreted together; then they grow by the same nourishment, and at birth they reach together the light of day.
Regimen, in Hippocrates, trans. W. H. S. Jones (1931), Vol. 4, 273.
However far the calculating reason of the mathematician may seem separated from the bold flight of the artist’s phantasy, it must be remembered that these expressions are but momentary images snatched arbitrarily from among the activities of both. In the projection of new theories the mathematician needs as bold and creative a phantasy as the productive artist, and in the execution of the details of a composition the artist too must calculate dispassionately the means which are necessary for the successful consummation of the parts. Common to both is the creation, the generation, of forms out of mind.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 185. From the original German, “Wie weit auch der rechnende Verstand des Mathematikers von dem kühnen Fluge der Phantasie des Künstlers getrennt zu sein scheint, so bezeichnen diese Ausdrücke doch blosse Augenblicksbilder, die willkürlich aus der Thätigkeit Beider herausgerissen sind. Bei dem Entwurfe neuer Theorieen bedarf der Mathematiker einer ebenso kühnen und schöpferischen Phantasie wie der schaffende Künstler, und bei der Ausführung der Einzelheiten eines Werkes muss auch der Künstler kühl alle Mittel berechnen, welche zum Gelingen der Theile erforderlich sind. Gemeinsam ist Beiden die Hervorbringung, die Erzeugung der Gebilde aus dem Geiste.”
However far the mathematician’s calculating senses seem to be separated from the audacious flight of the artist’s imagination, these manifestations refer to mere instantaneous images, which have been arbitrarily torn from the operation of both. In designing new theories, the mathematician needs an equally bold and inspired imagination as creative as the artist, and in carrying out the details of a work the artist must unemotionally reckon all the resources necessary for the success of the parts. Common to both is the fabrication, the creation of the structure from the intellect.
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 4. Translated by Webmaster using online resources. From the original German, “Wie weit auch der rechnende Verstand des Mathematikers von dem kühnen Fluge der Phantasie des Künstlers getrennt zu sein scheint, so bezeichnen diese Ausdrücke doch blosse Augenblicksbilder, die willkürlich aus der Thätigkeit Beider herausgerissen sind. Bei dem Entwurfe neuer Theorieen bedarf der Mathematiker einer ebenso kühnen und schöpferischen Phantasie wie der schaffende Künstler, und bei der Ausführung der Einzelheiten eines Werkes muss auch der Künstler kühl alle Mittel berechnen, welche zum Gelingen der Theile erforderlich sind. Gemeinsam ist Beiden die Hervorbringung, die Erzeugung der Gebilde aus dem Geiste.”
I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.
Letter to Friedrich Bessel (4 Dec 1808). In Gauss-Bessel Briefwechsel (1880), 107. In Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 158.
I am more and more convinced that the ant colony is not so much composed of separate individuals as that the colony is a sort of individual, and each ant like a loose cell in it. Our own blood stream, for instance, contains hosts of white corpuscles which differ little from free-swimming amoebae. When bacteria invade the blood stream, the white corpuscles, like the ants defending the nest, are drawn mechanically to the infected spot, and will die defending the human cell colony. I admit that the comparison is imperfect, but the attempt to liken the individual human warrior to the individual ant in battle is even more inaccurate and misleading. The colony of ants with its component numbers stands half way, as a mechanical, intuitive, and psychical phenomenon, between our bodies as a collection of cells with separate functions and our armies made up of obedient privates. Until one learns both to deny real individual initiative to the single ant, and at the same time to divorce one's mind from the persuasion that the colony has a headquarters which directs activity … one can make nothing but pretty fallacies out of the polity of the ant heap.
In An Almanac for Moderns (1935), 121
I am not ... asserting that humans are either genial or aggressive by inborn biological necessity. Obviously, both kindness and violence lie with in the bounds of our nature because we perpetrate both, in spades. I only advance a structural claim that social stability rules nearly all the time and must be based on an overwhelmingly predominant (but tragically ignored) frequency of genial acts, and that geniality is therefore our usual and preferred response nearly all the time ... The center of human nature is rooted in ten thousand ordinary acts of kindness that define our days.
…...
I beg to present Columbus as a man of science and a man of faith. As a scientist, considering the time in which he lived, he eminently deserves our respect. Both in theory and in practice he was one of the best geographers and cosmographers of the age.
Address, in Chicago (12 Oct 1892). In E.S. Werner (ed.), Werner's Readings and Recitations (1908), 71.
I believe … that we can still have a genre of scientific books suitable for and accessible alike to professionals and interested laypeople. The concepts of science, in all their richness and ambiguity, can be presented without any compromise, without any simplification counting as distortion, in language accessible to all intelligent people … I hope that this book can be read with profit both in seminars for graduate students and–if the movie stinks and you forgot your sleeping pills–on the businessman’s special to Tokyo.
In Wonderful Life: The Burgess Shale and the Nature of History (1990), Preface, 16.
I consider it important, indeed urgently necessary, for intellectual workers to get together, both to protect their own economic status and, also, generally speaking, to secure their influence in the political field.
…...
I consider then, that generally speaking, to render a reason of an effect or Phaenomenon, is to deduce It from something else in Nature more known than it self, and that consequently there may be divers kinds of Degrees of Explication of the same thing. For although such Explications be the most satisfactory to the Understanding, wherein ’tis shewn how the effect is produc’d by the more primitive and Catholick Affection of Matter, namely bulk, shape and motion, yet are not these Explications to be despis’d, wherein particular effects are deduc’d from the more obvious and familiar Qualities or States of Bodies, … For in the search after Natural Causes, every new measure of Discovery does both instinct and gratifie the Understanding.
Physiological Essays (1669), 20.
I could not help laughing at the ease with which he explained his process of deduction. “When I hear you give your reasons,” I remarked, “the thing always appears to me to be so ridiculously simple that I could easily do it myself, though at each successive instance of your reasoning I am baffled, until you explain your process. And yet I believe that my eyes are as good as yours.”
“Quite so,” he answered, lighting a cigarette, and throwing himself down into an arm-chair. “You see, but you do not observe. The distinction is clear. For example, you have frequently seen the steps which lead up from the hall to this room.”
“Frequently.”
“How often?”
“'Well, some hundreds of times.”
“Then how many are there?”
“How many! I don't know.”
“Quite so! You have not observed. And yet you have seen. That is just my point. Now, I know that there are seventeen steps, because I have both seen and observed.”
“Quite so,” he answered, lighting a cigarette, and throwing himself down into an arm-chair. “You see, but you do not observe. The distinction is clear. For example, you have frequently seen the steps which lead up from the hall to this room.”
“Frequently.”
“How often?”
“'Well, some hundreds of times.”
“Then how many are there?”
“How many! I don't know.”
“Quite so! You have not observed. And yet you have seen. That is just my point. Now, I know that there are seventeen steps, because I have both seen and observed.”
From 'Adventure I.—A Scandal in Bohemia', Adventures of Sherlock Holmes, in The Strand Magazine: An Illustrated Monthly (Jul 1891), 2, 62.
I didn’t really decide that I wanted to be an astronaut for sure until the end of college. But even in elementary school and junior high, I was very interested in space and in the space program. I had both male and female heroes. One was a high school science teacher who was very important in encouraging me to pursue science. Because I was a tennis player, Billie Jean King was a hero of mine. And the early astronauts, John Glenn and Neil Armstrong, were heroes of mine as well.
Interview conducted on Scholastic website (20 Nov 1998).
I do not find that any one has doubted that there are four elements. The highest of these is supposed to be fire, and hence proceed the eyes of so many glittering stars. The next is that spirit, which both the Greeks and ourselves call by the same name, air. It is by the force of this vital principle, pervading all things and mingling with all, that the earth, together with the fourth element, water, is balanced in the middle of space.
In The Natural History of Pliny (1855), Vol. 1, 18.
I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
I don’t understand why people insist on pitting concepts of evolution and creation against each other. Why can’t they see that spiritualism and science are one? That bodies evolve and souls evolve and the universe is a fluid package that marries them both in a wonderful package called a human being.
The Art of Racing in the Rain. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 43
I end with a word on the new symbols which I have employed. Most writers on logic strongly object to all symbols. ... I should advise the reader not to make up his mind on this point until he has well weighed two facts which nobody disputes, both separately and in connexion. First, logic is the only science which has made no progress since the revival of letters; secondly, logic is the only science which has produced no growth of symbols.
I had gone on a walk on a fine Sabbath afternoon. I had entered the Green [of Glasgow] by the gate at the foot of Charlotte Street—had passed the old washing-house. I was thinking upon the engine at the time, and had gone as far as the herd's house, when the idea came into my mind that as steam was an elastic body it would rush into a vacuum, and if a communication were made between the cylinder and an exhausted vessel it would rush into it, and might be there condensed without cooling the cylinder. I then saw that I must get rid of the condensed steam and injection water if I used a jet, as in Newcomen's engine. Two ways of doing this occurred to me. First, the water might be run off by a descending pipe, if an outlet could be got at the depth of 35 or 36 feet, and any air might be extracted by a small pump. The second was to make the pump large enough to extract both water and air. ... I had not walked further than the Golf-house when the whole thing was arranged in my mind.
[In Robert Hart's words, a recollection of the description of Watt's moment of inspiration, in May 1765, for improving Thomas Newcomen's steam engine.]
[In Robert Hart's words, a recollection of the description of Watt's moment of inspiration, in May 1765, for improving Thomas Newcomen's steam engine.]
In Robert Hart, 'Reminiscences of James Watt' (read 2 Nov 1857), Transactions of the Glasgow Archaeological Society (1859), Vol. 1, 1. Note that these are not the verbatim words of James Watt, but are only a recollection of them by Robert Hart, who is quoting as best he can from memory of a conversation he and his brother had with James Watt that took place over 43 years previously. In his Reminiscences, Hart explains, “I have accordingly thrown together the following brief narrative:— As these meetings took place forty-three years since, many observations that were made at the time may have escaped me at present; yet, when the same subjects are touched on, I have as distinct recollection of his treatment of them as if it were yesterday.”
I have always been very fond of mathematics—for one short period, I even toyed with the possibility of abandoning chemistry in its favour. I enjoyed immensely both its conceptual and formal beauties, and the precision and elegance of its relationships and transformations. Why then did I not succumb to its charms? … because by and large, mathematics lacks the sensuous elements which play so large a role in my attraction to chemistry.I love crystals, the beauty of their forms and formation; liquids, dormant, distilling, sloshing! The fumes, the odors—good or bad, the rainbow of colors; the gleaming vessels of every size, shape and purpose.
In Arthur Clay Cope Address, Chicago (28 Aug 1973). In O. T. Benfey and P. J. T. Morris (eds.), Robert Burns Woodward. Architect and Artist in the World of Molecules (2001), 427.
I have always felt that astronomical hypotheses should not be regarded as articles of faith, but should only serve as a framework for astronomical calculations, so that it does not matter whether they were right or wrong, as long as the phenomena can be characterized precisely. For who could possibly be certain as to whether the uneven movement of the sun, if we follow the hypotheses of Ptolemy, can be explained by assuming an epicycle or eccentricity. Both assumptions are plausible. That’s why I would consider it quite desirable for you to tell something about that in the preface. In this way you would appease the Aristotelians and the theologians, whose opposition you dread.
From surviving fragment of a Letter (20 Apr 1541) answering a query from Copernicus as to whether he should publish his book (De Revolutionibus). From the German in Leopold Friedrich Prowe, Nicolaus Coppernicus (1883), Vol. 1, Part 2, 521-522. Translated from Prowe by Webmaster using web resources. Original German: “Hypothesen nicht als Glaubens-Artikel zu betrachten seien, sondern nur als Grundlage für die astronomischen Rechnungen zu dienen hätten, so dass es nicht darauf ankomme, ob sie richtig oder falsch seien, wofern sich nur die Erscheinungen dadurch genau bestimmen liessen. »Denn wer dürfte uns wohl darüber sichere Auskunft geben, ob die ungleiche Bewegung der Sonne, wenn wir den Hypothesen des Ptolemaeus folgen, durch Annahme eines Epicykels oder der Ekcentricität zu erklären sei. Beide Annahmen sind gestattet. Daher würde ich—so schliesst Osiander—es für recht wünschenswerth erachten, wenn Du hierüber in der Vorrede etwas beibrächtest. Auf diese Weise würdest Du die Aristoteliker und die Theologen milder stimmen, von denen Du befürchtest, dass sie heftigen Widerspruch kundthun werden.«” Compare Latin text, from Johannes Kepler, 'Apologia Tychonia', Astronomi Opera Omnia (1858), Vol. 1, 246: “De hypothesibus ego sic sensi semper, non esse articulos fidei, sed fundamenta calculi ita ut, etiamsi falsae sint, modo motuum φαινομενα exacte exhibeant, nihil referat; quis enim nos certiores reddet, an Solis inaequalis motus nomine epicycli an nomine eccentricitatis contingat, si Ptolemaei hypotheses sequamur, cum id possit utrumque. Quare plausibile fore videretur, si hac de re in praefatione nonnihil attingeres. Sic enim placidiores redderes peripatheticos et theologos, quos contradicturos metuis.”
I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations. … For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it.
Although this preface would have been assumed by contemporary readers to be written by Copernicus, it was unsigned. It is now believed to have been written and added at press time by Andreas Osiander (who was then overseeing the printing of the book). It suggests the earth’s motion as described was merely a mathematical device, and not to be taken as absolute reality. Text as given in 'To the Reader on the Hypotheses in this Work', Copernicus: On the Revolutions of the Heavenly Spheres (1543), translated by Alistair Matheson Duncan (1976), 22-3. By adding this preface, Osiander wished to stave off criticism by theologians. See also the Andreas Osiander Quotes page of this website.
I have procured some of the mice mentioned in my former letters, a young one and a female with young, both of which I have preserved in brandy. From the colour, shape, size, and manner of nesting, I make no doubt but that the species is nondescript [not known to science]. They are much smaller and more slender than the mus domesticus medius of Ray; and have more of the squirrel or dormouse colour ... They never enter into houses; are carried into ricks and barns with the sheaves; abound in harvest, and build their nests amidst the straws of the corn above the ground, and sometimes in thistles.
[Part of his observations on the harvest mouse, which he was the first to describe as a new species.]
[Part of his observations on the harvest mouse, which he was the first to describe as a new species.]
Letter XII (4 Nov 1767) in The Natural History of Selborne (1789, 1899), 31.
I have recently observed and stated that the serum of normal people is capable of clumping the red cells of other healthy individuals... As commonly expressed, it can be said that in these cases at least two different kinds of agglutinins exist, one kind in A, the other in B, both together in C. The cells are naturally insensitive to the agglutinins in their own serum.
Ueber Agglutinationserscheinungen normalen menschlichen Blutes', Wiener klinische Wochenschrift (1901), 14, 1132-1134. Trans. Pauline M. H. Mazumdar.
I have repeatedly had cause to refer to certain resemblances between the phenomena of irritability in the vegetable kingdom and those of the animal body, thus touching a province of investigation which has hitherto been far too little cultivated. In the last instance, indeed, I might say animal and vegetable life must of necessity agree in all essential points, including the phenomena of irritability also, since it is established that the animal organism is constructed entirely and simply from the properties of these substances that all vital movements both of plants and animals are to be explained.
Lectures on the Physiology of Plants (1887), 600.
I have said that the investigation for which the teeth of the shark had furnished an opportunity, was very near an end... But thereafter, while I was examining more carefully these details of both places and bodies [sedimentary deposits and shells], these day by day presented points of doubt to me as they followed one another in indissoluble connection, so that I saw myself again and again brought back to the starting-place, as it were, when I thought I was nearest the goal. I might compare those doubts to the heads of the Lernean Hydra, since when one of them had been got rid of, numberless others were born; at any rate, I saw that I was wandering about in a sort of labyrinth, where the nearer one approaches the exit, the wider circuits does one tread.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 206.
I know two people who have found it [the secret of success]. … Getting ready. Getting prepared. There were Edison and Lindbergh,—they both got ready before they started. I had to find that out too. I had to stop for ten years after I had started; I had to stop for ten years and get ready. I made my first car in 1893, but it was 1903 before I had it ready to sell. It is these simple things that young men ought to know, and they are hardest to grasp. Before everything else, get ready.
From Henry Ford and Ralph Waldo Trine, The Power that Wins (1929), 147. Often seen paraphrased as “Before everything else, getting ready is the secret of success,” for example, in Connie Robertson (ed.), The Wordsworth Dictionary of Quotations (1998), 129.
I like to look at mathematics almost more as an art than as a science; for the activity of the mathematician, constantly creating as he is, guided though not controlled by the external world of the senses, bears a resemblance, not fanciful I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are, do not make a painter or mathematician worthy of the name, nor indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist or good mathematician.
From 'Fundamental Conceptions and Methods in Mathematics', Bulletin American Mathematical Society (1904), 9, 133. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 182.
I like to think that when Medawar and his colleagues showed that immunological tolerance could be produced experimentally the new immunology was born. This is a science which to me has far greater potentialities both for practical use in medicine and for the better understanding of living process than the classical immunochemistry which it is incorporating and superseding.
'Immunological Recognition of Self', Nobel Lecture, 12 December 1960. In Nobel Lectures Physiology or Medicine 1942-1962 (1964), 689.
I read … that geometry is the art of making no mistakes in long calculations. I think that this is an underestimation of geometry. Our brain has two halves: one is responsible for the multiplication of polynomials and languages, and the other half is responsible for orientation of figures in space and all the things important in real life. Mathematics is geometry when you have to use both halves.
In S.H. Lui, 'An Interview with Vladimir Arnol’d', Notices of the AMS (Apr 1997) 44, No. 4, 438. Reprinted from the Hong Kong Mathematics Society (Feb 1996).
I realized both the upper and lower body must be held securely in place with one strap across the chest and one across the hips. The belt also needed an immovable anchorage point for the buckle as far down beside the occupant’s hip, so it could hold the body properly during a collision. It was just a matter of finding a solution that was simple, effective and could be put on conveniently with one hand.
as quoted in New York Times obituary, 26 Sep 2002
I respect Kirkpatrick both for his sponges and for his numinous nummulosphere. It is easy to dismiss a crazy theory with laughter that debars any attempt to understand a man’s motivation–and the nummulosphere is a crazy theory. I find that few men of imagination are not worth my attention. Their ideas may be wrong, even foolish, but their methods often repay a close study ... The different drummer often beats a fruitful tempo.
…...
I stand before you as somebody who is both physicist and a priest, and I want to hold together my scientific and my religious insights and experiences . I want to hold them together, as far as I am able, without dishonesty and without compartmentalism. I don’t want to be a priest on Sunday and a physicist on Monday; I want to be both on both days.
…...
I took this view of the subject. The medulla spinalis has a central division, and also a distinction into anterior and posterior fasciculi, corresponding with the anterior and posterior portions of the brain. Further we can trace down the crura of the cerebrum into the anterior fasciculus of the spinal marrow, and the crura of the cerebellum into the posterior fasciculus. I thought that here I might have an opportunity of touching the cerebellum, as it were, through the posterior portion of the spinal marrow, and the cerebrum by the anterior portion. To this end I made experiments which, though they were not conclusive, encouraged me in the view I had taken. I found that injury done to the anterior portion of the spinal marrow, convulsed the animal more certainly than injury done to the posterior portion; but I found it difficult to make the experiment without injuring both portions.
Idea of a New Anatomy of the Brain (1811), 21-22.
I trade both with the living and the dead for the enrichment of our native language.
I venture to maintain, that, if the general culture obtained in the Faculty of Arts were what it ought to be, the student would have quite as much knowledge of the fundamental principles of Physics, of Chemistry, and of Biology, as he needs, before he commenced his special medical studies. Moreover, I would urge, that a thorough study of Human Physiology is, in itself, an education broader and more comprehensive than much that passes under that name. There is no side of the intellect which it does not call into play, no region of human knowledge into which either its roots, or its branches, do not extend; like the Atlantic between the Old and the New Worlds, its waves wash the shores of the two worlds of matter and of mind; its tributary streams flow from both; through its waters, as yet unfurrowed by the keel of any Columbus, lies the road, if such there be, from the one to the other; far away from that Northwest Passage of mere speculation, in which so many brave souls have been hopelessly frozen up.
'Universities: Actual and Ideal' (1874). In Collected Essays (1893), Vol. 3, 220.
I was interested in truth from the point of view of salvation just as much as in truth from the point of view of scientific certainty. It appeared to me that there were two paths to truth, and I decided to follow both of them.
Explaining his decision, made at age 9, to become a scientist, followed within a month by his decision to also become a priest. In interview with Duncan Aikman, 'Lemaître Follows Two Paths to Truth', New York Times Magazine (19 Feb 1933), 3.
I was there when Abbe Georges Lemaître first proposed this [Big Bang] theory. ... There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. .... It is only myth that attempts to say how the universe came to be, either four thousand or twenty billion years ago.
[Expressing his belief that the Big Bang is a myth devised to explain creation. He said he heard Lemaître (who was, at the time both a member of the Catholic hierarchy and an accomplished scientist) say in private that this theory was a way to reconcile science with St. Thomas Aquinas' theological dictum of creatio ex nihilo—creation out of nothing.]
[Expressing his belief that the Big Bang is a myth devised to explain creation. He said he heard Lemaître (who was, at the time both a member of the Catholic hierarchy and an accomplished scientist) say in private that this theory was a way to reconcile science with St. Thomas Aquinas' theological dictum of creatio ex nihilo—creation out of nothing.]
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),196.
I would liken science and poetry in their natural independence to those binary stars, often different in colour, which Herschel’s telescope discovered to revolve round each other. “There is one light of the sun,” says St. Paul, “and another of the moon, and another of the stars: star differeth from star in glory.” It is so here. That star or sun, for it is both, with its cold, clear, white light, is SCIENCE: that other, with its gorgeous and ever-shifting hues and magnificent blaze, is POETRY. They revolve lovingly round each other in orbits of their own, pouring forth and drinking in the rays which they exchange; and they both also move round and shine towards that centre from which they came, even the throne of Him who is the Source of all truth and the Cause of all beauty.
'The Alleged Antagonism between Poetry and Chemistry.' In Jesse Aitken Wilson, Memoirs of George Wilson. Quoted in Natural History Society of Montreal, 'Reviews and Notices of Books,' The Canadian Naturalist and Geologist (1861) Vol. 6, 393.
I would not be confident in everything I say about the argument: but one thing I would fight for to the end, both in word and in deed if I were able—that if we believe we should try to find out what is not known, we should be better and braver and less idle than if we believed that what we do not know is impossible to find out and that we need not even try.
…...
If A denotes one of the two constant traits, for example, the dominating one, a the recessive, and the Aa the hybrid form in which both are united, then the expression:
A + 2Aa + a
gives the series for the progeny of plants hybrid in a pair of differing traits.
A + 2Aa + a
gives the series for the progeny of plants hybrid in a pair of differing traits.
'Experiments on Plant Hybrids' (1865). In Curt Stem and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 16.
If I were entering adulthood now instead of in the environment of fifty years ago, I would choose a career that kept me in touch with nature more than science. … Too few natural areas remain; both by intent and by indifference we have insulated ourselves from the wilderness that produced us.
In 'The Wisdom of Wilderness', Life (22 Dec 1967), 63, No. 25, 10.
If in a given community unchecked popular rule means unlimited waste and destruction of the natural resources—soil, fertility, waterpower, forests, game, wild-life generally—which by right belong as much to subsequent generations as to the present generation, then it is sure proof that the present generation is not yet really fit for self-control, that it is not yet really fit to exercise the high and responsible privilege of a rule which shall be both by the people and for the people. The term “for the people” must always include the people unborn as well as the people now alive, or the democratic ideal is not realized.
In A Book-Lover's Holidays in the Open (1916), 319.
If in the citation of work that we have both done together only one of us is named, and especially in a journal [Annalen der Chemie] in which both are named on the title page, about which everyone knows that you are the actual editor, and this editor allows that to happen and does not show the slightest consideration to report it, then everyone will conclude that this represents an agreement between us, that the work is yours alone, and that I am a jackass.
Letter from Wohler to Liebig (15 Nov 1840). In A. W. Hofmann (ed.), Aus Justus Liebigs und Friedrich Wohlers Briefwechsel (1888), Vol. 1, 166. Trans. W. H. Brock.
If it were possible for us to have so deep an insight into a man's character as shown both in inner and in outer actions, that every, even the least, incentive to these actions and all external occasions which affect them were so known to us that his future conduct could be predicted with as great a certainty as the occurrence of a solar or lunar eclipse, we could nevertheless still assert that the man is free.
Critique of Practical Reason (1788). In L. W. Beck (ed. & trans.), Critique of Practical Reason and Other Writings in Moral Philosophy (1949), 204-5.
If politics is the art of the possible, research is surely the art of the soluble. Both are immensely practical-minded affairs.
In 'The Act of Creation', a book review (of Arthur Koestler’s book, The Act of Creation) in New Statesman (19 Jun 1964). Collected in The Strange Case of the Spotted Mice and Other Classic Essays on Science (1996), 42. Also collected in Medawar’s The Art of the Soluble: Creativity and Originality in Science (1967), 7.
If the juices of the body were more chymically examined, especially by a naturalist, that knows the ways of making fixed bodies volatile, and volatile fixed, and knows the power of the open air in promoting the former of those operations; it is not improbable, that both many things relating to the nature of the humours, and to the ways of sweetening, actuating, and otherwise altering them, may be detected, and the importance of such discoveries may be discerned.
Quoted In Barbara Kaplan (ed.) Divulging of Useful Truths in Physick: The Medical Agenda of Robert Boyle (1993), 92.
If the observation of the amount of heat the sun sends the earth is among the most important and difficult in astronomical physics, it may also be termed the fundamental problem of meteorology, nearly all whose phenomena would become predictable, if we knew both the original quantity and kind of this heat.
In Report of the Mount Whitney Expedition, quoted in Charles Greeley Abbot, Adventures in the World of Science (1958), 17. Also quoted and cited in David H. Devorkin, 'Charles Greeley Abbot', Biographical Memoirs (1998), 4.
If this seems complex, the reason is because Tao is both simple and complex. It is complex when we try to understand it, and simple when we allow ourselves to experience it.
In Gary William Flake, The Computational Beauty of Nature (2000), 327.
If thou examinest a man having a break in the column of his nose, his nose being disfigured, and a [depression] being in it, while the swelling that is on it protrudes, [and] he had discharged blood from both his nostrils, thou shouldst say concerning him: “One having a break in the column of his nose. An ailment which I will treat. “Thou shouldst cleanse [it] for him [with] two plugs of linen. Thou shouldst place two [other] plugs of linen saturated with grease in the inside of his two nostrils. Thou shouldst put [him] at his mooring stakes until the swelling is drawn out. Thou shouldst apply for him stiff rolls of linen by which his nose is held fast. Thou shouldst treat him afterward [with] lint, every day until he recovers.
(circa 1700 B.C.) From “The Edwin Smith Surgical Papyrus”, an ancient Egyptian document regarded as the earliest known historical record of scientific thought. As translated in James Henry Breasted, The Edwin Smith Surgical Papyrus: Published in Facsimile and Hieroglyphic Transliteration with Translation and Commentary (1930), 440.
If you ask your mother for one fried egg for breakfast and she gives you two fried eggs and you eat both of them, who is better in arithmetic, you or your mother?
From 'Arithmetic', Harvest Poems, 1910-1960 (1960), 116.
If you could see what I almost daily see in my practice … persons … in the very last stages of wretched existence, emaciated to a skeleton, with both tables of the skull almost completely perforated in many places, half the nose gone, with rotten jaws, ulerated throats, breaths most pestiferous more intolerable than poisonous upas, limbs racked with the pains of the Inquisition, minds as imbecile as the puling babe, a grievous burden to themselves and a disgusting spectacle to others, you would exclaim as I have often done, 'O! the lamentable want of science that dictates the abuse (use) of that noxious drug calomel!'
[Calomel is the mercury compound, Hg2Cl2.]
[Calomel is the mercury compound, Hg2Cl2.]
Quoted in Wooster Beach, A Treatise on Anatomy, Physiology, and Health (1848), 177.
Imagination comes first in both artistic and scientific creations, but in science there is only one answer and that has to be correct.
In 'Discoverers of the Double Helix', The Daily Telegraph (27 Apr 1987), in Max Perutz (ed.), Is Science Necessary: Essays on Science and Scientists (1991), 182.
In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”
In 'Einstein's Impact on Theoretical Physics', collected in Jong-Ping Hsu, Leonard Hsu (eds.), JingShin Theoretical Physics Symposium in Honor of Professor Ta-You Wu (1998), 70. Reprinted from Physics Today (Jun 1980), 49. The article was adapted from a talk given at the Second Marcel Grossman meeting, held in Trieste, Italy (Jul 1979), in honor of the 100th anniversary of the birth of Albert Einstein.
In all chemical investigations, it has justly been considered an important object to ascertain the relative weights of the simples which constitute a compound. But unfortunately the enquiry has terminated here; whereas from the relative weights in the mass, the relative weights of the ultimate particles or atoms of the bodies might have been inferred, from which their number and weight in various other compounds would appear, in order to assist and to guide future investigations, and to correct their results. Now it is one great object of this work, to shew the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle.
If there are two bodies, A and B, which are disposed to combine, the following is the order in which the combinations may take place, beginning with the most simple: namely,
1 atom of A + 1 atom of B = 1 atom of C, binary
1 atom of A + 2 atoms of B = 1 atom of D, ternary
2 atoms of A + 1 atom of B = 1 atom of E, ternary
1 atom of A + 3 atoms of B = 1 atom of F, quaternary
3 atoms of A and 1 atom of B = 1 atom of G, quaternary
If there are two bodies, A and B, which are disposed to combine, the following is the order in which the combinations may take place, beginning with the most simple: namely,
1 atom of A + 1 atom of B = 1 atom of C, binary
1 atom of A + 2 atoms of B = 1 atom of D, ternary
2 atoms of A + 1 atom of B = 1 atom of E, ternary
1 atom of A + 3 atoms of B = 1 atom of F, quaternary
3 atoms of A and 1 atom of B = 1 atom of G, quaternary
A New System of Chemical Philosophy (1808), Vol. 1, 212-3.
In attempting to explain geological phenomena, the bias has always been on the wrong side; there has always been a disposition to reason á priori on the extraordinary violence and suddenness of changes, both in the inorganic crust of the earth, and in organic types, instead of attempting strenuously to frame theories in accordance with the ordinary operations of nature.
Letter to Rev. W. Whewell (7 Mar 1837). Quoted in Mrs Lyell (ed.), Life, Letters and Journals of Sir Charles Lyell, Bart (1881), Vol. 2, 3.
In both social and natural sciences, the body of positive knowledge grows by the failure of a tentative hypothesis to predict phenomena the hypothesis professes to explain; by the patching up of that hypothesis until someone suggests a new hypothesis that more elegantly or simply embodies the troublesome phenomena, and so on ad infinitum. In both, experiment is sometimes possible, sometimes not (witness meteorology). In both, no experiment is ever completely controlled, and experience often offers evidence that is the equivalent of controlled experiment. In both, there is no way to have a self-contained closed system or to avoid interaction between the observer and the observed. The Gödel theorem in mathematics, the Heisenberg uncertainty principle in physics, the self-fulfilling or self-defeating prophecy in the social sciences all exemplify these limitations.
Inflation and Unemployment (1976), 348.
In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.
In 'Geometry', Encyclopedia Britannica (9th edition).
In formal logic a contradiction is the signal of a defeat, but in the evolution of real knowledge it marks the first step in progress toward a victory. This is one great reason for the utmost toleration of variety of opinion. Once and forever, this duty of toleration has been summed up in the words, “Let both grow together until the harvest.”
In 'Religion and Science', The Atlantic (Aug 1925).
In my opinion, there is absolutely no trustworthy proof that talents have been improved by their exercise through the course of a long series of generations. The Bach family shows that musical talent, and the Bernoulli family that mathematical power, can be transmitted from generation to generation, but this teaches us nothing as to the origin of such talents. In both families the high-watermark of talent lies, not at the end of the series of generations, as it should do if the results of practice are transmitted, but in the middle. Again, talents frequently appear in some member of a family which has not been previously distinguished.
In 'On Heredity', Essays upon Heredity and Kindred Biological Problems (1889), Vol. 1, 95-96.
In order that an inventory of plants may be begun and a classification of them correctly established, we must try to discover criteria of some sort for distinguishing what are called “species”. After a long and considerable investigation, no surer criterion for determining species had occurred to me than distinguishing features that perpetuate themselves in propagation from seed. Thus, no matter what variations occur in the individuals or the species, if they spring from the seed of one and the same plant, they are accidental variations and not such as to distinguish a species. For these variations do not perpetuate themselves in subsequent seeding. Thus, for example, we do not regard caryophylli with full or multiple blossoms as a species distinct from caryophylli with single blossoms, because the former owe their origin to the seed of the latter and if the former are sown from their own seed, they once more produce single-blossom caryophylli. But variations that never have as their source seed from one and the same species may finally be regarded as distinct species. Or, if you make a comparison between any two plants, plants which never spring from each other's seed and never, when their seed is sown, are transmuted one into the other, these plants finally are distinct species. For it is just as in animals: a difference in sex is not enough to prove a difference of species, because each sex is derived from the same seed as far as species is concerned and not infrequently from the same parents; no matter how many and how striking may be the accidental differences between them; no other proof that bull and cow, man and woman belong to the same species is required than the fact that both very frequently spring from the same parents or the same mother. Likewise in the case of plants, there is no surer index of identity of species than that of origin from the seed of one and the same plant, whether it is a matter of individuals or species. For animals that differ in species preserve their distinct species permanently; one species never springs from the seed of another nor vice versa.
— John Ray
Historia Plantarum (1686), Vol. 1, 40. Trans. Edmund Silk. Quoted in Barbara G. Beddall, 'Historical Notes on Avian Classification', Systematic Zoology (1957), 6, 133-4.
In our daily lives, we enjoy the pervasive benefits of long-lived robotic spacecraft that provide high-capacity worldwide telecommunications; reconnaissance of Earth’s solid surface and oceans, with far-reaching cultural and environmental implications; much-improved weather and climatic forecasts; improved knowledge about the terrestrial effects of the Sun’s radiations; a revolutionary new global navigational system for all manner of aircraft and many other uses both civil and military; and the science of Earth itself as a sustainable abode of life.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004).
In science it is no crime to be wrong, unless you are (inappropriately) laying claim to truth. What matters is that science as a whole is a self-correcting mechanism in which both new and old notions are constantly under scrutiny. In other words, the edifice of scientific knowledge consists simply of a body of observations and ideas that have (so far) proven resistant to attack, and that are thus accepted as working hypotheses about nature.
In The Monkey in the Mirror: Essays on the Science of What Makes Us Human (2003), 9.
In science, attempts at formulating hierarchies are always doomed to eventual failure. A Newton will always be followed by an Einstein, a Stahl by a Lavoisier; and who can say who will come after us? What the human mind has fabricated must be subject to all the changes—which are not progress—that the human mind must undergo. The 'last words' of the sciences are often replaced, more often forgotten. Science is a relentlessly dialectical process, though it suffers continuously under the necessary relativation of equally indispensable absolutes. It is, however, possible that the ever-growing intellectual and moral pollution of our scientific atmosphere will bring this process to a standstill. The immense library of ancient Alexandria was both symptom and cause of the ossification of the Greek intellect. Even now I know of some who feel that we know too much about the wrong things.
Voices in the Labyrinth: Nature, Man, and Science (1979), 46.
In the 1860s, Pasteur not only applied his germ theory to create “Pasteurization,” rescuing France’s wine and vinegar industries, but also found both the cause and cure of silkworm disease, saving growers millions of dollars. When Napoleon asked the scientist why he had not legitimately profited by his findings, Pasteur replied: “In France scientists would consider they lowered themselves by doing so.”
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 190.
In the last fifteen years we have witnessed an event that, I believe, is unique in the history of the natural sciences: their subjugation to and incorporation into the whirls and frenzies of disgusting publicity and propaganda. This is no doubt symptomatic of the precarious position assigned by present-day society to any form of intellectual activity. Such intellectual pursuits have at all times been both absurd and fragile; but they become ever more ludicrous when, as is now true of science, they become mass professions and must, as homeless pretentious parasites, justify their right to exist in a period devoted to nothing but the rapid consumption of goods and amusements. These sciences were always a divertissement in the sense in which Pascal used the word; but what is their function in a society living under the motto lunam et circenses? Are they only a band of court jesters in search of courts which, if they ever existed, have long lost their desire to be amused?
Voices in the Labyrinth: Nature, Man, and Science (1979), 27.
In the mountains of Parma and Piacenza, multitudes of shells and corals filled with worm-holes may be seen still adhering to the rocks, and when I was making the great horse at Milan a large sack of those which had been found in these parts was brought to my workshop by some peasants... The red stone of the mountains of Verona is found with shells all intermingled, which have become part of this stone... And if you should say that these shells have been and still constantly are being created in such places as these by the nature of the locality or by potency of the heavens in these spots, such an opinion cannot exist in brains possessed of any extensive powers of reasoning because the years of their growth are numbered upon the outer coverings of their shells; and both small and large ones may be seen; and these would not have grown without feeding, or fed without movement, and here [embedded in rock] they would not have been able to move... The peaks of the Apennines once stood up in a sea, in the form of islands surrounded by salt water... and above the plains of Italy where flocks of birds are flying today, fishes were once moving in large shoals.
'Physical Geography', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938), Vol. 1, 355-6, 359.
In the sense that [truth] means the reality about a human being it is probably impossible for a biographer to achieve. In the sense that it means a reasonable presentation of all the available facts it is more nearly possible, but even this limited goal is harder to reach than it appears to be. A biographer needs to be both humble and cautious.
Describing the difficulty of historical sources giving conflicting facts. From 'Getting at the Truth', The Saturday Review (19 Sep 1953), 36, No. 38, 11. Excerpted in Meta Riley Emberger and Marian Ross Hall, Scientific Writing (1955), 399.
In the temple of science are many mansions, and various indeed are they that dwell therein and the motives that have led them thither. Many take to science out of a joyful sense of superior intellectual power; science is their own special sport to which they look for vivid experience and the satisfaction of ambition; many others are to be found in the temple who have offered the products of their brains on this altar for purely utilitarian purposes. Were an angel of the Lord to come and drive all the people belonging to these two categories out of the temple, the assemblage would be seriously depleted, but there would still be some men, of both present and past times, left inside. Our Planck is one of them, and that is why we love him.
Address at Physical Society, Berlin (1918), for Max Planck’s 60th birthday, 'Principles of Research' in Essays in Science (1934, 2004), 1.
In the training and in the exercise of medicine a remoteness abides between the field of neurology and that of mental health, psychiatry. It is sometimes blamed to prejudice on the part of the one side or the other. It is both more grave and less grave than that. It has a reasonable basis. It is rooted in the energy-mind problem. Physiology has not enough to offer about the brain in relation to the mind to lend the psychiatrist much help.
In 'The Brain Collaborates With Psyche', Man On His Nature: The Gifford Lectures, Edinburgh 1937-8 (1940), 283.
In the year 1692, James Bernoulli, discussing the logarithmic spiral [or equiangular spiral, ρ = αθ] … shows that it reproduces itself in its evolute, its involute, and its caustics of both reflection and refraction, and then adds: “But since this marvellous spiral, by such a singular and wonderful peculiarity, pleases me so much that I can scarce be satisfied with thinking about it, I have thought that it might not be inelegantly used for a symbolic representation of various matters. For since it always produces a spiral similar to itself, indeed precisely the same spiral, however it may be involved or evolved, or reflected or refracted, it may be taken as an emblem of a progeny always in all things like the parent, simillima filia matri. Or, if it is not forbidden to compare a theorem of eternal truth to the mysteries of our faith, it may be taken as an emblem of the eternal generation of the Son, who as an image of the Father, emanating from him, as light from light, remains ὁμοούσιος with him, howsoever overshadowed. Or, if you prefer, since our spira mirabilis remains, amid all changes, most persistently itself, and exactly the same as ever, it may be used as a symbol, either of fortitude and constancy in adversity, or, of the human body, which after all its changes, even after death, will be restored to its exact and perfect self, so that, indeed, if the fashion of Archimedes were allowed in these days, I should gladly have my tombstone bear this spiral, with the motto, ‘Though changed, I arise again exactly the same, Eadem numero mutata resurgo.’”
In 'The Uses of Mathesis', Bibliotheca Sacra, Vol. 32, 516-516. [The Latin phrase “simillima filia matri” roughly translates as “the daughter resembles the mother”. “Spira mirabilis” is Latin for “marvellous spiral”. The Greek word (?µ???s???) translates as “consubstantial”, meaning of the same substance or essence (used especially of the three persons of the Trinity in Christian theology). —Webmaster]
In the year of our Lord 729, two comets appeared around the sun, striking terror into all who saw them. One comet rose early and preceded the sun, while the other followed the setting sun at evening, seeming to portend awful calamity to east and west alike. Or else, since one comet was the precursor of day and the other of night, they indicated that mankind was menaced by evils at both times. They appeared in the month of January, and remained visible for about a fortnight, pointing their fiery torches northward as though to set the welkin aflame. At this time, a swarm of Saracens ravaged Gaul with horrible slaughter; … Both the outset and course of Ceolwulfs reign were filled by so many grave disturbances that it is quite impossible to know what to write about them or what the outcome will be.
— Bede
From Historia Ecclesiastica Gentis Anglorum, Book V, Chap. XXIII., as translated by Leo Sherley-Price, revised by R.E. Latham, Ecclesiastical History of the English People (1955, 1990), 323. Note: The observation likely was on a single comet seen twice each day. The event is also in both the Laud and Parker manuscripts of The Anglo-Saxon Chronicle.
In the year of our Lord’s incarnation 729, two comets appeared about the sun, to the great terror of the beholders. One of them went before the rising sun in the morning, the other followed him when he set at night, as it were presaging much destruction to the east and west; one was the forerunner of the day, and the other of the night, to signify that mortals were threatened with calamities at both times. They carried their flaming tails towards the north, as it were ready to set the world on fire. They appeared in January, and continued nearly a fortnight. At which time a dreadful plague of Saracens ravaged France with miserable slaughter; … the beginning
and progress of Ceolwulf’s reign were so filled with commotions, that it cannot yet be known what is to be said concerning them, or what end they will have.
— Bede
From Historia Ecclesiastica Gentis Anglorum, Book V, Chap. XXIII, as translated in J.A. Giles (ed.), The Venerable Bede’s Ecclesiastical History of England. Also the Anglo-Saxon Chronicle (1894), 291-292. The editor reprinted the translation based on the 1723 work of John Stevens into modern English. Note: The observation likely was on a single comet seen twice each day. The event is also in both the Laud and Parker manuscripts of The Anglo-Saxon Chronicle.
In years gone by, we would just take, take, take from the oceans but today we realize this is not an option, that the oceans keep us alive, and that we need to tread more carefully. This is now both a governance issue and a choice issue.
In 'Can We Stop Killing Our Oceans Now, Please?', Huffington Post (14 Aug 2013).
Included in this ‘almost nothing,’ as a kind of geological afterthought of the last few million years, is the first development of self-conscious intelligence on this planet–an odd and unpredictable invention of a little twig on the mammalian evolutionary bush. Any definition of this uniqueness, embedded as it is in our possession of language, must involve our ability to frame the world as stories and to transmit these tales to others. If our propensity to grasps nature as story has distorted our perceptions, I shall accept this limit of mentality upon knowledge, for we receive in trade both the joys of literature and the core of our being.
…...
Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
Is the very mechanism for the universe to come into being meaningless or unworkable or both unless the universe is guaranteed to produce life, consciousness and observership somewhere and for some little time in its history-to-be?
Quoted in P.C.W. Davies, God and the New Physics (1984), 39, from J.A. Wheeler, 'Genesis and observership', Foundational Problems in the Special Science (1977), 39.
It appears to be law that you cannot have a deep sympathy with both man and nature.
Journal entry (11 Apr 1852).
It follows from the theory of relativity that mass and energy are both different manifestations of the same thing—a somewhat unfamiliar conception for the average man. Furthermore E=MC2, in which energy is put equal to mass multiplied with the square of the velocity of light, showed that a very small amount of mass may be converted into a very large amount of energy... the mass and energy were in fact equivalent.
As expressed in the Einstein film, produced by Nova Television (1979). Quoted in Alice Calaprice, The Quotable Einstein (1996), 183.
It has been the final aim of Lie from the beginning to make progress in the theory of differential equations; as subsidiary to this may be regarded both his geometrical developments and the theory of continuous groups.
In Lectures on Mathematics (1911), 24.
It has hitherto been a serious impediment to the progress of knowledge, that is in investigating the origin or causes of natural productions, recourse has generally been had to the examination, both by experiment and reasoning, of what might be rather than what is. The laws or processes of nature we have every reason to believe invariable. Their results from time to time vary, according to the combinations of influential circumstances; but the process remains the same. Like the poet or the painter, the chemist may, and no doubt often' does, create combinations which nature never produced; and the possibility of such and such processes giving rise to such and such results, is no proof whatever that they were ever in natural operation.
Considerations on Volcanoes (1825), 243.
It has long been a complaint against mathematicians that they are hard to convince: but it is a far greater disqualification both for philosophy, and for the affairs of life, to be too easily convinced; to have too low a standard of proof. The only sound intellects are those which, in the first instance, set their standards of proof high. Practice in concrete affairs soon teaches them to make the necessary abatement: but they retain the consciousness, without which there is no sound practical reasoning, that in accepting inferior evidence because there is no better to be had, they do not by that acceptance raise it to completeness.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611.
It is ... indisputable that the orogenic movements which uplift the hills have been at the basis of geological history. To them the great accumulation of sediments which now form so large a part of continental land are mainly due. There can be no doubt of the fact that these movements have swayed the entire history, both inorganic and organic, of the world in which we live.
Radioactivity and Geology (1909), 115-6.
It is a misfortune to pass at once from observation to conclusion, and to regard both as of equal value; but it befalls many a student