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Direct Quotes (84 quotes)

A great reform in geological speculation seems now to have become necessary. … It is quite certain that a great mistake has been made—that British popular geology at the present time is in direct opposition to the principles of Natural Philosophy.
From Sir W. Thomson, Address (27 Feb 1868), to the Geological Society of Glasgow, 'On Geological Time', Transactions of the Geological Society of Glasgow 3, collected in Popular Lectures and Addresses (1894), Vol. 2, 10 & 44. As Epigraph in Thomas Henry Huxley, 'Geological Reform' (1869), Collected Essays: Discourses, Biological and Geological (1894), 306.
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A man’s value to the community depends primarily on how far his feelings, thoughts, and actions are directed towards promoting the good of his fellows. We call him good or bad according to how he stands in this matter. It looks at first sight as if our estimate of a man depended entirely on his social qualities.
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A science cannot be played with. If an hypothesis is advanced that obviously brings into direct sequence of cause and effect all the phenomena of human history, we must accept it, and if we accept it, we must teach it.
In The Degradation of the Democratic Dogma (1919), 131.
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All scientists must focus closely on limited targets. Whether or not one’s findings on a limited subject will have wide applicability depends to some extent on chance, but biologists of superior ability repeatedly focus on questions the answers to which either have wide ramifications or lead to new areas of investigation. One procedure that can be effective is to attempt both reduction and synthesis; that is, direct a question at a phenomenon on one integrative level, identify its mechanism at a simpler level, then extrapolate its consequences to a more complex level of integration.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 230-231,
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America has always been greatest when we dared to be great. We can reach for greatness again. We can follow our dreams to distant stars, living and working in space for peaceful, economic, and scientific gain. Tonight, I am directing NASA to develop a permanently manned space station and to do it within a decade.
From State of the Union Address (25 Jan 1984).
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As the skies appear to a man, so is his mind. Some see only clouds there; some, prodigies and portents; some rarely look up at all; their heads, like the brutes, are directed toward Earth. Some behold there serenity, purity, beauty ineffable. The world runs to see the panorama, when there is a panorama in the sky which few go to see.
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Christian Science … is the direct denial both of science and of Christianity, for Science rests wholly on the recognition of truth and Christianity on the recognition of pain.
From The Illustrated London News (1 Nov 1930), 177, Part 2, 750. In 'More on American Optimism', Collected Works (1990), Vol. 35, 406-407.
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Civilisations as yet have only been created and directed by a small intellectual aristocracy, never by crowds. Crowds are only powerful for destruction.
From original French, “Les civilisations n’ont été créées et guidées jusqu’ici que par une petite aristocratie intellectuelle, jamais par les foules. Les foules n’ont de puissance que pour détruire,” in Psychologie des Foules (1895), Preface, 6. English text in The Crowd: A Study of the Popular Mind (1897), Introduction, xviii. Also seen translated as, “All the civilizations we know have been created and directed by small intellectual aristocracies, never by people in the mass. The power of crowds is only to destroy.”
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Debate is an art form. It is about the winning of arguments. It is not about the discovery of truth. There are certain rules and procedures to debate that really have nothing to do with establishing fact–which creationists have mastered. Some of those rules are: never say anything positive about your own position because it can be attacked, but chip away at what appear to be the weaknesses in your opponent’s position. They are good at that. I don’t think I could beat the creationists at debate. I can tie them. But in courtrooms they are terrible, because in courtrooms you cannot give speeches. In a courtroom you have to answer direct questions about the positive status of your belief. We destroyed them in Arkansas. On the second day of the two-week trial we had our victory party!
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Despite the high long-term probability of extinction, every organism alive today, including every person reading this paper, is a link in an unbroken chain of parent-offspring relationships that extends back unbroken to the beginning of life on earth. Every living organism is a part of an enormously long success story—each of its direct ancestors has been sufficiently well adapted to its physical and biological environments to allow it to mature and reproduce successfully. Viewed thus, adaptation is not a trivial facet of natural history, but a biological attribute so central as to be inseparable from life itself.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 330.
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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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Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.
Ampère gives this example drawn from geometry to illustrate his meaning for “direct synthesis” when deductions following from more simple, already-known theorems leads to a new discovery. In James R. Hofmann, André-Marie Ampère (1996), 159. Cites Académie des Sciences Ampère Archives, box 261.
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Engineering is the art of directing the great sources of power in nature for the use and the convenience of people. In its modern form engineering involves people, money, materials, machines, and energy. It is differentiated from science because it is primarily concerned with how to direct to useful and economical ends the natural phenomena which scientists discover and formulate into acceptable theories. Engineering therefore requires above all the creative imagination to innovate useful applications of natural phenomena. It seeks newer, cheaper, better means of using natural sources of energy and materials.
In McGraw Hill, Science and Technology Encyclopedia
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Engineering is the art of organizing and directing men and controlling the forces and materials of nature for the benefit of the human race.
1907
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Engineering is the art or science of utilizing, directing or instructing others in the utilization of the principles, forces, properties and substance of nature in the production, manufacture, construction, operation and use of things ... or of means, methods, machines, devices and structures ...
(1920}
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Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bn) / n = x, donc Dieu existe; repondez!

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.
In Budget of Paradoxes (1878), 251. [The declaration in French expresses, “therefore God exists; please answer!” This Euler-Diderot anecdote, as embellished by De Morgan, is generally regarded as entirely fictional. Diderot before he became an encyclopedist was an accomplished mathematician and fully capable of recognizing—and responding to—the absurdity of an algebraic expression in proving the existence of God. See B.H. Brown, 'The Euler-Diderot Anecdote', The American Mathematical Monthly (May 1942), 49, No. 5, 392-303. —Webmaster.]
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Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error.
In 'Lecture 7', Lectures on the History of Moral Philosophy in England (1852), 101.
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Experiments in geology are far more difficult than in physics and chemistry because of the greater size of the objects, commonly outside our laboratories, up to the earth itself, and also because of the fact that the geologic time scale exceeds the human time scale by a million and more times. This difference in time allows only direct observations of the actual geologic processes, the mind having to imagine what could possibly have happened in the past.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 455-6.
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For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.
In Théorie Nouvelle de la Rotation des Corps (1834). As translated by Charles Thomas Whitley in Outlines of a New Theory of Rotatory Motion (1834), 4.
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Forests and trees make significant direct contributions to the nutrition of poor households ... [as] rural communities in Central Africa obtained a critical portion of protein and fat in their diets through hunting wildlife from in and around forests. The five to six million tonnes of bushmeat eaten yearly in the Congo Basin is roughly equal to the total amount of beef produced annually in Brazil – without the accompanying need to clear huge swathes of forest for cattle.
In 'Forests and food security: What we know and need to know', Forest News online blog by the Center for International Forestry Research (20 Apr 2011).
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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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Heavy dependence on direct observation is essential to biology not only because of the complexity of biological phenomena, but because of the intervention of natural selection with its criterion of adequacy rather than perfection. In a system shaped by natural selection it is inevitable that logic will lose its way.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 229.
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Human personality resembles a coral reef: a large hard/dead structure built and inhabited by tiny soft/live animals. The hard/dead part of our personality consists of habits, memories, and compulsions and will probably be explained someday by some sort of extended computer metaphor. The soft/live part of personality consists of moment-to-moment direct experience of being. This aspect of personality is familiar but somewhat ineffable and has eluded all attempts at physical explanation.
Quoted in article 'Nick Herbert', in Gale Cengage Learning, Contemporary Authors Online (2002).
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I am among the most durable and passionate participants in the scientific exploration of the solar system, and I am a long-time advocate of the application of space technology to civil and military purposes of direct benefit to life on Earth and to our national security.
In 'Is Human Spaceflight Obsolete?' Quoted in Issues in Science and Technology (Summer 2004).
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I belong to those theoreticians who know by direct observation what it means to make a measurement. Methinks it were better if there were more of them.
Referring to his laboratory experience during his assistantship in experimental physics, as quoted in Walter Moore, Schrödinger: Life and Thought (1989, 1998), 58-59. Moore describes that Schrödinger in his early days in the laboratory, “learned to believe that physics is not based upon mathematical fantasies but on a solid ground of experimental observations.”
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I have no patience with the doctrine of “pure science,”—that science is science only as it is uncontaminated by application in the arts of life: and I have no patience with the spirit that considers a piece of work to be legitimate only as it has direct bearing on the arts and affairs of men. We must discover all things that are discoverable and make a record of it: the application will take care of itself.
In 'The Survey Idea in Country Life', collected in John Phelan, Readings in Rural Sociology (1920), 480.
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I think all museums should be directed toward 12-year-old boys. They’re the brightest group you can find and this is the age when you can arouse their curiosity and interest.
As quoted in Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 147.
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If a man is in need of rescue, an airplane can come in and throw flowers on him, and that’s just about all. But a direct lift aircraft could come in and save his life.
From 'Igor Sikorsky the Aviation Pioneer Speaks', Igor I. Sikorsky Historical Archives, sikorskyarchives.com.
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If we turn to the problems to which the calculus owes its origin, we find that not merely, not even primarily, geometry, but every other branch of mathematical physics—astronomy, mechanics, hydrodynamics, elasticity, gravitation, and later electricity and magnetism—in its fundamental concepts and basal laws contributed to its development and that the new science became the direct product of these influences.
Opening of Presidential Address (27 Apr 1907) to the American Mathematical Society, 'The Calculus in Colleges and Technical Schools', published in Bulletin of the American Mathematical Society (Jun 1907), 13, 449.
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If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.
In Novi Comm. Petr., Vol. 4, Preface.
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In a dispassionate comparison of the relative values of human and robotic spaceflight, the only surviving motivation for continuing human spaceflight is the ideology of adventure. But only a tiny number of Earth’s six billion inhabitants are direct participants. For the rest of us, the adventure is vicarious and akin to that of watching a science fiction movie.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004). [Note: published one year after the loss of seven lives in the Space Shuttle Columbia disaster. —Webmaster]
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In the world of science different levels of esteem are accorded to different kinds of specialist. Mathematicians have always been eminently respectable, and so are those who deal with hard lifeless theories about what constitutes the physical world: the astronomers, the physicists, the theoretical chemists. But the more closely the scientist interests himself in matters which are of direct human relevance, the lower his social status. The real scum of the scientific world are the engineers and the sociologists and the psychologists. Indeed, if a psychologist wants to rate as a scientist he must study rats, not human beings. In zoology the same rules apply. It is much more respectable to dissect muscle tissues in a laboratory than to observe the behaviour of a living animal in its natural habitat.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
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Ironically one’s scientific obsolescence is a direct result of the creativity of his peers.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 229.
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It certainly strikes the beholder with astonishment, to perceive what vast difficulties can be overcome by the pigmy arms of little mortal man, aided by science and directed by superior skill.
About his visit to Lockport on the Erie Canal, in Letter IX, to a friend in England from Lockport, New York (25 Jul 1831), collected in Narrative of a Tour in North America (1834), Vol. 1, 233-234,
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It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability. That a scientific investigation pursued on account of its probability will generally lead to truth, rather than falsehood, is at the best only probable.
In A Treatise on Probability (1921), 322.
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It is an irony of fate that I myself have been the recipient of excessive admiration and reverence from my fellow-beings, through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the few ideas to which I have with my feeble powers attained through ceaseless struggle. I am quite aware that for any organisation to reach its goals, one man must do the thinking and directing and generally bear the responsibility. But the led must not be coerced, they must be able to choose their leader.
In 'What I Believe', Forum and Century (1930), 84, 193-194.
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It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
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It is not failure but success that is forcing man off this earth. It is not sickness but the triumph of health... Our capacity to survive has expanded beyond the capacity of Earth to support us. The pains we are feeling are growing pains. We can solve growth problems in direct proportion to our capacity to find new worlds... If man stays on Earth, his extinction is sure even if he lasts till the sun expands and destroys him... It is no longer reasonable to assume that the meaning of life lies on this earth alone. If Earth is all there is for man, we are reaching the foreseeable end of man.
…...
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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Life is an offensive, directed against the repetitious mechanism of the Universe.
In Adventures of Ideas (1933), 102.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics … belongs to every inquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by observation. In its pure and simple form the syllogism cannot be directly compared with all experience, or it would not have required an Aristotle to discover it. It must be transmuted into all the possible shapes in which reasoning loves to clothe itself. The transmutation is the mathematical process in the establishment of the law.
From Memoir (1870) read before the National Academy of Sciences, Washington, printed in 'Linear Associative Algebra', American Journal of Mathematics (1881), 4, 97-98.
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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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My passionate sense of social justice and social responsibility has always contrasted oddly with my pronounced lack of need for direct contact with other human beings and human communities.
…...
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Nature has not arranged her productions on a single and direct line. They branch at every step, and in every direction, and he who attempts to reduce them into departments is left to do it by the lines of his own fancy.
In Letter (22 Feb 1814) to Dr. John Manners. Collected in The Writings of Thomas Jefferson (1905), Vol 13, 99.
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No occupation is more worthy of an intelligent and enlightened mind, than the study of Nature and natural objects; and whether we labour to investigate the structure and function of the human system, whether we direct our attention to the classification and habits of the animal kingdom, or prosecute our researches in the more pleasing and varied field of vegetable life, we shall constantly find some new object to attract our attention, some fresh beauties to excite our imagination, and some previously undiscovered source of gratification and delight.
In A Practical Treatise on the Cultivation of the Dahlia (1838), 1-2.
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Obviously we biologists should fit our methods to our materials. An interesting response to this challenge has been employed particularly by persons who have entered biology from the physical sciences or who are distressed by the variability in biology; they focus their research on inbred strains of genetically homogeneous laboratory animals from which, to the maximum extent possible, variability has been eliminated. These biologists have changed the nature of the biological system to fit their methods. Such a bold and forthright solution is admirable, but it is not for me. Before I became a professional biologist, I was a boy naturalist, and I prefer a contrasting approach; to change the method to fit the system. This approach requires that one employ procedures which allow direct scientific utilization of the successful long-term evolutionary experiments which are documented by the fascinating diversity and variability of the species of animals which occupy the earth. This is easy to say and hard to do.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 232.
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Organisms ... are directed and limited by their past. They must remain imperfect in their form and function, and to that extent unpredictable since they are not optimal machines. We cannot know their future with certainty, if only because a myriad of quirky functional shifts lie within the capacity of any feature, however well adapted to a present role.
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Purpose directs energy, and purpose makes energy.
From Sermon, collected in The Pattern in the Mount and Other Sermons (1885), 6.
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Reflexion is careful and laborious thought, and watchful attention directed to the agreeable effect of one’s plan. Invention, on the other hand, is the solving of intricate problems and the discovery of new principles by means of brilliancy and versatility.
Vitruvius
In De Architectura, Book 1, Chap 2, Sec. 2. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 14.
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Results rarely specify their causes unambiguously. If we have no direct evidence of fossils or human chronicles, if we are forced to infer a process only from its modern results, then we are usually stymied or reduced to speculation about probabilities. For many roads lead to almost any Rome.
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Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.
Letter collected in Tamworth Reading Room: Letters on an Address Delivered by Sir Robert Peel, Bart., M.P. on the Establishment of a Reading Room at Tamworth (1841), 32. Excerpted in John Henry Newman, An Essay in Aid of a Grammar of Assent (1870), 89 & 94 footnote.
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Science is a dynamic undertaking directed to lowering the degree of the empiricism involved in solving problems; or, if you prefer, science is a process of fabricating a web of interconnected concepts and conceptual schemes arising from experiments and ob
Modern Science and Modern Man, p. 62, New York (1952).
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Science is often regarded as the most objective and truth-directed of human enterprises, and since direct observation is supposed to be the favored route to factuality, many people equate respectable science with visual scrutiny–just the facts ma’am, and palpably before my eyes. But science is a battery of observational and inferential methods, all directed to the testing of propositions that can, in principle, be definitely proven false ... At all scales, from smallest to largest, quickest to slowest, many well-documented conclusions of science lie beyond the strictly limited domain of direct observation. No one has ever seen an electron or a black hole, the events of a picosecond or a geological eon.
…...
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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Taxonomy is often regarded as the dullest of subjects, fit only for mindless ordering and sometimes denigrated within science as mere “stamp collecting” (a designation that this former philatelist deeply resents). If systems of classification were neutral hat racks for hanging the facts of the world, this disdain might be justified. But classifications both reflect and direct our thinking. The way we order represents the way we think. Historical changes in classification are the fossilized indicators of conceptual revolutions.
In Hen’s Teeth and Horse’s Toes: Further Reflections in Natural History (1983, 2010), 72
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The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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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 discovery of the conic sections, attributed to Plato, first threw open the higher species of form to the contemplation of geometers. But for this discovery, which was probably regarded in Plato’s tune and long after him, as the unprofitable amusement of a speculative brain, the whole course of practical philosophy of the present day, of the science of astronomy, of the theory of projectiles, of the art of navigation, might have run in a different channel; and the greatest discovery that has ever been made in the history of the world, the law of universal gravitation, with its innumerable direct and indirect consequences and applications to every department of human research and industry, might never to this hour have been elicited.
In 'A Probationary Lecture on Geometry, Collected Mathematical Papers, Vol. 2 (1908), 7.
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The examples which a beginner should choose for practice should be simple and should not contain very large numbers. The powers of the mind cannot be directed to two things at once; if the complexity of the numbers used requires all the student’s attention, he cannot observe the principle of the rule which he is following.
In Study and Difficulties of Mathematics (1902), chap. 3.
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The fact is that up to now the free society has not been good for the intellectual. It has neither accorded him a superior status to sustain his confidence nor made it easy for him to acquire an unquestioned sense of social usefulness. For he derives his sense of usefulness mainly from directing, instructing, and planning-from minding other people’s business-and is bound to feel superfluous and neglected where people believe themselves competent to manage individual and communal affairs, and are impatient of supervision and regulation. A free society is as much a threat to the intellectual’s sense of worth as an automated economy is to the workingman’s sense of worth. Any social order that can function with a minimum of leadership will be anathema to the intellectual.
In 'Concerning Individual Freedom', The Ordeal of Change (1963), 141.
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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 history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, “The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics.” It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoiter and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken.
In History of Mathematics (1897), 1-2.
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The individual, if left alone from birth would remain primitive and beast-like in his thoughts and feelings to a degree that we can hardly conceive. The individual is what he is and has the significance that he has not so much in virtue of his individuality, but rather as a member of a great human society, which directs his material and spiritual existence from the cradle to the grave.
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The mathematician is in much more direct contact with reality. … [Whereas] the physicist’s reality, whatever it may be, has few or none of the attributes which common sense ascribes instinctively to reality. A chair may be a collection of whirling electrons.
In A Mathematician's Apology (1940, 2012), 128.
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The most conspicuous scientific and technical achievements of our age—nuclear bombs, rockets, computers—are all direct products of war.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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The most direct, and in a sense the most important, problem which our conscious knowledge of Nature should enable us to solve is the anticipation of future events, so that we may arrange our present affairs in accordance with such anticipation. As a basis for the solution of this problem we always make use of our knowledge of events which have already occurred, obtained by chance observation or by prearranged experiment.
In Heinrich Hertz, D.E. Jones (trans.) and J.T. Walley (trans.), 'Introduction', The Principles of Mechanics (1899), 1.
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The physician being, then, truly a blind man, armed with a club, who, as chance directs the weight of his blow, will be certain of annihilating nature or the disease.
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The seventeenth century witnessed the birth of modern science as we know it today. This science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science—a dependence on numbers, on real numbers of actual experience.
From The Triumph of Numbers: How Counting Shaped Modern Life (2005), 36.
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The student should not lose any opportunity of exercising himself in numerical calculation and particularly in the use of logarithmic tables. His power of applying mathematics to questions of practical utility is in direct proportion to the facility which he possesses in computation.
In Study and Difficulties of Mathematics (1902), chap. 12.
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The true man of science will know nature better by his finer organization; he will smell, taste, see, hear, feel, better than other men. His will be a deeper and finer experience.
In 'Natural history of Massachusetts', The Dial: A Magazine for Literature, Philosophy, and Religion (Jul 1842), 3, No. 1, 40.
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There are, as we have seen, a number of different modes of technological innovation. Before the seventeenth century inventions (empirical or scientific) were diffused by imitation and adaption while improvement was established by the survival of the fittest. Now, technology has become a complex but consciously directed group of social activities involving a wide range of skills, exemplified by scientific research, managerial expertise, and practical and inventive abilities. The powers of technology appear to be unlimited. If some of the dangers may be great, the potential rewards are greater still. This is not simply a matter of material benefits for, as we have seen, major changes in thought have, in the past, occurred as consequences of technological advances.
Concluding paragraph of "Technology," in Dictionary of the History of Ideas (1973), Vol. 4, 364.
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There is not wholly unexpected surprise, but surprise nevertheless, that mathematics has direct application to the physical world about us.
In The American Mathematical Monthly (1949), 56, 19. Excerpted in John Ewing (ed,), A Century of Mathematics: Through the Eyes of the Monthly (1996), 186.
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Today, in directly harnessing the power of the Sun, we're taking the energy that God gave us, the most renewable energy that we will ever see, and using it to replace our dwindling supplies of fossil fuels.
Speech, at dedication of solar panels on the White House roof, 'Solar Energy Remarks Announcing Administration Proposals' (20 Jun 1979).
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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We do not learn by inference and deduction, and the application of mathematics to philosophy, but by direct intercourse and sympathy.
In 'Natural History of Massachusetts', The Dial: A Magazine for Literature, Philosophy, and Religion (Jul 1842), 3, No. 1, 40.
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When Cayley had reached his most advanced generalizations he proceeded to establish them directly by some method or other, though he seldom gave the clue by which they had first been obtained: a proceeding which does not tend to make his papers easy reading. …
His literary style is direct, simple and clear. His legal training had an influence, not merely upon his mode of arrangement but also upon his expression; the result is that his papers are severe and present a curious contrast to the luxuriant enthusiasm which pervades so many of Sylvester’s papers. He used to prepare his work for publication as soon as he carried his investigations in any subject far enough for his immediate purpose. … A paper once written out was promptly sent for publication; this practice he maintained throughout life. … The consequence is that he has left few arrears of unfinished or unpublished papers; his work has been given by himself to the world.
In Proceedings of London Royal Society (1895), 58, 23-24.
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When we survey our lives and endeavours we soon observe that almost the whole of our actions and desires are bound up with the existence of other human beings. We see that our whole nature resembles that of the social animals. We eat food that others have grown, wear clothes that others have made, live in houses that others have built. The greater part of our knowledge and beliefs has been communicated to us by other people through the medium of a language which others have created. Without language our mental capacities would be poor indeed, comparable to those of the higher animals; we have, therefore, to admit that we owe our principal advantage over the beasts to the fact of living in human society. The individual, if left alone from birth would remain primitive and beast-like in his thoughts and feelings to a degree that we can hardly conceive. The individual is what he is and has the significance that he has not so much in virtue of his individuality, but rather as a member of a great human society, which directs his material and spiritual existence from the cradle to the grave.
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Without initiation into the scientific spirit one is not in possession of the best tools humanity has so far devised for effectively directed reflection. [Without these one] fails to understand the full meaning of knowledge.
Democracy and Education: an Introduction to the Philosophy of Education (1916), 223.
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[In the case of research director, Willis R. Whitney, whose style was to give talented investigators as much freedom as possible, you may define “serendipity” as] the art of profiting from unexpected occurrences. When you do things in that way you get unexpected results. Then you do something else and you get unexpected results in another line, and you do that on a third line and then all of a sudden you see that one of these lines has something to do with the other. Then you make a discovery that you never could have made by going on a direct road.
Quoted in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 355.
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[Napoleon] directed Bourrienne to leave all his letters unopened for three weeks, and then observed with satisfaction how large a part of the correspondence had thus disposed of itself, and no longer required an answer.
Lecture, 'Napoleon', collected in Representative Men (1850), 177.
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[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
In Examination of Sir William Hamilton's Philosophy (1878), 607.
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[The root cap of a plant], having the power of directing the movements of the adjoining parts, acts like the brain of one of the lower animals; the brain being seated within the anterior end of the body, receiving impressions from the sense-organs, and directing the several movements.
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[To identify ancient sites] The primary requirement is a human skeleton or artifacts that are clearly the work of humans. Next, this evidence must lie in situ within undisturbed geological deposits. The artifacts should be directly associated with stratigraphy. Finally, the minimum age of the site must be determined by a direct link with fossils of known age or with material that has been reliably dated.
As quoted in Sharman Apt Russell, When the Land Was Young: Reflections on American Archaeology (2001), 22.
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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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Sophie Germain
Gertrude Elion
Ernest Rutherford
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Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
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Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
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Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
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Francis Crick
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Francis Bacon
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- 10 -
Aristotle
John Watson
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Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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