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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index I > Category: Illustration

Illustration Quotes (48 quotes)

Carolus Linnaeus quote: A herbarium is better than any illustration; every botanist should make one.

A herbarium is better than any illustration; every botanist should make one.
Philosophia Botanica (1751), aphorism 11. Trans. Frans A. Statfleu, Linnaeus and the Linnaeans: The Spreading of their Ideas in Systematic Botany, 1735-1789 (1971), 38.
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A map of the moon... should be in every geological lecture room; for no where can we have a more complete or more magnificent illustration of volcanic operations. Our sublimest volcanoes would rank among the smaller lunar eminences; and our Etnas are but spitting furnaces.
'On the Volcanoes of the Moon', American Journal of Science, 1846, 2 (2nd Series), 347.
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John Ray quote: A multitude of words doth rather obscure than illustrate, they being a burden to the memory, and the first apt t
A multitude of words doth rather obscure than illustrate, they being a burden to the memory, and the first apt to be forgotten, before we come to the last. So that he that uses many words for the explaining of any subject, doth, like the cuttle-fish, hide himself, for the most part, in his own ink.
John Ray
The Wisdom of God Manifested in the Works of the Creation (1691).
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As I am writing, another illustration of ye generation of hills proposed above comes into my mind. Milk is as uniform a liquor as ye chaos was. If beer be poured into it & ye mixture let stand till it be dry, the surface of ye curdled substance will appear as rugged & mountanous as the Earth in any place.
Letter to Thomas Burnet (Jan 1680/1. In H. W. Turnbull (ed.), The Correspondence of Isaac Newton, 1676-1687 (1960), Vol. 2, 334.
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At the sea shore you pick up a pebble, fashioned after a law of nature, in the exact form that best resists pressure, and worn as smooth as glass. It is so perfect that you take it as a keepsake. But could you know its history from the time when a rough fragment of rock fell from the overhanging cliff into the sea, to be taken possession of by the under currents, and dragged from one ocean to another, perhaps around the world, for a hundred years, until in reduced and perfect form it was cast upon the beach as you find it, you would have a fit illustration of what many principles, now in familiar use, have endured, thus tried, tortured and fashioned during the ages.
From Address (1 Aug 1875), 'The Growth of Principles' at Saratoga. Collected in William L. Snyder (ed.), Great Speeches by Great Lawyers: A Collection of Arguments and Speeches (1901), 246.
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Büchsel in his reminiscences from the life of a country parson relates that he sought his recreation in Lacroix’s Differential Calculus and thus found intellectual refreshment for his calling. Instances like this make manifest the great advantage which occupation with mathematics affords to one who lives remote from the city and is compelled to forego the pleasures of art. The entrancing charm of mathematics, which captivates every one who devotes himself to it, and which is comparable to the fine frenzy under whose ban the poet completes his work, has ever been incomprehensible to the spectator and has often caused the enthusiastic mathematician to be held in derision. A classic illustration is the example of Archimedes….
From Die Entwickelung der Mathematik im Zusammenhange mit der Ausbreitung der Kultur (1893), 22. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 186. From the original German, “Wenn Büchsel in seinen Erinnerungen aus dem Leben eines Landgeistlichen erzählt, dass er in der Differentialrechnung von Lacroix Erholung gesucht und geistige Erfrischung ftir seinen Beruf gefunden habe, so erkennen wir darin den grossen Vorzug, den die Beschaftigung mit der Mathematik für jemanden hat, der fern von einer Stadt lebt und auf ihre Kunstgenüsse verzichten muss. Der berückende Zauber der Mathematik, dem jeder unterliegt, der sich ihr ergiebt, und der dem holden Wahnsinn vergleichbar ist, unter dessen Bann der Dichter sein Work vollendet, ist dem betrachtenden Mitmenschen immer unbegreiflich gewesen und hat den begeisterten Mathematiker oft zum Gespött werden lassen. Als klassisches Beispiel wird jedem Schüler Archimedes…”
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For the sake of persons of ... different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid coloring of a physical illustration, or in the tenuity and paleness of a symbolic expression.
…...
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GRAVITATION, n. The tendency of all bodies to approach one another with a strength proportioned to the quantity of matter they contain—the quantity of matter they contain being ascertained by the strength of their tendency to approach one another. This is a lovely and edifying illustration of how science, having made A the proof of B, makes B the proof of A.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  123.
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He that could teach mathematics well, would not be a bad teacher in any of [physics, chemistry, biology or psychology] unless by the accident of total inaptitude for experimental illustration; while the mere experimentalist is likely to fall into the error of missing the essential condition of science as reasoned truth; not to speak of the danger of making the instruction an affair of sensation, glitter, or pyrotechnic show.
In Education as a Science (1879), 298.
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I ought to call myself an agnostic; but, for all practical purposes, I am an atheist. I do not think the existence of the Christian God any more probable than the existence of the Gods of Olympus or Valhalla. To take another illustration: nobody can prove that there is not between the Earth and Mars a china teapot revolving in an elliptical orbit, but nobody thinks this sufficiently likely to be taken into account in practice. I think the Christian God just as unlikely.
Letter (1958) to Mr Major. Collected in Dear Bertrand Russell: A Selection of his Correspondence with the General Public, 1950 - 1968 (1969), 41-42.
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I think chemistry is being frittered away by the hairsplitting of the organic chemists; we have new compounds discovered, which scarcely differ from the known ones and when discovered are valueless—very illustrations perhaps of their refinements in analysis, but very little aiding the progress of true science.
Letter to William Grove (5 Jan 1845), The Letters of Faraday and Schoenbein, 1836-1862 (1899), Footnote, 209.
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If texts are unified by a central logic of argument, then their pictorial illustrations are integral to the ensemble, not pretty little trifles included only for aesthetic or commercial value. Primates are visual animals, and (particularly in science) illustration has a language and set of conventions all its own.
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In a sense Shapley’s telling me that space was transparent, which I shouldn’t have believed, illustrates a fundamental problem in science, believing what people tell you. Go and find it out for yourself. That same error has persisted in my life and in many other people’s. Authorities are not always authorities on everything; they often cling to their own mistakes.
Oral History Transcript of interview with Dr. Jesse Greenstein by Paul Wright (31 Jul 1974), on website of American Institute of Physics.
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In less than eight years “The Origin of Species” has produced conviction in the minds of a majority of the most eminent living men of science. New facts, new problems, new difficulties as they arise are accepted, solved, or removed by this theory; and its principles are illustrated by the progress and conclusions of every well established branch of human knowledge.
From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author in the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.
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In Man the brain presents an ascensive step in development, higher and more strongly marked than that by which the preceding subclass was distinguished from the one below it. Not only do the cerebral hemispheres overlap the olfactory lobes and cerebellum, but they extend in advance of the one, and further back than the other. Their posterior development is so marked, that anatomists have assigned to that part the character of a third lobe; it is peculiar to the genus Homo, and equally peculiar is the 'posterior horn of the lateral ventricle,' and the 'hippocampus minor,' which characterize the hind lobe of each hemisphere. The superficial grey matter of the cerebrum, through the number and depth of the convolutions, attains its maximum of extent in Man. Peculiar mental powers are associated with this highest form of brain, and their consequences wonderfully illustrate the value of the cerebral character; according to my estimate of which, I am led to regard the genus Homo, as not merely a representative of a distinct order, but of a distinct subclass of the Mammalia, for which I propose a name of 'ARCHENCEPHALA.'
'On the Characters, Principles of Division, and Primary Groups of the Class MAMMALIA' (1857), Journal of the Proceedings of the Linnean Society of London (1858), 2, 19-20.
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In preparing the present volume, it has been the aim of the author to do full justice to the ample material at his command, and, where possible, to make the illustrations tell the main story to anatomists. The text of such a memoir may soon lose its interest, and belong to the past, but good figures are of permanent value. [Justifying elaborate illustrations in his monographs.]
In Dinocerata: a monograph of an extinct order of gigantic mammals (1884), Preface, xvii.
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In truth, ideas and principles are independent of men; the application of them and their illustration is man's duty and merit. The time will come when the author of a view shall be set aside, and the view only taken cognizance of. This will be the millennium of Science.
Notes of hints to Mr Ramsey, Professor of Geology, University College London, 1847. In George Wilson and Archibald Geikie, Memoir of Edward Forbes F.R.S. (1861), 429.
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It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
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It is a remarkable illustration of the ranging power of the human intellect that a principle first detected in connection with the clumsy puffing of the early steam engines should be found to apply to the whole world, and possibly, even to the whole cosmic universe.
In Man and Energy (1955, 1963), 132.
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It was a dark and stormy night, so R. H. Bing volunteered to drive some stranded mathematicians from the fogged-in Madison airport to Chicago. Freezing rain pelted the windscreen and iced the roadway as Bing drove on—concentrating deeply on the mathematical theorem he was explaining. Soon the windshield was fogged from the energetic explanation. The passengers too had beaded brows, but their sweat arose from fear. As the mathematical description got brighter, the visibility got dimmer. Finally, the conferees felt a trace of hope for their survival when Bing reached forward—apparently to wipe off the moisture from the windshield. Their hope turned to horror when, instead, Bing drew a figure with his finger on the foggy pane and continued his proof—embellishing the illustration with arrows and helpful labels as needed for the demonstration.
In 'R. H. Bing', Biographical Memoirs: National Academy of Sciences (2002), 49. Anecdote based on the recollections of Bing's colleagues, Steve Armentrout and C. E. Burgess. The narrative was given in a memorial tribute at the University of Texas at Austin.
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Most classifications, whether of inanimate objects or of organisms, are hierarchical. There are “higher” and “lower” categories, there are higher and lower ranks. What is usually overlooked is that the use of the term “hierarchy” is ambiguous, and that two fundamentally different kinds of arrangements have been designated as hierarchical. A hierarchy can be either exclusive or inclusive. Military ranks from private, corporal, sergeant, lieutenant, captain, up to general are a typical example of an exclusive hierarchy. A lower rank is not a subdivision of a higher rank; thus, lieutenants are not a subdivision of captains. The scala naturae, which so strongly dominated thinking from the sixteenth to the eighteenth century, is another good illustration of an exclusive hierarchy. Each level of perfection was considered an advance (or degradation) from the next lower (or higher) level in the hierarchy, but did not include it.
The Growth of Biological Thought: Diversity, Evolution and Inheritance (1982), 205-6.
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Mr. Dalton's aspect and manner were repulsive. There was no gracefulness belonging to him. His voice was harsh and brawling; his gait stiff and awkward; his style of writing and conversation dry and almost crabbed. In person he was tall, bony, and slender. He never could learn to swim: on investigating this circumstance he found that his spec. grav. as a mass was greater than that of water; and he mentioned this in his lectures on natural philosophy in illustration of the capability of different persons for attaining the art of swimming. Independence and simplicity of manner and originality were his best qualities. Though in comparatively humble circumstances he maintained the dignity of the philosophical character. As the first distinct promulgator of the doctrine that the elements of bodies unite in definite proportions to form chemical compounds, he has acquired an undying fame.
Dr John Davy's (brother of Humphry Davy) impressions of Dalton written in c.1830-31 in Malta.
John Davy
Quoted in W. C. Henry, Memoirs of the Life and Scientific Researches of John Dalton (1854), 217-8.
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Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does.
In 'Reminiscences of an Octogenarian Mathematician', The American Mathematical Monthly (Nov 1971), 78, No. 9, 960-961.
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Perhaps the most impressive illustration of all is to suppose that you could label the molecules in a tumbler of water. ... threw it anywhere you please on the earth, and went away from the earth for a few million years while all the water on the earth, the oceans, rivers, lakes and clouds had had time to mix up perfectly. Now supposing that perfect mixing had taken place, you come back to earth and draw a similar tumbler of water from the nearest tap, how many of those marked molecules would you expect to find in it? Well, the answer is 2000. There are 2000 times more molecules in a tumbler of water than there are tumblers of water in the whole earth.
In Lecture (1936) on 'Forty Years of Atomic Theory', collected in Needham and Pagel (eds.) in Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 99-100.
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Quantum provides us with a striking illustration of the fact that though we can fully understand a connection … we can only speak of it in images and parables. We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.
In conversation during first meeting with Werner Heisenberg (summer 1920), as quoted in Werner Heisenberg and Arnold J. Pomerans (trans.), Physics and Beyond: Encounters and Conversations (1971), 41. As cited in Philip Kuberski, The Forgèd Feature: Toward a Poetics of Uncertainty: New and Selected Essays (1995), 177-178.
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Science appears to us with a very different aspect after we have found out that it is not in lecture rooms only, and by means of the electric light projected on a screen, that we may witness physical phenomena, but that we may find illustrations of the highest doctrines of science in games and gymnastics, in travelling by land and by water, in storms of the air and of the sea, and wherever there is matter in motion.
'Introductory Lecture on Experimental Physics' (1871). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 243.
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Some persons have contended that mathematics ought to be taught by making the illustrations obvious to the senses. Nothing can be more absurd or injurious: it ought to be our never-ceasing effort to make people think, not feel.
Seven Lectures on Shakespeare and Milton (1856) 24.
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Take the rose—most people think it very beautiful: I don’t care for It at all. I prefer the cactus, for the simple reason that it has a more interesting personality. It has wonderfully adapted itself to its surroundings! It is the best illustration of the theory of evolution in plant life.
From George MacAdam, 'Steinmetz, Electricity's Mastermind, Enters Politics', New York Times (2 Nov 1913), SM3.
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The artist does not illustrate science; … [but] he frequently responds to the same interests that a scientist does, and expresses by a visual synthesis what the scientist converts into analytical formulae or experimental demonstrations.
'The Arts', in Charles Austin Beard, Whither Mankind: a Panorama of Modern Civilization (1928, 1971), 296.
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The contents of this section will furnish a very striking illustration of the truth of a remark, which I have more than once made in my philosophical writings, and which can hardly be too often repeated, as it tends greatly to encourage philosophical investigations viz. That more is owing to what we call chance, that is, philosophically speaking, to the observation of events arising from unknown causes, than to any proper design, or pre-conceived theory in this business. This does not appear in the works of those who write synthetically upon these subjects; but would, I doubt not, appear very strikingly in those who are the most celebrated for their philosophical acumen, did they write analytically and ingenuously.
'On Dephlogisticated Air, and the Constitution of the Atmosphere', in The Discovery of Oxygen, Part I, Experiments by Joseph Priestley 1775 (Alembic Club Reprint, 1894), 5.
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The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.
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The existing premises, wholly altered by geologic science, are no longer those of Hume. The foot-print in the sand—to refer to his happy illustration—does now stand alone. Instead of one, we see many footprints, each in turn in advance of the print behind it, and on a higher level.
Lecture to the Edinburgh Philosophical Institution, 'Geology in its Bearings on the Two Theologies, Part 1', collected in The Testimony of the Rocks: or, Geology in Its Bearings on the Two Theologies, Natural and Revealed (1857), 223.
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The floating vapour is just as true an illustration of the law of gravity as the falling avalanche.
The Century Illustrated Monthly Magazine, May 1883 to October 1883 (1883), 26, 539.
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The history of aëronautic adventure affords a curious illustration of the same [dip of the horizon] principle. The late Mr. Sadler, the celebrated aeronaut, ascended on one occasion in a balloon from Dublin, and was wafted across the Irish Channel, when, on his approach to the Welsh coast, the balloon descended nearly to the surface of the sea. By this time the sun was set, and the shades of evening began to close in. He threw out nearly all his ballast, and suddenly sprang upwards to a great height, and by so doing brought his horizon to dip below the sun, producing the whole phenomenon of a western sunrise. Subsequently descending in Wales, he of course witnessed a second sunset on the same evening.
This describes how a rapidly ascending balloonist can see more of a setting sun, from the top down, as the viewer gradually rises more and thus sees further, beyond the curvature of the earth. The sun gradually appears as if at sunrise. It is the reverse of the view of a ship sailing toward the horizon which disappears from its hull up to the tip of the mast. In Outlines of Astronomy (1849), 20. A similar description appeared earlier, in Astronomy (1833), 36, which also footnoted Herschel's comment that he had this anecdote from Dr. Lardner, who was present at the ascent
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The peculiar taste both in pure and in mixed nature of those relations about which it is conversant, from its simple and definite phraseology, and from the severe logic so admirably displayed in the concatenation of its innumerable theorems, are indeed immense, and well entitled to separate and ample illustration.
In Philosophy of the Human Mind (1816), Vol. 2, Chap. 2, Sec. 3, 157.
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The progress of the individual mind is not only an illustration, but an indirect evidence of that of the general mind. The point of departure of the individual and of the race being the same, the phases of the mind of a man correspond to the epochs of the mind of the race. Now, each of us is aware, if he looks back upon his own history, that he was a theologian in his childhood, a metaphysician in his youth, and a natural philosopher in his manhood. All men who are up to their age can verify this for themselves.
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 3.
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The role of hypothesis in research can be discussed more effectively if we consider first some examples of discoveries which originated from hypotheses. One of the best illustrations of such a discovery is provided by the story of Christopher Columbus’ voyage; it has many of the features of a classic discovery in science. (a) He was obsessed with an idea—that since the world is round he could reach the Orient by sailing West, (b) the idea was by no means original, but evidently he had obtained some additional evidence from a sailor blown off his course who claimed to have reached land in the west and returned, (c) he met great difficulties in getting someone to provide the money to enable him to test his idea as well as in the actual carrying out of the experimental voyage, (d) when finally he succeeded he did not find the expected new route, but instead found a whole new world, (e) despite all evidence to the contrary he clung to the bitter end to his hypothesis and believed that he had found the route to the Orient, (f) he got little credit or reward during his lifetime and neither he nor others realised the full implications of his discovery, (g) since his time evidence has been brought forward showing that he was by no means the first European to reach America.
The Art of Scientific Investigation (1950), 41.
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The science of the geologist seems destined to exert a marked influence on that of the natural theologian... Not only—to borrow from Paley's illustration—does it enable him to argue on the old grounds, from the contrivance exhibited in the watch found on the moor, that the watch could not have lain upon the moor for ever; but it establishes further, on different and more direct evidence, that there was a time when absolutely the watch was not there; nay, further, so to speak, that there was a previous time in which no watches existed at all, but only water-clocks; yet further, that there was at time in which there we not even water-clocks, but only sun-dials; and further, an earlier time still in which sun-dials were not, nor an measurers of time of any kind.
Lecture to the Edinburgh Philosophical Institution, 'Geology in its Bearings on the Two Theologies, Part 1', collected in The Testimony of the Rocks: or, Geology in Its Bearings on the Two Theologies, Natural and Revealed (1857), 211.
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The stories of Whitney’s love for experimenting are legion. At one time he received a letter asking if insects could live in a vacuum. Whitney took the letter to one of the members of his staff and asked the man if he cared to run an experiment on the subject. The man replied that there was no point in it, since it was well established that life could not exist without a supply of oxygen. Whitney, who was an inveterate student of wild life, replied that on his farm he had seen turtles bury themselves in mud each fall, and, although the mud was covered with ice and snow for months, emerge again in the spring. The man exclaimed, “Oh, you mean hibernation!” Whitney answered, “I don’t know what I mean, but I want to know if bugs can live in a vacuum.”
He proceeded down the hall and broached the subject to another member of the staff. Faced with the same lack of enthusiasm for pursuing the matter further, Whitney tried another illustration. “I’ve been told that you can freeze a goldfish solidly in a cake of ice, where he certainly can’t get much oxygen, and can keep him there for a month or two. But if you thaw him out carefully he seems none the worse for his experience.” The second scientist replied, “Oh, you mean suspended animation.” Whitney once again explained that his interest was not in the terms but in finding an answer to the question.
Finally Whitney returned to his own laboratory and set to work. He placed a fly and a cockroach in a bell jar and removed the air. The two insects promptly keeled over. After approximately two hours, however, when he gradually admitted air again, the cockroach waved its feelers and staggered to its feet. Before long, both the cockroach and the fly were back in action.
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357-358.
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The tendency of the sciences has long been an increasing proclivity of separation and dismemberment … The mathematician turns away from the chemist; the chemist from the naturalist; the mathematician, left to himself divides himself into a pure mathematician and a mixed mathematician, who soon part company … And thus science, even mere physical science, loses all traces of unity. A curious illustration of this result may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively. We are informed that this difficulty was felt very oppressively by the members of the British Association for the Advancement of Science, at their meetings at York, Oxford and Cambridge, in the last three summers. There was no general term by which these gentlemen could describe themselves with reference to their pursuits … some ingenious gentleman [William Whewell] proposed that, by analogy with artist, they might form Scientist, and added that there could be no scruple … when we have words such as sciolist, economist, and atheist—but this was not generally palatable.
In Review of Mrs Somerville, 'On the Connexion of the Physical Sciences', The Quarterly Review (1834), 51, 58-61.
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The varieties of chemical substances actually found in living things are vastly more restricted than the possible varieties. A striking illustration is that if one molecule each of all the possible types of proteins were made, they would together weigh more than the observable universe. Obviously there are a fantastically large number of protein types that are not made by living cells.
In The Closing Circle: Nature, Man, and Technology (2014).
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Their specific effect on the glucosides might thus be explained by assuming that the intimate contact between the molecules necessary for the release of the chemical reaction is possible only with similar geometrical configurations. To give an illustration I will say that enzyme and glucoside must fit together like lock and key in order to be able to exercise a chemical action on each other. This concept has undoubtedly gained in probability and value for stereochemical research, after the phenomenon itself was transferred from the biological to the purely chemical field. It is an extension of the theory of asymmetry without being a direct consequence of it: for the conviction that the geometrical structure of the molecule even for optical isomers exercises such a great influence on the chemical affinities, in my opinion could only be gained by new actual observations.
'Einfluss der Configuration auf die wirkung der Enzyme', Berichte der deutschen Chemischen Gesellschaft, 1894, 27, 2985-93. Trans. B. Holmstedt and G. Liljestrand (eds.) Readings in Pharmacology (1963), 251.
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Whereas, to borrow an illustration from mathematics, life was formerly an equation of, say, 100 unknown quantities, it is now one of 99 only, inasmuch as memory and heredity have been shown to be one and the same thing.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 57.
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Why are atoms so small? ... Many examples have been devised to bring this fact home to an audience, none of them more impressive than the one used by Lord Kelvin: Suppose that you could mark the molecules in a glass of water, then pour the contents of the glass into the ocean and stir the latter thoroughly so as to distribute the marked molecules uniformly throughout the seven seas; if you then took a glass of water anywhere out of the ocean, you would find in it about a hundred of your marked molecules.
What is life?: the Physical Aspect of the Living Cell (1944). Collected in What is Life? with Mind And Matter & Autobiographical Sketches (1967, 1992), 6-7.
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[My Book] will endeavour to establish the principle[s] of reasoning in ... [geology]; and all my geology will come in as illustration of my views of those principles, and as evidence strengthening the system necessarily arising out of the admission of such principles, which... are neither more nor less than that no causes whatever have from the earliest time to which we can look back, to the present, ever acted, but those now acting; and that they never acted with different degrees of energy from that which they now exert.
Letter to Roderick Murchison Esq. (15 Jan 1829). In Mrs Lyell (ed.), The Life, Letters and Journals of Sir Charles Lyell, Bart (1881), Vol. 1, 234.
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[The] weakness of biological balance studies has aptly been illustrated by comparison with the working of a slot machine. A penny brings forth one package of chewing gum; two pennies bring forth two. Interpreted according to the reasoning of balance physiology, the first observation is an indication of the conversion of copper into gum; the second constitutes proof.
[Co-author with David Rittenberg (1906-70).]
'The Application of Isotopes to the Study of Intermediary Metabolism', Science (1938), 87, 222.
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[To elucidate using models] the different combining powers in elementary atoms, I … select my illustrations from that most delightful of games, croquet. Let the croquet balls represent our atoms, and let us distinguish the atoms of different elements by different colours. The white balls are hydrogen, the green ones chlorine atoms; the atoms of fiery oxygen are red, those of nitrogen, blue; the carbon atoms, lastly, are naturally represented by black balls. But we have, in addition, exhibit the different combining powers of these atoms … by screwing into the balls a number of metallic arms (tubes and pins), which correspond respectively to the combining powers of the atoms represented … to join the balls … in imitation of the atomic edifices represented.
Paper presented at the Friday Discourse of the the Royal Institution (7 Apr 1865). 'On the Combining Power of Atoms', Proceedings of the Royal Institution (1865), 4, No. 42, 416.
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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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