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Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
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Home > Category Index for Science Quotations > Category Index C > Category: Course

Course Quotes (413 quotes)

...it is not to be taken in the sense of our day, which we reckon by the course of the sun; but it must have another meaning, applicable to the
three days mentioned before the creation of the heavenly bodies.
iv.26
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“Crawling at your feet,” said the Gnat … “you may observe a Bread-and-Butterfly. …”
“And what does it live on?”
“Weak tea with cream in it.”
A new difficulty came into Alice's head. “Supposing it couldn't find any?” she suggested.
“Then it would die, of course.”
“But that must happen very often,” Alice remarked thoughtfully.
“It always happens,” said the Gnat.
In Through the Looking Glass: And what Alice Found There (1893), 66-67.
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“Every moment dies a man,/ Every moment one is born”:
I need hardly point out to you that this calculation would tend to keep the sum total of the world's population in a state of perpetual equipoise whereas it is a well-known fact that the said sum total is constantly on the increase. I would therefore take the liberty of suggesting that in the next edition of your excellent poem the erroneous calculation to which I refer should be corrected as follows:
'Every moment dies a man / And one and a sixteenth is born.” I may add that the exact figures are 1.167, but something must, of course, be conceded to the laws of metre.
Unpublished letter to Tennyson in response to his Vision of Sin (1842). Quoted in Philip and Emily Morrison, Charles Babbage and his Calculating Engines: Selected Writings by Charles Babbage and Others (1961), xxiii.
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“Men die of the diseases which they have studied most,” remarked the surgeon, snipping off the end of a cigar with all his professional neatness and finish. “It’s as if the morbid condition was an evil creature which, when it found itself closely hunted, flew at the throat of its pursuer. If you worry the microbes too much they may worry you. I’ve seen cases of it, and not necessarily in microbic diseases either. There was, of course, the well-known instance of Liston and the aneurism; and a dozen others that I could mention.”
First lines of 'The Surgeon Talks', in Round the Red Lamp: Being Facts and Fancies of Medical Life (1894), 316.
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“Of course they answer to their names?” the Gnat remarked carelessly.
“I never knew them to do it,” [said Alice.]
“What’s the use of them having names,” said the Gnat, “if they won’t answer to them?”
“No use to them,” said Alice; “but it’s useful to the people that name them, I suppose.”
In Through the Looking Glass and What Alice Found There (1871, 1897), 55.
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“She can’t do Subtraction.” said the White Queen. “Can you do Division? Divide a loaf by a knife—what's the answer to that?”
“I suppose-” Alice was beginning, but the Red Queen answered for her.
“Bread-and-butter, of course.”
Through the Looking Glass and What Alice Found There (1871, 1897), 189-190.
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“Try another Subtraction sum. Take a bone from a dog: what remains?” [asked the Red Queen]
Alice considered. “The bone wouldn't remain, of course, if I took it—and the dog wouldn’t remain; it would come to bite me—and I’m sure I shouldn’t remain!”
“Then you think nothing would remain?” said the Red Queen.
“I think that’s the answer.”
“Wrong, as usual,” said the Red Queen, “the dog's temper would remain.”
Through the Looking Glass and What Alice Found There (1871, 1897), 190-191.
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[About research with big particle accelerators such as the Large Hadron Collider.] I think the primary justification for this sort of science that we do is fundamental human curiosity. ... It's true, of course, that every previous generation that's made some breakthrough in understanding nature has seen those discoveries translated into new technologies, new possibilities for the human race. That may well happen with the Higgs boson. Quite frankly, at the moment I don't see how you can use the Higgs boson for anything useful.
As quoted in Alan Boyle, 'Discovery of Doom? Collider Stirs Debate', article (8 Sep 2008) on a msnbc.com web page.
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[About the mechanical properties of the molecules of a chemical substance being studied:] They could be measured, but that would have taken several months. So someone said, ‘Let’s get Teller in and make him guess the data.’ We got him into a room and locked the door, so no one else could get at him, and he asked questions and did some figuring at the blackboard. He got the answers in about two hours, not entirely accurately, of course, but—as we found out when we got around to verifying them—close enough for the purpose.
Recalls the first time she was ever really awed by mental abilities of Edward Teller. She had joined the Manhattan Project, and needed data on the physical properties of molecules of a certain substance to get started on her assigned task of calculating its chemical properties. As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 61.
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[Alchemists] finde out men so covetous of so much happiness, whom they easily perswade that they shall finde greater Riches in Hydargyrie [mercury], than Nature affords in Gold. Such, whom although they have twice or thrice already been deluded, yet they have still a new Device wherewith to deceive um again; there being no greater Madness…. So that the smells of Coles, Sulphur, Dung, Poyson, and Piss, are to them a greater pleasure than the taste of Honey; till their Farms, Goods, and Patrimonies being wasted, and converted into Ashes and Smoak, when they expect the rewards of their Labours, births of Gold, Youth, and Immortality, after all their Time and Expences; at length, old, ragged, famisht, with the continual use of Quicksilver [mercury] paralytick, onely rich in misery, … a laughing-stock to the people: … compell’d to live in the lowest degree of poverty, and … at length compell’d thereto by Penury, they fall to Ill Courses, as Counterfeiting of Money.
In The Vanity of the Arts and Sciences (1530), translation (1676), 313.
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[Decimal currency is desirable because] by that means all calculations of interest, exchange, insurance, and the like are rendered much more simple and accurate, and, of course, more within the power of the great mass of people. Whenever such things require much labor, time, and reflection, the greater number who do not know, are made the dupes of the lesser number who do.
Letter to Congress (15 Jan 1782). 'Coinage Scheme Proposed by Robert Morris, Superintendent of Finance', from MS. letters and reports of the Superintendent of Finance, No, 137, Vol. 1, 289-300. Reprinted as Appendix, in Executive Documents, Senate of the U.S., Third Session of the Forty-Fifth Congress, 1878-79 (1879), 430.
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[I]magine you want to know the sex of your unborn child. There are several approaches. You could, for example, do what the late film star ... Cary Grant did before he was an actor: In a carnival or fair or consulting room, you suspend a watch or a plumb bob above the abdomen of the expectant mother; if it swings left-right it's a boy, and if it swings forward-back it's a girl. The method works one time in two. Of course he was out of there before the baby was born, so he never heard from customers who complained he got it wrong. ... But if you really want to know, then you go to amniocentesis, or to sonograms; and there your chance of being right is 99 out of 100. ... If you really want to know, you go to science.
In 'Wonder and Skepticism', Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.
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[J.J.] Sylvester’s methods! He had none. “Three lectures will be delivered on a New Universal Algebra,” he would say; then, “The course must be extended to twelve.” It did last all the rest of that year. The following year the course was to be Substitutions-Théorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. “I must give one lecture a week on those,” he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not unfrequent in his lectures: “I haven’t proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc.” At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then another and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 265-266.
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[To one of his students he saw in a school dramatic production:] I’ve always been proud that Course X leaves little time for outside activities. You have proved me wrong so far and I’m glad you have. But don’t push your luck too far!
As quoted in A Dollar to a Doughnut: The Doc Lewis Story (1953), 49, which was a privately printed collection of anecdotes published by former students upon his retirement. Note that “X” was the actual designation of his chemical engineering course at MIT. The boy was a Course X student who had played the leading “lady” in the previous MIT Tech Show. The anecdote continues: “A word to the wise was sufficient—the leading lady that year was not from Course X.”
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[William Gull] endeavoured, above all things, to study the natural history of disease, uncomplicated by the action of unnecessary drugs, and he resented all useless interference with the course of nature. He would say of meddlesome poly-pharmacy—“Fools rush in, where angels fear to tread.”
Stated in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xxv-xxvi.
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The Mighty Task is Done

At last the mighty task is done;
Resplendent in the western sun
The Bridge looms mountain high;
Its titan piers grip ocean floor,
Its great steel arms link shore with shore,
Its towers pierce the sky.

On its broad decks in rightful pride,
The world in swift parade shall ride,
Throughout all time to be;
Beneath, fleet ships from every port,
Vast landlocked bay, historic fort,
And dwarfing all the sea.

To north, the Redwood Empires gates;
To south, a happy playground waits,
In Rapturous appeal;
Here nature, free since time began,
Yields to the restless moods of man,
Accepts his bonds of steel.

Launched midst a thousand hopes and fears,
Damned by a thousand hostile sneers,
Yet Neer its course was stayed,
But ask of those who met the foe
Who stood alone when faith was low,
Ask them the price they paid.

Ask of the steel, each strut and wire,
Ask of the searching, purging fire,
That marked their natal hour;
Ask of the mind, the hand, the heart,
Ask of each single, stalwart part,
What gave it force and power.

An Honored cause and nobly fought
And that which they so bravely wrought,
Now glorifies their deed,
No selfish urge shall stain its life,
Nor envy, greed, intrigue, nor strife,
Nor false, ignoble creed.

High overhead its lights shall gleam,
Far, far below lifes restless stream,
Unceasingly shall flow;
For this was spun its lithe fine form,
To fear not war, nor time, nor storm,
For Fate had meant it so.

Written upon completion of the building of the Golden Gate Bridge, May 1937. In Allen Brown, Golden Gate: biography of a Bridge (1965), 229.
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[Criticizing as “appalingly complacent” a Conservative Government report that by the '60s, Britain would be producing all the scientists needed] Of course we shall, if we don't give science its proper place in our national life. We shall no doubt be training all the bullfighters we need, because we don't use many.
Address at the Imperial College of Science and Technology, London (28 Feb 1963). In 'Hailsham Chided on Science's Role', New York Times (1 Mar 1963), 2. Also in 'The Manhunters: British Minister Blames American Recruiters for Emigration of Scientists',Science Magazine (8 Mar 1963), 893.
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Copernicus, who rightly did condemn
This eldest systeme, form’d a wiser scheme;
In which he leaves the Sun at Rest, and rolls
The Orb Terrestial on its proper Poles;
Which makes the Night and Day by this Career,
And by its slow and crooked Course the Year.
The famous Dane, who oft the Modern guides,
To Earth and Sun their Provinces divides:
The Earth’s Rotation makes the Night and Day,
The Sun revolving through th’ Eccliptic Way
Effects the various seasons of the Year,
Which in their Turn for happy Ends appear.
This Scheme or that, which pleases best, embrace,
Still we the Fountain of their Motion trace.
Kepler asserts these Wonders may be done
By the Magnetic Vertue of the Sun,
Which he, to gain his End, thinks fit to place
Full in the Center of that mighty Space,
Which does the Spheres, where Planets roll, include,
And leaves him with Attractive Force endu’d.
The Sun, thus seated, by Mechanic Laws,
The Earth, and every distant Planet draws;
By which Attraction all the Planets found
Within his reach, are turn'd in Ether round.
In Creation: A Philosophical Poem in Seven Books (1712), book 2, l. 430-53, p.78-9.
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Der bis zur Vorrede, die ihn abweist, gelangte Leser hat das Buch für baares Geld gekauft und frägt, was ihn schadlos hält? – Meine letzte Zuflucht ist jetzt, ihn zu erinnern, daß er ein Buch, auch ohne es gerade zu lesen, doch auf mancherlei Art zu benutzen weiß. Es kann, so gut wie viele andere, eine Lücke seiner Bibliothek ausfüllen, wo es sich, sauber gebunden, gewiß gut ausnehmen wird. Oder auch er kann es seiner gelehrten Freundin auf die Toilette, oder den Theetisch legen. Oder endlich er kann ja, was gewiß das Beste von Allem ist und ich besonders rathe, es recensiren.
The reader who has got as far as the preface and is put off by that, has paid money for the book, and wants to know how he is to be compensated. My last refuge now is to remind him that he knows of various ways of using a book without precisely reading it. It can, like many another, fill a gap in his library, where, neatly bound, it is sure to look well. Or he can lay it on the dressing-table or tea-table of his learned lady friend. Or finally he can review it; this is assuredly the best course of all, and the one I specially advise.
In Preface, written at Dresden in August 1818, first German edition, Die Welt als Wille und Vorstellung, 4 Bücher nebst einem Anhange der die Kritik der Kentischen Philosophie (1819), xv-xvi. As translated by E.F.J. Payne in The World as Will and Representation (1958, 1969), Vol. 1, xvii. In the preface, Schopenhauer is joking that some readers of his book may find his work does not interest them.
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Le savant n’étudie pas la nature parce que cela est utile; il l’étudie parce qu’il y prend plaisir et il y prend plaisir parce qu’elle est belle. Si la nature n’était pas belle, elle ne vaudrait pas la peine d’être connue, la vie ne vaudrait pas la peine d’être vécue.
The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.
In Science et Méthode (1920), 48, as translated by Francis Maitland, in Science and Method (1908, 1952), 15.
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The Annotated Alice, of course, does tie in with math, because Lewis Carroll was, as you know, a professional mathematician. So it wasn’t really too far afield from recreational math, because the two books are filled with all kinds of mathematical jokes. I was lucky there in that I really didn’t have anything new to say in The Annotated Alice because I just looked over the literature and pulled together everything in the form of footnotes. But it was a lucky idea because that’s been the best seller of all my books.
In Anthony Barcellos, 'A Conversation with Martin Gardner', The Two-Year College Mathematics Journal (Sep 1979), 10, No. 4, 241.
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A general course in mathematics should be required of all officers for its practical value, but no less for its educational value in training the mind to logical forms of thought, in developing the sense of absolute truthfulness, together with a confidence in the accomplishment of definite results by definite means.
In 'Mathematics at West Point and Annapolis', United States Bureau of Education, Bulletin 1912, No. 2, 11.
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A bird maintains itself in the air by imperceptible balancing, when near to the mountains or lofty ocean crags; it does this by means of the curves of the winds which as they strike against these projections, being forced to preserve their first impetus bend their straight course towards the sky with divers revolutions, at the beginning of which the birds come to a stop with their wings open, receiving underneath themselves the continual buffetings of the reflex courses of the winds.
'Flight', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938), Vol. 1, 471.
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A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.
In 'On the Development of the Methods of Theoretical Physics in Recent Times', Populäre Schriften, Essay 14. Address (22 Sep 1899) to the Meeting of Natural Scientists at Munich. Collected in Brian McGuinness (ed.), Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, Selected Writings (1974), 79.
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A great deal of the universe does not need any explanation. Elephants, for instance. Once molecules have learnt to compete and to create other molecules in their own image, elephants, and things resembling elephants, will in due course be found roaming around the countryside ... Some of the things resembling elephants will be men.
The Creation (1981), 3.
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A machine is not a genie, it does not work by magic, it does not possess a will, and … nothing comes out which has not been put in, barring of course, an infrequent case of malfunctioning. … The “intentions” which the machine seems to manifest are the intentions of the human programmer, as specified in advance, or they are subsidiary intentions derived from these, following rules specified by the programmer. … The machine will not and cannot do any of these things until it has been instructed as to how to proceed. ... To believe otherwise is either to believe in magic or to believe that the existence of man’s will is an illusion and that man’s actions are as mechanical as the machine’s.
In Science, September 16, 1960.
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A Miracle is a Violation of the Laws of Nature; and as a firm and unalterable Experience has established these Laws, the Proof against a Miracle, from the very Nature of the Fact, is as entire as any Argument from Experience can possibly be imagined. Why is it more than probable, that all Men must die; that Lead cannot, of itself, remain suspended in the Air; that Fire consumes Wood, and is extinguished by Water; unless it be, that these Events are found agreeable to the Laws of Nature, and there is required a Violation of these Laws, or in other Words, a Miracle to prevent them? Nothing is esteem'd a Miracle, if it ever happen in the common Course of Nature... There must, therefore, be a uniform Experience against every miraculous Event, otherwise the Event would not merit that Appellation. And as a uniform Experience amounts to a Proof, there is here a direct and full Proof, from the Nature of the Fact, against the Existence of any Miracle; nor can such a Proof be destroy'd, or the Miracle render'd credible, but by an opposite Proof, which is superior.
An Enquiry Concerning Human Understanding (1748), 180-181.
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A 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.
'New Colour Variety of the Guinea Pig', Science, 1908, 28, 250-252.
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A myth is, of course, not a fairy story. It is the presentation of facts belonging to one category in the idioms appropriate to another. To explode a myth is accordingly not to deny the facts but to re-allocate them.
In The Concept of Mind (1949), 8.
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A noteworthy and often-remarked similarity exists between the facts and methods of geology and those of linguistic study. The science of language is, as it were, the geology of the most modern period, the Age of the Man, having for its task to construct the history of development of the earth and its inhabitants from the time when the proper geological record remains silent … The remains of ancient speech are like strata deposited in bygone ages, telling of the forms of life then existing, and of the circumstances which determined or affected them; while words are as rolled pebbles, relics of yet more ancient formations, or as fossils, whose grade indicates the progress of organic life, and whose resemblances and relations show the correspondence or sequence of the different strata; while, everywhere, extensive denudation has marred the completeness of the record, and rendered impossible a detailed exhibition of the whole course of development.
In Language and the Study of Language (1867), 47.
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A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 140-141.
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A single ray of light from a distant star falling upon the eye of a tyrant in bygone times, may have altered the course of his life, may have changed the destiny of nations, may have transformed the surface of the globe, so intricate, so inconceivably complex are the processes of nature.
Lecture (Feb 1893) delivered before the Franklin Institute, Philadelphia, 'On Light and Other High Frequency Phenomena,' collected in Thomas Commerford Martin and Nikola Tesla, The Inventions, Researches and Writings of Nikola Tesla (1894), 298.
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A strict materialist believes that everything depends on the motion of matter. He knows the form of the laws of motion though he does not know all their consequences when applied to systems of unknown complexity.
Now one thing in which the materialist (fortified with dynamical knowledge) believes is that if every motion great & small were accurately reversed, and the world left to itself again, everything would happen backwards the fresh water would collect out of the sea and run up the rivers and finally fly up to the clouds in drops which would extract heat from the air and evaporate and afterwards in condensing would shoot out rays of light to the sun and so on. Of course all living things would regrede from the grave to the cradle and we should have a memory of the future but not of the past.
The reason why we do not expect anything of this kind to take place at any time is our experience of irreversible processes, all of one kind, and this leads to the doctrine of a beginning & an end instead of cyclical progression for ever.
Letter to Mark Pattison (7 Apr 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 360-1.
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A visitor to Niels Bohr's country cottage, noticing a horseshoe hanging on the wall, teasing the eminent scientist about this ancient superstition. “Can it be true that you, of all people, believe it will bring you luck?'
'Of course not,' replied Bohr, 'but I understand it brings you luck whether you believe it or not.'”
As described in Clifton Fadiman (ed.), André Bernard (ed.), Bartlett's Book of Anecdotes (2000), 68.
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Admit for a moment, as a hypothesis, that the Creator had before his mind a projection of the whole life-history of the globe, commencing with any point which the geologist may imagine to have been a fit commencing point, and ending with some unimaginable acme in the indefinitely distant future. He determines to call this idea into actual existence, not at the supposed commencing point, but at some stage or other of its course. It is clear, then, that at the selected stage it appears, exactly as it would have appeared at that moment of its history, if all the preceding eras of its history had been real.
Omphalos: An Attempt to Untie the Geological Knot (1857), 351.
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After having produced aquatic animals of all ranks and having caused extensive variations in them by the different environments provided by the waters, nature led them little by little to the habit of living in the air, first by the water's edge and afterwards on all the dry parts of the globe. These animals have in course of time been profoundly altered by such novel conditions; which so greatly influenced their habits and organs that the regular gradation which they should have exhibited in complexity of organisation is often scarcely recognisable.
Hydrogéologie (1802), trans. A. V. Carozzi (1964), 69-70.
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Again there is another great and powerful cause why the sciences have made but little progress; which is this. It is not possible to run a course aright when the goal itself has not been rightly placed.
Translation of Novum Organum, LXXXI. In Francis Bacon, James Spedding, The Works of Francis Bacon (1864), Vol. 8, 113.
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Against filling the Heavens with fluid Mediums, unless they be exceeding rare, a great Objection arises from the regular and very lasting Motions of the Planets and Comets in all manner of Courses through the Heavens.
From Opticks: Or, A Treatise of the Reflections, Refractions, Inflections and Colours of Light (1718), 339.
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All disease, at some period or other of its course, is more or less a reparative process, not necessarily accompanied with suffering: an effort of nature to remedy a process of poisoning or of decay, which has taken place weeks, months, sometimes years beforehand, unnoticed.
In Notes on Nursing: What It Is and What It Is Not (1859), 5.
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All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions.
In 'Report of the Secretary', Sixth Annual Report of the Board of Regents of the Smithsonian Institution for 1851 (1852), 10.
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All of us are interested in our roots. Generally this interest is latent in youth, and grows with age. Until I reached fifty I thought that history of science was a refuge for old scientists whose creative juices had dried up. Now of course I know that I was wrong! As we grow older, we become more interested in the past, in family history, local history, etc. Astronomy is, or was when I started in it, almost a family.
In Organizations and Strategies in Astronomy (2002), Vol. 3, 206.
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All palaetiological sciences, all speculations which attempt to ascend from the present to the remote past, by the chain of causation, do also, by an inevitable consequence, urge us to look for the beginning of the state of things which we thus contemplate; but in none of these cases have men been able, by the aid of science, to arrive at a beginning which is homogeneous with the known course of events. The first origin of language, of civilization, of law and government, cannot be clearly made out by reasoning and research; and just as little, we may expect, will a knowledge of the origin of the existing and extinct species of plants and animals, be the result of physiological and geological investigation.
In History of the Inductive Sciences (1837), Vol. 3, 581.
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All the fifty years of conscious brooding have brought me no closer to answer the question, “What are light quanta?” Of course today every rascal thinks he knows the answer, but he is deluding himself.
(1951). Quoted in Raymond W. Lam, Seasonal Affective Disorder and Beyond (1998), 1.
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All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.
In Lectures on the Logic of Arithmetic (1903), Preface, 18-19.
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Although I was four years at the University [of Wisconsin], I did not take the regular course of studies, but instead picked out what I thought would be most useful to me, particularly chemistry, which opened a new world, mathematics and physics, a little Greek and Latin, botany and and geology. I was far from satisfied with what I had learned, and should have stayed longer.
[Enrolled in Feb 1861, left in 1863 without completing a degree, and began his first botanical foot journey.]
John Muir
The Story of My Boyhood and Youth (1913), 286.
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Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of seconds necessary for the boiling of an egg, he perceived, after waiting a minute, that he held the egg in his hand, and had placed his seconds watch (an instrument of great value on account of its mathematical precision) to boil!
This absence of mind reminds one of the mathematician Ampere, who one day, as he was going to his course of lectures, noticed a little pebble on the road; he picked it up, and examined with admiration the mottled veins. All at once the lecture which he ought to be attending to returned to his mind; he drew out his watch; perceiving that the hour approached, he hastily doubled his pace, carefully placed the pebble in his pocket, and threw his watch over the parapet of the Pont des Arts.
Popular Astronomy: a General Description of the Heavens (1884), translated by J. Ellard Gore, (1907), 93.
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And do you know what “the world” is to me? Shall I show it to you in my mirror? This world: a monster of energy, without beginning, without end; a firm, iron magnitude of force that does not grow bigger or smaller, that does not expend itself but only transforms itself; as a whole, of unalterable size, a household without expenses or losses, but likewise without increase or income; enclosed by “nothingness”' as by a boundary; not by something blurry or wasted, not something endlessly extended, but set in a definite space as a definite force, and not a space that might be “empty” here or there, but rather as force throughout, as a play of forces and waves of forces, at the same time one and many, increasing here and at the same time decreasing there; a sea of forces flowing and rushing together, eternally changing, eternally flooding back, with tremendous years of recurrence, with an ebb and a flood of its forms; out of the simplest forms striving toward the most complex, out of the stillest, most rigid, coldest forms toward the hottest, most turbulent, most self-contradictory, and then again returning home to the simple out of this abundance, out of the play of contradictions back to the joy of concord, still affirming itself in this uniformity of its courses and its years, blessing itself as that which must return eternally, as a becoming that knows no satiety, no disgust, no weariness: this, my Dionysian world of the eternally self-creating, the eternally self-destroying, this mystery world of the twofold voluptuous delight, my “beyond good and evil,” without goal, unless the joy of the circle itself is a goal; without will, unless a ring feels good will toward itself-do you want a name for this world? A solution for all its riddles? A light for you, too, you best-concealed, strongest, most intrepid, most midnightly men?—This world is the will to power—and nothing besides! And you yourselves are also this will to power—and nothing besides!
The Will to Power (Notes written 1883-1888), book 4, no. 1067. Trans. W. Kaufmann and R. J. Hollingdale and ed. W. Kaufmann (1968), 549-50.
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And having thus passed the principles of arithmetic, geometry, astronomy, and geography, with a general compact of physics, they may descend in mathematics to the instrumental science of trigonometry, and from thence to fortification, architecture, engineering, or navigation. And in natural philosophy they may proceed leisurely from the history of meteors, minerals, plants, and living creatures, as far as anatomy. Then also in course might be read to them out of some not tedious writer the institution of physic. … To set forward all these proceedings in nature and mathematics, what hinders but that they may procure, as oft as shall be needful, the helpful experiences of hunters, fowlers, fishermen, shepherds, gardeners, apothecaries; and in other sciences, architects, engineers, mariners, anatomists.
In John Milton and Robert Fletcher (ed.), 'On Education', The Prose Works of John Milton: With an Introductory Review (1834), 100.
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Anyone who considers arithmetical methods of producing random digits is, of course, in the state of sin. For, as has been pointed out several times, there is no such thing as a random number—there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
In paper delivered at a symposium on the Monte Carlo method. 'Various Techniques Used in Connection with Random Digits', Journal of Research of the National Bureau of Standards, Appl. Math. Series, Vol. 3 (1951), 3, 36. Reprinted in John von Neumann: Collected Works (1963), Vol. 5, 700. Also often seen misquoted (?) as “Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.”
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As long as museums and universities send out expeditions to bring to light new forms of living and extinct animals and new data illustrating the interrelations of organisms and their environments, as long as anatomists desire a broad comparative basis human for anatomy, as long as even a few students feel a strong curiosity to learn about the course of evolution and relationships of animals, the old problems of taxonomy, phylogeny and evolution will gradually reassert themselves even in competition with brilliant and highly fruitful laboratory studies in cytology, genetics and physiological chemistry.
'Genetics Versus Paleontology', The American Naturalist, 1917, 51, 623.
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As soon as we got rid of the backroom attitude and brought our apparatus fully into the Department with an inexhaustible supply of living patients with fascinating clinical problems, we were able to get ahead really fast. Any new technique becomes more attractive if its clinical usefulness can be demonstrated without harm, indignity or discomfort to the patient... Anyone who is satisfied with his diagnostic ability and with his surgical results is unlikely to contribute much to the launching of a new medical science. He should first be consumed with a divine discontent with things as they are. It greatly helps, of course, to have the right idea at the right time, and quite good ideas may come, Archimedes fashion, in one's bath..
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As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer. But Euclid for children is barbarous.
Electro-Magnetic Theory (1893), Vol. 1, 148. In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 130.
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At the present time it is of course quite customary for physicists to trespass on chemical ground, for mathematicians to do excellent work in physics, and for physicists to develop new mathematical procedures. … Trespassing is one of the most successful techniques in science.
In Dynamics in Psychology (1940, 1973), 116.
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At this point, however, I have no intention whatever of criticizing the false teachings of Galen, who is easily first among the professors of dissection, for I certainly do not wish to start off by gaining a reputation for impiety toward him, the author of all good things, or by seeming insubordinate to his authority. For I am well aware how upset the practitioners (unlike the followers of Aristotle) invariably become nowadays, when they discover in the course of a single dissection that Galen has departed on two hundred or more occasions from the true description of the harmony, function, and action of the human parts, and how grimly they examine the dissected portions as they strive with all the zeal at their command to defend him. Yet even they, drawn by their love of truth, are gradually calming down and placing more faith in their own not ineffective eyes and reason than in Galen’s writings.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, iv, as translated by William Frank Richardson, in On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), Preface, liv.
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Bearing in mind that it is from the vitality of the atmospheric particles that all the mischief arises, it appears that all that is requisite is to dress the wound with some material capable of killing these septic germs, provided that any substance can be found reliable for this purpose, yet not too potent as a caustic. In the course of the year 1864 I was much struck with an account of the remarkable effects produced by carbolic acid upon the sewage of the town of Carlisle, the admixture of a very small proportion not only preventing all odour from the lands irrigated with the refuse material, but, as it was stated, destroying the entozoa which usually infest cattle fed upon such pastures.
'On a New Method of Treating Compound Fracture, Abscesses, etc: With Observations on the Conditions of Supperation', Part 1, The Lancet (1867), 327.
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Because the region of the Celestial World is of so great and such incredible magnitude as aforesaid, and since in what has gone before it was at least generally demonstrated that this comet continued within the limits of the space of the Aether, it seems that the complete explanation of the whole matter is not given unless we are also informed within narrower limits in what part of the widest Aether, and next to which orbs of the Planets [the comet] traces its path, and by what course it accomplishes this.
De Mundi Aetherei Recentioribus Phaenomenis (On Recent Phenomena in the Aetherial World) (1588). Quoted in M. Boas Hall, The Scientific Renaissance 1450-1630 (1962), 115.
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Because words pass away as soon as they strike upon the air, and last no longer than their sound, men have by means of letters formed signs of words. Thus the sounds of the voice are made visible to the eye, not of course as sounds, but by means of certain signs.
In 'Origin of Writing', Christian Doctrine, Book 2, as translated by J.F. Shaw, collected in A Select Library of the Nicene and Post-Nicene Fathers of the Christian Church: Volume II: St. Augustin’s City of God and Christian Doctrine (1907), 536.
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Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit.
'The Meaning and Limits of Exact Science', Science (30 Sep 1949), 110, No. 2857, 325. Advance reprinting of chapter from book Max Planck, Scientific Autobiography (1949), 110.
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Before his [Sir Astley Cooper’s] time, operations were too often frightful alternatives or hazardous compromises; and they were not seldom considered rather as the resource of despair than as a means of remedy; he always made them follow, as it were, in the natural course of treatment; he gave them a scientific character; and he moreover, succeeded, in a great degree, in divesting them of their terrors, by performing them unostentatiously, simply, confidently, and cheerfully, and thereby inspiring the patient with hope of relief, where previously resignation under misfortune had too often been all that could be expected from the sufferer.
In John Forbes (ed.), British and Foreign Medical Review (Jul 1840), 10, No. 19, 104. In Bransby Blake Cooper, The Life of Sir Astley Cooper (1843), Vol. 2, 37.
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Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611. [The French phrase, à peu près means “approximately”. —Webmaster]
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But … the working scientist … is not consciously following any prescribed course of action, but feels complete freedom to utilize any method or device whatever which in the particular situation before him seems likely to yield the correct answer. … No one standing on the outside can predict what the individual scientist will do or what method he will follow.
In Reflections of a Physicist: A Collection of Essays (1955, 1980), 83.
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But nothing of a nature foreign to the duties of my profession [clergyman] engaged my attention while I was at Leeds so much as the, prosecution of my experiments relating to electricity, and especially the doctrine of air. The last I was led into a consequence of inhabiting a house adjoining to a public brewery, where first amused myself with making experiments on fixed air [carbon dioxide] which found ready made in the process of fermentation. When I removed from that house, I was under the necessity making the fixed air for myself; and one experiment leading to another, as I have distinctly and faithfully noted in my various publications on the subject, I by degrees contrived a convenient apparatus for the purpose, but of the cheapest kind. When I began these experiments I knew very little of chemistry, and had in a manner no idea on the subject before I attended a course of chymical lectures delivered in the Academy at Warrington by Dr. Turner of Liverpool. But I have often thought that upon the whole, this circumstance was no disadvantage to me; as in this situation I was led to devise an apparatus and processes of my own, adapted to my peculiar views. Whereas, if I had been previously accustomed to the usual chemical processes, I should not have so easily thought of any other; and without new modes of operation I should hardly have discovered anything materially new.
Memoirs of Dr. Joseph Priestley, in the Year 1795 (1806), Vol. 1, 61-2.
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But the whole vital process of the earth takes place so gradually and in periods of time which are so immense compared with the length of our life, that these changes are not observed, and before their course can be recorded from beginning to end whole nations perish and are destroyed.
Aristotle
Meteorology, 351b, 8-13. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 573.
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But the World being once fram’d, and the course of Nature establish’d, the Naturalist, (except in some few cases, where God, or Incorporeal Agents interpose), has recourse to the first Cause but for its general and ordinary Support and Influence, whereby it preserves Matter and Motion from Annihilation or Desition; and in explicating particular phenomena, considers onely the Size, Shape, Motion, (or want of it) Texture, and the resulting Qualities and Attributes of the small particles of Matter.
The Origine of Formes and Qualities (1666), 194.
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By the death of Mr. O. Chanute the world has lost one whose labors had to an unusual degree influenced the course of human progress. If he had not lived the entire history of progress in flying would have been other than it has been.
Writing in Aeronautics in Jan 1911 about Chanute's death, collected in Wilbur Wright and Orville Wright, The Papers of Wilbur and Orville Wright: Volume Two 1906-1948 (1953), 1013.
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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).
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Children are told that an apple fell on Isaac Newton’s head and he was led to state the law of gravity. This, of course, is pure foolishness. What Newton discovered was that any two particles in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This is not learned from a falling apple, but by observing quantities of data and developing a mathematical theory that can be verified by additional data. Data gathered by Galileo on falling bodies and by Johannes Kepler on motions of the planets were invaluable aids to Newton. Unfortunately, such false impressions about science are not universally outgrown like the Santa Claus myth, and some people who don’t study much science go to their graves thinking that the human race took until the mid-seventeenth century to notice that objects fall.
In How to Tell the Liars from the Statisticians (1983), 127.
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Clearly it is not reason that has failed. What has failed—as it has always failed—is the attempt to achieve certainty, to reach an absolute, to find the course of human events to a final end. ... It is not reason that has promised to eliminate risk in human undertakings; it is the emotional needs of men.
In The Quest For Identity (1958), 135.
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Consciously and systematically Klein sought to enthrall me with the problems of mathematical physics, and to win me over to his conception of these problems as developed it in lecture courses in previous years. I have always regarded Klein as my real teacher only in things mathematical, but also in mathematical physics and in my conception of mechanics.
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 526. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
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Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.
Science and Method (1908), trans. Francis Maitland (1914), 254-5.
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Constant, or free, life is the third form of life; it belongs to the most highly organized animals. In it, life is not suspended in any circumstance, it unrolls along a constant course, apparently indifferent to the variations in the cosmic environment, or to the changes in the material conditions that surround the animal. Organs, apparatus, and tissues function in an apparently uniform manner, without their activity undergoing those considerable variations exhibited by animals with an oscillating life. This because in reality the internal environment that envelops the organs, the tissues, and the elements of the tissues does not change; the variations in the atmosphere stop there, so that it is true to say that physical conditions of the environment are constant in the higher animals; it is enveloped in an invariable medium, which acts as an atmosphere of its own in the constantly changing cosmic environment. It is an organism that has placed itself in a hot-house. Thus the perpetual changes in the cosmic environment do not touch it; it is not chained to them, it is free and independent.
Lectures on the Phenomena of Life Common to Animals and Plants (1878), trans. Hebbel E. Hoff, Roger Guillemin and Lucienne Guillemin (1974), 83.
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Contingency is rich and fascinating; it embodies an exquisite tension between the power of individuals to modify history and the intelligible limits set by laws of nature. The details of individual and species’s lives are not mere frills, without power to shape the large-scale course of events, but particulars that can alter entire futures, profoundly and forever.
Reprinted from column, 'This View of Life',Natural History magazine, in Eight Little Piggies (1993), 77.
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Darwin’s book is very important and serves me as a basis in natural science for the class struggle in history. One has to put up with the crude English method of development, of course. Despite all deficiencies not only is the death-blow dealt here for the first time to “teleology” in the natural sciences, but their rational meaning is empirically explained.
Karl Marx
Marx to Lasalle, 16 Jan 1861. In Marx-Engels Selected Correspondence, 1846-95, trans. Donna Torr (1934), 125.
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Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”
In article 'Mathematics', Encyclopedia Britannica (1911, 11th ed.), Vol. 17, 880. In the 2006 DVD edition of the encyclopedia, the definition of mathematics is given as “The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects.” [Premiss is a variant form of “premise”. —Webmaster]
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Differences between individuals are the raw materials for evolutionary change and for the evolution of adaptations, yet of course most physiologists treat these differences as noise that is to be filtered out. From the standpoint of physiological ecology, the traditional emphasis of physiologists on central tendencies rather than on variance has some unhappy consequences. Variation is not just noise; it is also the stuff of evolution and a central attribute of living systems. The physiological differences between individuals in the same species or population, and also the patterns of variation in different groups, must not be ignored.
From 'Interspecific comparison as a tool for ecological physiologists', collected in M.E. Feder, A.F. Bennett, W.W. Burggren, and R.B. Huey, (eds.), New Directions in Ecological Physiology (1987), 32-33,
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Discoveries are always accidental; and the great use of science is by investigating the nature of the effects produced by any process or contrivance, and of the causes by which they are brought about, to explain the operation and determine the precise value of every new invention. This fixes as it were the latitude and longitude of each discovery, and enables us to place it in that part of the map of human knowledge which it ought to occupy. It likewise enables us to use it in taking bearings and distances, and in shaping our course when we go in search of new discoveries.
In The Complete Works of Count Rumford (1876), Vol. 4, 270.
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Doubly galling was the fact that at the same time my roommate was taking a history course … filled with excitement over a class discussion. … I was busy with Ampere’s law. We never had any fascinating class discussions about this law. No one, teacher or student, ever asked me what I thought about it.
In Understanding the Universe: An Inquiry Approach to Astronomy and the Nature of Scientific Research (2013), ix.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Dr. Paget was conducting a school examination, and in the course of his questions he happened to ask a small child the meaning of “Average.” He was utterly bewildered by the reply, “The thing that hens lay on,” until the child explained that he had read in a book that hens lay on an average so many eggs a year.
Anecdote jotted down by Lewis Carroll to possibly send to the magazine Punch, as given in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 157.
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During Alfvén's visit he gave a lecture at the University of Chicago, which was attended by [Enrico] Fermi. As Alfvén described his work, Fermi nodded his head and said, 'Of course.' The next day the entire world of physics said. 'Oh, of course.'
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988), 195.
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Each new scientific development is due to the pressure of some social need. Of course … insatiable curiosity … is still nothing but a response either to an old problem of nature, or to one arising from new social circumstances.
In 'The Teaching of the History of Science', The Scientific Monthly (Sep 1918), 194.
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Energy is the measure of that which passes from one atom to another in the course of their transformations. A unifying power, then, but also, because the atom appears to become enriched or exhausted in the course of the exchange, the expression of structure.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 42. Originally published in French as Le Phénomene Humain (1955).
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Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.
Vitruvius
In De Architectura, Book 1, Chap 6, Sec. 9. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 27-28.
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Every complete set of chromosomes contains the full code; so there are, as a rule, two copies of the latter in the fertilized egg cell, which forms the earliest stage of the future individual. In calling the structure of the chromosome fibres a code-script we mean that the all-penetrating mind, once conceived by Laplace, to which every causal connection lay immediately open, could tell from their structure whether the egg would develop, under suitable conditions, into a black cock or into a speckled hen, into a fly or a maize plant, a rhododendron, a beetle, a mouse or a woman. To which we may add, that the appearances of the egg cells are very often remarkably similar; and even when they are not, as in the case of the comparatively gigantic eggs of birds and reptiles, the difference is not so much in the relevant structures as in the nutritive material which in these cases is added for obvious reasons.
But the term code-script is, of course, too narrow. The chromosome structures are at the same time instrumental in bringing about the development they foreshadow. They are law-code and executive power?or, to use another simile, they are architect's plan and builder’s craft-in one.
In What is Life? : The Physical Aspect of the Living Cell (1944), 20-21.
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Every great advance in science has issued from a new audacity of imagination. What are now working conceptions, employed as a matter of course because they have withstood the tests of experiment and have emerged triumphant, were once speculative hypotheses.
'The Copernican Revolution', in The Quest for Certainty: A Study of the Relation of Knowledge and Action (1929), 294. Collected in John Dewey. Volume 4: The Later Works, 1925-1953: 1929 The Quest for Certainty (1984), 247. The first sentence is used as the motto of The Bronx High School of Science, New York.
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Everything that we call Invention or Discovery in the higher sense of the word is the serious exercise and activity of an original feeling for truth, which, after a long course of silent cultivation, suddenly flashes out into fruitful knowledge.
In The Maxims and Reflections of Goethe (1906), 193.
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Evolution is an obstacle course not a freeway; the correct analogue for long-term success is a distant punt receiver evading legions of would-be tacklers in an oddly zigzagged path toward a goal, not a horse thundering down the flat.
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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.
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Finally I got to carbon, and as you all know, in the case of carbon the reaction works out beautifully. One goes through six reactions, and at the end one comes back to carbon. In the process one has made four hydrogen atoms into one of helium. The theory, of course, was not made on the railway train from Washington to Ithaca … It didn’t take very long, it took about six weeks, but not even the Trans-Siberian railroad [has] taken that long for its journey.
'Pleasure from Physics', From A Life of Physics: Evening Lectures at the International Centre for Theoretical Physics, Trieste, Italy. A Special Supplement of the IAEA Bulletin (1968), 14.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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For a modern ruler the laws of conservation and transformation of energy, when the vivifing stream takes its source, the ways it wends its course in nature, and how, under wisdom and knowledge, it may be intertwined with human destiny, instead of careering headlong to the ocean, are a study at least as pregnant with consequences to life as any lesson taught by the long unscientific history of man.
Science and Life (1920), 5.
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For if as scientists we seek simplicity, then obviously we try the simplest surviving theory first, and retreat from it only when it proves false. Not this course, but any other, requires explanation. If you want to go somewhere quickly, and several alternate routes are equally likely to be open, no one asks why you take the shortest. The simplest theory is to be chosen not because it is the most likely to be true but because it is scientifically the most rewarding among equally likely alternatives. We aim at simplicity and hope for truth.
Problems and Projects (1972), 352.
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For the most part we humans live with the false impression of security and a feeling of being at home in a seemingly trustworthy physical and human environment. But when the expected course of everyday life is interrupted, we are like shipwrecked people on a miserable plank in the open sea, having forgotten where they came from and not knowing whither they are drifting. But once we fully accept this, life becomes easier and there is no longer any disappointment.
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Former arbiters of taste must have felt (as so many apostles of ‘traditional values’ and other highminded tags for restriction and conformity do today) that maintaining the social order required a concept of unalloyed heroism. Human beings so designated as role models had to embody all virtues of the paragon–which meant, of course, that they could not be described in their truly human and ineluctably faulted form.
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Formerly one sought the feeling of the grandeur of man by pointing to his divine origin: this has now become a forbidden way, for at its portal stands the ape, together with other gruesome beasts, grinning knowingly as if to say: no further in this direction! One therefore now tries the opposite direction: the way mankind is going shall serve as proof of his grandeur and kinship with God. Alas this, too, is vain! At the end of this way stands the funeral urn of the last man and gravedigger (with the inscription “nihil humani a me alienum puto”). However high mankind may have evolved—and perhaps at the end it will stand even lower than at the beginning!— it cannot pass over into a higher order, as little as the ant and the earwig can at the end of its “earthly course” rise up to kinship with God and eternal life. The becoming drags the has-been along behind it: why should an exception to this eternal spectacle be made on behalf of some little star or for any little species upon it! Away with such sentimentalities!
Daybreak: Thoughts on the Prejudices of Morality (1881), trans. R. J. Hollingdale (1982), 32.
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From astronomy we find the east, west, south, and north, as well as the theory of the heavens, the equinox, solstice, and courses of the stars. If one has no knowledge of these matters, he will not be able to have any comprehension of the theory of sundials.
Vitruvius
In De Architectura, Book 1, Chap 1, Sec. 10. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 10.
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Furthermore, it’s equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today's organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it’s inconceivable, how any kind of description of the latter, complex organism could have existed in the earlier one. It’s not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produce, something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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Groups do not have experiences except insofar as all their members do. And there are no experiences... that all the members of a scientific community must share in the course of a [scientific] revolution. Revolutions should be described not in terms of group experience but in terms of the varied experiences of individual group members. Indeed, that variety itself turns out to play an essential role in the evolution of scientific knowledge.
Thomas S. Kuhn's Foreword to Paul Hoyningen-Huene, Reconstructing Scientific Revolutions: Thomas S Kuhn's Philosophy of Science (1993), xiii.
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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.
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He [Winston Churchill] is rather like a layer cake. One layer was certainly seventeenth century. The eighteenth century in him is obvious. There was the nineteenth century, and a large slice, of course, of the twentieth century; and another, curious, layer which may possibly have been the twenty-first.
As quoted in Peter Stansky, Churchill: A Profile (1973), 197.
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How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.
Max Planck, Walter Henry Johnston, The Universe in the Light of Modern Physics (1931), 58.
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How many and how curious problems concern the commonest of the sea-snails creeping over the wet sea-weed! In how many points of view may its history be considered! There are its origin and development, the mystery of its generation, the phenomena of its growth, all concerning each apparently insignificant individual; there is the history of the species, the value of its distinctive marks, the features which link it with the higher and lower creatures, the reason why it takes its stand where we place it in the scale of creation, the course of its distribution, the causes of its diffusion, its antiquity or novelty, the mystery (deepest of mysteries) of its first appearance, the changes of the outline of continents and of oceans which have taken place since its advent, and their influence on its own wanderings.
On the Natural History of European Seas. In George Wilson and Archibald Geikie, Memoir of Edward Forbes F.R.S. (1861), 547-8.
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How to start on my adventure—how to become a forester—was not so simple. There were no schools of Forestry in America. … Whoever turned his mind toward Forestry in those days thought little about the forest itself and more about its influences, and about its influence on rainfall first of all. So I took a course in meteorology, which has to do with weather and climate. and another in botany, which has to do with the vegetable kingdom—trees are unquestionably vegetable. And another in geology, for forests grow out of the earth. Also I took a course in astronomy, for it is the sun which makes trees grow. All of which is as it should be, because science underlies the forester’s knowledge of the woods. So far I was headed right. But as for Forestry itself, there wasn’t even a suspicion of it at Yale. The time for teaching Forestry as a profession was years away.
In Breaking New Ground (1947, 1998), 3.
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Humanity, in the course of time, had to endure from the hands of science two great outrages against its naive self-love. The first was when humanity discovered that our earth was not the center of the universe…. The second occurred when biological research robbed man of his apparent superiority under special creation, and rebuked him with his descent from the animal kingdom, and his ineradicable animal nature.
From a series of 28 lectures for laymen, Part Three, 'General Theory of the Neurons', Lecture 18, 'Traumatic Fixation—the Unconscious' collected in Sigmund Freud and G. Stanley Hall (trans.), A General Introduction to Psychoanalysis (1920), 246-247.
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I advise my students to listen carefully the moment they decide to take no more Mathematics courses. They might be able to hear the sound of closing doors.
From 'Everybody a Mathematician', CAIP Quarterly (Fall 1989), 2, as quoted and cited, as a space filler following article Reinhard C. Laubenbacher and Michael Siddoway, 'Great Problems of Mathematics: A Summer Workshop for High School Students', The College Mathematics Journal (Mar 1994), 25, No. 2, 114.
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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.
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I am trying to get the hang of this new fangled writing machine, but I am not making a shining success of it. However, this is the first attempt I have ever made & yet I perceive I shall soon & easily acquire a fine facility in its use. … The machine has several virtues. I believe it will print faster than I can write. One may lean back in his chair & work it. It piles an awful stack of words on one page. It don't muss things or scatter ink blots around. Of course it saves paper.
Letter (9 Dec 1874). Quoted in B. Blivens, Jr., The Wonderful Writing Machine (1954), 61.
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I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems.
Autobiography in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 115.
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I ask any one who has adopted the calling of an engineer, how much time he lost when he left school, because he had to devote himself to pursuits which were absolutely novel and strange, and of which he had not obtained the remotest conception from his instructors? He had to familiarize himself with ideas of the course and powers of Nature, to which his attention had never been directed during his school-life, and to learn, for the first time, that a world of facts lies outside and beyond the world of words.
From After-Dinner Speech (Apr 1869) delivered before the Liverpool Philomathic Society, 'Scientific Education', collected in Lay Sermons, Addresses, and Reviews (1870), 63. Previously published in Macmillan’s Magazine.
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I attended Davy's lectures to renew my stock of metaphors.
In 1802 Coleridge attended an entire course of Humphry Davy's lectures at the Royal Institution, and took over 60 pages of notes.
Quoted in Sir Harold Hartley, Humphry Davy (1971), 45.
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I cannot find anything showing early aptitude for acquiring languages; but that he [Clifford] had it and was fond of exercising it in later life is certain. One practical reason for it was the desire of being able to read mathematical papers in foreign journals; but this would not account for his taking up Spanish, of which he acquired a competent knowledge in the course of a tour to the Pyrenees. When he was at Algiers in 1876 he began Arabic, and made progress enough to follow in a general way a course of lessons given in that language. He read modern Greek fluently, and at one time he was furious about Sanskrit. He even spent some time on hieroglyphics. A new language is a riddle before it is conquered, a power in the hand afterwards: to Clifford every riddle was a challenge, and every chance of new power a divine opportunity to be seized. Hence he was likewise interested in the various modes of conveying and expressing language invented for special purposes, such as the Morse alphabet and shorthand. … I have forgotten to mention his command of French and German, the former of which he knew very well, and the latter quite sufficiently; …
In paper, 'William Kingdon Clifford', The Fortnightly Review (1879), 31, 671. Published in advance of Leslie Stephen and Frederick Pollock (eds.), Clifford’s Lectures and Essays (1879), Vol. 1, Introduction, 9. The 'Introduction' was written by Pollock.
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I completed my formal education having been one of the first students in geophysics at three great universities. By today’s standards my studies were extremely casual, but I had learned to work hard, taking courses which it turned out were often irrelevant, old-fashioned, and frequently wrong. Nevertheless, the very casualness encouraged independence in thought and action.
In 'Early Days in University Geophysics', Annual Review of Earth and Planetary Sciences (1982), 10, 7.
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I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.
Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.
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I couldn’t help picturing [the Steady State universe] as a sort of 1950s advertisement, with a pipe-smoking father sitting comfortably in his living room, next to the radiogram, with a wife knitting submissively in the background, and a small boy playing with Meccano on the carpet. The father would remove his pipe and twinkle knowledgeably as he said “Of course, I’m with Steady State Insurance,” and a caption underneath would say “You Know Where You Are With a STEADY STATE Policy.”
In short essay, 'The Origin of the Universe,' 1-2. Written after hearing Stephen Hawking’s lecture (2006) at Oxford, about the origin of the universe.
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I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
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I found the invention was applicable to painting, and would also contribute to facilitate the study of geography: for I have applied it to some maps, the rivers of which I represented in silver, and in the cities in gold. The rivers appearing, as it were, in silver streams, have a most pleasing effect on the sight, and relieve the eye of that painful search for the course, and origin, of rivers, the minutest branches of which can be splendidly represented this way.
Description of an outcome of her experiments originally investigating 'the possibility of making cloths of gold, silver and other metals by chemical processes.'
Preface to An Essay on Combustion with a View to a New Art of Dyeing and Painting (1794), iii-iv. In Marilyn Bailey Ogilvie and Joy Dorothy Harvey, The Biographical Dictionary of Women in Science (2000), 478.
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I had a dislike for [mathematics], and ... was hopelessly short in algebra. ... [One extraordinary teacher of mathematics] got the whole year's course into me in exactly six [after-school] lessons of half an hour each. And how? More accurately, why? Simply because he was an algebra fanatic—because he believed that algebra was not only a science of the utmost importance, but also one of the greatest fascination. ... [H]e convinced me in twenty minutes that ignorance of algebra was as calamitous, socially and intellectually, as ignorance of table manners—That acquiring its elements was as necessary as washing behind the ears. So I fell upon the book and gulped it voraciously. ... To this day I comprehend the binomial theorem.
In Prejudices: third series (1922), 261-262.
For a longer excerpt, see H. L. Mencken's Recollections of School Algebra.
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I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.
Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 414.
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I have before mentioned mathematics, wherein algebra gives new helps and views to the understanding. If I propose these it is not to make every man a thorough mathematician or deep algebraist; but yet I think the study of them is of infinite use even to grown men; first by experimentally convincing them, that to make anyone reason well, it is not enough to have parts wherewith he is satisfied, and that serve him well enough in his ordinary course. A man in those studies will see, that however good he may think his understanding, yet in many things, and those very visible, it may fail him. This would take off that presumption that most men have of themselves in this part; and they would not be so apt to think their minds wanted no helps to enlarge them, that there could be nothing added to the acuteness and penetration of their understanding.
In The Conduct of the Understanding, Sect. 7.
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Srinivasa Ramanujan quote: I have not trodden through a conventional university course, but I am striking out a new path for mys
I have not trodden through a conventional university course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling.”
First letter to G.H. Hardy (16 Jan 1913). In Collected Papers of Srinivasa Ramanujan (1927), xxiii. Hardy notes he did “seem to remember his telling me that his friends had given him some assistance” in writing the letter because Ramanujan's “knowledge of English, at that stage of his life, could scarcely have been sufficient.”
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I have satisfied myself that the [cosmic] rays are not generated by the formation of new matter in space, a process which would be like water running up a hill. Nor do they come to any appreciable amount from the stars. According to my investigations the sun emits a radiation of such penetrative power that it is virtually impossible to absorb it in lead or other substances. ... This ray, which I call the primary solar ray, gives rise to a secondary radiation by impact against the cosmic dust scattered through space. It is the secondary radiation which now is commonly called the cosmic ray, and comes, of course, equally from all directions in space. [The article continues: The phenomena of radioactivity are not the result of forces within the radioactive substances but are caused by this ray emitted by the sun. If radium could be screened effectively against this ray it would cease to be radioactive, he said.]
Quoted in 'Tesla, 75, Predicts New Power Source', New York Times (5 Jul 1931), Section 2, 1.
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I have shown first in the course of this investigation that the infective matter is independently animate, and further that one could think of the independently animate matter as either animal and plant organisms or elementary parts of animals, which have achieved a relative individuality.
'On Miasmata and Contagia', trans. G. Rosen, Bulletin of the Institute of the History of Medicine (1938), 6, 957.
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I hold every man a debtor to his profession; from the which as men of course do seek to receive countenance and profit, so ought they of duty to endeavour themselves, by way of amends, to be a help and ornament thereunto. This is performed, in some degree, by the honest and liberal practice of a profession; where men shall carry a respect not to descend into any course that is corrupt and unworthy thereof, and preserve themselves free from the abuses wherewith the same profession is noted to be infected: but much more is this performed, if a man be able to visit and strengthen the roots and foundation of the science itself; thereby not only gracing it in reputation and dignity, but also amplifying it in profession and substance.
Opening sentences of Preface, Maxims of Law (1596), in The Works of Francis Bacon: Law tracts. Maxims of the Law (1803), Vol. 4, 10.
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I purpose, in return for the honour you do us by coming to see what are our proceedings here, to bring before you, in the course of these lectures, the Chemical History of a Candle. I have taken this subject on a former occasion; and were it left to my own will, I should prefer to repeat it almost every year—so abundant is the interest that attaches itself to the subject, so wonderful are the varieties of outlet which it offers into the various departments of philosophy. There is not a law under which any part of this universe is governed which does not come into play, and is touched upon in these phenomena. There is no better, there is no more open door by which you can enter the study of natural philosophy, than by considering the physical phenomena of a candle.
A Course of Six Lectures on the Chemical History of a Candle (1861), 13-4.
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I remember my first look at the great treatise of Maxwell’s when I was a young man… I saw that it was great, greater and greatest, with prodigious possibilities in its power… I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly… It will be understood that I preach the gospel according to my interpretation of Maxwell.
From translations of a letter (24 Feb 1918), cited in Paul J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age (2002), 24. Nahin footnotes that the words are not verbatim, but are the result of two translations. Heaviside's original letter in English was quoted, translated in to French by J. Bethenode, for the obituary he wrote, "Oliver Heaviside", in Annales des Posies Telegraphs (1925), 14, 521-538. The quote was retranslated back to English in Nadin's book. Bethenode footnoted that he made the original translation "as literally as possible in order not to change the meaning." Nadin assures that the retranslation was done likewise. Heaviside studyied Maxwell's two-volume Treatise on Electricity and Magnetism.
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I suspect there could be life and intelligence out there in forms that we can't conceive. And there could, of course, be forms of intelligence beyond human capacity—beyond as much as we are beyond a chimpanzee.
As quoted by Robin McKie in 'Aliens Can't Hear Us, Says Astronomer', The Guardian (27 Jan 2010), reporting on “a special meeting on the search for extraterrestrial intelligence” on 26 Jan 2010.
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I took a course in speed reading course … and I was able to go through read War and Peace in twenty minutes. It’s about Russia.
As quoted in Reader's Digest (Oct 1967), 91, 120.
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I venture to assert that the feelings one has when the beautiful symbolism of the infinitesimal calculus first gets a meaning, or when the delicate analysis of Fourier has been mastered, or while one follows Clerk Maxwell or Thomson into the strange world of electricity, now growing so rapidly in form and being, or can almost feel with Stokes the pulsations of light that gives nature to our eyes, or track with Clausius the courses of molecules we can measure, even if we know with certainty that we can never see them I venture to assert that these feelings are altogether comparable to those aroused in us by an exquisite poem or a lofty thought.
In paper (May 1891) read before Bath Branch of the Teachers’ Guild, published in The Practical Teacher (July 1891), reprinted as 'Geometry', in Frederic Spencer, Chapters on the Aims and Practice of Teaching (1897), 194.
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If a single cell, under appropriate conditions, becomes a man in the space of a few years, there can surely be no difficulty in understanding how, under appropriate conditions, a cell may, in the course of untold millions of years, give origin to the human race.
Principles of Biology (1865, 1872), 350.
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If I were summing up the qualities of a good teacher of medicine, I would enumerate human sympathy, moral and intellectual integrity, enthusiasm, and ability to talk, in addition, of course, to knowledge of his subject.
Anonymous
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If Louis Pasteur were to come out of his grave because he heard that the cure for cancer still had not been found, NIH would tell him, “Of course we'll give you assistance. Now write up exactly what you will be doing during the three years of your grant.” Pasteur would say, “Thank you very much,” and would go back to his grave. Why? Because research means going into the unknown. If you know what you are going to do in science, then you are stupid! This is like telling Michelangelo or Renoir that he must tell you in advance how many reds and how many blues he will buy, and exactly how he will put those colors together.
Interview for Saturday Evening Post (Jan/Feb 1981), 30.
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If there ever was a misnomer, it is “exact science.” Science has always been full of mistakes. The present day is no exception. And our mistakes are good mistakes; they require a genius to correct. Of course, we do not see our own mistakes.
In Edward Teller, Wendy Teller and Wilson Talley, Conversations on the Dark Secrets of Physics (1991, 2013), 37.
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If there is real love, it is not difficult to exercise tolerance, for tolerance is the daughter of love—it is the truly Christian trait, which, of course, Christians of today do not practice.
English translation of the original German, “Liebt man sich wirklich, so ist es ja nicht schwer, die Toleranz zu üben, denn die Toleranz ist die Tochter der Liebe—es ist die eigentlich christliche Eigenschaft, die freilich von der heutigen Christenwelt nicht geübt wird.” In a letter to his father (7 Apr 1851), published in Briefe an seite Eltern, 1839 bis 1864 (1907).
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If this “critical openminded attitude” … is wanted, the question at once arises, Is it science that should be studied in order to achieve it? Why not study law? A judge has to do everything that a scientist is exhorted to do in the way of withholding judgment until all the facts are in, and then judging impartially on the merits of the case as well as he can. … Why not a course in Sherlock Holmes? The detectives, or at least the detective-story writers, join with the scientists in excoriating “dogmatic prejudice, lying, falsification of facts, and data, and willful fallacious reasoning.”
In Science is a Sacred Cow (1950), 191.
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If we ascribe the ejection of the proton to a Compton recoil from a quantum of 52 x 106 electron volts, then the nitrogen recoil atom arising by a similar process should have an energy not greater than about 400,000 volts, should produce not more than about 10,000 ions, and have a range in the air at N.T.P. of about 1-3mm. Actually, some of the recoil atoms in nitrogen produce at least 30,000 ions. In collaboration with Dr. Feather, I have observed the recoil atoms in an expansion chamber, and their range, estimated visually, was sometimes as much as 3mm. at N.T.P.
These results, and others I have obtained in the course of the work, are very difficult to explain on the assumption that the radiation from beryllium is a quantum radiation, if energy and momentum are to be conserved in the collisions. The difficulties disappear, however, if it be assumed that the radiation consists of particles of mass 1 and charge 0, or neutrons. The capture of the a-particle by the Be9 nucleus may be supposed to result in the formation of a C12 nucleus and the emission of the neutron. From the energy relations of this process the velocity of the neutron emitted in the forward direction may well be about 3 x 109 cm. per sec. The collisions of this neutron with the atoms through which it passes give rise to the recoil atoms, and the observed energies of the recoil atoms are in fair agreement with this view. Moreover, I have observed that the protons ejected from hydrogen by the radiation emitted in the opposite direction to that of the exciting a-particle appear to have a much smaller range than those ejected by the forward radiation.
This again receives a simple explanation on the neutron hypothesis.
'Possible Existence of a Neutron', Letter to the Editor, Nature, 1932, 129, 312.
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If we continue on our current course, the damage that has been the defining feature of my lifetime will be eclipsed by the damage coming in the next. … Science predicts that were I born today, I would be witness to the 2030s—The Amazon Rainforest, cut down until it can no longer produce enough moisture, degrades into a dry savannah, bringing catastrophic species loss—and altering the global water cycle.
From narration to Netflix TV program, A Life on Our Planet: My Witness Statement and a Vision for the Future (4 Oct 2020).
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If we drove an automobile the way we try to run civilization, I think we would face backwards, looking through the back window, admiring where we came from, and not caring where we are going. If you want a good life you must look to the future. … I think it is all right to have courses in history. But history is the “gonest” thing in the world. … Let’s keep history, but let’s take a small part of the time and study where we are going. … We can do something about the unmade history.
As quoted in book review, T.A. Boyd, 'Charles F. Kettering: Prophet of Progress', Science (30 Jan 1959), 256.
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If we knew all the laws of Nature, we should need only one fact or the description of one actual phenomenon to infer all the particular results at that point. Now we know only a few laws, and our result is vitiated, not, of course, by any confusion or irregularity in Nature, but by our ignorance of essential elements in the calculation. Our notions of law and harmony are commonly confined to those instances which we detect, but the harmony which results from a far greater number of seemingly conflicting, but really concurring, laws which we have not detected, is still more wonderful. The particular laws are as our points of view, as to the traveler, a mountain outline varies with every step, and it has an infinite number of profiles, though absolutely but one form. Even when cleft or bored through, it is not comprehended in its entireness.
In Walden (1878), 311.
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If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.
Science and Method (1914, 2003), 25.
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If you throw a stone in a pond... the waves which strike against the shores are thrown back towards the spot where the stone struck; and on meeting other waves they never intercept each other’s course... In a small pond one and the same stroke gives birth to many motions of advance and recoil.
…...
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If, in the course of a thousand or two thousand years, science arrives at the necessity of renewing its points of view, that will not mean that science is a liar. Science cannot lie, for it’s always striving, according to the momentary state of knowledge, to deduce what is true. When it makes a mistake, it does so in good faith. It’s Christianity that’s the liar. It’s in perpetual conflict with itself.
In Adolf Hitler, Hugh Redwald Trevor-Roper, translated by Norman Cameron and R. H. Stevens, '14 October 1941', Secret Conversations (1941 - 1944) (1953), 51
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If, then, the motion of every particle of matter in the universe were precisely reversed at any instant, the course of nature would be simply reversed for ever after. The bursting bubble of foam at the foot of a waterfall would reunite and descend into the water; the thermal motions would reconcentrate their energy, and throw the mass up the fall in drops re-forming into a close column of ascending water. Heat which had been generated by the friction of solids and dissipated by conduction, and radiation, and radiation with absorption, would come again to the place of contact, and throw the moving body back against the force to which it had previously yielded. Boulders would recover from the mud materials required to rebuild them into their previous jagged forms, and would become reunited to the mountain peak from which they had formerly broken away. And if also the materialistic hypothesis of life were true, living creatures would grow backwards, with conscious knowledge of the future but no memory of the past, and would become again unborn.
In 'The Kinetic Theory of the Dissipation of Energy', Nature (1874), 9, 442.
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In a class I was taking there was one boy who was much older than the rest. He clearly had no motive to work. I told him that, if he could produce for me, accurately to scale, drawings of the pieces of wood required to make a desk like the one he was sitting at, I would try to persuade the Headmaster to let him do woodwork during the mathematics hours—in the course of which, no doubt, he would learn something about measurement and numbers. Next day, he turned up with this task completed to perfection. This I have often found with pupils; it is not so much that they cannot do the work, as that they see no purpose in it.
In Mathematician's Delight (1943), 52.
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In a sense, of course, probability theory in the form of the simple laws of chance is the key to the analysis of warfare;… My own experience of actual operational research work, has however, shown that its is generally possible to avoid using anything more sophisticated. … In fact the wise operational research worker attempts to concentrate his efforts in finding results which are so obvious as not to need elaborate statistical methods to demonstrate their truth. In this sense advanced probability theory is something one has to know about in order to avoid having to use it.
In 'Operations Research', Physics Today (Nov 1951), 19. As cited by Maurice W. Kirby and Jonathan Rosenhead, 'Patrick Blackett (1897)' in Arjang A. Assad (ed.) and Saul I. Gass (ed.),Profiles in Operations Research: Pioneers and Innovators (2011), 25.
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In its earliest development knowledge is self-sown. Impressions force themselves upon men’s senses whether they will or not, and often against their will. The amount of interest in which these impressions awaken is determined by the coarser pains and pleasures which they carry in their train or by mere curiosity; and reason deals with the materials supplied to it as far as that interest carries it, and no further. Such common knowledge is rather brought than sought; and such ratiocination is little more than the working of a blind intellectual instinct. It is only when the mind passes beyond this condition that it begins to evolve science. When simple curiosity passes into the love of knowledge as such, and the gratification of the æsthetic sense of the beauty of completeness and accuracy seems more desirable that the easy indolence of ignorance; when the finding out of the causes of things becomes a source of joy, and he is accounted happy who is successful in the search, common knowledge passes into what our forefathers called natural history, whence there is but a step to that which used to be termed natural philosophy, and now passes by the name of physical science.
In this final state of knowledge the phenomena of nature are regarded as one continuous series of causes and effects; and the ultimate object of science is to trace out that series, from the term which is nearest to us, to that which is at the farthest limit accessible to our means of investigation.
The course of nature as it is, as it has been, and as it will be, is the object of scientific inquiry; whatever lies beyond, above, or below this is outside science. But the philosopher need not despair at the limitation on his field of labor; in relation to the human mind Nature is boundless; and, though nowhere inaccessible, she is everywhere unfathomable.
The Crayfish: an Introduction to the Study of Zoölogy (1880), 2-3. Excerpted in Popular Science (Apr 1880), 16, 789-790.
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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.
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In my understanding of God I start with certain firm beliefs. One is that the laws of nature are not broken. We do not, of course, know all these laws yet, but I believe that such laws exist. I do not, therefore, believe in the literal truth of some miracles which are featured in the Christian Scriptures, such as the Virgin Birth or water into wine. ... God works, I believe, within natural laws, and, according to natural laws, these things happen.
Essay 'Science Will Never Give Us the Answers to All Our Questions', collected in Henry Margenau, and Roy Abraham Varghese (eds.), Cosmos, Bios, Theos (1992), 66.
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In order to seek truth, it is necessary once in the course of our life, to doubt, as far as possible, of all things.
From the original Latin: “Veritatem inquirenti, semel in vita de omnibus, quantum fieri potest, esse dubitandum,” Principles of Philosophy (1644). Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition I, 5. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 193. Also seen translated as: “If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.”
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In our search after the Knowledge of Substances, our want of Ideas, that are suitable to such a way of proceeding, obliges us to a quite different method. We advance not here, as in the other (where our abstract Ideas are real as well as nominal Essences) by contemplating our Ideas, and considering their Relations and Correspondencies; that helps us very little, for the Reasons, and in another place we have at large set down. By which, I think it is evident, that Substances afford Matter of very little general Knowledge; and the bare Contemplation of their abstract Ideas, will carry us but a very little way in the search of Truth and Certainty. What then are we to do for the improvement of our Knowledge in Substantial beings? Here we are to take a quite contrary Course, the want of Ideas of their real essences sends us from our own Thoughts, to the Things themselves, as they exist.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 9, 644.
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In physics, mathematics, and astronautics [elderly] means over thirty; in the other disciplines, senile decay is sometimes postponed to the forties. There are, of course, glorious exceptions; but as every researcher just out of college knows, scientists of over fifty are good for nothing but board meetings, and should at all costs be kept out of the laboratory!
Defining 'elderly scientist' as in Clarke's First Law.
'Hazards of Prophecy: The Failure of Imagination'. In the collection. Profiles of the Future: An Enquiry into the Limits of the Possible (1962, rev. 1973), 14-15.
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In the animal world we have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life: understood, of course, in its wide Darwinian sense—not as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress. The mutual protection which is obtained in this case, the possibility of attaining old age and of accumulating experience, the higher intellectual development, and the further growth of sociable habits, secure the maintenance of the species, its extension, and its further progressive evolution. The unsociable species, on the contrary, are doomed to decay.
Mutual Aid: A Factor of Evolution (1902), 293.
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In the beginning the gods did not at all reveal all things clearly to mortals, but by searching men in the course of time find them out better.
Quoted in Arthur Fairbanks (ed. And trans.), The First Philosophers of Greece (1898), 71, fragment 16.
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In the course of centuries the naïve self-love of men has had to submit to two major blows at the hands of science. The first was when they learnt that our earth was not the centre of the universe but only a tiny fragment of a cosmic system of scarcely imaginable vastness… the second blow fell when biological research destroyed man’s supposedly privileged place in creation and proved his descent from the animal kingdom and his ineradicable animal nature… But human megalomania will have suffered its third and most wounding blow from the psychological research of the present time which seeks to prove to the ego that it is not even master in its own house, but must content itself with scanty information of what is going on unconsciously in its mind.
Introductory Lectures on Psychoanalyis (1916), in James Strachey (ed.), The Standard Edition of the Complete Psychological Works of Sigmund Freud (1963), Vol. 16, 284-5.
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In the course of individual development, inherited characters appear, in general, earlier than adaptive ones, and the earlier a certain character appears in ontogeny, the further back must lie in time when it was acquired by its ancestors.
Allgemeine Entwickelungsgeschichte der Organismen (1866), Vol. 2, 298. Trans. Stephen Jay Gould, Ontogeny and Phylogeny (1977), 81.
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In the course of normal speaking the inhibitory function of the will is continuously directed to bringing the course of ideas and the articulatory movements into harmony with each other. If the expressive movement which which follows the idea is retarded through mechanical causes, as is the case in writing ... such anticipations make their appearance with particular ease.
Folk Psychology (1900)
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In the course of the history of the earth innumerable events have occurred one after another, causing changes of states, all with certain lasting consequences. This is the basis of our developmental law, which, in a nutshell, claims that the diversity of phenomena is a necessary consequence of the accumulation of the results of all individual occurrences happening one after another... The current state of the earth, thus, constitutes the as yet most diverse final result, which of course represents not a real but only a momentary end-point.
Ober das Entwicklung der Erde, (1867), 5-6.
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In the course of the last century science has become so dizzy with its successes, that it has forgotten to ask the pertinent questions—or refused to ask them under the pretext that they are meaningless, and in any case not the scientists concern.
In The Ghost in the Machine (1967), xi.
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In the course of this short tour, I became convinced that we must turn to the New World if we wish to see in perfection the oldest monuments of the earth’s history, so far at least as relates to its earliest inhabitants.
Travels in North America (1845), Vol. 1, 19.
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In the fight which we have to wage incessantly against ignorance and quackery among the masses and follies of all sorts among the classes, diagnosis, not drugging, is our chief weapon of offence. Lack of systematic personal training in the methods of the recognition of disease leads to the misapplication of remedies, to long courses of treatment when treatment is useless, and so directly to that lack of confidence in our methods which is apt to place us in the eyes of the public on a level with empirics and quacks.
Address to the Canadian Medical Association, Montreal (17 Sep 1902), 'Chauvinism in Medicine', published in The Montreal Medical Journal (1902), 31, 267. Collected in Aequanimitas, with Other Addresses to Medical Students, Nurses and Practitioners of Medicine (1904), 299.
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In the history of science and throughout the whole course of its progress we see certain epochs following one another more or less rapidly. Some important view is expressed, it may be original or only revived; sooner or later it receives recognition; fellow-Workers spring up; the outcome of it finds its way into the schools; it is taught and handed down; and we observe, unhappily, that it does not in the least matter whether the view be true or false. In either case its course is the same; in either case it comes in the end to he a mere phrase, a lifeless word stamped on the memory.
In The Maxims and Reflections of Goethe (1906), 184.
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In the light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion, and the final emergence into the light—only those who have experienced it can understand that.
Quoted in Banesh Hoffmann and Helen Dukas, Albert Einstein: Creator and Rebel (1972), 124.
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In the long course of cell life on this earth it remained, for our age for our generation, to receive the full ownership of our inheritance. We have entered the cell, the Mansion of our birth, and started the inventory of our acquired wealth.
Talking about the new information revealed by electron microscopy Nobel Lecture, The Coming Age of the Cell, 12 Dec 1974
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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.
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Inductive reasoning is, of course, good guessing, not sound reasoning, but the finest results in science have been obtained in this way. Calling the guess a “working hypothesis,” its consequences are tested by experiment in every conceivable way.
In Higher Mathematics for Students of Chemistry and Physics (1902), 2.
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Instead of saying that a man behaves because of the consequences which are to follow his behavior, we simply say that he behaves because of the consequences which have followed similar behavior in the past. This is, of course, the Law of Effect or operant conditioning.
In Science and Human Behavior (1953), 87.
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Into whatsoever houses I enter, I will enter to help the sick, and I will abstain from all intentional wrong-doing and harm, especially from abusing the bodies of man or woman, bond or free. And whatsoever I shall see or hear in the course of my profession, as well as outside my profession in my intercourse with men, if it be what should not be published abroad, I will never divulge, holding such things to be holy secrets.
Oath, in Hippocrates, trans. W. H. S. Jones (1923), Vol. 1, 301.
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Introductory physics courses are taught at three levels: physics with calculus, physics without calculus, and physics without physics.
Anonymous
…...
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Investigators are commonly said to be engaged in a search for the truth. I think they themselves would usually state their aims less pretentiously. What the experimenter is really trying to do is to learn whether facts can be established which will be recognized as facts by others and which will support some theory that in imagination he has projected. But he must be ingenuously honest. He must face facts as they arise in the course of experimental procedure, whether they are favourable to his idea or not. In doing this he must be ready to surrender his theory at any time if the facts are adverse to it.
The Way of an Investigator: A Scientist's Experiences in Medical Research (1945), 34.
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Is it not true that for every person the course of life is along the line of least resistance, and that in this the movement of humanity is like the movement of material bodies?
In preface to Scientific Memoirs (1878), xiv.
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Is not Cuvier the greatest poet of our age? Of course Lord Byron has set down in fine words certain of our souls’ longings; but our immortal naturalist has reconstructed whole worlds out of bleached bones. Like Cadmus, he has rebuilt great cities from teeth, repopulated thousands of forests with all the mysteries of zoology from a few pieces of coal, discovered races of giants in the foot of a mammoth.
From 'La Peau de Chagrin' (1831). As translated as by Helen Constantine The Wild Ass’s Skin (2012), 19.
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Is what you are doing fun? Of course, physics is also fun—indeed it is an enjoyable way of life. One reason physics is fun is that each element of progress transforms an area of ignorance into knowledge, but it also creates, as a by-product, an amount of new and additional ignorance in excess of that which was reduced to understanding. Thus, the volume of delicious ignorance we produce is ever-expanding, like our exponentially exploding universe.
In 'Physics and the APS in 1979', Physics Today (Apr 1980), 33, No. 4, 50.
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It cannot, of course, be stated with absolute certainty that no elements can combine with argon; but it appears at least improbable that any compounds will be formed.
As surmised in Gases of the Atmosphere (1896, 1905), 193. [The first argon compound was finally made a century later (Aug 2000), argon fluorohydride, HArF, but unstable above 40 K (–233 °C). —Webmaster]
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It has become, in my view, a bit too trendy to regard the acceptance of death as something tantamount to intrinsic dignity. Of course I agree with the preacher of Ecclesiastes that there is a time to love and a time to die - and when my skein runs out I hope to face the end calmly and in my own way. For most situations, however, I prefer the more martial view that death is the ultimate enemy - and I find nothing reproachable in those who rage mightily against the dying of the light.
Bully for Brontosaurus: Reflections on Natural History (1991).
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It is a good principle in science not to believe any “fact”—however well attested—until it fits into some accepted frame of reference. Occasionally, of course, an observation can shatter the frame and force the construction of a new one, but that is extremely rare. Galileos and Einsteins seldom appear more than once per century, which is just as well for the equanimity of mankind.
In Opening of Chap 14, 'Search', 2061: Odyssey Three (1987, 1989), 62.
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It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing the microscope that prodigious smallness which is also a vastness, and now in seeking in geological ages the traces of a past that attracts us because of its remoteness.
…...
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It is imperative in the design process to have a full and complete understanding of how failure is being obviated in order to achieve success. Without fully appreciating how close to failing a new design is, its own designer may not fully understand how and why a design works. A new design may prove to be successful because it has a sufficiently large factor of safety (which, of course, has often rightly been called a “factor of ignorance”), but a design's true factor of safety can never be known if the ultimate failure mode is unknown. Thus the design that succeeds (ie, does not fail) can actually provide less reliable information about how or how not to extrapolate from that design than one that fails. It is this observation that has long motivated reflective designers to study failures even more assiduously than successes.
In Design Paradigms: Case Histories of Error and Judgment in Engineering (1994), 31. books.google.comHenry Petroski - 1994
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It is more important that a proposition be interesting than it be true. … But of course a true proposition is more apt to be interesting than a false one.
In Adventures of Ideas (1933, 1967), 244.
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It is not clear to anyone, least of all the practitioners, how science and technology in their headlong course do or should influence ethics and law, education and government, art and social philosophy, religion and the life of the affections. Yet science is an all-pervasive energy, for it is at once a mode of thought, a source of strong emotion, and a faith as fanatical as any in history.
Science: The Glorious Entertainment (1964), 3.
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It is not improbable that some of the presentations which come before the mind in sleep may even be causes of the actions cognate to each of them. For as when we are about to act [in waking hours], or are engaged in any course of action, or have already performed certain actions, we often find ourselves concerned with these actions, or performing them, in a vivid dream.
Aristotle
In Mortimer Jerome Adler, Charles Lincoln Van Doren (eds.) Great Treasury of Western Thought: A Compendium of Important Statements on Man and His Institutions by the Great Thinkers in Western History (1977), 352
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It is not the organs—that is, the character and form of the animal's bodily parts—that have given rise to its habits and particular structures. It is the habits and manner of life and the conditions in which its ancestors lived that have in the course of time fashioned its bodily form, its organs and qualities.
Attributed.
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It is often claimed that knowledge multiplies so rapidly that nobody can follow it. I believe this is incorrect. At least in science it is not true. The main purpose of science is simplicity and as we understand more things, everything is becoming simpler. This, of course, goes contrary to what everyone accepts.
Edward Teller, Wendy Teller, Wilson Talley, Conversations on the Dark Secrets of Physics (1991, 2002), 2.
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It is only by historical analysis that we can discover what makes up man, since it is only in the course of history that he is formed.
'The Dualism of Human Nature and its Social Conditions' (1914), trans. Charles Blend, in Kurt H. Wolff (ed.), Emile Durkheim, 1858-1917 (1960), 325.
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It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
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It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs.
In Adventures of a Mathematician (1976), Prologue, 5. Also used as epigraph in Richard Rhodes, The Making of the Atomic Bomb (1986), 11. The scribbles were those of scientists during the Manhattan Project at Los Alamos, while discussing the design the atomic bomb.
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It is the destiny of wine to be drunk, and it is the destiny of glucose to be oxidized. But it was not oxidized immediately: its drinker kept it in his liver for more than a week, well curled up and tranquil, as a reserve aliment for a sudden effort; an effort that he was forced to make the following Sunday, pursuing a bolting horse. Farewell to the hexagonal structure: in the space of a few instants the skein was unwound and became glucose again, and this was dragged by the bloodstream all the way to a minute muscle fiber in the thigh, and here brutally split into two molecules of lactic acid, the grim harbinger of fatigue: only later, some minutes after, the panting of the lungs was able to supply the oxygen necessary to quietly oxidize the latter. So a new molecule of carbon dioxide returned to the atmosphere, and a parcel of the energy that the sun had handed to the vine-shoot passed from the state of chemical energy to that of mechanical energy, and thereafter settled down in the slothful condition of heat, warming up imperceptibly the air moved by the running and the blood of the runner. 'Such is life,' although rarely is it described in this manner: an inserting itself, a drawing off to its advantage, a parasitizing of the downward course of energy, from its noble solar form to the degraded one of low-temperature heat. In this downward course, which leads to equilibrium and thus death, life draws a bend and nests in it.
The Periodic Table (1975), trans. Raymond Rosenthal (1984), 192-3.
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It is true that I am the father [of the H-bomb] in the biological sense that I performed a necessary function and let nature take its course. After that a child had to be born. It might he robust or it might be stillborn, but something had to be born. The process of conception was by no means a pleasure: it was filled with difficulty and anxiety….
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 72.
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It is usual to say that the two sources of experience are Observation and Experiment. When we merely note and record the phenomena which occur around us in the ordinary course of nature we are said to observe. When we change the course of nature by the intervention of our will and muscular powers, and thus produce unusual combinations and conditions of phenomena, we are said to experiment. [Sir John] Herschel has justly remarked that we might properly call these two modes of experience passive and active observation. In both cases we must certainly employ our senses to observe, and an experiment differs from a mere observation in the fact that we more or less influence the character of the events which we observe. Experiment is thus observation plus alteration of conditions.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 400.
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It isn’t easy to become a fossil. … Only about one bone in a billion, it is thought, becomes fossilized. If that is so, it means that the complete fossil legacy of all the Americans alive today—that’s 270 million people with 206 bones each—will only be about 50 bones, one-quarter of a complete skeleton. That’s not to say, of course, that any of these bones will ever actually be found.
In A Short History of Nearly Everything (2003), 321-322.
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It must happen that in some cases the author is not understood, or is very imperfectly understood; and the question is what is to be done. After giving a reasonable amount of attention to the passage, let the student pass on, reserving the obscurity for future efforts. … The natural tendency of solitary students, I believe, is not to hurry away prematurely from a hard passage, but to hang far too long over it; the just pride that does not like to acknowledge defeat, and the strong will that cannot endure to be thwarted, both urge to a continuance of effort even when success seems hopeless. It is only by experience we gain the conviction that when the mind is thoroughly fatigued it has neither the power to continue with advantage its course in .an assigned direction, nor elasticity to strike out a new path; but that, on the other hand, after being withdrawn for a time from the pursuit, it may return and gain the desired end.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 68.
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It must never be forgotten that education is not a process of packing articles in a trunk. Such a simile is entirely inapplicable. It is, of course, a process completely of its own peculiar genus. Its nearest analogue is the assimilation of food by a living organism: and we all know how necessary to health is palatable food under suitable conditions.
In 'The Rhythmic Claims of Freedom and Discipline', The Aims of Education and Other Essays (1929), 42.
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It seems to me that the view toward which we are tending is that the specificity in gene action is always a chemical specificity, probably the production of enzymes which guide metabolic processes along particular channels. A given array of genes thus determines the production of a particular kind of protoplasm with particular properties—such, for example, as that of responding to surface forces by the formation of a special sort of semipermeable membrane, and that of responding to trivial asymmetries in the play of external stimuli by polarization, with consequent orderly quantitative gradients in all physiologic processes. Different genes may now be called into play at different points in this simple pattern, either through the local formation of their specific substrates for action, or by activation of a mutational nature. In either case the pattern becomes more complex and qualitatively differentiated. Successive interactions of differentiated regions and the calling into play of additional genes may lead to any degree of complexity of pattern in the organism as a largely self-contained system. The array of genes, assembled in the course of evolution, must of course be one which determines a highly self­regulatory system of reactions. On this view the genes are highly specific chemically, and thus called into play only under very specific conditions; but their morphological effects, if any, rest on quantitative influences of immediate or remote products on growth gradients, which are resultants of all that has gone on before in the organism.
In 'Genetics of Abnormal Growth in the Guinea Pig', Cold Spring Harbor Symposia on Quantitative Biology (1934), 2, 142.
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It seems very strange … that in the course of the world’s history so obvious an improvement should never have been adopted. … The next generation of Britishers would be the better for having had this extra hour of daylight in their childhood.
In Report, and Special Report, from the Select Committee on the Daylight Saving Bill: Minutes of Evidence (1908), 116.
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It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it.
From Letter (24 Mar 1954) in Einstein archives. Quoted by Helen Dukas and Banesh Hoffman, Albert Einstein: The Human Side (1979, 2013), 43. Dukas was Einstein’s personal secretary for 28 years, so she knew his philosophy well.
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It will be possible, through the detailed determination of amino-acid sequences of hemoglobin molecules and of other molecules too, to obtain much information about the course of the evolutionary process, and to illuminate the question of the origin of species.
'Molecular Disease and Evolution'. Typescript of the Rudolph Virchow Lecture (5 Nov 1962). Quoted in T. Hager, Force of Nature: The Life of Linus Pauling (1997), 541.
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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It would, of course, be a poor lookout for the advancement of science if young men started believing what their elders tell them, but perhaps it is legitimate to remark that young Turks look younger, or more Turkish ... if the conclusions they eventually reach are different from what anyone had said before.
In Nature, 1969.
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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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John Bardeen was an avid golfer and a good one. Whenever possible, he sought out golf courses during research or consulting trips. According to the stories, he was as proud of hitting a “hole in one” as he was to win a second Nobel Prize.
In 'John Bardeen: A Place to Win Two Nobel Prizes and Make a Hole in One', collected in Lillian Hoddeson (ed.), No Boundaries: University of Illinois Vignettes (2004), Chap. 16, 257.
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Just as the musician is able to form an acoustic image of a composition which he has never heard played by merely looking at its score, so the equation of a curve, which he has never seen, furnishes the mathematician with a complete picture of its course. Yea, even more: as the score frequently reveals to the musician niceties which would escape his ear because of the complication and rapid change of the auditory impressions, so the insight which the mathematician gains from the equation of a curve is much deeper than that which is brought about by a mere inspection of the curve.
In Jahresbericht der Deutschen Mathematiker Vereiningung, 13, 864. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 190
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Knowing, henceforth, the physiognomy of the disease when allowed to run its own course, you can, without risk of error, estimate the value of the different medications which have been employed. You will discover which remedies have done no harm, and which have notably curtailed the duration of the disease; and thus for the future you will have a standard by which to measure the value of the medicine which you see employed to counteract the malady in question. What you have done in respect of one disease, you will be able to do in respect of many; and by proceeding in this way you will be able, on sure data, to pass judgment on the treatment pursued by your masters.
In Armand Trousseau, as translated by P. Victor and John Rose Cormack, Lectures on Clinical Medicine: Delivered at the Hôtel-Dieu, Paris (1873), Vol. 1, 40-41.
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Laplace considers astronomy a science of observation, because we can only observe the movements of the planets; we cannot reach them, indeed, to alter their course and to experiment with them. “On earth,” said Laplace, “we make phenomena vary by experiments; in the sky, we carefully define all the phenomena presented to us by celestial motion.” Certain physicians call medicine a science of observations, because they wrongly think that experimentation is inapplicable to it.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 18. A footnote cites Laplace, Système du monde, Chap. 2.
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Leave the beaten track occasionally and dive into the woods. Every time you do so you will be certain to find something that you have never seen before. Of course, it will be a little thing, but do not ignore it. Follow it up, explore all around it: one discovery will lead to another, and before you know it, you will have something worth thinking about to occupy your mind. All really big discoveries are the results of thought.
Address (22 May 1914) to the graduating class of the Friends’ School, Washington, D.C. Printed in 'Discovery and Invention', The National Geographic Magazine (1914), 25, 650.
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Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.
Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?
Pensées (1670), Section 1, aphorism 43. In H. F. Stewart (ed.), Pascal’s Pensées (1950), 19.
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Look at life as an energy economy game. Each day, ask yourself, Are my energy expenditures (actions, reactions, thoughts, and feelings) productive or nonproductive? During the course of my day, have I accumulated more stress or more peace?
Doc Childre and Howard Martin
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Looking back over the last thousand years, one can divide the development of the machine and the machine civilization into three successive but over-lapping and interpenetrating phases: eotechnic, paleotechnic, neotechnic … Speaking in terms of power and characteristic materials, the eotechnic phase is a water-and-wood complex: the paleotechnic phase is a coal-and-wood complex… The dawn-age of our modern technics stretches roughly from the year 1000 to 1750. It did not, of course, come suddenly to an end in the middle of the eighteenth century. A new movement appeared in industrial society which had been gathering headway almost unnoticed from the fifteenth century on: after 1750 industry passed into a new phase, with a different source of power, different materials, different objectives.
Technics and Civilisation (1934), 109.
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Man has generally been preoccupied with obtaining as much “production” from the landscape as possible, by developing and maintaining early successional types of ecosystems, usually monocultures. But, of course, man does not live by food and fiber alone; he also needs a balanced CO2-O2 atmosphere, the climactic buffer provided by oceans and masses of vegetation, and clean (that is, unproductive) water for cultural and industrial uses. Many essential life-cycle resources, not to mention recreational and esthetic needs, are best provided man by the less 'productive' landscapes. In other words, the landscape is not just a supply depot but is also the oikos—the home—in which we must live.
'The Strategy of Ecosystem Development. An Understanding of Ecological Succession Provides a Basis for Resolving Man's Conflict with Nature', Science (1969), 164, 266.
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Man is the Reasoning Animal. Such is the claim. I think it is open to dispute. Indeed, my experiments have proven to me that he is the Unreasoning Animal. … It seems plain to me that whatever he is he is not a reasoning animal. His record is the fantastic record of a maniac. I consider that the strongest count against his intelligence is the fact that with that record back of him he blandly sets himself up as the head animal of the lot: whereas by his own standards he is the bottom one.
In truth, man is incurably foolish. Simple things which the other animals easily learn, he is incapable of learning. Among my experiments was this. In an hour I taught a cat and a dog to be friends. I put them in a cage. In another hour I taught them to be friends with a rabbit. In the course of two days I was able to add a fox, a goose, a squirrel and some doves. Finally a monkey. They lived together in peace; even affectionately.
Next, in another cage I confined an Irish Catholic from Tipperary, and as soon as he seemed tame I added a Scotch Presbyterian from Aberdeen. Next a Turk from Constantinople; a Greek Christian from Crete; an Armenian; a Methodist from the wilds of Arkansas; a Buddhist from China; a Brahman from Benares. Finally, a Salvation Army Colonel from Wapping. Then I stayed away two whole days. When I came back to note results, the cage of Higher Animals was all right, but in the other there was but a chaos of gory odds and ends of turbans and fezzes and plaids and bones and flesh—not a specimen left alive. These Reasoning Animals had disagreed on a theological detail and carried the matter to a Higher Court.
In Mark Twain and Bernard DeVoto (ed.), Letters from the Earth: Uncensored Writings (1962), 180-181. [Note: As a humorous, irreverent consideration of Man and Christianity, these essays (written c.1909) remained unpublished for over 50 years after Twain’s death (1910), because his daughter and literary executor (Clara Clemens Samossoud) felt that some of the pieces did not accurately represent her father’s beliefs, but eventually, she consented to their publication.]
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Man, being the servant and interpreter of Nature, can do and understand so much and so much only as he has observed in fact or thought of the course of nature; beyond this he neither knows anything nor can do anything.
From Novum Organum (1620), Book 1, Aphorism 1. As translated from the original Latin, “Homo enim naturae minister et interpres tantum facit et intelligit, quantum de naturae ordine, opere vel mente, observaverit: nec amplius scit, aut potest.” in The New Organon: Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man), collected in James Spedding, Robert Ellis and Douglas Heath (eds.), The Works of Francis Bacon (1857), Vol. 4, 47. Also seen translated as “Man, as the minister and interpreter of nature, is limited in act and understanding by his observation of the order of nature; neither his understanding nor his power extends farther,” in Robert Routledge, Discoveries and Inventions of the 19th Century (1891), 697.
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Many consider that the conflict of religion and science is a temporary phase, and that in due course the two mighty rivers of human understanding will merge into an even mightier Amazon of comprehension. I take the opposite view, that reconciliation is impossible. I consider that Science is mightier than the Word, and that the river of religion will (or, at least, should) atrophy and die.
In 'Religion - The Antithesis to Science', Chemistry & Industry (Feb 1997).
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Many orthodox people speak as though it were the business of sceptics to disprove received dogmas rather than of dogmatists to prove them. This is, of course, a mistake.
In unpublished manuscript, 'Is There a God', (5 Mar 1952) written for the magazine, Illustrated. Collected in Bertrand Russell, John G. Slater (ed.) and Peter Köllner (ed.) The Collected Papers of Bertrand Russell: Volume II: Last Philosophical Testament: 1943-68 (1997), 547.
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Many will, no doubt, prefer to retain old unsystematic names as far as possible, but it is easy to see that the desire to avoid change may carry us too far in this direction; it will undoubtedly be very inconvenient to the present generation of chemists to abandon familiar and cherished names, but nevertheless it may be a wise course to boldly face the difficulty, rather than inflict on coming generations a partially illogical and unsystematic nomenclature.
'International Conference on Chemical Nomenclature', Nature (19 May 1892), 46, 57.
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Mathematics appreciation is more than a course. It is an attitude that we should cultivate in every mathematics course.
In 'Loving Math Infinitely', The Chronicle of Higher Education (19 Jan 2001).
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Mathematics is often considered a difficult and mysterious science, because of the numerous symbols which it employs. Of course, nothing is more incomprehensible than a symbolism which we do not understand. … But this is not because they are difficult in themselves. On the contrary they have invariably been introduced to make things easy. … [T]he symbolism is invariably an immense simplification. It … represents an analysis of the ideas of the subject and an almost pictorial representation of their relations to each other.
In Introduction to Mathematics (1911), 59-60.
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Mathematics is the study which forms the foundation of the course [at West Point Military Academy]. This is necessary, both to impart to the mind that combined strength and versatility, the peculiar vigor and rapidity of comparison necessary for military action, and to pave the way for progress in the higher military sciences.
In Congressional Committee on Military Affairs, 1834, United States Bureau of Education, Bulletin 1912, No. 2, 10.
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Mathematics pursues its own course unrestrained, not indeed with an unbridled licence which submits to no laws, but rather with the freedom which is determined by its own nature and in conformity with its own being.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1869), 20. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 12. From the original German, “Die Mathematik folgt frei ihren eigenen Bahnen; zwar nicht mit der zügellosen Freiheit, die keinen Gesetzen unterliegt, sondern mit der Freiheit, die sich aus ihrer Natur heraus und mit ihr in Uebereinstimmung selbst determinirt.”
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Medicine deals with the states of health and disease in the human body. It is a truism of philosophy that a complete knowledge of a thing can only be obtained by elucidating its causes and antecedents, provided, of course, such causes exist. In medicine it is, therefore, necessary that causes of both health and disease should be determined.
Avicenna
'Concerning the Subject-Matter of Medicine', in The Canon of Medicine, adapted by L. Bakhtiar (1999), 11.
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Modern physics has changed nothing in the great classical disciplines of, for instance, mechanics, optics, and heat. Only the conception of hitherto unexplored regions, formed prematurely from a knowledge of only certain parts of the world, has undergone a decisive transformation. This conception, however, is always decisive for the future course of research.
In Philosophical Problems of Nuclear Science: Eight Lectures (1952), 18.
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Mortal as I am, I know that I am born for a day. But when I follow at my pleasure the serried multitude of the stars in their circular course, my feet no longer touch the earth.
Ptolemy
…...
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Mountains have been formed by one [or other] of the causes of the formation of stone, most probably from agglutinative clay which slowly dried and petrified during ages of which we have no record. It seems likely that this habitable world was in former days uninhabitable and, indeed, submerged beneath the ocean. Then, becoming exposed little by little, it petrified in the course of ages.
Avicenna
Congelatione et Conglutinatione Lapidium (1021-23), trans. E. J. Hohnyard and D. C. Mandeville (1927), 28.
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Mutations merely furnish random raw material for evolution, and rarely, if ever determine the course of the process.
From 'Fisher and Ford on the Sewall Wright Effect', American Scientist (Jul 1951), 39, No. 3, 452. Collected in Sewall Wright and ‎William B. Provine, Evolution: Selected Papers (1986), 515.
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My decision to begin research in radio astronomy was influenced both by my wartime experience with electronics and antennas and by one of my teachers, Jack Ratcliffe, who had given an excellent course on electromagnetic theory during my final undergraduate year.
From Autobiography in Wilhelm Odelberg (ed.), Les Prix Nobel en 1974/Nobel Lectures (1975)
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My father’s collection of fossils was practically unnamed, but the appearance of Phillips’ book [Geology of the Yorkshire Coast], in which most of our specimens were figured, enabled us to remedy this defect. Every evening was devoted by us to accomplishing the work. This was my first introduction to true scientific study. … Phillips’ accurate volume initiated an entirely new order of things. Many a time did I mourn over the publication of this book, and the consequences immediately resulting from it. Instead of indulging in the games and idleness to which most lads are prone, my evenings throughout a long winter were devoted to the detested labour of naming these miserable stones. Such is the short-sightedness of boyhood. Pursuing this uncongenial work gave me in my thirteenth year a thorough practical familiarity with the palaeontological treasures of Eastern Yorkshire. This early acquisition happily moulded the entire course of my future life.
In Reminiscences of a Yorkshire naturalist (1896), 12.
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My mother, my dad and I left Cuba when I was two [January, 1959]. Castro had taken control by then, and life for many ordinary people had become very difficult. My dad had worked [as a personal bodyguard for the wife of Cuban president Batista], so he was a marked man. We moved to Miami, which is about as close to Cuba as you can get without being there. It’s a Cuba-centric society. I think a lot of Cubans moved to the US thinking everything would be perfect. Personally, I have to say that those early years were not particularly happy. A lot of people didn’t want us around, and I can remember seeing signs that said: “No children. No pets. No Cubans.” Things were not made easier by the fact that Dad had begun working for the US government. At the time he couldn’t really tell us what he was doing, because it was some sort of top-secret operation. He just said he wanted to fight against what was happening back at home. [Estefan’s father was one of the many Cuban exiles taking part in the ill-fated, anti-Castro Bay of Pigs invasion to overthrow dictator Fidel Castro.] One night, Dad disappeared. I think he was so worried about telling my mother he was going that he just left her a note. There were rumors something was happening back home, but we didn’t really know where Dad had gone. It was a scary time for many Cubans. A lot of men were involved—lots of families were left without sons and fathers. By the time we found out what my dad had been doing, the attempted coup had taken place, on April 17, 1961. Initially he’d been training in Central America, but after the coup attempt he was captured and spent the next two years as a political prisoner in Cuba. That was probably the worst time for my mother and me. Not knowing what was going to happen to Dad. I was only a kid, but I had worked out where my dad was. My mother was trying to keep it a secret, so she used to tell me Dad was on a farm. Of course, I thought that she didn’t know what had really happened to him, so I used to keep up the pretense that Dad really was working on a farm. We used to do this whole pretending thing every day, trying to protect each other. Those two years had a terrible effect on my mother. She was very nervous, just going from church to church. Always carrying her rosary beads, praying her little heart out. She had her religion, and I had my music. Music was in our family. My mother was a singer, and on my father’s side there was a violinist and a pianist. My grandmother was a poet.
…...
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My picture of the world is drawn in perspective and not like a model to scale. The foreground is occupied by human beings and the stars are all as small as three-penny bits. I don't really believe in astronomy, except as a complicated description of part of the course of human and possibly animal sensation. I apply my perspective not merely to space but also to time. In time the world will cool and everything will die; but that is a long time off still and its present value at compound discount is almost nothing.
From a paper read to the Apostles, a Cambridge discussion society (1925). In 'The Foundations of Mathematics' (1925), collected in Frank Plumpton Ramsey and D.H. Mellor (ed.), Philosophical Papers (1990), Epilogue, 249. Citation to the paper, in Nils-Eric Sahlin, The Philosophy of F.P. Ramsey (1990), 225.
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My practice as a scientist is atheistic. That is to say, when I set up an experiment I assume that no god, angel or devil is going to interfere with its course; and this assumption has been justified by such success as I have achieved in my professional career. I should therefore be intellectually dishonest if I were not also atheistic in the affairs of the world.
In Fact and Faith (1934), vi.
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My second fixed idea is the uselessness of men above sixty years of age, and the incalculable benefit it would be in commercial, political, and in professional life, if as a matter of course, men stopped work at this age.
In farewell address, Johns Hopkins University, 'The Fixed Period', as quoted in Harvey Cushing, The Life of Sir William Osier (1925), vol. 1, 666. He was reflecting on his own intention to retire (now age 55) because he felt a teacher should have a fixed period of service. The title of his address was from an Anthony Trollope novel The Fixed Period which discussed the retiring of college teachers at age 60.
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Nat Sci 5 has turned more scientists into poets, and more poets into scientists, than any course ever taught on this campus.
In the Confidential Guide published by The Harvard Crimson, as quoted on his web page by Elijah Wald about the introductory biology course (Nat Sci 5) taught for decades by his father, George Wald.
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Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules [i.e. atoms] out of which these systems are built—the foundation stones of the material universe—remain unbroken and unworn. They continue to this day as they were created—perfect in number and measure and weight.
Lecture to the British Association at Bradford, 'Molecules', Nature (1873), 8, 437-441. Reprinted in James Clerk Maxwell and W. D. Niven, editor, The Scientific Papers of James Clerk Maxwell (2003), 377. By
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Natural selection is not the wind which propels the vessel, but the rudder which, by friction, now on this side and now on that, shapes the course.
Asa Gray
Illustrating the Darwinian Doctrine, in his essay 'Evolutionary Teleology,' in Darwiniana: Essays and Reviews Pertaining to Darwinism (1876), 386.
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No history of civilization can be tolerably complete which does not give considerable space to the explanation of scientific progress. If we had any doubts about this, it would suffice to ask ourselves what constitutes the essential difference between our and earlier civilizations. Throughout the course of history, in every period, and in almost every country, we find a small number of saints, of great artists, of men of science. The saints of to-day are not necessarily more saintly than those of a thousand years ago; our artists are not necessarily greater than those of early Greece; they are more likely to be inferior; and of course, our men of science are not necessarily more intelligent than those of old; yet one thing is certain, their knowledge is at once more extensive and more accurate. The acquisition and systematization of positive knowledge is the only human activity which is truly cumulative and progressive. Our civilization is essentially different from earlier ones, because our knowledge of the world and of ourselves is deeper, more precise, and more certain, because we have gradually learned to disentangle the forces of nature, and because we have contrived, by strict obedience to their laws, to capture them and to divert them to the gratification of our own needs.
Introduction to the History of Science (1927), Vol. 1, 3-4.
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Nothing can be more fatal to progress than a too confident reliance upon mathematical symbols; for the student is only too apt to take the easier course, and consider the formula and not the fact as the physical reality.
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, viii.
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Now and then, in the course of the century, a great man of science, like Darwin; a great poet, like Keats; a fine critical spirit, like M. Renan; a supreme artist, like Flaubert, has been able to isolate himself, to keep himself out of reach of the clamorous claims of others, to stand “under the shelter of the wall,” as Plato puts it, and so to realise the perfection of what was in him, to his own incomparable gain, and to the incomparable and lasting gain of the whole world.
In Sebastian Melmoth (1908), 133-134.
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Occurrences that other men would have noted only with the most casual interest became for Whitney exciting opportunities to experiment. Once he became disturbed by a scientist's seemingly endless pursuit of irrelevant details in the course of an experiment, and criticized this as being as pointless as grabbing beans out of a pot, recording the numbers, and then analyzing the results. Later that day, after he had gone home, his simile began to intrigue him, and he asked himself whether it would really be pointless to count beans gathered in such a random manner. Another man might well have dismissed this as an idle fancy, but to Whitney an opportunity to conduct an experiment was not to be overlooked. Accordingly, he set a pot of beans beside his bed, and for several days each night before retiring he would take as many beans as he could grasp in one hand and make a note of how many were in the handful. After several days had passed he was intrigued to find that the results were not as unrewarding as he had expected. He found that each handful contained more beans than the one before, indicating that with practice he was learning to grasp more and more beans. “This might be called research in morphology, the science of animal structure,” he mused. “My hand was becoming webbed … so I said to myself: never label a real experiment useless, it may reveal something unthought of but worth knowing.”
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 358-359.
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October 9, 1863
Always, however great the height of the balloon, when I have seen the horizon it has roughly appeared to be on the level of the car though of course the dip of the horizon is a very appreciable quantity or the same height as the eye. From this one might infer that, could the earth be seen without a cloud or anything to obscure it, and the boundary line of the plane approximately the same height as the eye, the general appearance would be that of a slight concavity; but I have never seen any part of the surface of the earth other than as a plane.
Towns and cities, when viewed from the balloon are like models in motion. I shall always remember the ascent of 9th October, 1863, when we passed over London about sunset. At the time when we were 7,000 feet high, and directly over London Bridge, the scene around was one that cannot probably be equalled in the world. We were still so low as not to have lost sight of the details of the spectacle which presented itself to our eyes; and with one glance the homes of 3,000,000 people could be seen, and so distinct was the view, that every large building was easily distinguishable. In fact, the whole of London was visible, and some parts most clearly. All round, the suburbs were also very distinct, with their lines of detached villas, imbedded as it were in a mass of shrubs; beyond, the country was like a garden, its fields, well marked, becoming smaller and smaller as the eye wandered farther and farther away.
Again looking down, there was the Thames, throughout its whole length, without the slightest mist, dotted over its winding course with innumerable ships and steamboats, like moving toys. Gravesend was visible, also the mouth of the Thames, and the coast around as far as Norfolk. The southern shore of the mouth of the Thames was not so clear, but the sea beyond was seen for many miles; when at a higher elevation, I looked for the coast of France, but was unable to see it. On looking round, the eye was arrested by the garden-like appearance of the county of Kent, till again London claimed yet more careful attention.
Smoke, thin and blue, was curling from it, and slowly moving away in beautiful curves, from all except one part, south of the Thames, where it was less blue and seemed more dense, till the cause became evident; it was mixed with mist rising from the ground, the southern limit of which was bounded by an even line, doubtless indicating the meeting of the subsoils of gravel and clay. The whole scene was surmounted by a canopy of blue, everywhere free from cloud, except near the horizon, where a band of cumulus and stratus extended all round, forming a fitting boundary to such a glorious view.
As seen from the earth, the sunset this evening was described as fine, the air being clear and the shadows well defined; but, as we rose to view it and its effects, the golden hues increased in intensity; their richness decreased as the distance from the sun increased, both right and left; but still as far as 90º from the sun, rose-coloured clouds extended. The remainder of the circle was completed, for the most part, by pure white cumulus of well-rounded and symmetrical forms.
I have seen London by night. I have crossed it during the day at the height of four miles. I have often admired the splendour of sky scenery, but never have I seen anything which surpassed this spectacle. The roar of the town heard at this elevation was a deep, rich, continuous sound the voice of labour. At four miles above London, all was hushed; no sound reached our ears.
Travels in the Air (1871), 99-100.
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Of course I know that “knickers” begins with a “k”. I’ve been to Oxford—it’s one of the first things they teach you.
As quoted in William Reville, 'The Science of Writing a Good Joke', The Irish Times (5 Jun 2000).
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Of course we have no means of staying back for any length of Time, any more than a savage or an animal has of staying six feet above the ground. But a civilized man is better off than the savage in this respect. He can go up against gravitation in a balloon, and why should he not hope that ultimately he may be able to stop or accelerate his drift along the Time-Dimension, or even turn about and travel the other way?
In The Time Machine (1898), 13.
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Of course, Behaviourism “works.” So does torture. Give me a no-nonsense, down-to-earth behaviourist, a few drugs, and simple electrical appliances, and in six months I will have him reciting the Athanasian Creed in public.
A Certain World: A Commonplace Book (1971),33.
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Often the great scientists, by turning the problem around a bit, changed a defect to an asset. For example, many scientists when they found they couldn't do a problem finally began to study why not. They then turned it around the other way and said, “But of course, this is what it is” and got an important result.
'You and Your Research', Bell Communications Research Colloquium Seminar, 7 Mar 1986.
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Oh! That the Chemist’s magic art
Could crystallize this sacred treasure!…
That very law which moulds a tear,
And bids it trickle from its source;
That law preserves the earth a sphere,
And guides the planets in their course.
Referring to the Law of Gravitation. From Poem, 'On a Tear' (c.1813-15), in Samuel Rogers et al., The Poetical Works of Rogers, Campbell, J. Montombery, Lamb, and Kirke White (1836), 101.
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On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
'The Work of Nicholas Bourbaki'American Mathematical Monthly (1970), 77, 134. In Carl C. Gaither, Alma E. Cavazos-Gaither, Mathematically Speaking: a Dictionary of Quotations (), 194.
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On the 20th of May 1747, I took twelve patients in the scurvy, on board the Salisbury at sea. Their cases were as similar as I could have them. They all in general had putrid gums, the spots and lassitude, with weakness of their knees. They lay together in one place, being a proper apartment for the sick in the fore-hold; and had one diet common to all, viz, water-gruel sweetened with sugar in the morning; fresh mutton-broth often times for dinner; at other times puddings, boiled biscuit with sugar, &c.; and for supper, barley and raisins, rice and currents, sago and wine, or the like.
Two of these were ordered each a quart of cider a-day. Two others took twenty-five gutta of elixir vitriol three times a-day, upon an empty stomach; using a gargle strongly acidulated with it for their mouths. Two others took two spoonfuls of vinegar three times a-day, upon an empty stomach; having their gruels and their other food well acidulated with it, as also the gargle for their mouth. Two of the worst patients, with the tendons in the ham rigid, (a symptom none of the rest had), were put under a course of sea-water. Of this they drank half a pint every day, and sometimes more or less as it operated, by way of gentle physics. The others had each two oranges and one lemon given them every day. These they eat with greediness, at different times, upon an empty stomach. They continued but six days under this course, having consumed the quantity that could be spared. The two remaining patients, took the bigness of a nutmeg three times a-day, of an electuary recommended by an hospital-surgeon, made of garlic, mustard-seed, rad. raphan. balsam of Peru, and gum myrrh; using for common drink, barley-water well acidulated with tamarinds; by a decoction of which, with the addition of cremor tartar, they were gently purged three or four times during the course.
The consequence was, that the most sudden and visible good effects were perceived from the use of the oranges and lemons; one of those who had taken them, being at the end of six days fit for duty. …
Next to the oranges, I thought the cider had the best effects.
A Treatise of the Scurvy (1753), 191-193. Quoted in Carleton Ellis and Annie Louise Macleod, Vital Factors of Foods: Vitamins and Nutrition (1922), 229-230.
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One doesn’t really understand what mathematics is until at least halfway through college when one takes abstract math courses and learns about proofs.
In 'A Personal Profile of Karen K. Uhlenbeck', collected in Susan Ambrose et al., Journeys of Women in Science and Engineering, No Universal Constants (1999).
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One of the great commandments of science is, 'Mistrust arguments from authority'. (Scientists, being primates, and thus given to dominance hierarchies, of course do not always follow this commandment.)
The Demon-Haunted World: Science as a Candle in the Dark (1996), 31.
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Only human beings were given the power of speech, because only to them was it necessary. It was not necessary that either angels or the lower animals should be able to speak; rather, this power would have been wasted on them, and nature, of course, hates to do anything superfluous. … As for the lower animals, since they are guided only by their natural instinct, it was not necessary for them to be given the power of speech. For all animals that belong to the same species are identical in respect of action and feeling; and thus they can know the actions and feelings of others by knowing their own. Between creatures of different species, on the other hand, not only was speech unnecessary, but it would have been injurious, since there could have been no friendly exchange between them.
In Dante Alighieri and Steven Botterill (trans.), De Vulgari Eloquentia (1305), Book 1, Chap 2. from the Latin original.
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Our attention will focus on the institutional context of technological innovation rather than … individual inventors, for the actual course of work that leads to the conception and use of technology always involves a group that has worked for a considerable period of time on the basic idea before success is achieved.
In The Social Context of Innovation: Bureaucrats, Families, and Heroes in the Early Industrial Revolution as Foreseen in Bacon’s New Atlantis (1982, 2003), 3.
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Our great mistake in education is ... the worship of book-learning—the confusion of instruction and education. We strain the memory instead of cultivating the mind. … We ought to follow exactly the opposite course with children—to give them a wholesome variety of mental food, and endeavour to cultivate their tastes, rather than to fill their minds with dry facts.
The Pleasures of Life (Appleton, 1887), 183-184, or (2007), 71.
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Our model of Nature should not be like a building—a handsome structure for the populace to admire, until in the course of time some one takes away a corner stone and the edifice comes toppling down. It should be like an engine with movable parts. We need not fix the position of any one lever; that is to be adjusted from time to time as the latest observations indicate. The aim of the theorist is to know the train of wheels which the lever sets in motion—that binding of the parts which is the soul of the engine.
In 'The Internal Constitution of the Stars', The Scientific Monthly (Oct 1920), 11, No. 4, 302.
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Pain is a sensation produced by something contrary to the course of nature and this sensation is set up by one of two circumstances: either a very sudden change of the temperament (or the bad effect of a contrary temperament) or a solution of continuity.
Avicenna
'A General Discussion of the Causes of Pain', in The Canon of Medicine, adapted by L. Bakhtiar (1999), 246.
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Palliative care should be an integral part of cancer care and not be associated exclusively with terminal care. Many patients need it early in the course of their disease.
Anonymous
Improving the Quality of Cancer Care. A Report of the Expert Advisory Group on Cancer to the Chief Medical Officers of England and Wales (1995). Quoted in Jessica Corner and Christopher Bailey, Cancer Nursing (2001),543.
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People give ear to an upstart astrologer [Copernicus] who strove to show that the earth revolves, not the heavens or the firmament, the sun and the moon. Whoever wishes to appear clever must devise some new system, which of all systems is of course the very best. This fool wishes to reverse the entire science of astronomy.
c. 1543, in The Experts Speak by Christopher Cerf and Victor Navasky (1998).
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People like you and I, though mortal of course like everyone else, do not grow old no matter how long we live...[We] never cease to stand like curious children before the great mystery into which we were born.
…...
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People travel to wonder at the height of mountains, at the huge waves of the sea, at the long courses of rivers, at the vast compass of the ocean, at the circular motion of the stars; and they pass by themselves without wondering.
In Circulations: Webster's Quotations, Facts and Phrases, 1.
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Physicists do, of course, show a healthy respect for High Voltage, Radiation, and Liquid Hydrogen signs. They are not reckless. I can think of only six who have been killed on the job.
In Adventures of a Physicist (1987), 14.
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Picture yourself during the early 1920's inside the dome of the [Mount Wilson Observatory]. … [Milton] Humason is showing [Harlow] Shapley stars he had found in the Andromeda Nebula that appeared and disappeared on photographs of that object. The famous astronomer very patiently explains that these objects could not be stars because the Nebula was a nearby gaseous cloud within our own Milky Way system. Shapley takes his handkerchief from his pocket and wipes the identifying marks off the back of the photographic plate.
Of course, Hubble came along in 1924 and showed that it was just these Cepheid variable stars in the Andromeda Nebula which proved it was a separate galaxy system.
In Quasars, Redshifts and Controversies (1998), 168. Arp writes that this was “a piece of real history which I happen to know because it was told to me by one of the participants. It dramatically illustrate the critical role of discordant evidence.”
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Plants, generally speaking, meet the impact of the terrestrial environment head on, although of course they in turn modify the physical environment by adventitious group activity. The individual plant cannot select its habitat; its location is largely determined by the vagaries of the dispersal of seeds or spores and is thus profoundly affected by chance. Because of their mobility and their capacity for acceptance or rejection terrestrial animals, in contrast, can and do actively seek out and utilize the facets of the environment that allow their physiological capacities to function adequately. This means that an animal by its behavior can fit the environment to its physiology by selecting situations in which its physiological capacities can cope with physical conditions. If one accepts this idea, it follows that there is no such thing as The Environment, for there exist as many different terrestrial environments as there are species of animals.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
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Preferring a search for objective reality over revelation is another way of satisfying religious hunger. It is an endeavor almost as old as civilization and intertwined with traditional religion, but it follows a very different course—a stoic’s creed, an acquired taste, a guidebook to adventure plotted across rough terrain. It aims to save the spirit, not by surrender but by liberation of the human mind. Its central tenet, as Einstein knew, is the unification of knowledge. When we have unified enough certain knowledge, we will understand who we are and why we are here. If those committed to the quest fail, they will be forgiven. When lost, they will find another way.
In Consilience: The Unity of Knowledge (1998), 5.
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Primates stand at a turning point in the course of evolution. Primates are to the biologist what viruses are to the biochemist. They can be analysed and partly understood according to the rules of a simpler discipline, but they also present another level of complexity: viruses are living chemicals, and primates are animals who love and hate and think.
'The Evolution of Primate Behavior: A survey of the primate order traces the progressive development of intelligence as a way of life', American Scientist (1985), 73, 288.
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Put glibly:
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
Of course, you seldom, if ever, see either pure state.
In The Art of Doing Science and Engineering: Learning to Learn (1975, 2005), 5.
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Quality control is achieved most efficiently, of course, not by the inspection operation itself, but by getting at causes.
As coauthor with Harry Gutekius Romig in Sampling Inspection Tables: Single and Double Sampling (1944), 41.
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Relations between authors and referees are, of course, almost always strained. Authors are convinced that the malicious stupidity of the referee is alone preventing them from laying their discoveries before an admiring world. Referees are convinced that authors are too arrogant and obtuse to recognize blatant fallacies in their own reasoning, even when these have been called to their attention with crystalline lucidity. All physicists know this, because all physicists are both authors and referees, but it does no good. The ability of one person to hold both views is an example of what Bohr called complementarity.
In Boojums All the Way Through: Communicating Science in a Prosaic Age (1990), 19-20.
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Religion reveals the meaning of life, and science only applies this meaning to the course of circumstances.
My Religion, translated by Huntington Smith (3rd Ed., 1885), 121.
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Say’st thou, “The Course of Nature governs All?”
The Course of Nature is the Art of GOD.
The Complaint: or, Night-Thoughts on Life, Death, and Immortality (1742, 1750), Night 9, 273.
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Science starts with preconception, with the common culture, and with common sense. It moves on to observation, is marked by the discovery of paradox, and is then concerned with the correction of preconception. It moves then to use these corrections for the designing of further observation and for more refined experiment. And as it moves along this course the nature of the evidence and experience that nourish it becomes more and more unfamiliar; it is not just the language that is strange [to common culture].
From 'The Growth of Science and the Structure of Culture', Daedalus (Winter 1958), 87, No. 1, 67.
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Sea-water is, of course, opaque and this is the first difficulty that faces the oceanographer. Most of the tools needed to investigate the sea must use physical principles which are more complicated than the optical methods that are so satisfactory for studying the surface features of the land.
In 'Man Explores the Sea', Journal of the Royal Society of Arts (Sep 1963), 111, No. 5086, 786.
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She would have solved it, but it would have come out in stages. For the feminists, however, she has become a doomed heroine, and they have seized upon her as an icon, which is not, of course, her fault. Rosalind was not a feminist in the ordinary sense, but she was determined to be treated equally like anybody else.
'Rosalind Franklin and the Discovery of the Structure of DNA'. Cited in Brenda Maddox, The Dark Lady of DNA (2002), 326.
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Signs and symptoms indicate the present, past and future states of the three states of the body (health, illness, neutrality). According to Galen, knowledge of the present state is of advantage only to the patient as it helps him to follow the proper course of management. Knowledge of the past state is useful only to the physician inasmuch as its disclosure by him to the patient brings him a greater respect for his professional advice. Knowledge of the future state is useful to both. It gives an opportunity to the patient to be forewarned to adopt necessary preventative measures and it enhances the reputation of the physician by correctly forecasting the future developments.
Avicenna
'The Signs and Symptoms (Diagnosis): General Remarks,' in The Canon of Medicine, adapted by L. Bakhtiar (1999), 259.
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Since many cases are known in which the specificities of antigens and enzymes appear to bear a direct relation to gene specificities, it seems reasonable to suppose that the gene’s primary and possibly sole function is in directing the final configurations of protein molecules.
Assuming that each specific protein of the organism has its unique configuration copied from that of a gene, it follows that every enzyme whose specificity depends on a protein should be subject to modification or inactivation through gene mutation. This would, of course, mean that the reaction normally catalyzed by the enzyme in question would either have its rate or products modified or be blocked entirely.
Such a view does not mean that genes directly “make” proteins. Regardless of precisely how proteins are synthesized, and from what component parts, these parts must themselves be synthesized by reactions which are enzymatically catalyzed and which in turn depend on the functioning of many genes. Thus in the synthesis of a single protein molecule, probably at least several hundred different genes contribute. But the final molecule corresponds to only one of them and this is the gene we visualize as being in primary control.
In 'Genetics and Metabolism in Neurospora', Physiological Reviews, 1945, 25, 660.
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Since the invention of the microprocessor, the cost of moving a byte of information around has fallen on the order of 10-million-fold. Never before in the human history has any product or service gotten 10 million times cheaper-much less in the course of a couple decades. That’s as if a 747 plane, once at $150 million a piece, could now be bought for about the price of a large pizza.
…...
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So it is clear, since there will be no end to time and the world is eternal, that neither the Tanais nor the Nile has always been flowing, but that the region whence they flow was once dry; for their action has an end, but time does not. And this will be equally true of all other rivers. But if rivers come into existence and perish and the same parts of the earth were not always moist, the sea must needs change correspondingly. And if the sea is always advancing in one place and receding in another it is clear that the same parts of the whole earth are not always either sea or land, but that all this changes in the course of time.
Aristotle
Meteorology, 353a, 14-24. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 575.
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Some people believe in fate, others don’t. I do, and I don't. It may seem at times as if invisible fingers move us about like puppets on strings. But for sure, we are not born to be dragged along. We can grab the strings ourselves and adjust our course at every crossroad, or take off at any little trail into the unknown.
Opening paragraph in 'Foreword to the 35th Anniversary Edition', Kon-Tiki: Across the Pacific by Raft (1990), xi.
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Some recent work by E. Fermi and L. Szilard, which has been communicated to me in manuscript, leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. Certain aspects of the situation seem to call for watchfulness and, if necessary, quick action on the part of the Administration. …
In the course of the last four months it has been made probable … that it may become possible to set up nuclear chain reactions in a large mass of uranium, by which vast amounts of power and large quantities of new radium-like elements would be generated. Now it appears almost certain that this could be achieved in the immediate future.
This new phenomenon would also lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may thus be constructed. A single bomb of this type, carried by boat or exploded in a port, might well destroy the whole port altogether with some of the surrounding territory. However, such bombs might well prove to be too heavy for transportation by air.
Letter to President Franklin P. Roosevelt, (2 Aug 1939, delivered 11 Oct 1939). In Otto Nathan and Heinz Norden (Eds.) Einstein on Peace (1960, reprinted 1981), 294-95.
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Sometime in my early teens, I started feeling an inner urgency, ups and downs of excitement and frustration, caused by such unlikely occupations as reading Granville’s course of calculus ... I found this book in the attic of a friend’s apartment. Among other standard stuff, it contained the notorious epsilon-delta definition of continuous functions. After struggling with this definition for some time (it was the hot Crimean summer, and I was sitting in the shadow of a dusty apple tree), I got so angry that I dug a shallow grave for the book between the roots, buried it there, and left in disdain. Rain started in an hour. I ran back to the tree and exhumed the poor thing. Thus, I discovered that I loved it, regardless.
'Mathematics as Profession and vocation', in V. Arnold et al. (eds.), Mathematics: Frontiers and Perspectives (2000), 153. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 79.
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Sometimes dreams alter the course of an entire life.
…...
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Students using astrophysical textbooks remain essentially ignorant of even the existence of plasma concepts, despite the fact that some of them have been known for half a century. The conclusion is that astrophysics is too important to be left in the hands of astrophysicists who have gotten their main knowledge from these textbooks. Earthbound and space telescope data must be treated by scientists who are familiar with laboratory and magnetospheric physics and circuit theory, and of course with modern plasma theory.
[Lamenting the traditional neglect of plasma physics]
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),197.
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Suicide is merely the product of the general condition of society, and that the individual felon only carries into effect what is a necessary consequence of preceding circumstances. In a given state of society, a certain number of persons must put an end to their own life. This is the general law; and the special question as to who shall commit the crime depends of course upon special laws; which, however, in their total action, must obey the large social law to which they are all subordinate. And the power of the larger law is so irresistible, that neither the love of life nor the fear of another world can avail any thing towards even checking its operation.
In History of Civilization in England (1857, 1904), 15-16.
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Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]
In Darwinism, chap. 15.
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The 'stream' we call science always flows forward; sometimes reactionary beavers block its flow, but the stream is never defeated by this; it accumulates, gathers strength; its waters get over the barrage and continue on their course. The advancement of science is the advancement of God, for science is nothing but human intelligence, and human intelligence is the most valuable treasure God has bequeathed us.
From the play Galileo Galilei (2001) .
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The 4th sort of creatures... which moved through the 3 former sorts, were incredibly small, and so small in my eye that I judged, that if 100 of them lay [stretched out] one by another, they would not equal the length of a grain of course Sand; and according to this estimate, ten hundred thousand of them could not equal the dimensions of a grain of such course Sand. There was discover’d by me a fifth sort, which had near the thickness of the former, but they were almost twice as long.
The first time bacteria were observed.
Letter to H. Oldenburg, 9 Oct 1676. In The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 95.
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The achievements of the Beagle did not just depend on FitzRoy’s skill as a hydrographer, nor on Darwin’s skill as a natural scientist, but on the thoroughly effective fashion in which everyone on board pulled together. Of course Darwin and FitzRoy had their quarrels, but all things considered, they were remarkably infrequent. To have shared such cramped quarters for nearly five years with a man often suffering from serious depression, prostrate part of the time with sea sickness, with so little friction, Darwin must have been one of the best-natured people ever! This is, indeed, apparent in his letters. And anyone who has participated in a scientific expedition will agree that when he wrote from Valparaiso in July 1834 that ‘The Captain keeps all smooth by rowing everyone in turn, which of course he has as much right to do as a gamekeeper to shoot partridges on the first of September’, he was putting a finger on an important ingredient in the Beagle’s success.
From Introduction to The Beagle Record (1979, 2012), 9.
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The advanced course in physics began with Rutherford’s lectures. I was the only woman student who attended them and the regulations required that women should sit by themselves in the front row. There had been a time when a chaperone was necessary but mercifully that day was past. At every lecture Rutherford would gaze at me pointedly, as I sat by myself under his very nose, and would begin in his stentorian voice: “Ladies and Gentlemen”. All the boys regularly greeted this witticism with thunderous applause, stamping with their feet in the traditional manner, and at every lecture I wished I could sink into the earth. To this day I instinctively take my place as far back as possible in a lecture room.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 118.
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The aim of scientific thought, then, is to apply past experience to new circumstances; the instrument is an observed uniformity in the course of events. By the use of this instrument it gives us information transcending our experience, it enables us to infer things that we have not seen from things that we have seen; and the evidence for the truth of that information depends on our supposing that the uniformity holds good beyond our experience.
'On the Aims and Instruments of Scientific Thought,' a Lecture delivered before the members of the British Association, at Brighton, on 19 Aug 1872, in Leslie Stephen and Frederick Pollock (eds.), Lectures and Essays, by the Late William Kingdon Clifford (1886), 90.
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The alternating current will kill people, of course. So will gunpowder, and dynamite, and whisky, and lots of other things; but we have a system whereby the deadly electricity of the alternating current can do no harm unless a man is fool enough to swallow a whole dynamo.
(1884). As quoted in Francis Ellington Leupp, George Westinghouse: His Life and Achievements (1918), 149.
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The bird which is drawn to the water by its need of finding there the prey on which it lives, separates the digits of its feet in trying to strike the water and move about on the surface. The skin which unites these digits at their base acquires the habit of being stretched by these continually repeated separations of the digits; thus in course of time there are formed large webs which unite the digits of ducks, geese, etc., as we actually find them. In the same way efforts to swim, that is to push against the water so as to move about in it, have stretched the membranes between the digits of frogs, sea-tortoises, the otter, beaver, etc.
On the other hand, a bird which is accustomed to perch on trees and which springs from individuals all of whom had acquired this habit, necessarily has longer digits on its feet and differently shaped from those of the aquatic animals that I have just named. Its claws in time become lengthened, sharpened and curved into hooks, to clasp the branches on which the animal so often rests.
We find in the same way that the bird of the water-side which does not like swimming and yet is in need of going to the water's edge to secure its prey, is continually liable to sink into the mud. Now this bird tries to act in such a way that its body should not be immersed in the liquid, and hence makes its best efforts to stretch and lengthen its legs. The long-established habit acquired by this bird and all its race of continually stretching and lengthening its legs, results in the individuals of this race becoming raised as though on stilts, and gradually obtaining long, bare legs, denuded of feathers up to the thighs and often higher still.
Philosophie Zoologique (1809), Vol. 1, 249-50, trans. Hugh Elliot (1914), 119-20.
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The blood, the fountain whence the spirits flow,
The generous stream that waters every part,
And motion, vigour, and warm life conveys
To every Particle that moves or lives;
This vital fluid, thro' unnumber'd tubes
Pour'd by the heart, and to the heart again
Refunded; scourg'd forever round and round;
Enrag'd with heat and toil, at last forgets
Its balmy nature; virulent and thin
It grows; and now, but that a thousand gates
Are open to its flight, it would destroy
The parts it cherish' d and repair'd before.
Besides, the flexible and tender tubes
Melt in the mildest, most nectareous tide
That ripening Nature rolls; as in the stream
Its crumbling banks; but what the vital force
Of plastic fluids hourly batters down,
That very force, those plastic particles
Rebuild: so mutable the state of man.
For this the watchful appetite was given,
Daily with fresh materials to repair
This unavoidable expense of life,
This necessary waste of flesh and blood.
Hence the concoctive powers, with various art,
Subdue the cruder aliments to chyle;
The chyle to blood; the foamy purple tide
To liquors, which through finer arteries
To different parts their winding course pursue;
To try new changes, and new forms put on,
Or for the public, or some private use.
The Art of Preserving Health (1744), book 2, I. 12-23, p.15-16.
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The changing of Bodies into Light, and Light into Bodies, is very conformable to the Course of Nature, which seems delighted with Transmutations.
Opticks, 2nd edition (1718), Book 3, Query 30, 349.
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The commissioners of the treasury moved the king, for the relief of his estate, to disafforest some forests of his, explaining themselves of such forests as lay out of the way, not near any of the king’s houses, nor in the course of his progress; whereof he should never have use nor pleasure. “Why,” saith the king, “do you think that Solomon had use and pleasure of all his three hundred concubines?”
In 'A Collection of Apophthegms, New and Old' (1625). As given in Essays, Moral, Economical, and Political: A New Edition, With the Latin Quotations Translated (1813), No. 9, 262. King James I was named in the preceding Apophthegm No. 3.
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The conclusion forced upon me in the course of a life devoted to natural science is that the universe as it is assumed to be in physical science is only an idealized world, while the real universe is the spiritual universe in which spiritual values count for everything.
The Sciences and Philosophy: Gifford Lectures, University of Glasgow, 1927 & 1925 (1929), 273.
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The course of the line we indicated as forming our grandest terrestrial fold [along the shores of Japan] returns upon itself. It is an endless fold, an endless band, the common possession of two sciences. It is geological in origin, geographical in effect. It is the wedding ring of geology and geography, uniting them at once and for ever in indissoluble union.
Presidential Address to the Geology Section, Report of the British Association for the Advancement of Science (1892), 705.
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The development of an organism … may be considered as the execution of a 'developmental program' present in the fertilized egg. … A central task of developmental biology is to discover the underlying algorithm from the course of development.
Aristid Lindenmayer and Grzegorz Rozenberg, Automata, Languages, Development (1976), v.
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The difficulties connected with my criterion of demarcation (D) are important, but must not be exaggerated. It is vague, since it is a methodological rule, and since the demarcation between science and nonscience is vague. But it is more than sharp enough to make a distinction between many physical theories on the one hand, and metaphysical theories, such as psychoanalysis, or Marxism (in its present form), on the other. This is, of course, one of my main theses; and nobody who has not understood it can be said to have understood my theory.
The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the 'means of production' would lead to social, political, and ideological developments, rather than the other way round.
But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin's and Stalin's ideology that Russia must push forward with its industrialization ('Socialism is dictatorship of the proletariat plus electrification') which promoted the new development of the means of production.
Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).
However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.
Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler's break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)
The point is very clear. Neither Freud nor Adler excludes any particular person's acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud's theory; the theory was compatible with everything that could happen—even without any special immunization treatment.
Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.
'The Problem of Demarcation' (1974). Collected in David Miller (ed.) Popper Selections (1985), 127-128.
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The discovery of the conic sections, attributed to Plato, first threw open the higher species of form to the contemplation of geometers. But for this discovery, which was probably regarded in Plato’s tune and long after him, as the unprofitable amusement of a speculative brain, the whole course of practical philosophy of the present day, of the science of astronomy, of the theory of projectiles, of the art of navigation, might have run in a different channel; and the greatest discovery that has ever been made in the history of the world, the law of universal gravitation, with its innumerable direct and indirect consequences and applications to every department of human research and industry, might never to this hour have been elicited.
In 'A Probationary Lecture on Geometry, Collected Mathematical Papers, Vol. 2 (1908), 7.
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The education of the intellect is a great business, but an unconsecrated intellect is a sight than which the sun in all his daily course can see no sadder.
From a book review giving the quote in an extract from John W. Chadwick’s book, The Education of Conscience in Herald of Health (Mar 1876), 27, 135. Note that this is clearly identified as the work of JOHN Chadwick. IMPORTANT NOTE: It is thus apparently NOT a quote by Edwin Chadwick, to whom it is attributed in 19th century quote collections, and now virally spread across the web. John Chadwick writes sermons; Edwin Chadwick writes on public health and clearly this quote is typical of lines from a sermon. The error traces back at least as early as Tryon Edwards, A Dictionary of Thoughts: Being a Cyclopedia of Laconic Quotations (1891), 266. Edwards gives the quote in the body of the text, attributed with the single word, “Chadwick,” then, in the prefatory material, the 'Index of Authors' lists only “Chadwick, Erwin”. Since the book review cited above makes clear the quote was written in a book by John W. Chadwick, Tryon Edwards must be in error.
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The efforts of most human-beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. Beneath the effort directed toward the accumulation of worldly goods lies all too frequently the illusion that this is the most substantial and desirable end to be achieved; but there is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual's own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.
In letter (1 May 1935), Letters to the Editor, 'The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician', New York Times (4 May 1935), 12.
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The endeavour to observe oneself must inevitably introduce changes into the course of mental events,—changes which could not have occurred without it, and whose usual consequence is that the very process which was to have been observed disappears from consciousness.
In Principles of Physiological Psychology (1873, 1904), Vol. 1, 5.
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The fertilized ovum of a mouse and a whale look much alike, but differences quickly show up in the course of their development. If we could study their molecules with the naked eyes, we would see the differences from the start.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 73.
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The fertilized ovum of a mouse and a whale look much alike, but differences quickly show up in the course of their development. If we could study their molecules with the naked eyes, we would see the differences from the start.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 73.
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The first drizzling shower is born...
[Then] the flood comes down,
Threatening with deluge this devoted town. ...
Now from all parts the swelling kennels flow,
And bear their trophies with them as they go:
Filth of all hues and odors seem to tell
What street they sailed from, by their sight and smell.
They, as each torrent drives with rapid force,
From Smithfield or St. Pulchre’s shape their course,
And in huge confluence joined at Snow Hill ridge,
Fall from the conduit prone to Holborn Bridge.
Sweepings from butchers’ stalls, dung, guts, and blood.
Drowned puppies, stinking sprats, all drenched in mud,
Dead cats, and turnip tops, come tumbling down the flood.
Poem, 'A Description of a City Shower', first published in the Tatler, No. 238 (17 Oct 1710). Reprinted in Pope and Swift's Miscellanies in Prose and Verse (1711, 1721), 225-227. Swift wrote at the time in London that the street surface open gutters (kennels) were the primary means for handling stormwater flows and disposing of every kind of human and animal waste. “Devoted” means overwhelmed. Smithfield was a market with butchers' shops and cattle and sheep pens. St. Sepulchre refers to a church in Holborn. The Holborn Conduit was taken down in 1746. Below Holborn Bridge ran the Fleet Ditch (a stagnant remnant of the former Fleet River after its water supply had been diverted). It was joined by a stream called Snow Hill. Notes printed with the poem collected in Jay Parini, The Wadsworth Anthology Of Poetry (2005), 723-724.
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The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up, or to the number of people who subsequently join them after the show/match/party/gig, or to the number of people who leave when they see who else has turned up.
The second nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive. Recipriversexclusons now play a vital part in many branches of math, including statistics and accountancy and also form the basic equations used to engineer the Somebody Else’s Problem field.
The third and most mysterious piece of nonabsoluteness of all lies in the relationship between the number of items on the check [bill], the cost of each item, the number of people at the table and what they are each prepared to pay for. (The number of people who have actually brought any money is only a subphenomenon of this field.)
Life, the Universe and Everything (1982, 1995), 47-48.
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The footsteps of Nature are to be trac'd, not only in her ordinary course, but when she seems to be put to her shifts, to make many doublings and turnings, and to use some kind of art in endeavouring to avoid our discovery.
Micrographia (1665, reprint 2008), 17.
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The framing of hypotheses is, for the enquirer after truth, not the end, but the beginning of his work. Each of his systems is invented, not that he may admire it and follow it into all its consistent consequences, but that he may make it the occasion of a course of active experiment and observation. And if the results of this process contradict his fundamental assumptions, however ingenious, however symmetrical, however elegant his system may be, he rejects it without hesitation. He allows no natural yearning for the offspring of his own mind to draw him aside from the higher duty of loyalty to his sovereign, Truth, to her he not only gives his affections and his wishes, but strenuous labour and scrupulous minuteness of attention.
Philosophy of the Inductive Sciences (1847), Vol. 2, 57.
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The game of Chess is not merely an idle amusement. Several very valuable qualities of the mind, useful in the course of human life, are to be acquired or strengthened by it so as to become habits ready on all occasions.
In The Morals of Chess. As quoted in The Gentleman's Magazine, and Historical Chronicle (1787), 590.
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The generation of seeds ... is therefore marvelous and analogous to the other productions of living things. For first of all an umbilicus appears. ... Its extremity gradually expands and after gathering a colliquamentous ichor becomes analogous to an amnion. ... In the course of time the seed or fetus begins to become visible.
'On the Developmental Process', in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 850.
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The genotypic constitution of a gamete or a zygote may be parallelized with a complicated chemico-physical structure. This reacts exclusively in consequence of its realized state, but not in consequence of the history of its creation. So it may be with the genotypical constitution of gametes and zygotes: its history is without influence upon its reactions, which are determined exclusively by its actual nature. The genotype-conception is thus an 'ahistoric' view of the reactions of living beings—of course only as far as true heredity is concerned. This view is an analog to the chemical view, as already pointed out; chemical compounds have no compromising ante-act, H2O is always H2O, and reacts always in the same manner, whatsoever may be the 'history' of its formation or the earlier states of its elements. I suggest that it is useful to emphasize this 'radical' ahistoric genotype-conception of heredity in its strict antagonism to the transmission—or phenotype-view.
'The Genotype Conception of Heredity', The American Naturalist (1911), 45, 129.
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The golden age of mathematics—that was not the age of Euclid, it is ours. Ours is the age when no less than six international congresses have been held in the course of nine years. It is in our day that more than a dozen mathematical societies contain a growing membership of more than two thousand men representing the centers of scientific light throughout the great culture nations of the world. It is in our time that over five hundred scientific journals are each devoted in part, while more than two score others are devoted exclusively, to the publication of mathematics. It is in our time that the Jahrbuch über die Fortschritte der Mathematik, though admitting only condensed abstracts with titles, and not reporting on all the journals, has, nevertheless, grown to nearly forty huge volumes in as many years. It is in our time that as many as two thousand books and memoirs drop from the mathematical press of the world in a single year, the estimated number mounting up to fifty thousand in the last generation. Finally, to adduce yet another evidence of a similar kind, it requires not less than seven ponderous tomes of the forthcoming Encyclopaedie der Mathematischen Wissenschaften to contain, not expositions, not demonstrations, but merely compact reports and bibliographic notices sketching developments that have taken place since the beginning of the nineteenth century.
In Lectures on Science, Philosophy and Art (1908), 8.
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The great heroes and heroines of our society are of course the teachers, and in particular the teachers of kids in their first years. Once a child has been shown what the natural world is, it will live with them forever.
As quoted in Alexandra Pope, 'Attenborough Awarded RCGS Gold', Canadian Geographic, (May 2017), 137, No. 3, 73.
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The history of a species, or any natural phenomenon that requires unbroken continuity in a world of trouble, works like a batting streak. All are games of a gambler playing with a limited stake against a house with infinite resources. The gambler must eventually go bust. His aim can only be to stick around as long as possible, to have some fun while he’s at it, and, if he happens to be a moral agent as well, to worry about staying the course with honor.
In Bully for Brontosaurus: Reflections in Natural History (1991), 471-472.
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The history of aëronautic adventure affords a curious illustration of the same [dip of the horizon] principle. The late Mr. Sadler, the celebrated aeronaut, ascended on one occasion in a balloon from Dublin, and was wafted across the Irish Channel, when, on his approach to the Welsh coast, the balloon descended nearly to the surface of the sea. By this time the sun was set, and the shades of evening began to close in. He threw out nearly all his ballast, and suddenly sprang upwards to a great height, and by so doing brought his horizon to dip below the sun, producing the whole phenomenon of a western sunrise. Subsequently descending in Wales, he of course witnessed a second sunset on the same evening.
This describes how a rapidly ascending balloonist can see more of a setting sun, from the top down, as the viewer gradually rises more and thus sees further, beyond the curvature of the earth. The sun gradually appears as if at sunrise. It is the reverse of the view of a ship sailing toward the horizon which disappears from its hull up to the tip of the mast. In Outlines of Astronomy (1849), 20. A similar description appeared earlier, in Astronomy (1833), 36, which also footnoted Herschel's comment that he had this anecdote from Dr. Lardner, who was present at the ascent
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The History of Evolution of Organisms consists of two kindred and closely connected parts: Ontogeny, which is the history of the evolution of individual organisms, and Phylogeny, which is the history of the evolution of organic tribes. Ontogency is a brief and rapid recapitulation of Phylogeny, dependent on the physiological functions of Heredity (reproduction) and Adaptation (nutrition). The individual organism reproduces in the rapid and short course of its own evolution the most important of the changes in form through which its ancestors, according to laws of Heredity and Adaptation, have passed in the slow and long course of their palaeontological evolution.
Translated from his Generelle Morphologie (1866) as an epigraph to Chap. 1, The Evolution of Man, (1886), Vol 1, 1-2.
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The history of mathematics, as of any science, is to some extent the story of the continual replacement of one set of misconceptions by another. This is of course no cause for despair, for the newly instated assumptions very often possess the merit of being closer approximations to truth than those that they replace.
In 'Consistency and Completeness—A Résumé', The American Mathematical Monthly (May 1956), 63, No.5, 295.
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The hypothesis that man is not free is essential to the application of scientific method to the study of human behavior. The free inner man who is held responsible for the behavior of the external biological organism is only a prescientific substitute for the kinds of causes which are discovered in the course of a scientific analysis.
In Science and Human Behavior (1953), 447.
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The idea of making a fault a subject of study and not an object to be merely determined has been the most important step in the course of my methods of observation. If I have obtained some new results it is to this that I owe it.
'Notice sur les Travaux Scientifiques de Marcel Bertrand' (1894). In Geological Society of London, The Quarterly Journal of the Geological Society of London (May 1908), 64, li.
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The increasing technicality of the terminology employed is also a serious difficulty. It has become necessary to learn an extensive vocabulary before a book in even a limited department of science can be consulted with much profit. This change, of course, has its advantages for the initiated, in securing precision and concisement of statement; but it tends to narrow the field in which an investigator can labour, and it cannot fail to become, in the future, a serious impediment to wide inductive generalisations.
Year Book of Science (1892), preface, from review in Chemical News and Journal of Physical Science (14 Apr 1892), 65, 190.
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The lessons of science should be experimental also. The sight of a planet through a telescope is worth all the course on astronomy; the shock of the electric spark in the elbow outvalues all theories; the taste of the nitrous oxide, the firing of an artificial volcano, are better than volumes of chemistry.
The Prose Works of Ralph Waldo Emerson (1870), 552.
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The majority of mathematical truths now possessed by us presuppose the intellectual toil of many centuries. A mathematician, therefore, who wishes today to acquire a thorough understanding of modern research in this department, must think over again in quickened tempo the mathematical labors of several centuries. This constant dependence of new truths on old ones stamps mathematics as a science of uncommon exclusiveness and renders it generally impossible to lay open to uninitiated readers a speedy path to the apprehension of the higher mathematical truths. For this reason, too, the theories and results of mathematics are rarely adapted for popular presentation … This same inaccessibility of mathematics, although it secures for it a lofty and aristocratic place among the sciences, also renders it odious to those who have never learned it, and who dread the great labor involved in acquiring an understanding of the questions of modern mathematics. Neither in the languages nor in the natural sciences are the investigations and results so closely interdependent as to make it impossible to acquaint the uninitiated student with single branches or with particular results of these sciences, without causing him to go through a long course of preliminary study.
In Mathematical Essays and Recreations (1898), 32.
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The man who is thoroughly convinced of the universal operation of the law of causation cannot for a moment entertain the idea of a being who interferes in the course of events–provided, of course, that he takes the hypothesis of causality really seriously. He has no use for the religion of fear and equally little for social or moral religion. A God who rewards and punishes is inconceivable to him for the simple reason that a man’s actions are determined by necessity, external and internal, so that in God’s eyes he cannot be responsible, any more than an inanimate object is responsible for the motions it undergoes. Science has therefore been charged with undermining morality, but the charge is unjust. A man’s ethical behavior should be based effectually on sympathy, education, and social ties and needs; no religious basis is necessary. Man would indeed be in a poor way if he had to be restrained by fear of punishment and hopes of reward after death.
From 'Religion And Science', as collected in Ideas And Opinions (1954), 39, given its source as: “Written expressly for the New York Times Magazine. Appeared there November 9, 1930 (pp. 1-4). The German text was published in the Berliner Tageblatt, November 11, 1930.” The NYT Magazine article in full, is reprinted in Edward H. Cotton (ed.), Has Science Discovered God? A Symposium of Modern Scientific Opinion (1931), 101. This original version directly from the magazine has significantly different wording, beginning, “For anyone who is pervaded with the sense of causal law….” See this alternate form on the Albert Einstein Quotes page on this website. As for why the difference, Webmaster speculates the book form editor perhaps used a revised translation from Einstein’s German article.
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The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work.
In Presidential Address British Association for the Advancement of Science, Section A, (1890), Nature, 42, 467.
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The meaning of human life and the destiny of man cannot be separable from the meaning and destiny of life in general. 'What is man?' is a special case of 'What is life?' Probably the human species is not intelligent enough to answer either question fully, but even such glimmerings as are within our powers must be precious to us. The extent to which we can hope to understand ourselves and to plan our future depends in some measure on our ability to read the riddles of the past. The present, for all its awesome importance to us who chance to dwell in it, is only a random point in the long flow of time. Terrestrial life is one and continuous in space and time. Any true comprehension of it requires the attempt to view it whole and not in the artificial limits of any one place or epoch. The processes of life can be adequately displayed only in the course of life throughout the long ages of its existence.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 9.
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The method I take to do this is not yet very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course (as a Specimen of the Political Arithmetic I have long aimed at) to express myself in Terms of Number, Weight, or Measure; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature.
From Essays in Political Arithmetic (1679, 1755), 98.
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The neutral zone of selective advantage in the neighbourhood of zero is thus so narrow that changes in the environment, and in the genetic constitution of species, must cause this zone to be crossed and perhaps recrossed relatively rapidly in the course of evolutionary change, so that many possible gene substitutions may have a fluctuating history of advance and regression before the final balance of selective advantage is determined.
'The Distribution of Gene Ratios for Rare Mutations', Proceedings of the Royal Society of Edinburgh, 1930, 50, 219.
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The only object of theoretical physics is to calculate results that can be compared with experiment... it is quite unnecessary that any satisfactory description of the whole course of the phenomena should be given.
The Principles of Quantum Mechanics (1930), 7.
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The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits—he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher—the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do—and if a man does his best, what else can you ask of him?
The Rise of Scientific Philosophy (1951, 1973), 248-9. Collected in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 376.
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The practice of that which is ethically best—what we call goodness or virtue—involves a course of conduct which, in all respects, is opposed to that which leads to success in the cosmic struggle for existence. In place of ruthless self-assertion it demands self-restraint; in place of thrusting aside, or treading down, all competitors, it requires that the individual shall not merely respect, but shall help his fellows… It repudiates the gladiatorial theory of existence… Laws and moral precepts are directed to the end of curbing the cosmic process.
'Evolution and Ethics' (1893). In Collected Essays (1894), Vol. 9, 81-2.
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The prediction of nuclear winter is drawn not, of course, from any direct experience with the consequences of global nuclear war, but rather from an investigation of the governing physics. (The problem does not lend itself to full experimental verification—at least not more than once.)[co-author with American atmospheric chemist Richard P. Turco (1943- )]
A Path Where No Man Thought: Nuclear Winter and the End of the Arms Race (1990), 26.
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The primary rocks, … I regard as the deposits of a period in which the earth’s crust had sufficiently cooled down to permit the existence of a sea, with the necessary denuding agencies,—waves and currents,—and, in consequence, of deposition also; but in which the internal heat acted so near the surface, that whatever was deposited came, matter of course, to be metamorphosed into semi-plutonic forms, that retained only the stratification. I dare not speak of the scenery of the period. We may imagine, however, a dark atmosphere of steam and vapour, which for age after age conceals the face of the sun, and through which the light of moon or star never penetrates; oceans of thermal water heated in a thousand centres to the boiling point; low, half-molten islands, dim through the log, and scarce more fixed than the waves themselves, that heave and tremble under the impulsions of the igneous agencies; roaring geysers, that ever and anon throw up their intermittent jets of boiling fluid, vapour, and thick steam, from these tremulous lands; and, in the dim outskirts of the scene, the red gleam of fire, shot forth from yawning cracks and deep chasms, and that bears aloft fragments of molten rock and clouds of ashes. But should we continue to linger amid a scene so featureless and wild, or venture adown some yawning opening into the abyss beneath, where all is fiery and yet dark,—a solitary hell, without suffering or sin,—we would do well to commit ourselves to the guidance of a living poet of the true faculty,—Thomas Aird and see with his eyes.
Lecture Sixth, collected in Popular Geology: A Series of Lectures Read Before the Philosophical Institution of Edinburgh, with Descriptive Sketches from a Geologist's Portfolio (1859), 297-298.
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The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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The progress of Science is generally regarded as a kind of clean, rational advance along a straight ascending line; in fact it has followed a zig-zag course, at times almost more bewildering than the evolution of political thought. The history of cosmic theories, in particular, may without exaggeration be called a history of collective obsessions and controlled schizophrenias; and the manner in which some of the most important individual discoveries were arrived at reminds one more of a sleepwalker’s performance than an electronic brain’s.
From 'Preface', in The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), 15.
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The purpose of the present course is the deepening and development of difficulties underlying contemporary theory...
…...
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The pursuit of knowledge is but a course between two ignorances, as human life is itself only a wayfaring from grave to grave.
In Philosophy of Sir William Hamilton (1853), 517.
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The question is not: How can we justify the unobstructed teaching of evolution in public schools? The question, of course, is: How can we not?
In online article, 'The Day That Botany Took on Bobby Jindal by Just Being Itself', Huffington Post (5 Aug 2013).
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The results of mathematics are seldom directly applied; it is the definitions that are really useful. Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do. This you cannot see unless you take a course in abstract differential equations. What applies is the cultural background you get from a course in differential equations, not the specific theorems. If you want to learn French, you have to live the life of France, not just memorize thousands of words. If you want to apply mathematics, you have to live the life of differential equations. When you live this life, you can then go back to molecular biology with a new set of eyes that will see things you could not otherwise see.
In 'A Mathematician's Gossip', Indiscrete Thoughts (2008), 213.
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The role of hypothesis in research can be discussed more effectively if we consider first some examples of discoveries which originated from hypotheses. One of the best illustrations of such a discovery is provided by the story of Christopher Columbus’ voyage; it has many of the features of a classic discovery in science. (a) He was obsessed with an idea—that since the world is round he could reach the Orient by sailing West, (b) the idea was by no means original, but evidently he had obtained some additional evidence from a sailor blown off his course who claimed to have reached land in the west and returned, (c) he met great difficulties in getting someone to provide the money to enable him to test his idea as well as in the actual carrying out of the experimental voyage, (d) when finally he succeeded he did not find the expected new route, but instead found a whole new world, (e) despite all evidence to the contrary he clung to the bitter end to his hypothesis and believed that he had found the route to the Orient, (f) he got little credit or reward during his lifetime and neither he nor others realised the full implications of his discovery, (g) since his time evidence has been brought forward showing that he was by no means the first European to reach America.
The Art of Scientific Investigation (1950), 41.
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The ruthless destruction of their forests by the Chinese is one of the reasons why famine and plague today hold this nation in their sinister grasp. Denudation, wherever practiced, leaves naked soil; floods and erosion follow, and when the soil is gone men must also go—and the process does not take long. The great plains of Eastern China were centuries ago transformed from forest into agricultural land. The mountain plateau of Central China have also within a few hundred years been utterly devastated of tree growth, and no attempt made at either natural or artificial reforestation. As a result, the water rushes off the naked slopes in veritable floods, gullying away the mountain sides, causing rivers to run muddy with yellow soil, and carrying enormous masses of fertile earth to the sea. Water courses have also changed; rivers become uncontrollable, and the water level of the country is lowered perceptibly. In consequence, the unfortunate people see their crops wither and die for lack of water when it is most needed.
Statement (11 May 1921) by United States Department of Agriculture (USDA) concerning the famine in China in seven out of every ten years. Reported in 'Blames Deforestation: Department of Agriculture Ascribes Chinese Famine to it', New York Times (12 May 1921), 12.
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The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.
In Essai sur les machines en général (1783), conclusion, as translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840 (1990), Vol. 1, 32.
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René Descartes quote: The seeker after truth must, once in the course of his life, doubt everything, as far as is possible.
The seeker after truth must, once in the course of his life, doubt everything, as far as is possible.
In Principles of Philosophy Part 1, 1, As translated by Cottingham, Stoothoff and Murdoch in Descartes: Selected Philosophical Writings (1988, 1999), 160.
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The self-fulfilling prophecy is, in the beginning, a false definition of the situation evoking a new behavior which makes the originally false conception come true. The specious validity of the self-fulfilling prophecy perpetuates a reign of error. For the prophet will cite the actual course of events as proof that he was right from the very beginning. … Such are the perversities of social logic.
In article, 'The Self-Fulfilling Prophecy', The Antioch Review (Summer 1948), 8, No. 2, 195-196. Included as Chap. 7 of Social Theory and Social Structure (1949), 181-195. Note: Merton coined the expression “self-fulfilling prophecy.”
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The subsequent course of nature, teaches, that God, indeed, gave motion to matter; but that, in the beginning, he so guided the various motion of the parts of it, as to contrive them into the world he design'd they should compose; and establish'd those rules of motion, and that order amongst things corporeal, which we call the laws of nature. Thus, the universe being once fram'd by God, and the laws of motion settled, and all upheld by his perpetual concourse, and general providence; the same philosophy teaches, that the phenomena of the world, are physically produced by the mechanical properties of the parts of matter; and, that they operate upon one another according to mechanical laws. 'Tis of this kind of corpuscular philosophy, that I speak.
'The Excellence and Grounds of the Mechanical Philosophy', In P. Shaw (ed.), The Philosophical Works of Robert Boyle (1725), Vol. 1, 187.
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The successive series of stratified formations are piled on one another, almost like courses of masonry.
Geology and Mineralogy, Considered with Reference to Natural Theology (1836), Vol. 1, 37.
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The sun, moving as it does, sets up processes of change and becoming and decay, and by its agency the finest and sweetest water is every day carried up and is dissolved into vapour and rises to the upper region, where it is condensed again by the cold and so returns to the earth. This, as we have said before, is the regular course of nature.
Aristotle
Meteorology (350 B.C.), Book II, translated by E. W. Webster. Internet Classics Archive, (classics.mit.edu).
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The University of Cambridge, in accordance with that law of its evolution, by which, while maintaining the strictest continuity between the successive phases of its history, it adapts itself with more or less promptness to the requirements of the times, has lately instituted a course of Experimental Physics.
'Introductory Lecture on Experimental Physics', (1871). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 241.Course;Experiment;Cambridge;History;Promptness;Adapt;Requirement
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The view of the moon that we’ve been having recently is really spectacular. It fills about three-quarters of the hatch window, and of course we can see the entire circumference even though part of it is in complete shadow and part of it is in earthshine. It’s a view worth the price of the trip.
…...
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The whole of the developments and operations of analysis are now capable of being executed by machinery ... As soon as an Analytical Engine exists, it will necessarily guide the future course of science.
Passages From the Life of a Philosopher (1864), 136-137.
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The whole subject of the X rays is opening out wonderfully, Bragg has of course got in ahead of us, and so the credit all belongs to him, but that does not make it less interesting. We find that an X ray bulb with a platinum target gives out a sharp line spectrum of five wavelengths which the crystal separates out as if it were a diffraction grating. In this way one can get pure monochromatic X rays. Tomorrow we search for the spectra of other elements. There is here a whole new branch of spectroscopy, which is sure to tell one much about the nature of an atom.
Letter to his mother (18 May 1913). In J. L. Heilbron (ed.), H. G. J. Moseley: The Life and Letters of an English Physicist 1887-1915 (1974), 205.
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The word “universe” means the general assemblage of all nature, and it also means the heaven that is made up of the constellations and the courses of the stars.
Vitruvius
In De Architectura, Book 9, Chap 1, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 257.
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Then if the first argument remains secure (for nobody will produce a neater one, than the length of the periodic time is a measure of the size of the spheres), the order of the orbits follows this sequence, beginning from the highest: The first and highest of all is the sphere of the fixed stars, which contains itself and all things, and is therefore motionless. It is the location of the universe, to which the motion and position of all the remaining stars is referred. For though some consider that it also changes in some respect, we shall assign another cause for its appearing to do so in our deduction of the Earth’s motion. There follows Saturn, the first of the wandering stars, which completes its circuit in thirty years. After it comes Jupiter which moves in a twelve-year long revolution. Next is Mars, which goes round biennially. An annual revolution holds the fourth place, in which as we have said is contained the Earth along with the lunar sphere which is like an epicycle. In fifth place Venus returns every nine months. Lastly, Mercury holds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun. For who in this most beautiful of temples would put this lamp in any other or better place than the one from which it can illuminate everything at the same time? Aptly indeed is he named by some the lantern of the universe, by others the mind, by others the ruler. Trismegistus called him the visible God, Sophocles' Electra, the watcher over all things. Thus indeed the Sun as if seated on a royal throne governs his household of Stars as they circle around him. Earth also is by no means cheated of the Moon’s attendance, but as Aristotle says in his book On Animals the Moon has the closest affinity with the Earth. Meanwhile the Earth conceives from the Sun, and is made pregnant with annual offspring. We find, then, in this arrangement the marvellous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultation by the Sun and re-appearance. Indeed Mars in particular at the time when it is visible throughout the night seems to equal Jupiter in size, though marked out by its reddish colour; yet it is scarcely distinguishable among stars of the second magnitude, though recognized by those who track it with careful attention. All these phenomena proceed from the same course, which lies in the motion of the Earth. But the fact that none of these phenomena appears in the fixed stars shows their immense elevation, which makes even the circle of their annual motion, or apparent motion, vanish from our eyes.
'Book One. Chapter X. The Order of the Heavenly Spheres', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 49-51.
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Theorems are not to mathematics what successful courses are to a meal.
In Rota's 'Introduction' written (1980) to preface Philip J. Davis and Reuben Hersh, The Mathematical Experience (1981, 2012), xxii-xxiii.
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There are in this world optimists who feel that any symbol that starts off with an integral sign must necessarily denote something that will have every property that they should like an integral to possess. This of course is quite annoying to us rigorous mathematicians; what is even more annoying is that by doing so they often come up with the right answer.
In 'Integrals Devised for Special Purposes', Bulletin of the American Mathematical Society (1963), 69, 611.
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There are no better terms available to describe the difference between the approach of the natural and the social sciences than to call the former ‘objective’ and the latter ‘subjective.’ ... While for the natural scientist the contrast between objective facts and subjective opinions is a simple one, the distinction cannot as readily be applied to the object of the social sciences. The reason for this is that the object, the ‘facts’ of the social sciences are also opinions—not opinions of the student of the social phenomena, of course, but opinions of those whose actions produce the object of the social scientist.
…...
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There are two processes which we adopt consciously or unconsciously when we try to prophesy. We can seek a period in the past whose conditions resemble as closely as possible those of our day, and presume that the sequel to that period will, save for some minor alterations, be similar. Secondly, we can survey the general course of development in our immediate past, and endeavor to prolong it into the near future. The first is the method the historian; the second that of the scientist. Only the second is open to us now, and this only in a partial sphere.
From 'Fifty Years Hence', Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57, No. 3, 393.
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There are, I believe, very few maxims in philosophy that have laid firmer hold upon the mind, than that air, meaning atmospherical air (free from various foreign matters, which were always supposed to be dissolved, and intermixed with it) is a simple elementary substance, indestructible, and unalterable, at least as much so as water is supposed to be. In the course of my enquiries, I was, however, soon satisfied that atmospherical air is not an unalterable thing; for that the phlogiston with which it becomes loaded from bodies burning in it, and animals breathing it, and various other chemical processes, so far alters and depraves it, as to render it altogether unfit for inflammation, respiration, and other purposes to which it is subservient; and I had discovered that agitation in water, the process of vegetation, and probably other natural processes, by taking out the superfluous phlogiston, restore it to its original purity.
'On Dephlogisticated Air, and the Constitution of the Atmosphere', in The Discovery of Oxygen, Part I, Experiments by Joseph Priestley 1775 (Alembic Club Reprint, 1894), 6.
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There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material—these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative—a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures.
Reflections: Mathematics and Creativity', New Yorker (1972), 47, No. 53, 39-45. In Douglas M. Campbell, John C. Higgins (eds.), Mathematics: People, Problems, Results (1984), Vol. 2, 7.
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There may be some interest in one of my own discoveries in physics, entitled, “A Method of Approximating the Importance of a Given Physicist.” Briefly stated, after elimination of all differentials, the importance of a physicist can be measured by observation in the lobby of a building where the American Physical Society is in session. The importance of a given physicist varies inversely with his mean free path as he moves from the door of the meeting-room toward the street. His progress, of course, is marked by a series of scattering collisions with other physicists, during which he remains successively in the orbit of other individuals for a finite length of time. A good physicist has a mean free path of 3.6 ± 0.3 meters. The shortest m.f.p. measured in a series of observations between 1445 and 1947 was that of Oppenheimer (New York, 1946), the figure being 2.7 centimeters. I know. I was waiting for him on the street.
In 'A Newsman Looks at Physicists', Physics Today (May 1948), 1, No. 1, 33.
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There might have been a hundred or a thousand life-bearing planets, had the course of evolution of the universe been a little different, or there might have been none at all. They would probably add, that, as life and man have been produced, that shows that their production was possible; and therefore, if not now then at some other time, if not here then in some other planet of some other sun, we should be sure to have come into existence; or if not precisely the same as we are, then something a little better or a little worse.
From Conclusion to Man's Place in the Universe: A Study of the Results of Scientific Research (1903), 315.
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There really are not any spheres in the heavens ... Those which have been devised by the experts to save the appearances exist only in the imagination, for the purpose of enabling the mind to conceive the motion which the heavenly bodies trace in their course and, by the aid of geometry, to determine the motion numerically through the use of arithmetic.
J. L. E. Dreyer (ed.), Opera Omnia (1913-29), Vol. 4, 222. Trans. Edward Rosen, 'Nicholas Copernicus', in Charles C. Gillispie (ed.), Dictionary of Scientific Biography (1971), Vol. 3, 409.
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These parsons are so in the habit of dealing with the abstractions of doctrines as if there was no difficulty about them whatever, so confident, from the practice of having the talk all to themselves for an hour at least every week with no one to gainsay a syllable they utter, be it ever so loose or bad, that they gallop over the course when their field is Botany or Geology as if we were in the pews and they in the pulpit ... There is a story somewhere of an Englishman, Frenchman, and German being each called on to describe a camel. The Englishman immediately embarked for Egypt, the Frenchman went to the Jardin des Plantes, and the German shut himself up in his study and thought it out!
Letter to Asa Gray (29 Mar 1857). Quoted in Leonard Huxley, Life and Letters of Sir Joseph Dalton Hooker (1918), Vol. 1, 477.
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They had neither compass, nor astronomical instruments, nor any of the appliances of our time for finding their position at sea; they could only sail by the sun, moon, and stars, and it seems incomprehensible how for days and weeks, when these were invisible, they were able to find their course through fog and bad weather; but they found it, and in the open craft of the Norwegian Vikings, with their square sails, fared north and west over the whole ocean, from Novaya Zemlya and Spitsbergen to Greenland, Baffin Bay, Newfoundland, and North America.
In northern mists: Arctic exploration in early times - Volume 1 - Page 248 https://books.google.com/books?id=I1ugAAAAMAAJ Fridtjof Nansen - 1911
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They think that differential equations are not reality. Hearing some colleagues speak, it’s as though theoretical physics was just playing house with plastic building blocks. This absurd idea has gained currency, and now people seem to feel that theoretical physicists are little more than dreamers locked away ivory towers. They think our games, our little houses, bear no relation to their everyday worries, their interests, their problems, or their welfare. But I’m going to tell you something, and I want you to take it as a ground rule for this course. From now on I will be filling this board with equations. … And when I'm done, I want you to do the following: look at those numbers, all those little numbers and Greek letters on the board, and repeat to yourselves, “This is reality,” repeat it over and over.
Zig Zag, trans. Lisa Dillman (2008), 63.
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Those of us who were familiar with the state of inorganic chemistry in universities twenty to thirty years ago will recall that at that time it was widely regarded as a dull and uninteresting part of the undergraduate course. Usually, it was taught almost entirely in the early years of the course and then chiefly as a collection of largely unconnected facts. On the whole, students concluded that, apart from some relationships dependent upon the Periodic table, there was no system in inorganic chemistry comparable with that to be found in organic chemistry, and none of the rigour and logic which characterised physical chemistry. It was widely believed that the opportunities for research in inorganic chemistry were few, and that in any case the problems were dull and uninspiring; as a result, relatively few people specialized in the subject... So long as inorganic chemistry is regarded as, in years gone by, as consisting simply of the preparations and analysis of elements and compounds, its lack of appeal is only to be expected. The stage is now past and for the purpose of our discussion we shall define inorganic chemistry today as the integrated study of the formation, composition, structure and reactions of the chemical elements and compounds, excepting most of those of carbon.
Inaugural Lecture delivered at University College, London (1 Mar 1956). In The Renaissance of Inorganic Chemistry (1956), 4-5.
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Those who have handled sciences have been either men of experiment or men of dogmas. The men of experiment are like the ant; they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes a middle course; it gathers its material from the flowers of the garden and of the field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy; for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay it up in the memory whole, as it finds it; but lays it up in the understanding altered and digested. Therefore from a closer and purer league between these two faculties, the experimental and the rational (such as has never yet been made), much may be hoped.
From Novum Organum (1620), Book 1, Aphorism 95. 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, 92-3.
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Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men's efforts than good by their own. Those on the other hand who have taken a contrary course, and asserted that absolutely nothing can be known — whether it were from hatred of the ancient sophists, or from uncertainty and fluctuation of mind, or even from a kind of fullness of learning, that they fell upon this opinion — have certainly advanced reasons for it that are not to be despised; but yet they have neither started from true principles nor rested in the just conclusion, zeal and affectation having carried them much too far...
Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain. But the mental operation which follows the act of sense I for the most part reject; and instead of it I open and lay out a new and certain path for the mind to proceed in, starting directly from the simple sensuous perception.
Novum Organum (1620)
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Thomas Robert Malthus quote Nature has scattered the seeds of life
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Through the animal and vegetable kingdoms, Nature has scattered the seeds of life abroad with the most profuse and liberal hand; but has been comparatively sparing in the room and the nourishment necessary to rear them. The germs of existence contained in this spot of earth, if they could freely develop themselves, would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all-pervading law of nature, restrains them within the prescribed bounds. The race of plants and the race of animals shrink under this great restrictive law; and man cannot by any efforts of reason escape from it.
In An Essay on the Principle of Population (1798), 14-15.
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Thus ordered thinking arises out of the ordered course of nature in which man finds himself, and this thinking is from the beginning nothing more than the subjective reproduction of the regularity according to the law of natural phenomena. On the other hand, this reproduction is only possible by means of the will that controls the concatenation of ideas.
An Introduction to Psychology (1912)
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Time, which measures everything in our idea, and is often deficient to our schemes, is to nature endless and as nothing; it cannot limit that by which alone it had existence; and as the natural course of time, which to us seems infinite, cannot be bounded by any operation that may have an end, the progress of things upon this globe, that is, the course of nature, cannot be limited by time, which must proceed in a continual succession.
'Theory of the Earth', Transactions of the Royal Society of Edinburgh (1788), 1, 215.
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To ask what qualities distinguish good from routine scientific research is to address a question that should be of central concern to every scientist. We can make the question more tractable by rephrasing it, “What attributes are shared by the scientific works which have contributed importantly to our understanding of the physical world—in this case the world of living things?” Two of the most widely accepted characteristics of good scientific work are generality of application and originality of conception. . These qualities are easy to point out in the works of others and, of course extremely difficult to achieve in one’s own research. At first hearing novelty and generality appear to be mutually exclusive, but they really are not. They just have different frames of reference. Novelty has a human frame of reference; generality has a biological frame of reference. Consider, for example, Darwinian Natural Selection. It offers a mechanism so widely applicable as to be almost coexistent with reproduction, so universal as to be almost axiomatic, and so innovative that it shook, and continues to shake, man’s perception of causality.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230.
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To complete a PhD[,] I took courses in the history of philosophy. … As a result of my studies, I concluded that the traditional philosophy of science had little if anything to do with biology. … I had no use for a philosophy based on such an occult force as the vis vitalis. … But I was equally disappointed by the traditional philosophy of science, which was all based on logic, mathematics, and the physical sciences, and had adopted Descartes’ conclusion that an organism was nothing but a machine. This Cartesianism left me completely dissatisfied.
In 'Introduction', What Makes Biology Unique?: Considerations on the Autonomy of a Scientific Discipline (2007), 2.
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To complete a PhD[,] I took courses in the history of philosophy. … As a result of my studies, I concluded that the traditional philosophy of science had little if anything to do with biology. … I had no use for a philosophy based on such an occult force as the vis vitalis. … But I was equally disappointed by the traditional philosophy of science, which was all based on logic, mathematics, and the physical sciences, and had adopted Descartes’ conclusion that an organism was nothing but a machine. This Cartesianism left me completely dissatisfied.
In 'Introduction', What Makes Biology Unique?: Considerations on the Autonomy of a Scientific Discipline (2007), 2.
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To the distracting occupations belong especially my lecture courses which I am holding this winter for the first time, and which now cost much more of my time than I like. Meanwhile I hope that the second time this expenditure of time will be much less, otherwise I would never be able to reconcile myself to it, even practical (astronomical) work must give far more satisfaction than if one brings up to B a couple more mediocre heads which otherwise would have stopped at A.
Letter to Friedrich Bessel (4 Dec 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 415.
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Traditions may be very important, but they can be extremely hampering as well, and whether or not tradition is of really much value I have never been certain. Of course when they are very fine, they do good, but it is very difficult of course ever to repeat the conditions under which good traditions are formed, so they may be and are often injurious and I think the greatest progress is made outside of traditions.
Quoted as the notations of an unnamed student in the auditorium when Councilman made impromptu biographical remarks at his last lecture as a teacher of undergraduates in medicine (19 Dec 1921). As quoted in obituary, 'William Thomas Councilman', by Harvey Cushing, Science (30 Jun 1933), 77, No. 2009, 613-618. Reprinted in National Academy Biographical Memoirs, Vol. 18, 159-160. The transcribed lecture was published privately in a 23-page booklet, A Lecture Delivered to the Second-Year Class of the Harvard Medical School at the Conclusion of the Course in Pathology, Dec. 19, 1921.
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True science is at length disencumbered of the empirical determinations which had accumulated in the course of many centuries.
Franz Cumont, translated by J.B. Baker, Astrology and Religion Among the Greeks and Romans (1912, 2007), 6.
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Until I became a published writer, I remained completely ignorant of books on how to write and courses on the subject ... they would have spoiled my natural style; made me observe caution; would have hedged me with rules.
In Isaac Asimov and Janet Asimov (ed.), It's Been a Good Life (2002), 38.
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We academic scientists move within a certain sphere, we can go on being useless up to a point, in the confidence that sooner or later some use will be found for our studies. The mathematician, of course, prides himself on being totally useless, but usually turns out to be the most useful of the lot. He finds the solution but he is not interested in what the problem is: sooner or later, someone will find the problem to which his solution is the answer.
'Concluding Remarks', Proceedings of the Royal Society of London, Series A, A Discussion of New Materials, 1964, 282, 152-3.
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We are, of course, extremely concerned that if this did, in fact, happen, that there is going to be a tremendous public outcry, and we will be concerned with what the Congress does, … Obviously, we are concerned about there being a backlash against the medical applications of this technology, which have, of course, the potential to cure millions of patients.
…...
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We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed.
In The Elements of Morality (1845), Vol 1, 1.
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We cannot, of course, give a definition of matter which will satisfy the metaphysician, but the naturalist may be content to know matter as that which can be perceived by the senses, or as that which can be acted upon by, or can exert, force.
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, 161.
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We do not know of any enzymes or other chemical defined organic substances having specifically acting auto-catalytic properties such as to enable them to construct replicas of themselves. Neither was there a general principle known that would result in pattern-copying; if there were, the basis of life would be easier to come by. Moreover, there was no evidence to show that the enzymes were not products of hereditary determiners or genes, rather than these genes themselves, and they might even be products removed by several or many steps from the genes, just as many other known substances in the cell must be. However, the determiners or genes themselves must conduct, or at least guide, their own replication, so as to lead to the formation of genes just like themselves, in such wise that even their own mutations become .incorporated in the replicas. And this would probably take place by some kind of copying of pattern similar to that postulated by Troland for the enzymes, but requiring some distinctive chemical structure to make it possible. By virtue of this ability of theirs to replicate, these genes–or, if you prefer, genetic material–contained in the nuclear chromosomes and in whatever other portion of the cell manifests this property, such as the chloroplastids of plants, must form the basis of all the complexities of living matter that have arisen subsequent to their own appearance on the scene, in the whole course of biological evolution. That is, this genetic material must underlie all evolution based on mutation and selective multiplication.
'Genetic Nucleic Acid', Perspectives in Biology and Medicine (1961), 5, 6-7.
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We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer.
From the German, “Wir fühlen, dass selbst, wenn alle möglichen wissenschaftlichen Fragen beantwortet sind, unsere Lebensprobleme noch gar nicht berührt sind. Freilich bleibt dann eben keine Frage mehr; und eben dies ist die Antwort,” in Logisch-Philosophische Abhandlung (1921). German text with English translation in Tractatus Logico-Philosophicus (1922), 186-187.
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We have no faculties for passing beyond ourselves, yet in ourselves are unfathomed depths, unexplored powers and relations which need fathoming and searching into. As Schopenhauer says, if we would understand nature our course must not only be horizontal, but perpendicular.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), li.
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We have now got what seems to be definite proof that an X ray which spreads out in a spherical form from a source as a wave through the aether can when it meets an atom collect up all its energy from all round and concentrate it on the atom. It is as if when a circular wave on water met an obstacle, the wave were all suddenly to travel round the circle and disappear all round and concentrate its energy on attacking the obstacle. Mechanically of course this is absurd, but mechanics have in this direction been for some time a broken reed.
Letter to Margery Moseley (2 Feb 1913). In J. L. Heilbron (ed.), H. G. J. Moseley: The Life and Letters of an English Physicist 1887-1915 (1974), 201.
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We have the opportunity of observing her [Nature] through these delicate and pellucid teguments of the bodies of Insects acting according to her usual course and way, undisturbed, whereas when we endeavour to pry into her secrets by breaking open the doors upon her, and dissecting and mangling creatures whil'st there is life yet within them, we find her indeed at work, but put into such disorder by the violence offer'd, as it may easily be imagin'd how differing a thing we should find, if we could, as we can with a Microscope, in these smaller creatures, quietly peep in at the windows, without frighting her out of her usual byas.
Micrographia, or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses with Observations and Inquiries thereupon (1665), 186.
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We may produce at will, from a sending station. an electrical effect in any particular region of the globe; we may determine the relative position or course of a moving object, such as a vessel at sea, the distance traversed by the same, or its speed.
In 'The Problem of Increasing Human Energy', Century Illustrated Monthly Magazine (Jun 1900), 60, 208-209.
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We must make the following remark: a proof, that after a certain time t1, the spheres must necessarily be mixed uniformly, whatever may be the initial distribution of states, cannot be given. This is in fact a consequence of probability theory, for any non-uniform distribution of states, no matter how improbable it may be, is still not absolutely impossible. Indeed it is clear that any individual uniform distribution, which might arise after a certain time from some particular initial state, is just as improbable as an individual non-uniform distribution; just as in the game of Lotto, any individual set of five numbers is as improbable as the set 1, 2, 3, 4, 5. It is only because there are many more uniform distributions than non-uniform ones that the distribution of states will become uniform in the course of time. One therefore cannot prove that, whatever may be the positions and velocities of the spheres at the beginning, the distributions must become uniform after a long time; rather one can only prove that infinitely many more initial states will lead to a uniform one after a definite length of time than to a non-uniform one. Loschmidt's theorem tells us only about initial states which actually lead to a very non-uniform distribution of states after a certain time t1; but it does not prove that there are not infinitely many more initial conditions that will lead to a uniform distribution after the same time. On the contrary, it follows from the theorem itself that, since there are infinitely many more uniform distributions, the number of states which lead to uniform distributions after a certain time t1, is much greater than the number that leads to non-uniform ones, and the latter are the ones that must be chosen, according to Loschmidt, in order to obtain a non-uniform distribution at t1.
From 'On the Relation of a General Mechanical Theorem to the Second Law of Thermodynamics' (1877), in Stephen G. Brush (ed.), Selected Readings in Physics (1966), Vol. 2, Irreversible Processes, 191-2.
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We need science education to produce scientists, but we need it equally to create literacy in the public. Man has a fundamental urge to comprehend the world about him, and science gives today the only world picture which we can consider as valid. It gives an understanding of the inside of the atom and of the whole universe, or the peculiar properties of the chemical substances and of the manner in which genes duplicate in biology. An educated layman can, of course, not contribute to science, but can enjoy and participate in many scientific discoveries which as constantly made. Such participation was quite common in the 19th century, but has unhappily declined. Literacy in science will enrich a person’s life.
In Popular Mechanics (Sep 1961), 256
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We should admit in theory what is already very largely a case in practice, that the main currency of scientific information is the secondary sources in the forms of abstracts, reports, tables, &c., and that the primary sources are only for detailed reference by very few people. It is possible that the fate of most scientific papers will be not to be read by anyone who uses them, but with luck they will furnish an item, a number, some facts or data to such reports which may, but usually will not, lead to the original paper being consulted. This is very sad but it is the inevitable consequence of the growth of science. The number of papers that can be consulted is absolutely limited, no more time can be spent in looking up papers, by and large, than in the past. As the number of papers increase the chance of any one paper being looked at is correspondingly diminished. This of course is only an average, some papers may be looked at by thousands of people and may become a regular and fixed part of science but most will perish unseen.
'The Supply of Information to the Scientist: Some Problems of the Present Day', The Journal of Documentation, 1957, 13, 195.
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We should take care not to make the intellect our god; it has, of course, powerful muscles, but no personality.
From NBC radio broadcast for the United Jewish Appeal (11 Apr 1943), 'The Goal of Human Existence.' Einstein Archives 28-587. Transcript reprinted in full in David E. Rowe and Robert Schulmann (eds.), Einstein on Politics (2007), 322. Also in Albert Einstein, Out of My Later Years: The Scientist, Philosopher, and Man Portrayed Through His Own Words (1956), 260-261.
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We think the heavens enjoy their spherical
Their round proportion, embracing all;
But yet their various and perplexed course,
Observed in divers ages, doth enforce
Men to find out so many eccentric parts,
Such diverse downright lines, such overthwarts,
As disproportion that pure form.
From poem, 'An Anatomy of the World: The First Anniversary', lines 251-257, as collected in The Poems of John Donne (1896), Vol. 2, 113.
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We think we understand the regular reflection of light and X rays - and we should understand the reflections of electrons as well if electrons were only waves instead of particles ... It is rather as if one were to see a rabbit climbing a tree, and were to say ‘Well, that is rather a strange thing for a rabbit to be doing, but after all there is really nothing to get excited about. Cats climb trees - so that if the rabbit were only a cat, we would understand its behavior perfectly.’ Of course, the explanation might be that what we took to be a rabbit was not a rabbit at all but was actually a cat. Is it possible that we are mistaken all this time in supposing they are particles, and that actually they are waves?
Franklin Institute Journal Vol. 205, 597. Cited in New Scientist (14 Apr 1977), 66.
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We will be misguided in our intentions if we point at one single thing and say that it will prevent war, unless, of course, that thing happens to be the will, the determination, and the resolve of people everywhere that nations will never again clash on the battlefield.
Opening address (7 Nov 1945) of Town Hall’s annual lecture series, as quoted in 'Gen. Groves Warns on Atom ‘Suicide’', New York Times (8 Nov 1945), 4. (Just three months before he spoke, two atom bombs dropped on Japan in Aug 1945 effectively ended WW II.)
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Western field-work conjures up images of struggle on horseback ... –toughing it out on one canteen a day as you labor up and down mountains. The value of a site is supposedly correlated with the difficulty of getting there. This, of course, is romantic drivel. Ease of access is no measure of importance. The famous La Brea tar pits are right in downtown Los Angeles. To reach the Clarkia lake beds, you turn off the main road at Buzzard’s Roost Trophy Company and drive the remaining fifty yards right up to the site.
…...
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What is possible can never be demonstrated to be false; and 'tis possible the course of nature may change, since we can conceive such a change. Nay, I will go farther, and assert, that he could not so much as prove by any probable arguments, that the future must be conformable to the past. All probable arguments are built on the supposition, that there is this conformity betwixt the future and the past, and therefore can never prove it. This conformity is a matter of fact, and if it must be proved, will admit of no proof but from experience. But our experience in the past can be a proof of nothing for the future, but upon a supposition, that there is a resemblance betwixt them. This therefore is a point, which can admit of no proof at all, and which we take for granted without any proof.
An Abstract of A Treatise on Human Nature (1740), ed. John Maynard Keynes and Piero Sraffa (1938), 15.
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What nature does in the course of long periods we do every day when we suddenly change the environment in which some species of living plant is situated.
Philosophie Zoologique (1809), Vol. 1, 226, trans. Hugh Elliot (1914), 109.
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What of the future of this adventure? What will happen ultimately? We are going along guessing the laws; how many laws are we going to have to guess? I do not know. Some of my colleagues say that this fundamental aspect of our science will go on; but I think there will certainly not be perpetual novelty, say for a thousand years. This thing cannot keep on going so that we are always going to discover more and more new laws … It is like the discovery of America—you only discover it once. The age in which we live is the age in which we are discovering the fundamental laws of nature, and that day will never come again. Of course in the future there will be other interests … but there will not be the same things that we are doing now … There will be a degeneration of ideas, just like the degeneration that great explorers feel is occurring when tourists begin moving in on a territory.
In The Character of Physical Law (1965, 1994), 166.
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What! Did Sir W[alter] R[aleigh] believe that a male and female ounce (and, if so, why not two tigers and lions, etc?) would have produced, in a course of generations, a cat, or a cat a lion? This is Darwinizing with a vengeance.
'Notes on Stillingfleet by S. T. Coleridge', The Athenaeum, no. 2474, 27 March 1875, 423.
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Whatever Nature undertakes, she can only accomplish it in a sequence. She never makes a leap. For example she could not produce a horse if it were not preceded by all the other animals on which she ascends to the horse’s structure as if on the rungs of a ladder. Thus every one thing exists for the sake of all things and all for the sake of one; for the one is of course the all as well. Nature, despite her seeming diversity, is always a unity, a whole; and thus, when she manifests herself in any part of that whole, the rest must serve as a basis for that particular manifestation, and the latter must have a relationship to the rest of the system.
Jeremy Naydler (ed.), Goethe On Science: An Anthology of Goethe's Scientific Writings (1996), 60
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When a Parliament, acting against the declared Sense of the Nation, would have appeared as surprising a phœnomenon in the moral World, as a retrograde Motion of the Sun, or any other signal Deviation of Things from their ordinary Course in the natural World.
In A Dissertation Upon Parties: In Several Letters to Caleb D’Anvers, Esq. (1733, 1735), 39.
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When a physician is called to a patient, he should decide on the diagnosis, then the prognosis, and then the treatment. … Physicians must know the evolution of the disease, its duration and gravity in order to predict its course and outcome. Here statistics intervene to guide physicians, by teaching them the proportion of mortal cases, and if observation has also shown that the successful and unsuccessful cases can be recognized by certain signs, then the prognosis is more certain.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 213.
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When an element A has an affinity for another substance B, I see no mechanical reason why it should not take as many atoms of B as are presented to it, and can possibly come into contact with it (which may probably be 12 in general), except so far as the repulsion of the atoms of B among themselves are more than a match for the attraction of an atom of A. Now this repulsion begins with 2 atoms of B to 1 atom of A, in which case the 2 atoms of B are diametrically opposed; it increases with 3 atoms of B to 1 of A, in which case the atoms are only 120° asunder; with 4 atoms of B it is still greater as the distance is then only 90; and so on in proportion to the number of atoms. It is evident from these positions, that, as far as powers of attraction and repulsion are concerned (and we know of no other in chemistry), binary compounds must first be formed in the ordinary course of things, then ternary and so on, till the repulsion of the atoms of B (or A, whichever happens to be on the surface of the other), refuse to admit any more.
Observations on Dr. Bostock's Review of the Atomic Principles of Chemistry', Nicholson's Journal, 1811, 29, 147.
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When Big Bang proponents make assertions such as … “the evidence taken together … hangs together beautifully,” they overlook observational facts that have been piling up for 25 years and that have now become overwhelming. Of course, if one ignores contradictory observations, one can claim to have an “elegant” or “robust” theory. But it isn’t science.
In 'Letters: Wrangling Over the Bang', Science News (27 Jul 1991), 140, No. 4, 51. Also quoted in Roy C. Martin, Astronomy on Trial: A Devastating and Complete Repudiation of the Big Bang Fiasco (1999), Appendix I, 217.
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When I undertake the dissection of a human cadaver I pass a stout rope tied like a noose beneath the lower jaw and through the two zygomas up to the top of the head, either more toward the forehead or more toward the occiput according as I want the cadaver to hang with its head up or down. The longer end of the noose I run through a pulley fixed to a beam in the room so that I may raise or lower the cadaver as it hangs there or may turn it round in any direction to suit my purpose; and should I so wish I can allow it to recline at an angle upon a table, since a table can easily be placed underneath the pulley. This is how the cadaver was suspended for drawing all the muscle tables... though while that one was being drawn the rope was passed around the occiput so as to show the muscles in the neck. If the lower jaw has been removed in the course of dissection, or the zygomas have been broken, the hollows for the temporal muscles will nonetheless hold the noose sufficiently firmly. You must take care not to put the noose around the neck, unless some of the muscles connected to the occipital bone have already been cut away. It is best to suspend the cadaver like this because a human body lying on a table is very difficult to turn over on to its chest or its back.
From De Humani Corporis Fabrica Libri Septem (1543), Book II, 268, as translated by William Frank Richardson and John Burd Carman, in 'How the Cadaver Can Be Held Erect While These Muscles are Dissected', On The Fabric of the Human Body: Book II: The Ligaments and Muscles (1998), 234.
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When only one course of action is possible, there is no difficulty in deciding what to do.
Aphorism as given by the fictional character Dezhnev Senior, in Fantastic Voyage II: Destination Brain (1987), 282.
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When we seek a textbook case for the proper operation of science, the correction of certain error offers far more promise than the establishment of probable truth. Confirmed hunches, of course, are more upbeat than discredited hypotheses. Since the worst traditions of ‘popular’ writing falsely equate instruction with sweetness and light, our promotional literature abounds with insipid tales in the heroic mode, although tough stories of disappointment and loss give deeper insight into a methodology that the celebrated philosopher Karl Popper once labeled as ‘conjecture and refutation.’
…...
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Whenever a textbook is written of real educational worth, you may be quite certain that some reviewer will say that it will be difficult to teach from it. Of course it will be difficult to teach from it. It it were easy, the book ought to be burned; for it cannot be educational. In education as elsewhere, the broad primrose path leads to a nasty place. This evil path is represented by a book or a set of lectures which will practically enable the student to learn by heart all the questions likely to be asked at the next external examination.
In 'The Aims of Education', The Aims of Education: & Other Essays (1917), 6-7.
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Whenever we pride ourselves upon finding a newer, stricter way of thought or exposition; whenever we start insisting too hard upon “operationalism” or symbolic logic or any other of these very essential systems of tramlines, we lose something of the ability to think new thoughts. And equally, of course, whenever we rebel against the sterile rigidity of formal thought and exposition and let our ideas run wild, we likewise lose. As I see it, the advances in scientific thought come from a combination of loose and strict thinking, and this combination is the most precious tool of science.
In 'Culture Contact and Schismogenesis' (1935), in Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution, and Epistemology (1972).
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Whether moral and social phenomena are really exceptions to the general certainty and uniformity of the course of nature; and how far the methods, by which so many of the laws of the physical world have been numbered among truths irrevocably acquired and universally assented to, can be made instrumental to the gradual formation of a similar body of received doctrine in moral and political science.
A System of Logic, Ratiocinative and Inductive (1858), v.
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While we cannot accurately predict the course of climate change in the coming decades, the risks we run if we don’t change our course are enormous. Prudent risk management does not equate uncertainty with inaction.
In letter (1 Feb 2013) to Energy Department employees announcing his decision not to serve a second term.
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While we keep an open mind on this question of vitalism, or while we lean, as so many of us now do, or even cling with a great yearning, to the belief that something other than the physical forces animates the dust of which we are made, it is rather the business of the philosopher than of the biologist, or of the biologist only when he has served his humble and severe apprenticeship to philosophy, to deal with the ultimate problem. It is the plain bounden duty of the biologist to pursue his course unprejudiced by vitalistic hypotheses, along the road of observation and experiment, according to the accepted discipline of the natural and physical sciences. … It is an elementary scientific duty, it is a rule that Kant himself laid down, that we should explain, just as far as we possibly can, all that is capable of such explanation, in the light of the properties of matter and of the forms of energy with which we are already acquainted.
From Presidential Address to Zoological Section of the British Association for the Advancement of Science. As quoted in H.V. Neal, 'The Basis of Individuality in Organisms: A Defense of Vitalism', Science (21 Jul 1916), 44 N.S., No. 1125, 82.
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Who shall declare the time allotted to the human race, when the generations of the most insignificant insect also existed for unnumbered ages? Yet man is also to vanish in the ever-changing course of events. The earth is to be burnt up, and the elements are to melt with fervent heat—to be again reduced to chaos—possibly to be renovated and adorned for other races of beings. These stupendous changes may be but cycles in those great laws of the universe, where all is variable but the laws themselves and He who has ordained them.
Physical Geography (1848), Vol. 1, 2-3.
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Whoever wishes to acquire a deep acquaintance with Nature must observe that there are analogies which connect whole branches of science in a parallel manner, and enable us to infer of one class of phenomena what we know of another. It has thus happened on several occasions that the discovery of an unsuspected analogy between two branches of knowledge has been the starting point for a rapid course of discovery.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 631.
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Why it is that animals, instead of developing in a simple and straightforward way, undergo in the course of their growth a series of complicated changes, during which they often acquire organs which have no function, and which, after remaining visible for a short time, disappear without leaving a trace ... To the Darwinian, the explanation of such facts is obvious. The stage when the tadpole breathes by gills is a repetition of the stage when the ancestors of the frog had not advanced in the scale of development beyond a fish.
In The Works of Francis Maitland Balfour (1885), Vol. 1, 702.
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With fame I become more and more stupid, which, of course, is a very common phenomenon. There is far too great a disproportion between what one is and what others think one is, or at least what they say they think one is. But one has to take it all with good humor.
From Letter (Christmas 1919) to his friend Heinrich Zangger, in Einstein archives. Quoted by Helen Dukas and Banesh Hoffman, Albert Einstein: The Human Side (1979, 2013), 8.
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With respect to those who may ask why Nature does not produce new beings? We may enquire of them in turn, upon what foundation they suppose this fact? What it is that authorizes them to believe this sterility in Nature? Know they if, in the various combinations which she is every instant forming, Nature be not occupied in producing new beings, without the cognizance of these observers? Who has informed them that this Nature is not actually assembling, in her immense elaboratory, the elements suitable to bring to light, generations entirely new, that will have nothing in common with those of the species at present existing? What absurdity then, or what want of just inference would there be, to imagine that the man, the horse, the fish, the bird will be no more? Are these animals so indispensably requisite to Nature, that without them she cannot continue her eternal course? Does not all change around us? Do we not ourselves change? ... Nature contains no one constant form.
The System of Nature (1770), trans. Samuel Wilkinson (1820), Vol. 1, 94-95.
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With time, I attempt to develop hypotheses that are more risky. I agree with [Karl] Popper that scientists need to be interested in risky hypotheses because risky hypotheses advance science by producing interesting thoughts and potential falsifications of theories (of course, personally, we always strive for verification—we love our theories after all; but we should be ready to falsify them as well.
'Grand Theories and Mid-Range Theories&3039;, essay in Ken G. Smith (ed.) and Michael A. Hitt (ed), Great Minds in Management: the Theory of Process Development (2005), 89.
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Within our bodies course the same elements that flame in the stars.
In The Incredible Machine (1986).
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Xenophanes of Kolophon ... believes that once the earth was mingled with the sea, but in the course of time it became freed from moisture; and his proofs are such as these: that shells are found in the midst of the land and among the mountains, that in the quarries of Syracuse the imprints of a fish and of seals had been found, and in Paros the imprint of an anchovy at some depth in the stone, and in Melite shallow impressions of all sorts of sea products. He says that these imprints were made when everything long ago was covered with mud, and then the imprint dried in the mud.
Doxographists, Zeller, Vorsokr. Phil. 543, n. 1. Quoted in Arthur Fairbanks (ed. And trans.), The First Philosophers of Greece (1898), 83.
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Yet as I cast my eye over the whole course of science I behold instances of false science, even more pretentious and popular than that of Einstein gradually fading into ineptitude under the searchlight; and I have no doubt that there will arise a new generation who will look with a wonder and amazement, deeper than now accompany Einstein, at our galaxy of thinkers, men of science, popular critics, authoritative professors and witty dramatists, who have been satisfied to waive their common sense in view of Einstein's absurdities.
In Elizabeth Dilling, A "Who's Who" and Handbook of Radicalism for Patriots (1934), 49.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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