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Home > Category Index for Science Quotations > Category Index P > Category: Place

Place Quotes (192 quotes)

“What place would you advise me to visit now?” he asked. “The planet Earth,” replied the geographer. “It has a good reputation.”
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[Archimedes] is said to have requested his friends and relations that when he was dead, they would place over his tomb a sphere containing a cylinder, inscribing it with the ratio which the containing solid bears to the contained.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity.
In Ueber das Verhältnis der Naturwissenschaften zur Gesammtheit der Wissenschaft, Vorträge und Reden (1896), Bd. 1, 176. Also seen translated as “In mathematics we see the conscious logical activity of our mind in its purest and most perfect form; here is made manifest to us all the labor and the great care with which it progresses, the precision which is necessary to determine exactly the source of the established general theorems, and the difficulty with which we form and comprehend abstract conceptions; but we also learn here to have confidence in the certainty, breadth, and fruitfulness of such intellectual labor”, in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 20. From the original German, “Hier sehen wir die bewusste logische Thätigkeit unseres Geistes in ihrer reinsten und vollendetsten Form; wir können hier die ganze Mühe derselben kennen lernen, die grosse Vorsicht, mit der sie vorschreiten muss, die Genauigkeit, welche nöthig ist, um den Umfang der gewonnenen allgemeinen Sätze genau zu bestimmen, die Schwierigkeit, abstracte Begriffe zu bilden und zu verstehen; aber ebenso auch Vertrauen fassen lernen in die Sicherheit, Tragweite und Fruchtbarkeit solcher Gedankenarbeit.”
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[Philosopher Lao-tse] is not dogmatic, and he does not go in for big, universal ideas. For instance, I like what he says about failure and success, “Failure is the foundation of success and the means by which it is achieved. Success is the lurking place of failure; but who can tell when the turning point will come?”
As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 74.
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[The sun] … which alone we should judge to be worthy of the most high God, if He should be pleased with a material domicile, and choose a place in which to dwell with the blessed angels.
As translated in Edwin Arthur Burtt, 'Kepler’s Early Acceptance of the New World-Scheme', The Metaphysical Foundations of Modern Physical Science: A Historical and and Critical Essay (1925), 48. From the Latin [as best as Webmaster can tell]: “[solem] … unum dignum omnes aestimaremus, in quo Deus Opt. Max., si corporeo domicilio delectaretur et capi loco posset, cum beatis angelis inhabitaret,” in Christian Frisch (ed.), Opera Omnia, Vol. 8, Part 1, 267.
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Here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!
Said by the fictional Red Queen character, in Through the Looking Glass and What Alice Found There (1872, 1896), 36.
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Mathematical truth has validity independent of place, personality, or human authority. Mathematical relations are not established, nor can they be abrogated, by edict. The multiplication table is international and permanent, not a matter of convention nor of relying upon authority of state or church. The value of π is not amenable to human caprice. The finding of a mathematical theorem may have been a highly romantic episode in the personal life of the discoverer, but it cannot be expected of itself to reveal the race, sex, or temperament of this discoverer. With modern means of widespread communication even mathematical notation tends to be international despite all nationalistic tendencies in the use of words or of type.
Anonymous
In 'Light Thrown on the Nature of Mathematics by Certain Aspects of Its Development', Mathematics in General Education (1940), 256. This is the Report of the Committee on the Function of Mathematics in General Education of the Commission on Secondary School Curriculum, which was established by the Executive Board of the Progressive Education Association in 1932.
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Omnes scientiae sunt connexae et fovent auxiliis sicut partes ejusdem totius, quarum quaelibet opus suum peragit non propter se sed pro aliis.
All sciences are connected; they lend each other material aid as parts of one great whole, each doing its own work, not for itself alone, but for the other parts; as the eye guides the body and the foot sustains it and leads it from place to place.
Opus Tertium [1266- 1268], chapter 4, Latin text quoted in J. B. Bury, The Idea of Progress (1920), 355 (footnote to page 25). In J. S. Brewer (ed.), Fr. Rogeri Bacon Opera ... inedita (1859), 18.
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Question: A hollow indiarubber ball full of air is suspended on one arm of a balance and weighed in air. The whole is then covered by the receiver of an air pump. Explain what will happen as the air in the receiver is exhausted.
Answer: The ball would expand and entirely fill the vessell, driving out all before it. The balance being of greater density than the rest would be the last to go, but in the end its inertia would be overcome and all would be expelled, and there would be a perfect vacuum. The ball would then burst, but you would not be aware of the fact on account of the loudness of a sound varying with the density of the place in which it is generated, and not on that in which it is heard.
Genuine student answer* to an Acoustics, Light and Heat paper (1880), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 181, Question 21. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.)
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~~[Questionable attribution]~~ Travel and change of place impart new vigor to the mind.
Found widely quoted and attributed to Seneca, but Webmaster, as yet, has not identified the primary source of these words (in verbatim translation) in the writings of Seneca. Conversely, Seneca says somewhat the opposite in his Epistle CIV on 'Travelling', as translated in The Epistles of Lucius Annæus Seneca (1786), Vol. 2, 242-243. Seneca quotes Socrates, “For it is said that Socrates, when a person was complaining to him that he had received very little benefit from travelling, made this reply: I do not wonder at it, since you travelled with yourself.” However Seneca was perhaps commenting on physical health, saying further, “Medicine is requisite for a sick man, not a journey. … Why then should you think a mind … can be cured merely by change of place?” However, please contact if you can help with a different Seneca source applying to mental health.
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A complete theory of evolution must acknowledge a balance between ‘external’ forces of environment imposing selection for local adaptation and ‘internal’ forces representing constraints of inheritance and development. Vavilov placed too much emphasis on internal constraints and downgraded the power of selection. But Western Darwinians have erred equally in practically ignoring (while acknowledging in theory) the limits placed on selection by structure and development–what Vavilov and the older biologists would have called ‘laws of form.’
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A few days afterwards, I went to him [the same actuary referred to in another quote] and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly. I told him that the law was involved in this circumstance. Take the table of the expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come. “You don’t mean that this always happens?”—“Try it.” He did try, again and again; and found it as I said. “This is, indeed, a curious thing; this is a discovery!” I might have sent him about trumpeting the law of life: but I contented myself with informing him that the same thing would happen with any table whatsoever in which the first column goes up and the second goes down.
In Budget of Paradoxes (1872), 172.
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A neat and orderly laboratory is unlikely. It is, after all, so much a place of false starts and multiple attempts.
[Unverified. Please contact Webmaster if you can identify the primary source.]
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A place for everything, and everything in its place.
In Thrift (1875), 13.
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A proposal…to bore a hole in the crust of the Earth and discover the conditions deep down below the surface…may remind us that the most secret places of Nature are, perhaps, not 10 to the n-th miles above our heads, but 10 miles below our feet.
From Presidential address to Section A of the British Association at Cardiff (24 Aug 1920). Published in 'The Internal Constitution of the Stars', The Observatory: A Monthly Review of Astronomy (Oct 1920), 43, No. 557, 341.
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A quarter-horse jockey learns to think of a twenty-second race as if it were occurring across twenty minutes—in distinct parts, spaced in his consciousness. Each nuance of the ride comes to him as he builds his race. If you can do the opposite with deep time, living in it and thinking in it until the large numbers settle into place, you can sense how swiftly the initial earth packed itself together, how swiftly continents have assembled and come apart, how far and rapidly continents travel, how quickly mountains rise and how quickly they disintegrate and disappear.
Annals of the Former World
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A Telescope = To see place.
Anagram
From 'The Anagram Hall of Fame' on the wordsmith.org website.
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A university should be a place of light, of liberty, and of learning.
Speech (11 Mar 1873) in the House of Commons, on University Education (Ireland) Bill, HC Deb 11 March 1873 vol 214 cc1814.
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All things on the earth are the result of chemical combination. The operation by which the commingling of molecules and the interchange of atoms take place we can imitate in our laboratories; but in nature they proceed by slow degrees, and, in general, in our hands they are distinguished by suddenness of action. In nature chemical power is distributed over a long period of time, and the process of change is scarcely to be observed. By acts we concentrate chemical force, and expend it in producing a change which occupies but a few hours at most.
In chapter 'Chemical Forces', The Poetry of Science: Or, Studies of the Physical Phenomena of Nature (1848), 235-236. Charles Dicken used this quote, with his own sub-head of 'Relative Importance Of Time To Man And Nature', to conclude his review of the book, published in The Examiner (1848).
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Always store beer in a dark place.
In 'From the Notebooks of Lazarus Long', Time Enough for Love: The Lives of Lazarus Long (1973), 256.
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Archaeology gives a sense of place. It grounds us within the landscape and every place is unique. … Archaeology can also give an understanding of where we come from.
From interview with Sarah Marsh, in “Being a Council Archaeologist is ‘Like Being a Detective’”, The Guardian (6 Sep 2013).
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Archimedes possessed so high a spirit, so profound a soul, and such treasures of highly scientific knowledge, that though these inventions [used to defend Syracuse against the Romans] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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As for the earth, out of it comes bread, but underneath it is turned up as by fire. Its stones are the place of sapphires, and it has dust of gold.
Bible
Bible: English Standard Version, Job Chap 28, verses 5-6.
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Building goes on briskly at the therapeutic Tower of Babel; what one recommends another condemns; what one gives in large doses another scarce dares to prescribe in small doses; and what one vaunts as a novelty another thinks not worth rescuing from merited oblivion. All is confusion, contradiction, inconceivable chaos. Every country, every place, almost every doctor, have their own pet remedies, without which they imagine their patients can not be cured; and all this changes every year, aye every mouth.
Weekly Medical Gazette, of Vienna
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But when science, passing beyond its own limits, assumes to take the place of theology, and sets up its own conception of the order of Nature as a sufficient account of its cause, it is invading a province of thought to which it has no claim, and not unreasonably provokes the hostility of its best friends.
Presidential Address (14 Aug 1872) to the British Association for the Advancement of Science, Brighton, reprinted in The Journal of the Society of Arts (16 Aug 1872), 20, No. 1030, 799, penultimate sentence.
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But, as we consider the totality of similarly broad and fundamental aspects of life, we cannot defend division by two as a natural principle of objective order. Indeed, the ‘stuff’ of the universe often strikes our senses as complex and shaded continua, admittedly with faster and slower moments, and bigger and smaller steps, along the way. Nature does not dictate dualities, trinities, quarterings, or any ‘objective’ basis for human taxonomies; most of our chosen schemes, and our designated numbers of categories, record human choices from a cornucopia of possibilities offered by natural variation from place to place, and permitted by the flexibility of our mental capacities. How many seasons (if we wish to divide by seasons at all) does a year contain? How many stages shall we recognize in a human life?
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Changes That Have Occurred in the Globe: When we have seen with our own eyes a mountain progressing into a plain; that is to say, an immense boulder separating from this mountain and covering the fields; an entire castle broken into pieces over the ground; a river swallowed up which then bursts out from its abyss; clear marks of a vast amount of water having once flooded regions now inhabited, and a hundred vestiges of other transformations, then we are much more willing to believe that great changes altered the face of the earth, than a Parisian lady who knows only that the place where her house was built was once a cultivated field. However, a lady from Naples who has seen the buried ruins of Herculaneum, is much less subject to the bias which leads us to believe that everything has always been as it is today.
From article 'Changements arrivées dans le globe', in Dictionnaire philosophique (1764), collected in Œuvres Complètes de Voltaire (1878), Vol. 2, 427-428. Translated by Ian Ellis, from the original French: “Changements arrivées dans le globe: Quand on a vu de ses yeux une montagne s’avancer dans une plaine, c’est-à-dire un immense rocher de cette montagne se détacher et couvrir des champs, un château tout entier enfoncé dans la terre, un fleuve englouti qui sort ensuite de son abîme, des marques indubitables qu’un vaste amas d’eau inondait autrefois un pays habité aujourd’hui, et cent vestiges d’autres révolutions, on est alors plus disposé à croire les grands changements qui ont altéré la face du monde, que ne l’est une dame de Paris qui sait seulement que la place où est bâtie sa maison était autrefois un champ labourable. Mais une dame de Naples, qui a vu sous terre les ruines d’Herculanum, est encore moins asservie au préjugé qui nous fait croire que tout a toujours été comme il est aujourd’hui.”
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Charlie Holloway (human): “What we hoped to achieve was to meet our makers. To get answers. Why they even made us in the first place.”
David (AI robot): “Why do you think your people made me?”
Charlie Holloway (human): “We made you because we could.”
David (AI robot): “Can you imagine how disappointing it would be for you to hear the same thing from your creator?”
Charlie Holloway (human): “I guess it’s good you can’t be disappointed.”
Prometheus (2012)
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City wisdom became almost entirely centered on the problems of human relationships, in contrast to the wisdom of any natural tribal group, where relationships with the rest of the animate and inanimate world are still given due place.
In Gaia, a New Look at Life on Earth (1979), 135.
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Coterminous with space and coeval with time is the kingdom of Mathematics; within this range her dominion is supreme; otherwise than according to her order nothing can exist; in contradiction to her laws nothing takes place. On her mysterious scroll is to be found written for those who can read it that which has been, that which is, and that which is to come.
From Presidential Address (Aug 1878) to the British Association, Dublin, published in the Report of the 48th Meeting of the British Association for the Advancement of Science (1878), 31.
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Darwinists are right to say that selection favours the organisms that leave alive the most progeny, but vigorous growth takes place within a constrained space where feedback from the environment allows the emergence of natural self-regulation.
In The Revenge of Gaia: Earth’s Climate Crisis & The Fate of Humanity (2006, 2007), 35.
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Different kinds of animals and plants live together in different places: camels in deserts, whales in the seas, gorillas in tropical forests. The totality of this diversity from the genetic level, through organisms to ecosystems and landscapes is termed collectively biological diversity.
From Reith Lecture, 'Biodiversity', on BBC Radio 4 (19 Apr 2000). Transcript and audio on BBC website.
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Dirichlet was not satisfied to study Gauss’ Disquisitiones arithmetical once or several times, but continued throughout life to keep in close touch with the wealth of deep mathematical thoughts which it contains by perusing it again and again. For this reason the book was never placed on the shelf but had an abiding place on the table at which he worked. … Dirichlet was the first one, who not only fully understood this work, but made it also accessible to others.
In Dirichlet, Werke, Bd. 2, 315. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 159.
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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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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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Everyone has talent. What is rare is the courage to follow that talent to dark place where it leads.
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Everything that comes into being seeks room for itself and desires duration: hence it drives something else from its place and shortens its duration.
In The Maxims and Reflections of Goethe (1906), 199.
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Exits sun; enters moon.
This moon is never alone.
Stars are seen all around.
These twinklers do not make a sound.
The tiny ones shine from their place.
Mother moon watches with a smiling face.
Its light is soothing to the eyes.
Night’s darkness hides its face.
Cool and calm is its light.
Heat and sweat are never felt.
Some days, moon is not seen.
Makes kids wonder, where had it been?
Partial eclipse shades the moon.
In summers it does not arrive soon.
Beautiful is this milky ball.
It is the love of one and all.
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For me, physics cultivates a perpetual state of wonder about the limits of thoughts, the workings of the universe, and our place in the vast space-time landscape that we call home.
Closing sentence of 'Introduction', The Physics Book: From Olbers’ Paradox to Schrödinger’s Cat: From the Big Bang to Quantum Resurrection, 250 Milestones in the History of Physics (2011), 15.
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For the world, I count it not an inn, but an hospital, and a place, not to live, but to die in.
In Religio Medici (1642, 1754), pt. 2, sec. 11, 203.
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Formal symbolic representation of qualitative entities is doomed to its rightful place of minor significance in a world where flowers and beautiful women abound.
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Gay-Lussac was quick, lively, ingenious and profound, with great activity of mind and great facility of manipulation. I should place him at the head of all the living chemists in France.
In Mary Elvira Weeks, Discovery of the Elements (1934), 161, citing J. Davy, Memoirs of the Life of Sir Humphry Davy, Bart. (1836) Vol. 1, 469.
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going to have an industrial society you must have places that will look terrible. Other places you set aside—to say, ‘This is the way it was.’
Assembling California
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Heroes of physics, Argonauts of our time
Who leaped the mountains, who crossed the seas …
You have confirmed in uncomfortable places
What Newton knew without leaving his study.
Discours en Vers sur l’Homme (1734), Quatrieme discours: de la Moderation (1738). English translation as in J. L. Heilbron, Weighing Imponderables and Other Quantitative Science around 1800 (1993), 224.
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How hard to realize that every camp of men or beast has this glorious starry firmament for a roof! In such places standing alone on the mountain-top it is easy to realize that whatever special nests we make - leaves and moss like the marmots and birds, or tents or piled stone - we all dwell in a house of one room - the world with the firmament for its roof - and are sailing the celestial spaces without leaving any track.
John Muir
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Hubble touches people. When you're looking that far out, you're giving people their place in the universe, it touches people. Science is often visual, so it doesn't need translation. It's like poetry, it touches you.
Interview (22 May 1997). On Academy of Achievement website.
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I am born into an environment–I know not whence I came nor whither I go nor who I am. This is my situation as yours, every single one of you. The fact that everyone always was in this same situation, and always will be, tells me nothing. Our burning question as to the whence and whither–all we can ourselves observe about it is the present environment. That is why we are eager to find out about it as much as we can. That is science, learning, knowledge; it is the true source of every spiritual endeavour of man. We try to find out as much as we can about the spatial and temporal surroundings of the place in which we find ourselves put by birth.
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I can certainly wish for new, large, and properly constructed instruments, and enough of them, but to state where and by what means they are to be procured, this I cannot do. Tycho Brahe has given Mastlin an instrument of metal as a present, which would be very useful if Mastlin could afford the cost of transporting it from the Baltic, and if he could hope that it would travel such a long way undamaged… . One can really ask for nothing better for the observation of the sun than an opening in a tower and a protected place underneath.
As quoted in James Bruce Ross and Mary Martin McLaughlin, The Portable Renaissance Reader (1968), 605.
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I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
In Florian Cajori, Teaching and History of Mathematics in the United States (1890), 266-267.
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I do not define time, space, place, and motion, as being well known to all. … [However] it will be convenient to distinguish them into Absolute and Relative, True and Apparent, Mathematical and Common.
Scholium following opening section of Definitions, Philosophia Naturalis Principia Mathematica (1687) as translated from the original Latin, in Andrew Motte, Newton's Principia: The Mathematical Principles of Natural Philosophy (1729), Vol. 1, 9.
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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 have said that the investigation for which the teeth of the shark had furnished an opportunity, was very near an end... But thereafter, while I was examining more carefully these details of both places and bodies [sedimentary deposits and shells], these day by day presented points of doubt to me as they followed one another in indissoluble connection, so that I saw myself again and again brought back to the starting-place, as it were, when I thought I was nearest the goal. I might compare those doubts to the heads of the Lernean Hydra, since when one of them had been got rid of, numberless others were born; at any rate, I saw that I was wandering about in a sort of labyrinth, where the nearer one approaches the exit, the wider circuits does one tread.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 206.
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I hear one day the word “mountain,” and I ask someone “what is a mountain? I have never seen one.”
I join others in discussions of mountains.
One day I see in a book a picture of a mountain.
And I decide I must climb one.
I travel to a place where there is a mountain.
At the base of the mountain I see there are lots of paths to climb.
I start on a path that leads to the top of the mountain.
I see that the higher I climb, the more the paths join together.
After much climbing the many paths join into one.
I climb till I am almost exhausted but I force myself and continue to climb.
Finally I reach the top and far above me there are stars.
I look far down and the village twinkles far below.
It would be easy to go back down there but it is so beautiful up here.
I am just below the stars.
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I learned a lot of different things from different schools. MIT is a very good place…. It has developed for itself a spirit, so that every member of the whole place thinks that it’s the most wonderful place in the world—it’s the center, somehow, of scientific and technological development in the United States, if not the world … and while you don’t get a good sense of proportion there, you do get an excellent sense of being with it and in it, and having motivation and desire to keep on…
From Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character (1985), 51.
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I shall tell you a great secret, my friend. Do not wait for the last judgment. It takes place every day.
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I strongly reject any conceptual scheme that places our options on a line, and holds that the only alternative to a pair of extreme positions lies somewhere between them. More fruitful perspectives often require that we step off the line to a site outside the dichotomy.
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I submit that the traditional definition of psychiatry, which is still in vogue, places it alongside such things as alchemy and astrology, and commits it to the category of pseudo-science.
In The Myth of Mental Illness: Foundations of a Theory of Personal Conduct (1961), 1.
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Iamblichus in his treatise On the Arithmetic of Nicomachus observes p. 47- “that certain numbers were called amicable by those who assimilated the virtues and elegant habits to numbers.” He adds, “that 284 and 220 are numbers of this kind; for the parts of each are generative of each other according to the nature of friendship, as was shown by Pythagoras. For some one asking him what a friend was, he answered, another I (ετεϑος εγω) which is demonstrated to take place in these numbers.” [“Friendly” thus: Each number is equal to the sum of the factors of the other.]
In Theoretic Arithmetic (1816), 122. (Factors of 284 are 1, 2, 4 ,71 and 142, which give the sum 220. Reciprocally, factors of 220 are 1, 2, 4, 5, 10, 11 ,22, 44, 55 and 110, which give the sum 284.) Note: the expression “alter ego” is Latin for “the other I.”
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If a hundred or a thousand people, all of the same age, of the same constitution and habits, were suddenly seized by the same illness, and one half of them were to place themselves under the care of doctors, such as they are in our time, whilst the other half entrusted themselves to Nature and to their own discretion, I have not the slightest doubt that there would be more cases of death amongst the former, and more cases of recovery among the latter.
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If I choose to impose individual blame for all past social ills, there will be no one left to like in some of the most fascinating periods of our history. For example ... if I place every Victorian anti-Semite beyond the pale of my attention, my compass of available music and literature will be pitifully small. Though I hold no shred of sympathy for active persecution, I cannot excoriate individuals who acquiesced passively in a standard societal judgment. Rail instead against the judgment, and try to understand what motivates men of decent will.
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If we want an answer from nature, we must put our questions in acts, not words, and the acts may take us to curious places. Some questions were answered in the laboratory, others in mines, others in a hospital where a surgeon pushed tubes in my arteries to get blood samples, others on top of Pike’s Peak in the Rocky Mountains, or in a diving dress on the bottom of the sea. That is one of the things I like about scientific research. You never know where it will take you next.
From essay 'Some Adventures of a Biologist', as quoted in Ruth Moore, Man, Time, And Fossils (1953), 174.
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If you keep your standards high, people will always find a place for you.
Anonymous
Found in The NIH Catalyst (May-June 2003), 11, No. 3, 8, as part of list 'A Scientist’s Dozen,' cited as “culled and adapted…from a variety of sources” by Howard Young.
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In crossing a heath, suppose I pitched my foot against a stone, and were asked how the stone came to be there, I might possibly answer, that, for any thing I knew to the contrary, it had lain there for ever: nor would it perhaps be very easy to shew the absurdity of this answer. But suppose I had found a watch upon the ground, and it should be enquired how the watch happened to be in that place, I should hardly think of the answer which I had before given, that, for any thing I knew, the watch might have always been there.
Natural Theology: or, Evidences of the Existence and Attributes of the Deity, Collected from the Appearances of Nature (1802), 1-2.
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In human freedom in the philosophical sense I am definitely a disbeliever. Everybody acts not only under external compulsion but also in accordance with inner necessity. Schopenhauer’s saying, that ‘a man can do what he wants, but not want what he wants,’ has been an inspiration to me since my youth up, and a continual consolation and unfailing well-spring of patience in the face of the hardships of life, my own and others. This feeling mercifully not only mitigates the sense of responsibility which so easily becomes paralysing, and it prevents us from taking ourselves and other people too seriously; it conduces to a view of life in which humour, above all, has its due place.
In The World As I See It (1934), 238.
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In India we have clear evidence that administrative statistics had reached a high state of organization before 300 B.C. In the Arthasastra of Kautilya … the duties of the Gopa, the village accountant, [include] “by setting up boundaries to villages, by numbering plots of grounds as cultivated, uncultivated, plains, wet lands, gardens, vegetable gardens, fences (váta), forests altars, temples of gods, irrigation works, cremation grounds, feeding houses (sattra), places where water is freely supplied to travellers (prapá), places of pilgrimage, pasture grounds and roads, and thereby fixing the boundaries of various villages, of fields, of forests, and of roads, he shall register gifts, sales, charities, and remission of taxes regarding fields.”
Editorial, introducing the new statistics journal of the Indian Statistical Institute, Sankhayā (1933), 1, No. 1. Also reprinted in Sankhyā: The Indian Journal of Statistics (Feb 2003), 65, No. 1, viii.
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In mathematics it [sophistry] had no place from the beginning: Mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly we find no parties among mathematicians, and hardly any disputes.
In Essays on the Intellectual Powers of Man, Essay 1, chap. 1.
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In matters of conscience, the law of majority has no place.
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In the center of everything rules the sun; for who in this most beautiful temple could place this luminary at another better place whence it can light up the whole at once? … In fact, the sun sitting on his royal throne guides the family of stars surrounding him. … In this arrangement we thus find an admirable harmony of the world, and a constant harmonious connection between the motion and the size of the orbits as could not be found otherwise.
In De Revolutionibus Orbium Coelestium (1543), Book 1, Ch. 10. As translated in Hermann Kesten, Copernicus and his World (1945), 182-183. From the original Latin: “In medio vero omnium residet Sol. Quis enim in hoc pulcherrimo templo lampadem hanc in alio vel meliori loco poneret, quam unde totum simul possit illuminare? … Ita profecto tanquam in solio regali Sol residens circum agentem gubernat Astrorum familiam. … Invenimus igitur sub hac ordinatione admirandam mundi symmetriam, ac certum harmoniae nexum motus et magnitudinis orbium: qualis alio modo reperiri non potest.” Corresponding translations also found in Charles Glenn Wallis (trans.), On the Revolutions of Heavenly Spheres (1939, 1995), 24-25, which gives: “In the center of all rests the sun. For who would place this lamp of a very beautiful temple in another or better place than this wherefrom it can illuminate everything at the same time? … And so the sun, as if resting on a kingly throne, governs the family of stars which wheel around. … Therefore in this ordering we find that the world has a wonderful commensurability and that there is a sure bond of harmony for the movement and magnitude of the orbital circles such as cannot be found in any other way.” The passage is translated in Robert Reinhold, 'After 500 Years, Now the Year of Copernicus', New York Times (28 Dec 1972), 33, as: “At rest in the middle of everything is the sun, for in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time? … As though seated on a royal throne, the sun governs the family of planets revolving around it.” Also seen translated in Edwin Arthur Burtt, The Metaphysical Foundations of Modern Physical Science (1925), 45, as: “Then in the middle of all stands the sun. For who, in our most beautiful temple, could set this light in another or better place, than that from which it can at once illuminate the whole? … And in fact does the sun, seated on his royal throne, guide his family of planets as they circle round him.” [Notice the original Latin reads “Astrorum familiam”, so the literal translation is “family of stars” rather than what we now call “planets.” —Webmaster]
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In the tropical and subtropical regions, endemic malaria takes first place almost everywhere among the causes of morbidity and mortality and it constitutes the principal obstacle to the acclimatization of Europeans in these regions.
From Nobel Lecture (11 Dec 1907), 'Protozoa as Causes of Diseases', collected in Nobel Lectures, Physiology or Medicine 1901-1921 (1967, 1999), 264.
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In this world [of art] the emotions of life find no place.
In Art (1913), 27.
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Induction and analogy are the special characteristics of modern mathematics, in which theorems have given place to theories and no truth is regarded otherwise than as a link in an infinite chain. “Omne exit in infinitum” is their favorite motto and accepted axiom.
In 'A Plea for the Mathematician', Nature, Vol. 1, 861. [The Latin phrase “Omne exit in infinitum” means “Everything goes to infinity”.
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Is man a peculiar organism? Does he originate in a wholly different way from a dog, bird, frog, or fish? and does he thereby justify those who assert that he has no place in nature, and no real relationship with the lower world of animal life? Or does he develop from a similar embryo, and undergo the same slow and gradual progressive modifications? The answer is not for an instant doubtful, and has not been doubtful for the last thirty years. The mode of man’s origin and the earlier stages of his development are undoubtedly identical with those of the animals standing directly below him in the scale; without the slightest doubt, he stands in this respect nearer the ape than the ape does to the dog. (1863)
As quoted in Ernst Haeckel and E. Ray Lankester (trans.) as epigraph for Chap. 12, The History of Creation (1886), Vol. 1, 364.
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It feels unacceptable to many people even to think of having a cosmology based on science. … They see fanciful origin stories as spicing up the culture. … Aspects of many origin stories can enrich our understanding of the scientific picture, but they cannot take its place.
As co-author with Nancy Ellen Abrams, in The View from the Center of the Universe: Discovering Our Extraordinary Place in the Cosmos (2006), 85.
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It is a custom often practiced by seafaring people to throw a bottle overboard, with a paper, stating the time and place at which it is done. In the absence of other information as to currents, that afforded by these mute little navigators is of great value.
In The Physical Geography of the Sea (1855), 28.
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It is hard to believe that a man is telling the truth when you know that you would lie if you were in his place.
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It is not always possible to know what one has learned, or when the dawning will arrive. You will continue to shift, sift, to shake out and to double back. The synthesis that finally occurs can be in the most unexpected place and the most unexpected time. My charge ... is to be alert to the dawnings.
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It is plainly the popularization of science that is responsible for the fever and instability apparent on all sides. To withhold knowledge from people, or to place unassimilable knowledge in their hands, are both equally effective, if you wish to render them helpless.
In The Art of Being Ruled (1926), 423.
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It is tautological to say that an organism is adapted to its environment. It is even tautological to say that an organism is physiologically adapted to its environment. However, just as in the case of many morphological characters, it is unwarranted to conclude that all aspects of the physiology of an organism have evolved in reference to a specific milieu. It is equally gratuitous to assume that an organism will inevitably show physiological specializations in its adaptation to a particular set of conditions. All that can be concluded is that the functional capacities of an organism are sufficient to have allowed persistence within its environment. On one hand, the history of an evolutionary line may place serious constraints upon the types of further physiological changes that are readily feasible. Some changes might require excessive restructuring of the genome or might involve maladaptive changes in related functions. On the other hand, a taxon which is successful in occupying a variety of environments may be less impressive in individual physiological capacities than one with a far more limited distribution.
In W.R. Dawson, G.A. Bartholomew, and A.F. Bennett, 'A Reappraisal of the Aquatic Specializations of the Galapagos Marine Iguana (Amblyrhynchus cristatus)', Evolution (1977), 31, 891.
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It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.
Proclus
In scholium to Book X of Euclid t. V, 417 as quoted and cited in Ettore Carruccio and Isabel Quigly (trans.), Mathematics And Logic in History And in Contemporary Thought (1964), 27.
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It may be said of some very old places, as of some very old books, that they are destined to be forever new. The nearer we approach them, the more remote they seem: the more we study them, the more we have yet to learn. Time augments rather than diminishes their everlasting novelty; and to our descendants of a thousand years hence it may safely be predicted that they will be even more fascinating than to ourselves. This is true of many ancient lands, but of no place is it so true as of Egypt.
Opening remark in Pharaohs, Fellahs and Explorers (1891), 3.
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It needs scarcely be pointed out that in placing Mathematics at the head of Positive Philosophy, we are only extending the application of the principle which has governed our whole Classification. We are simply carrying back our principle to its first manifestation. Geometrical and Mechanical phenomena are the most general, the most simple, the most abstract of all,— the most irreducible to others, the most independent of them; serving, in fact, as a basis to all others. It follows that the study of them is an indispensable preliminary to that of all others. Therefore must Mathematics hold the first place in the hierarchy of the sciences, and be the point of departure of all Education whether general or special.
In Auguste Comte and Harriet Martineau (trans.), The Positive Philosophy (1858), Introduction, Chap. 2, 50.
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It’s amazing how quickly nature consumes human places after we turn our backs on them. Life is a hungry thing.
…...
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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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Let no one say that I have said nothing new; the arrangement of the subject is new. When we play tennis, we both play with the same ball, but one of us places it better.
In Pensées (1670), Section 7, No. 9. From Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 14. From the French, “Qu’on ne dise pas que je n’ai rien dit de nouveau: la disposition des matières est nouvelle. Quand on joue à la paume, c’est une même balle dont on joue l’un et l’autre; mais l’un la place mieux,” in Oeuvres Complètes de Blaise Pascal (1864), Vol. 1, 287.
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Life and business are rather simple after all—to make a success of either, you've got to hang on to the knack of putting yourself into the other person's place.
c. 1891. On Wrigley Company web site.
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Life is inseparable from water. For all terrestrial animals, including birds, the inescapable need for maintaining an adequate state of hydration in a hostile, desiccating environment is a central persistent constraint which exerts a sustained selective pressure on every aspect of the life cycle. It has been said, with some justification, that the struggle for existence is a struggle for free energy for doing physiological work. It can be said with equal justification for terrestrial organisms that the struggle for existence is a struggle to maintain an aqueous internal environment in which energy transformations for doing work can take place.
In 'The water economy of seed-eating birds that survive without drinking', Proceedings of the International Ornithological Congress (1972), 15, 237-238.
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Life through many long periods has been manifested in a countless host of varying structures, all circumscribed by one general plan, each appointed to a definite place, and limited to an appointed duration. On the whole the earth has been thus more and more covered by the associated life of plants and animals, filling all habitable space with beings capable of enjoying their own existence or ministering to the enjoyment of others; till finally, after long preparation, a being was created capable of the wonderful power of measuring and weighing all the world of matter and space which surrounds him, of treasuring up the past history of all the forms of life, and considering his own relation to the whole. When he surveys this vast and co-ordinated system, and inquires into its history and origin, can he be at a loss to decide whether it be a work of Divine thought and wisdom, or the fortunate offspring of a few atoms of matter, warmed by the anima mundi, a spark of electricity, or an accidental ray of sunshine?
Life on the Earth: Its Origin and Succession (1860), 216-7.
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Lovely snowflakes! Each one falls in the appropriate place.
Zen
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 23
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Mathematical physics is in the first place physics and it could not exist without experimental investigations.
From inaugural lecture at Utrecht on the kinetic theory of matter and its modern development (1913), as quoted in Julio Antonio Gonzalo and Carmen Aragó López (eds.), Great Solid State Physicists of the 20th Century (2003), 157.
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Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well placed internal charges.
From In Mathematical Circles (1969), 7.
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Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
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Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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Men go into space to see whether it is the kind of place where other men, and their families and their children, can eventually follow them. A disturbingly high proportion of the intelligent young are discontented because they find the life before them intolerably confining. The moon offers a new frontier. It is as simple and splendid as that.
Editorial on the moon landing, The Economist (1969).
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Mere infants of the universe, with no feel for infinity, no sense of place in time and space, we human beings have yet to comprehend the enormity of what we are doing: In a geological second, we are unraveling complexities it took eternity to create.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 107.
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More dependence must be placed on facts than on reasonings, which must agree with facts.
Aristotle
Cited as De Gener. Animal., III., 10, 760. 639 in George Henry Lewes, Aristotle: A Chapter from the History of Science including analyses of Aristotle's scientific writings (1864),
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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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No one, it has been said, will ever look at the Moon in the same way again. More significantly can one say that no one will ever look at the earth in the same way. Man had to free himself from earth to perceive both its diminutive place in a solar system and its inestimable value as a life-fostering planet. As earthmen, we may have taken another step into adulthood. We can see our planet earth with detachment, with tenderness, with some shame and pity, but at last also with love.
In Earth Shine (1969). As quoted and cited in Joseph J. Kerski, Interpreting Our World: 100 Discoveries That Revolutionized Geography (2016), 93.
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Not every one of our desires can be immediately gratified. We’ve got to learn to wait patiently for our dreams to come true, especially on the path we’ve chosen. But while we wait, we need to prepare symbolically a place for our hopes and dreams.
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Now comes the reign of iron — and cased sloops are to take the place of wooden ships.
Quoted as “After Monitor-Virginia engagement,” without citation, in David M. Cooney, A Chronology of the U.S. Navy, 1775-1965 (1965), 92, also VE-398.
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Number, place, and combination … the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.
In Philosophical Magazine (1844), 84, 285; Collected Mathematical Papers, Vol. 1, 91.
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Of all the sciences that pertain to reason, Metaphysics and Geometry are those in which imagination plays the greatest part. … Imagination acts no less in a geometer who creates than in a poet who invents. It is true that they operate differently on their object. The first shears it down and analyzes it, the second puts it together and embellishes it. … Of all the great men of antiquity, Archimedes is perhaps the one who most deserves to be placed beside Homer.
From the original French: “La Métaphysique & la Géométrie sont de toutes les Sciences qui appartiennent à la raison, celles où l’imagination à le plus de part. … L’imagination dans un Géometre qui crée, n’agit pas moins que dans un Poëte qui invente. Il est vrai qu’ils operent différemment sur leur objet; le premier le dépouille & l’analyse, le second le compose & l’embellit. … De tous les grands hommes de l’antiquité, Archimede est peut-être celui qui mérite le plus d’être placé à côté d’Homere.” In Discours Preliminaire de L'Encyclopedie (1751), xvi. As translated by Richard N. Schwab and Walter E. Rex, Preliminary Discourse to the Encyclopedia of Diderot (1963, 1995), xxxvi. A footnote states “Note that ‘geometer’ in d’Alembert’s definition is a term that includes all mathematicians and is not strictly limited to practitioners of geometry alone.” Also seen in a variant extract and translation: “Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this …. The imagination in a mathematician who creates makes no less difference than in a poet who invents…. Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.” This latter translation may be from The Plan of the French Encyclopædia: Or Universal Dictionary of Arts, Sciences, Trades and Manufactures (1751). Webmaster has not yet been able to check for a verified citation for this translation. Can you help?
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Of all the strange “crimes” that humanity has legislated out of nothing, “blasphemy” is the most amazing—with “obscenity” and “indecent exposure” fighting it out for second and third place.
In 'From the Notebooks of Lazarus Long', Time Enough for Love: The Lives of Lazarus Long (1973), 259.
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Once in a while you get shown the light in the strangest of places if you look at it right.
Scarlet Begonias
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One cannot ignore half of life for the purposes of science, and then claim that the results of science give a full and adequate picture of the meaning of life. All discussions of “life” which begin with a description of man's place on a speck of matter in space, in an endless evolutionary scale, are bound to be half-measures, because they leave out most of the experiences which are important to use as human beings.
In Religion and the Rebel (1957), 309.
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One object of Life and Habit was to place the distrust of science upon a scientific basis.
In Samuel Butler and Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1920), Vol. 2, 266. About Butler’s own book, Life and Habit.
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One of the ways the telegraph changed us as humans was it gave us a new sense of what time it is. It gave us an understanding of simultaneity. It gave us the ability to synchronize clocks from one place to another. It made it possible for the world to have standard time and time zones and then Daylight Savings Time and then after that jetlag. All of that is due to the telegraph because, before that, the time was whatever it was wherever you were.
From transcript for video interview on bigthink website
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One precept for the scientist-to-be is already obvious. Do not place yourself in an environment where your advisor is already suffering from scientific obsolescence. If one is so unfortunate as to receive his training under a person who is either technically or intellectually obsolescent, one finds himself to be a loser before he starts. It is difficult to move into a position of leadership if one’s launching platform is a scientific generation whose time is already past.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 229.
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Our time is distinguished by wonderful achievements in the fields of scientific understanding and the technical application of those insights. Who would not be cheered by this? But let us not forget that human knowledge and skills alone cannot lead humanity to a happy and dignified life. Humanity has every reason to place the proclaimers of high moral standards and values above the discoverers of objective truth. What humanity owes to personalities like Buddha, Moses, and Jesus ranks for me higher than all the achievements of the inquiring constructive mind.
(Sep 1937). In Helen Dukas and Banesh Hoffman (eds.), Albert Einstein, the Human Side (1979), 70. The editors state that except being unrelated to “a ‘Preaching Mission’, nothing of any consequence is known of the circumstances that prompted its composition.”
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Our world is not an optimal place, fine tuned by omnipotent forces of selection. It is a quirky mass of imperfections, working well enough (often admirably); a jury-rigged set of adaptations built of curious parts made available by past histories in different contexts ... A world optimally adapted to current environments is a world without history, and a world without history might have been created as we find it. History matters; it confounds perfection and proves that current life transformed its own past.
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Plant breeding to be successful must be conducted like architecture. Definite plans must be carefully laid for the proposed creation; suitable materials selected with judgment, and these must he securely placed in their proper order and position.
From Paper read at the Annual Meeting of the American Breeders’ Association, at Columbia, Mo. (5-8 January 1909). In 'Another Mode of Species Forming', Popular Science Monthly (Sep 1909), 75, 265.
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Plants have all the same kinds of problems of survival that animals have. … They must find food, a place to live, a mate and they must get on with their neighbors and fight to survive.
In Nadine Brozan, 'Chronicle: Bringing the Secret Life of Plants to Light', New York Times (9 Oct 1995), Sec. A, 13. Attenborough was on a lecture tour about The Private Life of Plants, the title of his book and a six-part BBC TV series.
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Q: Which place has special childhood memories for you?
A: Charnwood Forest, Leicestershire.

Q: In which place do you feel most “at home”?
A: Richmond, Surrey, where I live near Richmond Hill.

Q: In which place have you felt ill at ease or uncomfortable?
A: The Democratic Republic of the Congo.
Q: Which place that you have visited has for you a “tingle factor?”
A: New Guinea.

Q: Which place that you have visited has given you most hope about the future?
A: A primary school.

Q: Which place would you like to revisit?
A: Tuscany.
In 'My Places: David Attenborough', Teaching Geography, (Summer 2008), 33, No. 2, 86.
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Science is not only compatible with spirituality; it is a profound source of spirituality. When we recognize our place in an immensity of light-years and in the passage of ages, when we grasp the intricacy, beauty, and subtlety of life, then that soaring feeling, that sense of elation and humility combined, is surely spiritual ... The notion that science and spirituality are somehow mutually exclusive does a disservice to both.
In Demon-Haunted World: Science as a Candle in the Dark (1995), 29.
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Several of the young people here [at the fifth White House Science Fair] are first-generation Americans. Their parents came here, in part, so their kids could develop their talents and make a difference in the world. … America is going to be stronger and smarter and healthier, and a much more interesting place because of you.
From remarks at the fifth White House Science Fair, in Press Release (23 Mar 2015).
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Solitude is the place of purification.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 183
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Space is to place as eternity is to time.
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Strong, deeply rooted desire is the starting point of all achievement. Just as the electron is the last unit of matter discernible to the scientist. DESIRE is the seed of all achievement; the starting place, back of which there is nothing, or at least there is nothing of which we have any knowledge.
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Surely the claim of mathematics to take a place among the liberal arts must now be admitted as fully made good. Whether we look at the advances made in modern geometry, in modern integral calculus, or in modern algebra, in each of these three a free handling of the material employed is now possible, and an almost unlimited scope is left to the regulated play of fancy. It seems to me that the whole of aesthetic (so far as at present revealed) may be regarded as a scheme having four centres, which may be treated as the four apices of a tetrahedron, namely Epic, Music, Plastic, and Mathematic. There will be found a common plane to every three of these, outside of which lies the fourth; and through every two may be drawn a common axis opposite to the axis passing through the other two. So far is certain and demonstrable. I think it also possible that there is a centre of gravity to each set of three, and that the line joining each such centre with the outside apex will intersect in a common point the centre of gravity of the whole body of aesthetic; but what that centre is or must be I have not had time to think out.
In 'Proof of the Hitherto Undemonstrated Fundamental Theorem of Invariants', Collected Mathematical Papers (1909), Vol. 3, 123.
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Take care of your body. It’s the only place you have to live.
Jim Rohn
Found quoted in various books, but without a citation. Webmaster has found no primary source yet. Can you help?
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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That night I lie out under the stars again. The Pleiades are there winking at me. I am no longer on my way from one place to another. I have changed lives. My life now is as black and white as night and day; a life of fierce struggle under the sun, and peaceful reflection under the night sky. I feel as though I am floating on a raft far, far away from any world I ever knew.
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The amount of knowledge which we can justify from evidence directly available to us can never be large. The overwhelming proportion of our factual beliefs continue therefore to be held at second hand through trusting others, and in the great majority of cases our trust is placed in the authority of comparatively few people of widely acknowledged standing.
Personal Knowledge (1958), 208.
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The animals of the Burgess Shale are holy objects–in the unconventional sense that this word conveys in some cultures. We do not place them on pedestals and worship from afar. We climb mountains and dynamite hillsides to find them. We quarry them, split them, carve them, draw them, and dissect them, struggling to wrest their secrets. We vilify and curse them for their damnable intransigence. They are grubby little creatures of a sea floor 530 million years old, but we greet them with awe because they are the Old Ones, and they are trying to tell us something.
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The axis cylinders of all nerve fibers (motor, secretory, sensitive and sensory, conducting centrifugally or centripetally) have been proved to proceed directly from the cells. A connection with a fiber network, or an origin from such a network, does not take place.
In 'Uber einige neuere Forschungen im Gebiete der Anatomie des Centralnervensystems', Deutsche Medizirusche Wochenschrlft (1891), 7, 1352. Trans. Edwin Clarke and L. S. Jacyna, Nineteenth Century Origins of Neuroscientific Concepts (1987), 99.
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The beautiful has its place in mathematics as elsewhere. The prose of ordinary intercourse and of business correspondence might be held to be the most practical use to which language is put, but we should be poor indeed without the literature of imagination. Mathematics too has its triumphs of the Creative imagination, its beautiful theorems, its proofs and processes whose perfection of form has made them classic. He must be a “practical” man who can see no poetry in mathematics.
In A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays (1908), 208.
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The canyon country does not always inspire love. To many it appears barren, hostile, repellent—a fearsome, mostly waterless land of rock and heat, sand dunes and quicksand. cactus, thornbush, scorpion, rattlesnake, and agoraphobic distances. To those who see our land in that manner, the best reply is, yes, you are right, it is a dangerous and terrible place. Enter at your own risk. Carry water. Avoid the noon-day sun. Try to ignore the vultures. Pray frequently.
The Journey Home
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The cell phone has transformed public places into giant phone-a-thons in which callers exist within narcissistic cocoons of private conversations. Like faxes, computer modems and other modern gadgets that have clogged out lives with phony urgency, cell phones represent the 20th Century’s escalation of imaginary need. We didn’t need cell phones until we had them. Clearly, cell phones cause not only a breakdown of courtesy, but the atrophy of basic skills.
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The chemist works along his own brilliant line of discovery and exposition; the astronomer has his special field to explore; the geologist has a well-defined sphere to occupy. It is manifest, however, that not one of these men can tell the whole tale, and make a complete story of creation. Another man is wanted. A man who, though not necessarily going into formal science, sees the whole idea, and speaks of it in its unity. This man is the theologian. He is not a chemist, an astronomer, a geologist, a botanist——he is more: he speaks of circles, not of segments; of principles, not of facts; of causes and purposes rather than of effects and appearances. Not that the latter are excluded from his study, but that they are so wisely included in it as to be put in their proper places.
In The People's Bible: Discourses Upon Holy Scripture: Vol. 1. Genesis (1885), 120.
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The dictionary is the only place where success comes before work.
Seen attributed to Mark Twain, likely falsely, because the quotation with that wording is not found in complilations of his work. On the Quote Investigator website, possible precursors are listed. The earliest QI found is from a Newcastle, Pennsylvania, newspaper (1925): “One way to find success without working for it is to look it up in the dictionary.” A closer match found by QI is in a column, 'The Press Box', by Stubby Currence in the Bluefield, West Virginia newspaper, Bluefield Daily Telegraph (1935): “BUFF SAYS: “The dictionary is the only place where you come to SUCCESS before you get to WORK.” It is unclear if the quip was in circulation earlier, and merely recited in these examples. Vince Lombardi used a similar wording much later.
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The dodo never had a chance. He seems to have been invented for the sole purpose of becoming extinct and that was all he was good for. … I’m not blaming the Dodo but he was a mess. He had an ugly face with a large hooked beak, a tail in the wrong place, wings too small … and a very prominent stomach.
In 'The Dodo', How to Become Extinct (1941), 163.
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The edge of the sea is a strange and beautiful place. All through the long history of Earth it has been an area of unrest where waves have broken heavily against the land, where the tides have pressed forward over the continents, receded, and then returned. For no two successive days is the shore line precisely the same. Not only do the tides advance and retreat in their eternal rhythms, but the level of the sea itself is never at rest. It rises or falls as the glaciers melt or grow, as the floor of the deep ocean basins shifts under its increasing load of sediments, or as the Earth’s crust along the continental margins warps up or down in adjustment to strain and tension. Today a little more land may belong to the sea, tomorrow a little less. Always the edge of the sea remains an elusive and indefinable boundary.
Opening paragraph in The Edge of the Sea (1955), 1.
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The future is not a result of choices among alternative paths offered by the present, but a place that is created-created first in the mind and will, created next in activity. The future is not some place we are going to, but one we are creating. The paths are not to be found, but made, and the activity of making them, changes both the maker and the destination.
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The goal is nothing other than the coherence and completeness of the system not only in respect of all details, but also in respect of all physicists of all places, all times, all peoples, and all cultures.
Acht Vorlesungen (1910), 'Vorwort': 4. Translated in J. L. Heilbron, The Dilemmas of an Upright Man (1986), 51.
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The habitat of an organism is the place where it lives, or the place where one would go to find it. The ecological niche, on the other hand, is the position or status of an organism within its community and ecosystem resulting from the organism’s structural adaptations, physiological responses and specific behavior (inherited and/or learned). The ecological niche of an organism depends not only on where it lives, but also on what it does. By analogy, it may be said that the habitat is the organism’s ‘address,’ and the niche is its ‘profession,’ biologically speaking.
Fundamentals of Ecology
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The highest wisdom has one science—the science of the All—the universal science which explains all creation, and the place man occupies in it.
As translated from the Russian by Nathan Haskell Dole, in War and Peace (1868, 1889), Vol. 1, 73.
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The historian of science may be tempted to claim that when paradigms change, the world itself changes with them. Led by a new paradigm, scientists adopt new instruments and look in new places. even more important, during revolutions, scientists see new and different things when looking with familiar instruments in places they have looked before. It is rather as if the professional community had been suddenly transported to another planet where familiar objects are seen in a different light and are joined by unfamiliar ones as well.
In The Structure of Scientific Revolutions (1962, 2nd ed. 1970). Excerpt 'Revolutions as Changes of World View', in Joseph Margolis and Jacques Catudal, The Quarrel between Invariance and Flux (2001), 35-36.
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The idea that time may vary from place to place is a difficult one, but it is the idea Einstein used, and it is correct—believe it or not.
…...
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The man of true genius never lives before his time, he never undertakes impossibilities, and always embarks on his enterprise at the suitable place and period. Though he may catch a glimpse of the coming light as it gilds the mountain top long before it reaches the eyes of his contemporaries, and he may hazard a prediction as to the future, he acts with the present.
Closing Address (19 Mar 1858) at the Exhibition of the Metropolitan Mechanics' Institute, of Washington. Published as a pamphlet by the M.M. Institute (1853). Collected in Smithsonian Miscellaneous Collections, Vol. 30.
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The mathematician's patterns … must be beautiful … Beauty is the first test; there is no permanent place in the world for ugly mathematics.
In A Mathematician's Apology (1940, 2012), 85.
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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 modern airplane creates a new geographical dimension. A navigable ocean of air blankets the whole surface of the globe. There are no distant places any longer: the world is small and the world is one.
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The moon is a very nice place. When we landed, we were 20 minutes behind. Because time on the Moon was so precious, what I remember most is trying to catch up.
As quoted in 'NASA Mourns the Passing of Astronaut John Young' (6 Jan 2018) on nasa.gov website.
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The more we study Art, the less we care for Nature. What Art really reveals to us is Nature’s lack of design, her curious crudities, her extraordinary monotony, her absolutely unfinished condition. … It is fortunate for us, however, that Nature is so imperfect, as otherwise we should have had no art at all. Art is our spirited protest, our gallant attempt to teach Nature her proper place. As for the infinite variety of Nature, that is a pure myth. It is not to be found in Nature herself. It resides in the imagination, or fancy, or cultivated blindness of the man who looks at her.
In 'Decay of Lying', The Writings of Oscar Wilde: Epigrams, Phrases and Philosophies For the Use of the Young (1907), 5.
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The most fundamental difference between compounds of low molecular weight and macromolecular compounds resides in the fact that the latter may exhibit properties that cannot be deduced from a close examination of the low molecular weight materials. Not very different structures can be obtained from a few building blocks; but if 10,000 or 100,000 blocks are at hand, the most varied structures become possible, such as houses or halls, whose special structure cannot be predicted from the constructions that are possible with only a few building blocks... Thus, a chromosome can be viewed as a material whose macromolecules possess a well defined arrangement, like a living room in which each piece of furniture has its place and not, as in a warehouse, where the pieces of furniture are placed together in a heap without design.
Quoted, without citation, in Ralph E. Oesper (ed.), The Human Side of Scientists (1975), 175.
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The name of Sir Isaac Newton has by general consent been placed at the head of those great men who have been the ornaments of their species. … The philosopher [Laplace], indeed, to whom posterity will probably assign a place next to Newton, has characterized the Principia as pre-eminent above all the productions of human intellect.
In Life of Sir Isaac Newton (1831), 1, 2.
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The Nubians never remember the native name for a river; thus their statements are of little value to geographical criticism. Hence they never speak of the River Bah or Ibba, for example, but always say the “Penio’s river,” because this is the name of the district head whose seat is on this river. In other places they are quite helpless…. This is a dreadful fact. Were the well-traveled and well-informed Arab leaders able to remember the names of the rivers, it would be wonderfully easy to draw a map of the entire country.
In August Petermann, Petermann’s Geographische Mittheilungen (1871), 137. As quoted and cited in Kathrin Fritsch, '"You Have Everything Confused And Mixed Up…!" Georg Schweinfurth, Knowledge And Cartography Of Africa In The 19th Century', History in Africa (2009), 36, 92.
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The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
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The persons who have been employed on these problems of applying the properties of matter and the laws of motion to the explanation of the phenomena of the world, and who have brought to them the high and admirable qualities which such an office requires, have justly excited in a very eminent degree the admiration which mankind feels for great intellectual powers. Their names occupy a distinguished place in literary history; and probably there are no scientific reputations of the last century higher, and none more merited, than those earned by great mathematicians who have laboured with such wonderful success in unfolding the mechanism of the heavens; such for instance as D ’Alembert, Clairaut, Euler, Lagrange, Laplace.
In Astronomy and General Physics (1833), Bk. 3, chap. 4, 327.
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The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren't the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown.
Interview for website of the Mathematical Association of America.
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The probability of an event is the reason we have to believe that it has taken place, or that it will take place.
In 'Règles générales des probabilités', Recherches sur la Probabilités des Jugemens (1837), Chap. 1, 30, as translated in George Boole, An Investigation of the Laws of Thought (1854), 244. From the original French, “La probabilité d’un événement est la raison que nous avons de croire qu’il aura ou qu’il a eu lieu.”
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The same algebraic sum of positive and negative charges in the nucleus, when the arithmetical sum is different, gives what I call “isotopes” or “isotopic elements,” because they occupy the same place in the periodic table. They are chemically identical, and save only as regards the relatively few physical properties which depend upon atomic mass directly, physically identical also. Unit changes of this nuclear charge, so reckoned algebraically, give the successive places in the periodic table. For any one “place” or any one nuclear charge, more than one number of electrons in the outer-ring system may exist, and in such a case the element exhibits variable valency. But such changes of number, or of valency, concern only the ring and its external environment. There is no in- and out-going of electrons between ring and nucleus.
Concluding paragraph of 'Intra-atomic Charge', Nature (1913), 92, 400. Collected in Alfred Romer, Radiochemistry and the Discovery of Isotopes (1970), 251-252.
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The scientist has marched in and taken the place of the poet. But one day somebody will find the solution to the problems of the world and remember, it will be a poet, not a scientist.
As quoted in The Star (1959). Collected in Jonathon Green, Morrow's International Dictionary of Contemporary Quotations (1982).
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The Senses place before us the Characters of the Book of Nature; but these convey no knowledge to us, till we have discovered the Alphabet by which they are to be read.
In 'Aphorisms Concerning Ideas', The Philosophy of the Inductive Sciences (1840), Vol. 1, xvii.
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The United States is the most powerful technically advanced country in the world to-day. Its influence on the shaping of international relations is absolutely incalculable. But America is a large country and its people have so far not shown much interest in great international problems, among which the problem of disarmament occupies first place today. This must be changed, if only in the essential interests of the Americans. The last war has shown that there are no longer any barriers between the continents and that the destinies of all countries are closely interwoven. The people of this country must realize that they have a great responsibility in the sphere of international politics. The part of passive spectator is unworthy of this country and is bound in the end to lead to disaster all round.
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The universe seems to me infinitely strange and foreign. At such a moment I gaze upon it with a mixture of anguish and euphoria; separate from the universe, as though placed at a certain distance outside it; I look and I see pictures, creatures that move in a kind of timeless time and spaceless space, emitting sounds that are a kind of language I no longer understand or ever register.
‘Interviews: Brief Notes for Radio’, Notes and Counter-Notes: Writings on the Theatre (1964), 136.
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The various elements had different places before they were arranged so as to form the universe. At first, they were all without reason and measure. But when the world began to get into order, fire and water and earth and air had only certain faint traces of themselves, and were altogether such as everything might be expected in the absence of God; this, I say, was their nature at that time, and God fashioned them by form and number.
Plato
In Plato and B. Jowett (trans.), The Dialogues of Plato: Republic (3rd ed., 1892), Vol. 3, 473.
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There are many different styles of composition. I characterize them always as Mozart versus Beethoven. When Mozart began to write at that time he had the composition ready in his mind. He wrote the manuscript and it was ‘aus einem Guss’ (casted as one). And it was also written very beautiful. Beethoven was an indecisive and a tinkerer and wrote down before he had the composition ready and plastered parts over to change them. There was a certain place where he plastered over nine times and one did remove that carefully to see what happened and it turned out the last version was the same as the first one.
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There are many modes of thinking about the world around us and our place in it. I like to consider all the angles from which we might gain perspective on our amazing universe and the nature of existence.
With co-author Kenneth William Ford Geons, Black Holes, and Quantum Foam: A Life in Physics (1998, 2010), 153.
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There is a road in the hearts of all of us, hidden and seldom traveled, which leads to an unknown, secret place.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 249
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There is no one central problem in philosophy, but countless little problems. Philosophy is like trying to open a safe with a combination lock: each little adjustment of the dials seems to achieve nothing, only when everything is in place does the door open.
From conversation with Rush Rhees (1930) as given by Rush Rhees in Ludwig Wittgenstein: Personal Recollections (1981), 96.
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There’s no value in digging shallow wells in a hundred places. Decide on one place and dig deep ... If you leave that to dig another well, all the first effort is wasted and there is no proof you won’t hit rock again.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 258
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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They cannot scare me with their empty spaces
Between stars—on stars where no human race is.
I have it in me so much nearer home
To scare myself with my own desert places.
Poem, ‘Desert Places’, in Collected Poems of Robert Frost 1939 (1945), 386.
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This is the most beautiful place on Earth. There are many such places. Every man, every woman, carries in heart and mind the image of the ideal place, the right place, the one true home, known or unknown, actual or visionary.
Opening sentences in 'The First morning', Desert Solitaire (1968,1988), 1.
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To go places and do things that have never been done before - that’s what living is all about.
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To the east was our giant neighbor Makalu, unexplored and unclimbed, and even on top of Everest the mountaineering instinct was sufficient strong to cause me to spend some moments conjecturing as to whether a route up that mountain might not exist. Far away across the clouds the great bulk of Kangchenjunga loomed on the horizon. To the west, Cho Oyu, our old adversary from 1952, dominated the scene and we could see the great unexplored ranges of Nepal stretching off into the distance. The most important photograph, I felt, was a shot down the north ridge, showing the North Col and the old route that had been made famous by the struggles of those great climbers of the 1920s and 1930s. I had little hope of the results being particularly successful, as I had a lot of difficulty in holding the camera steady in my clumsy gloves, but I felt that they would at least serve as a record. After some ten minutes of this, I realized that I was becoming rather clumsy-fingered and slow-moving, so I quickly replaced my oxygen set and experience once more the stimulating effect of even a few liters of oxygen. Meanwhile, Tenzing had made a little hole in the snow and in it he placed small articles of food – a bar of chocolate, a packet of biscuits and a handful of lollies. Small offerings, indeed, but at least a token gifts to the gods that all devoted Buddhists believe have their home on this lofty summit. While we were together on the South Col two days before, Hunt had given me a small crucifix that he had asked me to take to the top. I, too, made a hole in the snow and placed the crucifix beside Tenzing’s gifts.
As quoted in Whit Burnett, The Spirit of Adventure: The Challenge (1955), 349.
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To those devoid of imagination a blank place on the map is a useless waste; to others, the most valuable part.
In A Sand County Almanac, and Sketches Here and There (1949, 1987), 176.
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To us, men of the West, a very strange thing happened at the turn of the century; without noticing it, we lost science, or at least the thing that had been called by that name for the last four centuries. What we now have in place of it is something different, radically different, and we don’t know what it is. Nobody knows what it is.
From La Science et Nous (1941), translated as 'Classical Science and After', in Richard Rees (ed.), On Science, Necessity and the Love of God (1968), as quoted and cited in Robert Andrews, The Columbia Dictionary of Quotations (1993), 809-810. Also seen translated as, “Something happened to the people of the Western world at the beginning of the century, something quite strange: we lost science without even being aware of it, or at least, what had been called science for the last four centuries. What we now have under this name is something else, something radically different, and we do not know what it is. Probably no one knows what it is”, collected in Simone Weil: Late Philosophical Writings (2015), Chap. 10.
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True majorities, in a TV-dominated and anti-intellectual age, may need sound bites and flashing lights–and I am not against supplying such lures if they draw children into even a transient concern with science. But every classroom has one [Oliver] Sacks, one [Eric] Korn, or one [Jonathan] Miller, usually a lonely child with a passionate curiosity about nature, and a zeal that overcomes pressures for conformity. Do not the one in fifty deserve their institutions as well–magic places, like cabinet museums, that can spark the rare flames of genius?
…...
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We are placed here with certain talents and capabilities. It is up to each of us to use those talents and capabilities as best you can. If you do that, I think there is a power greater than any of us that will place the opportunities in our way, and if we use our talents properly, we will be living the kind of life we should live.
At NASA press conference (9 Apr 1959) to introduce the Mercury 7 astronauts. As quoted in Joseph N. Bell, Seven Into Space: The Story of the Mercury Astronauts (1960), 69.
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We live in an essential and unresolvable tension between our unity with nature and our dangerous uniqueness. Systems that attempt to place and make sense of us by focusing exclusively either on the uniqueness or the unity are doomed to failure. But we must not stop asking and questing because the answers are complex and ambiguous.
In 'Our Natural Place', Hen's Teeth and Horse’s Toes: Further Reflections in Natural History (1994, 2010), 250.
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We must build a picture of the human soul that works. … a recognition that the enemy is within us and that Nature has placed it there. … for a reason. And we must understand that reason to outwit her.
In 'Who is Lucifer?', The Lucifer Principle: A Scientific Expedition Into the Forces of History (1997), 4.
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We need constantly new accessions of truth as to the universe and better definition of the truths which are old. Such knowledge, tested and placed in order, we call science. Science is the gathered wisdom of the race.
From Presidential Address (5 Dec 1896) to the Biological Society of Washington, 'The Malarial Parasite and Other Pathogenic Protozoa', Popular Science Monthly (Mar 1897), 642.
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We no longer can talk of unearned “rights.” We’ll have to get back to working for “rights” to adequate food, housing, education, opportunity, a place in the sun—and not everybody is going to make the grade. I don’t see this obsession with the lowest strata of humanity, against all natural biologic experience. We must accept that life is unfair.
In Raymond Mungo, 'Dixy Lee Ray: How Madame Nuke Took Over Washington', Mother Jones (May 1977), 2, No. 4, 31.
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We urgently need [the landmark National Ocean Policy] initiative, as we use our oceans heavily: Cargo ships crisscross the sea, carrying goods between continents. Commercial and recreational fishing boats chase fish just offshore. Cruise ships cruise. Oil and gas drilling continues, but hopefully we will add renewable energy projects as well. Without planning, however, these various industrial activities amount to what we call “ocean sprawl,” steamrolling the resources we rely upon for our livelihoods, food, fun, and even the air we breathe. While humankind relies on many of these industries, we also need to keep the natural riches that support them healthy and thriving. As an explorer, I know firsthand there are many places in the ocean so full of life that they should be protected.
In 'A Blueprint for Our Blue Home', Huffington Post (18 Jul 2011).
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We were flying over America and suddenly I saw snow, the first snow we ever saw from orbit. I have never visited America, but I imagined that the arrival of autumn and winter is the same there as in other places, and the process of getting ready for them is the same. And then it struck me that we are all children of our Earth.
As quoted in Kevin W. Kelley (ed.), The Home Planet (1988). Source cited as “submitted by Lev Demin”.
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We will build the roads and bridges, the electric grids and digital lines that feed our commerce and bind us together. We'll restore science to its rightful place, and wield technology's wonders to raise health care's quality and lower its cost. We will harness the sun and the winds and the soil to fuel our cars and run our factories. And we will transform our schools and colleges and universities to meet the demands of a new age. All this we can do. All this we will do.
From First Inaugural Address (20 Jan 2009)
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What is a weed? I have heard it said that there are sixty definitions. For me, a weed is a plant out of place.
In Flowering Earth (1939), 156. Note that this definition was in use before Peattie was born, for example “the true definition of a weed is ‘a plant out of place’” appears in Alex Brown, The Coffee Planter's Manual (1880), 121.
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What now, dear reader, shall we make of our telescope? Shall we make a Mercury’s magic wand to cross the liquid aether with, and like Lucian lead a colony to the uninhabitied evening star, allured by the sweetness of the place?
In Preface to Dioptrics (1611), 86. Collected in Galileo Galilei, Johannes Kepler and Edward Stafford Carlos (trans.), The Sidereal Messenger of Galileo Galilei: And a Part of the Preface to Kepler’s Dioptrics (1880), 103.
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When intersected by a plane, the sphere displays in this section the circle, the genuine image of the created mind, placed in command of the body which it is appointed to rule; and this circle is to the sphere as the human mind is to the Mind Divine.
As quoted in Wolfgang Pauli, 'The Influence of Archetypal Ideas on the Scientific Theories of Kepler', as translated and collected in Writings on Physics and Philosophy (1994), 225. With Latin from Harmonia Mundi, Liber IV, Caput 1, collected in Christian Frisch (ed.), Opera Omnia (1864), Vol. 5, 223: “ plano vero sectum sphaericum circulum sectione repraesentat, mentis creatae, quae corpori regendo sit praefecta, genuinam imaginem, quae in ea proportione sit ad sphaericum, ut est mens humana ad divinam,”
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When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
Quoted, without citation, in The American Mathematical Monthly (Mar 1993), 100 No. 3, 286.
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When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring.
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Wherefore also these Kinds [elements] occupied different places even before the universe was organised and generated out of them. Before that time, in truth, all these were in a state devoid of reason or measure, but when the work of setting in order this Universe was being undertaken, fire and water and earth and air, although possessing some traces of their known nature, were yet disposed as everything is likely to be in the absence of God; and inasmuch as this was then their natural condition, God began by first marking them out into shapes by means of forms and numbers.
Plato
Timaeus 53ab, trans. R. G. Bury, in Plato: Timaeus, Critias, Cleitophon, Menexenus, Epistles (1929), 125-7.
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Whether it’s the science to slow global warming; the technology to protect our troops and confront bioterror and weapons of mass destruction; the research to find life-saving cures; or the innovations to remake our industries and create twenty-first century jobs—Today, more than ever before, science holds the key to our survival as a planet and our security and prosperity as a nation. It’s time we once again put science at the top of our agenda and work to restore America’s place as the world leader in science and technology.
From weekly Democratic address as President-Elect, online video (20 Dec 2008), announcing his selection of science and technology advisers. C-Span video 282995-102.
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Why do you so earnestly seek the truth in distant places?
Look for delusion and truth in the bottom of your own hearts.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 247
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With a single exception, it may be affirmed that units of volume now [1893] in use were originally in no way related to units of length, most of them being of accidental and now unknown origin. That a legal bushel in the United States must contain 2150.42 cubic inches is convincing evidence that the foot or the yard has no place in its ancestry.
From Address to the International Engineering Congress of the Columbia Exposition, Chicago, 1893. Published in Transactions of the American Society of Civil Engineers (Oct 1893), 121. Reprinted in 'Fundamental Units of Measure', Smithsonian Report for 1893 (1894), 136.
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Without the suitable conditions life could not exist. But both life and its conditions set forth the operations of inscrutable Power. We know not its origin; we know not its end. And the presumption, if not the degradation, rests with those who place upon the throne of the universe a magnified image of themselves, and make its doings a mere colossal imitation of their own.
In Forms of Water in Clouds and Rivers, Ice and Glaciers (1872), 125.
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Working on the final formulation of technological patents was a veritable blessing for me. It enforced many-sided thinking and also provided important stimuli to physical thought. Academia places a young person under a kind of compulsion to produce impressive quantities of scientific publications–a temptation to superficiality.
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You are in service to your patients, and a servant should know his place.
In Letters to a Young Doctor (1982), 53.
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You have only to take in what you please and leave out what you please; to select your own conditions of time and place; to multiply and divide at discretion; and you can pay the National Debt in half an hour. Calculation is nothing but cookery.
(1849). Epigraph, without citation, in M.J. Moroney, Facts From Figures (1951), 334.
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You may perceive something of the distinction which I think necessary to keep in view between art and science, between the artist and the man of knowledge, or the philosopher. The man of knowledge, the philosopher, is he who studies and acquires knowledge in order to improve his own mind; and with a desire of extending the department of knowledge to which he turns his attention, or to render it useful to the world, by discoveries, or by inventions, which may be the foundation of new arts, or of improvements in those already established. Excited by one or more of these motives, the philosopher employs himself in acquiring knowledge and in communicating it. The artist only executes and practises what the philosopher or man of invention has discovered or contrived, while the business of the trader is to retail the productions of the artist, exchange some of them for others, and transport them to distant places for that purpose.
From the first of a series of lectures on chemistry, collected in John Robison (ed.), Lectures on the Elements of Chemistry: Delivered in the University of Edinburgh (1807), Vol. 1, 3.
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Young writers find out what kinds of writers they are by experiment. If they choose from the outset to practice exclusively a form of writing because it is praised in the classroom or otherwise carries appealing prestige, they are vastly increasing the risk inherent in taking up writing in the first place.
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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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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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- 10 -
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