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Measure Quotes (104 quotes)

Numero pondere et mensura Deus omnia condidit.
God created everything by number, weight and measure.
On more than one occasion, Newton wrote these Latin words as his autograph, with his signature below. A photo of one example, dated “London 11 Sep 1722,” can be seen in I. Hargitta (ed.), Symmetry 2: Unifying Human Understanding (2014), 837. Reprinted from M. and B. Rozsondai, 'Symmetry Aspects of Bookbindings', Computers Math. Applic. (1989), 17, No. 4-6, 837. On this piece of paper, Newton dedicated these words to a Hungarian student, Ferenc Páriz Pápai Jr., whose album is now held by the Department of Manuscripts and Rare Books of the Library of the Hungarian Academy of Sciences (Shelf-number Tort. naplók, kis 8⁰ 6). The sentiment existed long before Newton used it. In the Bible, Wisdom of Solomon, 11:20, it appears as “Pondere, mensura, numero Deus omnia fecit,” (Vulgate) which the King James Version translates as “thou hast ordered all things in measure and number and weight.” Another Newton signed autograph with his Latin quote, dated 13 Jul 1716, sold (4 Apr 1991) for DM 9500 (about $31,000). See Dept of English, Temple University, The Scriblerian and the Kit-Cats (1991), 24-25, 230. A few years later, the sale (31 Mar 1998) of Newton's autograph cost the buyer $46,000. See Frank Ryan, Darwin's Blind Spot: Evolution Beyond Natural Selection (2002), 11-12. Other authors, including mathematicians, used the same Biblical passage. In Gilles Personne de Roberval's Aristarchi Samii de Mundi Systemate (1644), he frequently uses the abbreviation “P.N.E.M.” standing for “Pondere, mensura et mensura.” It was adopted as the motto of the Smeatonian Society of Engineers as “Omnia in Numero Pondere et Mensura.”
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A hundred times every day I remind myself that my inner and outer life depends on the labors of other men, living and dead, and that I must exert myself in order to give in the measure as I have received and am still receiving.
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A sufficient measure of civilization is the influence of good women.
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Academies have been instituted to guard the avenues of their languages, to retain fugitives, and repulse intruders; but their vigilance and activity have hitherto been vain; sounds are too volatile and subtile for legal restraints; to enchain syllables, and to lash the wind, are equally the undertakings of pride, unwilling to measure its desires by its strength.
From Dictionary of the English Language (1818), Vol. 1, Preface, xxiii. Note: Subtile means subtle.
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An event experienced is an event perceived, digested, and assimilated into the substance of our being, and the ratio between the number of cases seen and the number of cases assimilated is the measure of experience.
Address, opening of 1932-3 session of U.C.H. Medical School (4 Oct 1932), 'Art and Science in medicine', The Collected Papers of Wilfred Trotter, FRS (1941), 98.
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At some future period, not very distant as measured by centuries, the civilised races of man will almost certainly exterminate, and replace the savage races throughout the world.
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Attainment is a poor measure of capacity, and ignorance no proof of defect.
From 'The Binet-Simon Scale: Practical Use of the Method', Mental and Scholastic Tests (1921), 1.
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Better to withdraw confidence than measure it.
From the original French, “Mieux vaut retirer sa confiance que la mesurer”, in Actes de l'Académie Nationale des Sciences, Belles-Lettres et Arts de Bordeaux (1872), 479. English as in Franz Liszt, The Letters of Franz Liszt to Olga Von Meyendorff (1979), 82.
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Bring out number, weight, and measure in a year of dearth.
In 'Proverbs', The Poems: With Specimens of the Prose Writings of William Blake (1885), 279.
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Disorder increases with time because we measure time in the direction in which disorder increases.
In 'The Direction of Time', New Scientist (9 Jul 1987), 115, No. 1568, 47. Also in 'The Arrow of Time', A Brief History of Time: From the Big Bang to Black Holes (1988, 1998), Chap. 9, 152.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Embryology furnishes … the best measure of the true affinities existing between animals.
In 'Essay on Classification', Contributions to the Natural History of the United States of America (1857), Pt. 1, 85.
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Energy is the measure of that which passes from one atom to another in the course of their transformations. A unifying power, then, but also, because the atom appears to become enriched or exhausted in the course of the exchange, the expression of structure.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 42. Originally published in French as Le Phénomene Humain (1955).
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For terrestrial vertebrates, the climate in the usual meteorological sense of the term would appear to be a reasonable approximation of the conditions of temperature, humidity, radiation, and air movement in which terrestrial vertebrates live. But, in fact, it would be difficult to find any other lay assumption about ecology and natural history which has less general validity. … Most vertebrates are much smaller than man and his domestic animals, and the universe of these small creatures is one of cracks and crevices, holes in logs, dense underbrush, tunnels, and nests—a world where distances are measured in yards rather than miles and where the difference between sunshine and shadow may be the difference between life and death. Actually, climate in the usual sense of the term is little more than a crude index to the physical conditions in which most terrestrial animals live.
From 'Interaction of physiology and behavior under natural conditions', collected in R.I. Bowman (ed.), The Galapagos (1966), 40.
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Free men are aware of the imperfection inherent in human affairs, and they are willing to fight and die for that which is not perfect. They know that basic human problems can have no final solutions, that our freedom, justice, equality, etc. are far from absolute, and that the good life is compounded of half measures, compromises, lesser evils, and gropings toward the perfect. The rejection of approximations and the insistence on absolutes are the manifestation of a nihilism that loathes freedom, tolerance, and equity.
In The Temper of Our Time (1967), 103.
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Galileo … asserts that in all these phenomena we must measure all that is measurable, and try to make measurable all that is not directly measurable.
From the original French, “Galilée … déclare que dans tous ces phénomènes il faut mesurer tout ce qui est mesurable, et tâcher de rendre mesurable tout ce qui ne l’est pas directement,” in Galilée: Les Droits de la Science et la Méthode des Sciences Physiques (1868), 289. Notice the statement is not enclosed in quotation marks; they are the author’s words, not Galileo’s. Translation by Webmaster using Internet resources. Martin’s words are often repeated as an assumed quote by Galileo: Measure what is measurable, and make measurable what is not so. These words do not come verbatim from any known work by Galileo, and should only be used without quotation marks as Martin’s description of Galileo’s method. Nevertheless, quotation marks have been - erroneously - added in many books, for example, in the transcript of a radio talk by Hermann Weyl, 'Mathematics and the Laws of Nature', collected in Warren Weaver (ed.), The Scientists Speak (1947). Reprinted in Isabel S. Gordon and Sophie Sorkin (eds.), The Armchair Science Reader (1959), 301.
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Geometrical axioms are neither synthetic a priori conclusions nor experimental facts. They are conventions: our choice, amongst all possible conventions, is guided by experimental facts; but it remains free, and is only limited by the necessity of avoiding all contradiction. ... In other words, axioms of geometry are only definitions in disguise.
That being so what ought one to think of this question: Is the Euclidean Geometry true?
The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 110.
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Go, wondrous creature! mount where Science guides,
Go, measure earth, weigh air, and state the tides;
Instruct the planets in what orbs to run,
Correct old Time, and regulate the Sun.
In An Essay on Man (1736), Epistle II, lines 19-22, 10.
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How strange is the lot of us mortals! Each of us is here for a brief sojourn; for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people–first of all for those upon whose smiles and well-being our own happiness is wholly dependent, and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving.
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I am more of a sponge than an inventor. I absorb ideas from every source. I take half-matured schemes for mechanical development and make them practical. I am a sort of middleman between the long-haired and impractical inventor and the hard-headed businessman who measures all things in terms of dollars and cents. My principal business is giving commercial value to the brilliant but misdirected ideas of others.
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I cannot separate land and sea: to me they interfinger like a pattern in a moss agate, positive and negative shapes irrevocably interlocked. My knowledge of this peninsula depends on that understanding: of underwater canyons that are continuations of the land, of the shell fossils far inland that measure continuations of the sea in eons past.
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I remember one occasion when I tried to add a little seasoning to a review, but I wasn’t allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: “The author discusses valueless measures in pointless spaces.”
In I Want to be a Mathematician: An Automathography (1985), 120.
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I should like to urge some arguments for wilderness preservation that involve recreation,…. Hunting, fishing, hiking, mountain-climbing, camping, photography, and the enjoyment of natural scenery will all, surely, figure in your report. So will the wilderness as a genetic reserve, a scientific yardstick by which we may measure the world in its natural balance against the world in its man-made imbalance.
Letter (3 Dec 1960) written to David E. Pesonen of the Outdoor Recreation Resources Review Commission. Collected in 'Coda: Wilderness Letter', The Sound of Mountain Water: The Changing American West (1969), 145-146.
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I think that a particle must have a separate reality independent of the measurements. That is an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it.
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I think that harping on [earthquake] prediction is something between a will-o'-the-wisp and a red herring. Attention is thereby diverted away from positive measures to eliminate earthquake risk.
From interview in the Earthquake Information Bulletin (Jul-Aug 1971), 3, No. 4, as abridged in article on USGS website.
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I venture to assert that the feelings one has when the beautiful symbolism of the infinitesimal calculus first gets a meaning, or when the delicate analysis of Fourier has been mastered, or while one follows Clerk Maxwell or Thomson into the strange world of electricity, now growing so rapidly in form and being, or can almost feel with Stokes the pulsations of light that gives nature to our eyes, or track with Clausius the courses of molecules we can measure, even if we know with certainty that we can never see them I venture to assert that these feelings are altogether comparable to those aroused in us by an exquisite poem or a lofty thought.
In paper (May 1891) read before Bath Branch of the Teachers’ Guild, published in The Practical Teacher (July 1891), reprinted as 'Geometry', in Frederic Spencer, Chapters on the Aims and Practice of Teaching (1897), 194.
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If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured and far away.
In Walden: Or, Life in the Woods (1854, 1906), 358.
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If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous.
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If it were not for our conception of weights and measures we would stand in awe of the firefly as we do before the sun.
In Kahlil Gibran: The Collected Works (207), 204.
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In a nutshell, the universe is 4% visible, 23% undetectable and 73% unimaginable. Welcome to the cosmos, full of mass you can measure but not manhandle, driven by a force you can infer but not explain.
In 'Dark Side of Creation', The Guardian (12 Feb 2004).
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In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
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In the real changes which animals undergo during their embryonic growth, in those external transformations as well as in those structural modifications within the body, we have a natural scale to measure the degree or the gradation of those full grown animals which corresponds in their external form and in their structure, to those various degrees in the metamorphoses of animals, as illustrated by embryonic changes, a real foundation for zoological classification.
From Lecture 4, collected in Twelve Lectures on Comparative Embryology: Delivered Before the Lowell Institute in Boston: December and January 1848-9 (1849), 29.
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It has always seemed to me extreme presumptuousness on the part of those who want to make human ability the measure of what nature can and knows how to do, since, when one comes down to it, there is not one effect in nature, no matter how small, that even the most speculative minds can fully understand.
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It is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
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It is so hard for an evolutionary biologist to write about extinction caused by human stupidity ... Let me then float an unconventional plea, the inverse of the usual argument ... The extinction of Partula is unfair to Partula. That is the conventional argument, and I do not challenge its primacy. But we need a humanistic ecology as well, both for the practical reason that people will always touch people more than snails do or can, and for the moral reason that humans are legitimately the measure of all ethical questions–for these are our issues, not nature’s.
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Knowing, henceforth, the physiognomy of the disease when allowed to run its own course, you can, without risk of error, estimate the value of the different medications which have been employed. You will discover which remedies have done no harm, and which have notably curtailed the duration of the disease; and thus for the future you will have a standard by which to measure the value of the medicine which you see employed to counteract the malady in question. What you have done in respect of one disease, you will be able to do in respect of many; and by proceeding in this way you will be able, on sure data, to pass judgment on the treatment pursued by your masters.
In Armand Trousseau, as translated by P. Victor and John Rose Cormack, Lectures on Clinical Medicine: Delivered at the Hôtel-Dieu, Paris (1873), Vol. 1, 40-41.
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Laws are important and valuable in the exact natural sciences, in the measure that those sciences are universally valid.
In Max Weber with translation by Edward Shils and Henry A. Finch (eds.), The Methodology of the Social Sciences (1949), 80.
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Learning how to access a continuity of common sense can be one of your most efficient accomplishments in this decade. Can you imagine common sense surpassing science and technology in the quest to unravel the human stress mess? In time, society will have a new measure for confirming truth. It’s inside the people-not at the mercy of current scientific methodology. Let scientists facilitate discovery, but not invent your inner truth.
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Man has never been a particularly modest or self-deprecatory animal, and physical theory bears witness to this no less than many other important activities. The idea that thought is the measure of all things, that there is such a thing as utter logical rigor, that conclusions can be drawn endowed with an inescapable necessity, that mathematics has an absolute validity and controls experience—these are not the ideas of a modest animal. Not only do our theories betray these somewhat bumptious traits of self-appreciation, but especially obvious through them all is the thread of incorrigible optimism so characteristic of human beings.
In The Nature of Physical Theory (1936), 135-136.
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Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7. From the original French, “L’analyse mathématique est aussi étendue que la nature elle-même; elle définit tous les rapports sensibles, mesure les temps y les espaces, les forces, les températures; cette science difficile se forme avec lenteur, mais elle conserve tous les principes quelle a une fois acquis; elle s’accroît et s’affermit sans cesse au milieu de tant de variations et d’erreurs de l’esprit humain.”
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Mathematics associates new mental images with ... physical abstractions; these images are almost tangible to the trained mind but are far removed from those that are given directly by life and physical experience. For example, a mathematician represents the motion of planets of the solar system by a flow line of an incompressible fluid in a 54-dimensional phase space, whose volume is given by the Liouville measure
Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.
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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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Measure, time and number are nothing but modes of thought or rather of imagination.
Letter to Ludvicus Meyer (20 Apr 1663), in Correspondence of Spinoza (2003), 118.
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Measured objectively, what a man can wrest from Truth by passionate striving is utterly infinitesimal. But the striving frees us from the bonds of the self and makes us comrades of those who are the best and the greatest.
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Mere poets are sottish as mere drunkards are, who live in a continual mist, without seeing or judging anything clearly. A man should be learned in several sciences, and should have a reasonable, philosophical and in some measure a mathematical head, to be a complete and excellent poet.
In Notes and Observations on The Empress of Morocco (1674), 70.
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Money is a stupid measure of achievement, but unfortunately it is the only universal measure we have.
Seen quoted, without citation, since as early as The Forbes Scrapbook of Thoughts on the Business of Life (1950), 486. If you know a primary source, please contact Webmaster.
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Nature! … Incessant life, development, and movement are in her, but she advances not. She changes for ever and ever, and rests not a moment. Quietude is inconceivable to her, and she has laid her curse upon rest. She is firm. Her steps are measured, her exceptions rare, her laws unchangeable.
As quoted by T.H. Huxley, in Norman Lockyer (ed.), 'Nature: Aphorisms by Goethe', Nature (1870), 1, 9.
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Neither the absolute nor the relative size of the brain can be used to measure the degree of mental ability in animal or in man. So far as man is concerned, the weights of the brains or the volumes of the cranial cavities of a hundred celebrities of all branches of knowledge all over the world have been listed. … At the bottom of those lists are Gall, the famous phrenologist, Anatole France, the French novelist, and Gambetta, the French statesman, each with about 1,100 cc brain mass. The lists are topped by Dean Jonathan Swift, the English writer, Lord Byron, the English poet, and Turgenev, the Russian novelist, all with about 2,000 cc … Now our mental test! Had Turgenev really twice the mental ability of Anatole France?
In 'The Human Brain in the Light of Its Phylogenetic Development', Scientific Monthly (Aug 1948), 67, No. 2, 104-105. Collected in Sherwood Larned Washburn and ‎Davida Wolffson (eds.), The Shorter Anthropological Papers of Franz Weidenreich Published in the Period 1939-1948: A Memorial Volume (1949), 18.
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Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Now do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting.
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One of the grandest figures that ever frequented Eastern Yorkshire was William Smith, the distinguished Father of English Geology. My boyish reminiscence of the old engineer, as he sketched a triangle on the flags of our yard, and taught me how to measure it, is very vivid. The drab knee-breeches and grey worsted stockings, the deep waistcoat, with its pockets well furnished with snuff—of which ample quantities continually disappeared within the finely chiselled nostril—and the dark coat with its rounded outline and somewhat quakerish cut, are all clearly present to my memory.
From Reminiscences of a Yorkshire Naturalist (1896), 13.
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Pauli … asked me to tell him what was happening in America. I told him that Mrs. Wu is trying to measure whether parity is conserved. He answered me: “Mrs. Wu is wasting her time. I would bet you a large sum that parity is conserved.” When this letter came I already knew that parity is violated. I could have sent a telegram to Pauli that the bet was accepted. But I wrote him a letter. He said: “I could never let it out that this is possible. I am glad that we did not actually do the bet because I can risk to lose my reputation, but I cannot risk losing my capital.”
In Discussion after paper presented by Chien-Shiung Wu to the International Conference on the History of Original Ideas and Basic Discoveries, Erice, Sicily (27 Jul-4 Aug 1994), 'Parity Violation' collected in Harvey B. Newman, Thomas Ypsilantis (eds.), History of Original Ideas and Basic Discoveries in Particle Physics (1996), 381.
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Personally, I feel sorry for those who seem to measure their patriotism by how often and how viciously they can criticise our government.
As recorded in United States Congressional Serial Set (2000), 51.
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Phenomena unfold on their own appropriate scales of space and time and may be invisible in our myopic world of dimensions assessed by comparison with human height and times metered by human lifespans. So much of accumulating importance at earthly scales ... is invisible by the measuring rod of a human life. So much that matters to particles in the microscopic world of molecules ... either averages out to stability at our scale or simply stands below our limits of perception.
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Science is a speculative enterprise. The validity of a new idea and the significance of a new experimental finding are to be measured by the consequences—consequences in terms of other ideas and other experiments. Thus conceived, science is not a quest for certainty; it is rather a quest which is successful only to the degree that it is continuous.
In Science and Common Sense (1951), 25-26.
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Spirituality leaps where science cannot yet follow, because science must always test and measure, and much of reality and human experience is immeasurable.
Starhawk
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 43
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Suppose we divide the space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure “disorder” by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the “disorder” is less.
In 'Order And Entropy', The Feynman Lectures on Physics (1964), 46-7.
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Taking … the mathematical faculty, probably fewer than one in a hundred really possess it, the great bulk of the population having no natural ability for the study, or feeling the slightest interest in it*. And if we attempt to measure the amount of variation in the faculty itself between a first-class mathematician and the ordinary run of people who find any kind of calculation confusing and altogether devoid of interest, it is probable that the former could not be estimated at less than a hundred times the latter, and perhaps a thousand times would more nearly measure the difference between them.
[* This is the estimate furnished me by two mathematical masters in one of our great public schools of the proportion of boys who have any special taste or capacity for mathematical studies. Many more, of course, can be drilled into a fair knowledge of elementary mathematics, but only this small proportion possess the natural faculty which renders it possible for them ever to rank high as mathematicians, to take any pleasure in it, or to do any original mathematical work.]
In Darwinism, chap. 15.
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The astronomer may speak to you of his understanding of space, but he cannot give you his understanding. … And he who is versed in the science of numbers can tell of the regions of weight and measure, but he cannot conduct you thither.
In Kahlil Gibran: The Collected Works (207), 134.
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The book of Nature is the book of Fate. She turns the gigantic pages,—leaf after leaf,—never re-turning one. One leaf she lays down, a floor of granite; then a thousand ages, and a bed of slate; a thousand ages, and a measure of coal; a thousand ages, and a layer of marl and mud: vegetable forms appear; her first misshapen animals, zoophyte, trilobium, fish; then, saurians,—rude forms, in which she has only blocked her future statue, concealing under these unwieldy monsters the fine type of her coming king. The face of the planet cools and dries, the races meliorate, and man is born. But when a race has lived its term, it comes no more again.
From 'Fate', collected in The Complete Works of Ralph Waldo Emerson, Volume 6: The Conduct of Life (1860), 15. This paragraph is the prose version of his poem, 'Song of Nature'.
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The explorations of space end on a note of uncertainty. And necessarily so. … We know our immediate neighborhood rather intimately. With increasing distance our knowledge fades, and fades rapidly. Eventually, we reach the dim boundary—the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial. The search will continue. Not until the empirical resources are exhausted, need we pass on to the dreamy realms of speculation.
From conclusion of The Silliman Memorial Lectures Series delivered at Yale University (Fall 1935). Collected in The Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202.
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The first quality we know in matter is centrality,—we call it gravity,—which holds the universe together, which remains pure and indestructible in each mote, as in masses and planets, and from each atom rays out illimitable influence. To this material essence answers Truth, in the intellectual world,—Truth, whose centre is everywhere, and its circumference nowhere, whose existence we cannot disimagine,—the soundness and health of things, against which no blow can be struck but it recoils on the striker,—Truth, on whose side we always heartily are. And the first measure of a mind is its centrality, its capacity of truth, and its adhesion to it.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 477.
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The great mathematician, like the great poet or naturalist or great administrator, is born. My contention shall be that where the mathematic endowment is found, there will usually be found associated with it, as essential implications in it, other endowments in generous measure, and that the appeal of the science is to the whole mind, direct no doubt to the central powers of thought, but indirectly through sympathy of all, rousing, enlarging, developing, emancipating all, so that the faculties of will, of intellect and feeling learn to respond, each in its appropriate order and degree, like the parts of an orchestra to the “urge and ardor” of its leader and lord.
In Lectures on Science, Philosophy and Art (1908), 22.
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The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.
In Elementarmathematik von höheren Standpunkte aus (1909), Bd. 2, 392.
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The hours of Folly are measured by the clock, but of Wisdom no clock can measure.
In 'Proverbs', The Poems: With Specimens of the Prose Writings of William Blake (1885), 279.
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The long-range trend toward federal regulation, which found its beginnings in the Interstate Commerce Act of 1887 and the Sherman Act of 1890, which was quickened by a large number of measures in the Progressive era, and which has found its consummation in our time, was thus at first the response of a predominantly individualistic public to the uncontrolled and starkly original collectivism of big business. In America the growth of the national state and its regulative power has never been accepted with complacency by any large part of the middle-class public, which has not relaxed its suspicion of authority, and which even now gives repeated evidence of its intense dislike of statism. In our time this growth has been possible only under the stress of great national emergencies, domestic or military, and even then only in the face of continuous resistance from a substantial part of the public. In the Progressive era it was possible only because of widespread and urgent fear of business consolidation and private business authority. Since it has become common in recent years for ideologists of the extreme right to portray the growth of statism as the result of a sinister conspiracy of collectivists inspired by foreign ideologies, it is perhaps worth emphasizing that the first important steps toward the modern organization of society were taken by arch-individualists—the tycoons of the Gilded Age—and that the primitive beginning of modern statism was largely the work of men who were trying to save what they could of the eminently native Yankee values of individualism and enterprise.
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The mass of a body is a measure of its energy content.
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The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible, or all of which have the same chance.
In 'Règles générales des probabilités', Recherches sur la Probabilités des Jugemens (1837), Chap. 1, 31, as translated in George Boole, An Investigation of the Laws of Thought (1854), 244. From the original French, “La mesure de la probabilité d'un événement, est le rapport du nombre de cas favorables à cet événement, au nombre total de cas favorables ou contraires, et tous également possibles, ou qui ont tous une même chance.”
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The method I take to do this is not yet very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course (as a Specimen of the Political Arithmetic I have long aimed at) to express myself in Terms of Number, Weight, or Measure; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature.
From Essays in Political Arithmetic (1679, 1755), 98.
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The Ocean Health Index is like a thermometer of ocean health, which will allow us to determine how the patient is doing. The Index will be a measure of whether our policies are working, or whether we need new solutions.
As quoted in press release (14 Aug 2012), 'Ocean Health Index Provides First-Ever Global Benchmark of 171 Coastal Regions', on web page of Conservation International, conservation.org.
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The oldest empires,—what we called venerable antiquity, now that we have true measures of duration, show like creations of yesterday. … The old six thousand years of chronology become a kitchen clock,—no more a measure of time than an hour-glass or an egg-glass,—since the duration of geologic periods has come into view.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 475.
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The opinions that are held with passion are always those for which no good ground exists; indeed the passion is the measure of the holders lack of
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The owner of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process is the relation between what the worker produces and what he is paid, both measured in terms of real value. In so far as the labor contract is free what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists’ requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product.
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The purely formal sciences, logic and mathematics, deal with such relations which are independent of the definite content, or the substance of the objects, or at least can be. In particular, mathematics involves those relations of objects to each other that involve the concept of size, measure, number.
In Theorie der Complexen Zahlensysteme, (1867), 1. Translated by Webmaster using Google Translate from the original German, “Die rein formalen Wissenschaften, Logik und Mathematik, haben solche Relationen zu behandeln, welche unabhängig von dem bestimmten Inhalte, der Substanz der Objecte sind oder es wenigstens sein können.”
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The purely formal Sciences, logic and mathematics, deal with those relations which are, or can be, independent of the particular content or the substance of objects. To mathematics in particular fall those relations between objects which involve the concepts of magnitude, of measure and of number.
In Theorie der Complexen Zahlensysteme (1867), 1. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 4. From the original German, “Die rein formalen Wissenschaften, Logik und Mathematik, haben solche Relationen zu behandeln, welche unabhängig von dem bestimmten Inhalte, der Substanz der Objecte sind oder es wenigstens sein können. Der Mathematik fallen ins Besondere diejenigen Beziehungen der Objecte zu einander zu, die den Begriff der Grösse, des Maasses, der Zahl involviren.”
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The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.
On the Doctrine of Chances, with Later Reflections (1878), 61-2.
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The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.
In Popular Scientific Lectures (1910), 196.
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The true value of a human being is determined primarily by the measure and the sense in which he has attained to liberation from the self.
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The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal.
From review by James on W.K. Clifford, Lectures and Essays in The Nation (1879), 29, No. 749, 312. In Collected Essays and Reviews (1920), 138.
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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 could not be a language more universal and more simple, more exempt from errors and obscurities, that is to say, more worthy of expressing the invariable relations of natural objects. Considered from this point of view, it is coextensive with nature itself; it defines all the sensible relations, measures the times, the spaces, the forces, the temperatures; this difficult science is formed slowly, but it retains all the principles it has once acquired. It grows and becomes more certain without limit in the midst of so many errors of the human mind.
From Théorie Analytique de la Chaleur, Discours Préliminaire (Theory of Heat, Introduction), quoted as translated in F.R. Moulton, 'The Influence of Astronomy on Mathematics', Science (10 Mar 1911), N.S. Vol. 33, No. 845, 359.
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There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
From 'The Power of Words', collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.
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There is nothing in machinery, there is nothing in embankments and railways and iron bridges and engineering devices to oblige them to be ugly. Ugliness is the measure of imperfection.
repr. In The Works of H.G. Wells, vol. 9 (1925). A Modern Utopia, ch. 3, sct. 8 (1905).
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This tomb holds Diophantus Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father’s life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life.
Epigram-problem for age at his death (84). Original Greek with English translation in The Greek Anthology (1918), Vol. 5, 92-93.
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Those who see their lives as spoiled and wasted crave equality and fraternity more than they do freedom. If they clamor for freedom, it is but freedom to establish equality and uniformity. The passion for equality is partly a passion for anonymity: to be one thread of the many which make up a tunic; one thread not distinguishable from the others. No one can then point us out, measure us against others and expose our inferiority.
In The True Believer: Thoughts on the Nature of Mass Movements (1951), 31-32.
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To preach conservation at such a time, when all our resources, national and otherwise are being sacrificed in unprecedented measure, might seem to some anomalous, even ironical. ... But we firmly believe, and now are more acutely aware than ever, that conservation is basically related to the peace of the world and the future of the race.
Breaking New Ground
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To the exact descriptions he gave of the crystalline forms, he added the measure of their angles, and, which was essential, showed that these angles were constant for each variety. In one word, his crystallography was the fruit of an immense work, almost entirely new and most precious in its usefulness.<[About Jean-Baptiste Romé de l’Isle.]
(1795). As quoted in André Authier, Early Days of X-ray Crystallography (2013), 313.
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To the extent that remaining old-growth Douglas fir ecosystems possess unique structural and functional characteristics distinct from surrounding managed forests, the analogy between forest habitat islands and oceanic islands applies. Forest planning decision variables such as total acreage to be maintained, patch size frequency distribution, spatial distribution of patches, specific locations, and protective measures all need to be addressed.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), 6.
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True physics was founded the day when Galileo, rejecting fruitless speculations, conceived the idea … of defining the general form to give to experiments, by assigning for their immediate purpose the measure of all that can be measurable in natural phenomena.
From the original French, “La vraie physique a été fondée le jour où Galilée, rejetant des spéculations depuis si longtemps stériles, a conçu l’idée … de préciser la forme générale à donner aux expériences, en leur assignant pour objet immédiat la mesure de tout ce qui peut être mesurable dans les phénomènes naturels,” in De l’origine et des limites de la correspondance entre l’algèbre et la géométrie (1847), 375. English version by Webmaster using Google translate. This may be the basis of Thomas-Henri Martin describing Galileo’s experimental method , often translated as Measure what is measurable, and make measurable what is not so, from the original French in Galilée: Les droits de la science et la méthode des sciences physiques (1868), 289. Note that in both cases, the words were narrative by the authors, not quoting actual words by Galileo. What the authors wrote was in their own words, and should not be attributed to Galileo with quotation marks.
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Truth … and if mine eyes
Can bear its blaze, and trace its symmetries,
Measure its distance, and its advent wait,
I am no prophet—I but calculate.
From poem, 'The Prospects of the Future', collected in The Poetical Works of Charles Mackay: Now for the First Time Collected Complete in One Volume (1876), 447.
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Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.
In History of European Thought in the Nineteenth Century (1903), 630.
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We are Marxists, and Marxism teaches that in our approach to a problem we should start from objective facts, not from abstract definitions, and that we should derive our guiding principles, policies, and measures from an analysis of these facts.
As quoted in William Theodore De Bary, Sources of Chinese Tradition (1960), 929.
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We are more than just flesh and bones. There’s a certain spiritual nature and something of the mind that we can’t measure.… With all our sophisticated equipment, we cannot monitor or define it, and yet it’s there.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 44
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We need another, wiser, and perhaps a more mystical concept of animals. For the animal shall not be measured by man....They are not underlings. They are other nations, caught with ourselves in the net of life and time, fellow prisoners of the splendor and travail of Earth.
The Outermost House: A Year of Life On The Great Beach of Cape Cod (2003), 24-25.
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We see not only thought as participating in evolution as an anomaly or as an epiphenomenon; but evolution as so reducible to and identifiable with a progress towards thought that the movement of our souls expresses and measures the very stages of progress of evolution itself. Man discovers that he is nothing else than evolution become conscious of itself.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 221. Originally published in French as Le Phénomene Humain (1955).
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Western field-work conjures up images of struggle on horseback ... –toughing it out on one canteen a day as you labor up and down mountains. The value of a site is supposedly correlated with the difficulty of getting there. This, of course, is romantic drivel. Ease of access is no measure of importance. The famous La Brea tar pits are right in downtown Los Angeles. To reach the Clarkia lake beds, you turn off the main road at Buzzard’s Roost Trophy Company and drive the remaining fifty yards right up to the site.
…...
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When we look back beyond one hundred years over the long trails of history, we see immediately why the age we live in differs from all other ages in human annals. … It remained stationary in India and in China for thousands of years. But now it is moving very fast. … A priest from Thebes would probably have felt more at home at the council of Trent, two thousand years after Thebes had vanished, than Sir Isaac Newton at a modern undergraduate physical society, or George Stephenson in the Institute of Electrical Engineers. The changes have have been so sudden and so gigantic, that no period in history can be compared with the last century. The past no longer enables us even dimly to measure the future.
From 'Fifty Years Hence', Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57, No. 3, 393.
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You cannot do without one specialty. You must have some base-line to measure the work and attainments of others. For a general view of the subject, study the history of the sciences. Broad knowledge of all Nature has been the possession of no naturalist except Humboldt, and general relations constituted his specialty.
Lecture at a teaching laboratory on Penikese Island, Buzzard's Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 146.
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[About the mechanical properties of the molecules of a chemical substance being studied:] They could be measured, but that would have taken several months. So someone said, ‘Let’s get Teller in and make him guess the data.’ We got him into a room and locked the door, so no one else could get at him, and he asked questions and did some figuring at the blackboard. He got the answers in about two hours, not entirely accurately, of course, but—as we found out when we got around to verifying them—close enough for the purpose.
Recalls the first time she was ever really awed by mental abilities of Edward Teller. She had joined the Manhattan Project, and needed data on the physical properties of molecules of a certain substance to get started on her assigned task of calculating its chemical properties. As quoted in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 61.
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[Before the time of Benjamin Peirce it never occurred to anyone that mathematical research] was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone—a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country.
In 'The Story of Mathematics at Harvard', Harvard Alumni Bulletin (3 Jan 1924), 26, 376. Cited by R. C. Archibald in 'Benjamin Peirce: V. Biographical Sketch', The American Mathematical Monthly (Jan 1925), 32, No. 1, 10.
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[We are] a fragile species, still new to the earth, … here only a few moments as evolutionary time is measured, … in real danger at the moment of leaving behind only a thin layer of of our fossils, radioactive at that.
The Fragile Species (1992, 1996), 25.
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~~[Misattributed]~~ It was Galileo who said, “Measure what is measurable, and make measurable what is not so.”
No, Galileo did not “say” or write these words, from transcript of a radio talk 'Mathematics and the Laws of Nature', collected in Warren Weaver (ed.), The Scientists Speak (1947). Reprinted in Isabel S. Gordon and Sophie Sorkin (eds.), The Armchair Science Reader (1959), 301. Weyl is perhaps the source of the quotation marks that have resulted in the quote being attributed to Galileo. It is, in fact, a translation of the original French, “Galilée … déclare que dans tous ces phénomènes il faut mesurer tout ce qui est mesurable, et tâcher de rendre mesurable tout ce qui ne l’est pas directement,” in Thomas-Henri Martin, Galilée: Les Droits de la Science et la Méthode des Sciences Physiques (1868), 289. In English: Galileo … asserts that in all these phenomena we must measure all that is measurable, and try to make measurable all that is not directly measurable. Notice the origin statement is not enclosed in quotation marks; they are the biographer’s own words, not Galileo’s. These words do not come verbatim from any known work by Galileo, and should only be used without quotation marks as Martin’s description of Galileo’s method. Nevertheless, quotation marks have been - erroneously - added in many books, and some of those reference Weyl.
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~~[Misattributed]~~ Measure what is measurable, and make measurable what is not so.
Almost certainly, Galileo did NOT write this quote. No primary source to Galileo seems to be known. However, it IS found in a French author’s own words, as a description of Galileo's experimental outlook (i.e. WITHOUT quotation marks) in Thomas-Henri Martin, Galilée: les droits de la science et la méthode des sciences physiques (1868), 289. The countless repetitions since then never have a citation. Also variants are seen, for example, “Count what is countable, measure what is measurable, and what is not measurable, make measurable,” without citation, in Institute of Public Administration, Administration (1967), 15 175. The quote is included here to note its status.
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“In order to ascertain the height of the tree I must be in such a position that the top of the tree is exactly in a line with the top of a measuring-stick—or any straight object would do, such as an umbrella—which I shall secure in an upright position between my feet. Knowing then that the ratio that the height of the tree bears to the length of the measuring stick must equal the ratio that the distance from my eye to the base of the tree bears to my height, and knowing (or being able to find out) my height, the length of the measuring stick and the distance from my eye to the base of the tree, I can, therefore, calculate the height of the tree.”
“What is an umbrella?”
In Mr. Fortune’s Maggot (1927), 175.
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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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