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Who said: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.”
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Trace Quotes (39 quotes)


Combining in our survey then, the whole range of deposits from the most recent to the most ancient group, how striking a succession do they present:– so various yet so uniform–so vast yet so connected. In thus tracing back to the most remote periods in the physical history of our continents, one system of operations, as the means by which many complex formations have been successively produced, the mind becomes impressed with the singleness of nature's laws; and in this respect, at least, geology is hardly inferior in simplicity to astronomy.
The Silurian System (1839), 574.
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Consciousness is never experienced in the plural, only in the singular. Not only has none of us ever experienced more than one consciousness, but there is also no trace of circumstantial evidence of this ever happening anywhere in the world. If I say that there cannot be more than one consciousness in the same mind, this seems a blunt tautology–we are quite unable to imagine the contrary.
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Controlled research … endeavors to pick out of the web of nature’s activities some single strand and trace it towards its origin and its terminus and determine its relation to other strands.
In 'The Influence of Research in Bringing into Closer Relationship the Practice of Medicine and Public Health Activities', American Journal of Medical Sciences (Dec 1929), No. 178.
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Copernicus, the most learned man whom we are able to name other than Atlas and Ptolemy, even though he taught in a most learned manner the demonstrations and causes of motion based on observation, nevertheless fled from the job of constructing tables, so that if anyone computes from his tables, the computation is not even in agreement with his observations on which the foundation of the work rests. Therefore first I have compared the observations of Copernicus with those of Ptolemy and others as to which are the most accurate, but besides the bare observations, I have taken from Copernicus nothing other than traces of demonstrations. As for the tables of mean motion, and of prosthaphaereses and all the rest, I have constructed these anew, following absolutely no other reasoning than that which I have judged to be of maximum harmony.
Dedication to the Duke of Prussia, Prutenicae Tabulae (1551), 1585 edition, as quoted in Owen Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler (1993), 227.
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From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.
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I believe with Schopenhauer that one of the strongest motives that lead men to art and science is escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one’s own ever shifting desires. A finely tempered nature longs to escape from personal life into the world of objective perception and thought; this desire may be compared with the townsman’s irresistible longing to escape from his noisy, cramped surroundings into the silence of high mountains, where the eye ranges freely through the still, pure air and fondly traces out the restful contours apparently built for eternity.
Address at The Physical Society, Berlin (1918) for Max Planck’s 60th birthday, 'Principles of Research', collected in Essays in Science (1934) 2.
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I have presented the periodic table as a kind of travel guide to an imaginary country, of which the elements are the various regions. This kingdom has a geography: the elements lie in particular juxtaposition to one another, and they are used to produce goods, much as a prairie produces wheat and a lake produces fish. It also has a history. Indeed, it has three kinds of history: the elements were discovered much as the lands of the world were discovered; the kingdom was mapped, just as the world was mapped, and the relative positions of the elements came to take on a great significance; and the elements have their own cosmic history, which can be traced back to the stars.
In The Periodic Kingdom: A Journey Into the Land of the Chemical Elements (1995), Preface, viii.
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Iconography becomes even more revealing when processes or concepts, rather than objects, must be depicted–for the constraint of a definite ‘thing’ cedes directly to the imagination. How can we draw ‘evolution’ or ‘social organization,’ not to mention the more mundane ‘digestion’ or ‘self-interest,’ without portraying more of a mental structure than a physical reality? If we wish to trace the history of ideas, iconography becomes a candid camera trained upon the scholar’s mind.
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In physics we have dealt hitherto only with periodic crystals. To a humble physicist’s mind, these are very interesting and complicated objects; they constitute one of the most fascinating and complex material structures by which inanimate nature puzzles his wits. Yet, compared with the aperiodic crystal, they are rather plain and dull. The difference in structure is of the same kind as that between an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity and a masterpiece of embroidery, say a Raphael tapestry, which shows no dull repetition, but an elaborate, coherent, meaningful design traced by the great master.
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It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing the microscope that prodigious smallness which is also a vastness, and now in seeking in geological ages the traces of a past that attracts us because of its remoteness.
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It is clear that all the valuable things, material, spiritual, and moral, which we receive from society can be traced back through countless generations to certain creative individuals. The use of fire, the cultivation of edible plants, the steam engine–each was discovered by one man.
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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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It was one thing to declare that we had not yet discovered the traces of a beginning, and another to deny that the earth ever had a beginning.
As quoted in Charles Lyell, Principles of Geology: Being an Attempt to Explain the Former Changes of the Earth’s Surface (1833), Vol. 3, 383. The quote is Playfair’s comment on Hutton’s conclusion: “The result, therefore of our present inquiry is, that we find no vestige of a beginning, no prospect of an end.” In defence of Hutton, Playfair was pointing out that the doctrine of Hutton was not opposed to the belief of a creation. Hutton’s conclusion is in Dissertation on the Theory of the Earth (1795)
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It was one thing to declare that we had not yet discovered the trace of a beginning, and another to deny that the earth ever had a beginning.
Epigraph in Charles Clay, 'Observations on the Theory of the Earth’s Original Formation', Geological Sketches and Observations on Vegetable Fossil Remains (1839), 69.
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It’s impossible to move, to live, to operate at any level without leaving traces, bits, seemingly meaningless fragments of personal information.
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Nature! … She is the only artist; working-up the most uniform material into utter opposites; arriving, without a trace of effort, at perfection, at the most exact precision, though always veiled under a certain softness.
As quoted by T.H. Huxley, in Norman Lockyer (ed.), 'Nature: Aphorisms by Goethe', Nature (1870), 1, 10.
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No matter how we twist and turn we shall always come back to the cell. The eternal merit of Schwann does not lie in his cell theory that has occupied the foreground for so long, and perhaps will soon be given up, but in his description of the development of the various tissues, and in his demonstration that this development (hence all physiological activity) is in the end traceable back to the cell. Now if pathology is nothing but physiology with obstacles, and diseased life nothing but healthy life interfered with by all manner of external and internal influences then pathology too must be referred back to the cell.
In 'Cellular-Pathologie', Archiv für pathologische Anatomie und Physiologie und fur klinische Medizin (1855), 8, 13-14, as translated in LellandJ. Rather, 'Cellular Pathology', Disease, Life, and Man: Selected Essays by Rudolf Virchow (1958), 81.
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No other animals have ever lighted fires as far as we can tell. In field archeology, a charcoal deposit found in such a location that it could not have been made by a forest fire is taken as conclusive evidence of man. A circular dark disk in the soil five or six feet in diameter is such a find. … With … modern radioactive dating methods, we can trace man’s history.
In 'Man’s Place in the Physical Universe', Bulletin of the Atomic Scientists (Sep 1965), 21, No. 7, 15.
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Now, it may be stretching an analogy to compare epidemics of cholera—caused by a known agent—with that epidemic of violent crime which is destroying our cities. It is unlikely that our social problems can be traced to a single, clearly defined cause in the sense that a bacterial disease is ‘caused’ by a microbe. But, I daresay, social science is about as advanced in the late twentieth century as bacteriological science was in the mid nineteenth century. Our forerunners knew something about cholera; they sensed that its spread was associated with misdirected sewage, filth, and the influx of alien poor into crowded, urban tenements. And we know something about street crime; nowhere has it been reported that a member of the New York Stock Exchange has robbed ... at the point of a gun. Indeed, I am naively confident that an enlightened social scientist of the next century will be able to point out that we had available to us at least some of the clues to the cause of urban crime.
'Cholera at the Harvey,' Woods Hole Cantata: Essays on Science and Society (1985).
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Now, we propose in the first place to show, that this law of organic progress is the law of all progress. Whether it be in the development of the Earth, in the development in Life upon its surface, in the development of Society, of Government, of Manufactures, of Commerce, of Language, Literature, Science, Art, this same evolution of the simple into the complex, through a process of continuous differentiation, holds throughout. From the earliest traceable cosmical changes down to the latest results of civilization, we shall find that the transformation of the homogeneous into the heterogeneous is that in which Progress essentially consists.
'Progress: Its Law and Cause', Westminster Review (1857), 67, 446-7.
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Science has found that nothing can disappear without a trace. Nature does not know extinction. All it knows is transformation.
In This Week Magazine (24 Jan 1960), 2. As quoted in Martin A. Recio, From the Threshold of Heaven (2008), 102.
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Science never saw a ghost, nor does it look for any, but it sees everywhere the traces, and it is itself the agent, of a Universal Intelligence.
(2 Dec 1853). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: VI: December 1, 1853-August 31, 1854 (1906), 4.
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Science quickens and cultivates directly the faculty of observation, which in very many persons lies almost dormant through life, the power of accurate and rapid generalizations, and the mental habit of method and arrangement; it accustoms young persons to trace the sequence of cause and effect; it familiarizes then with a kind of reasoning which interests them, and which they can promptly comprehend; and it is perhaps the best corrective for that indolence which is the vice of half-awakened minds, and which shrinks from any exertion that is not, like an effort of memory, merely mechanical.
Anonymous
Report of the Royal Commission on Education (1861), Parliamentary Papers (1864), Vol 20, 32-33, as cited in Paul White, Thomas Huxley: Making the "Man of Science" (2003), 77, footnote. Also quoted in John Lubbock, The Pleasures of Life (1887, 2007), 63.
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So-called psychoanalysis is the occupation of lustful rationalists who trace everything in the world to sexual causes—with the exception of their occupation.
Trans. by Harry Zohn, originally published in Beim Wort genommen (1955). Half-Truths and One-and-a-Half Truths, University of Chicago Press (1990)
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The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.
The Value of Science (1905), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 208.
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The breaking up of the terrestrial globe, this it is we witness. It doubtless began a long time ago, and the brevity of human life enables us to contemplate it without dismay. It is not only in the great mountain ranges that the traces of this process are found. Great segments of the earth's crust have sunk hundreds, in some cases, even thousands, of feet deep, and not the slightest inequality of the surface remains to indicate the fracture; the different nature of the rocks and the discoveries made in mining alone reveal its presence. Time has levelled all.
The Face of the Earth (1904), Vol. 1, 604.
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The footsteps of Nature are to be trac'd, not only in her ordinary course, but when she seems to be put to her shifts, to make many doublings and turnings, and to use some kind of art in endeavouring to avoid our discovery.
Micrographia (1665, reprint 2008), 17.
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The philosophic spirit of inquiry may be traced to brute curiosity, and that to the habit of examining all things in search of food. Artistic genius is an expansion of monkey imitativeness.
In The Martyrdom of Man (14th ed., 1892), 392.
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The preservation of a few samples of undeveloped territory is one of the most clamant issues before us today. Just a few more years of hesitation and the only trace of that wilderness which has exerted such a fundamental influence in molding American character will lie in the musty pages of pioneer books. … To avoid this catastrophe demands immediate action.
…...
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The reputation of science which ought to be the most lasting, as synonymous with truth, is often the least so. One discovery supersedes another; and the progress of light throws the past into obscurity. What is become of the Blacks, the Lavoisiers, the Priestleys, in chemistry? … When any set of men think theirs the only science worth studying, and themselves the only infallible persons in it, it is a sign how frail the traces are of past excellence in it.
Characteristics: In the Manner of Rochefoucault's Maxims (1837), 148-149.
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There is no field of biological inquiry in which the influence of the Origin of Species is not traceable; the foremost men of science in every country are either avowed champions of its leading doctrines, or at any rate abstain from opposing them; a host of young and ardent investigators seek for and find inspiration and guidance in Mr. Darwin’s great work; and the general doctrine of Evolution, to one side of which it gives expression, finds in the phenomena of biology a firm base of operations whence it may conduct its conquest of the whole realm of nature.
From Lecture (19 Mar 1880) delivered at the Royal Institute 'The Coming of Age of The Origin of Species', printed in John Michels (ed.), Science (3 Jul 1880), 1, 15.
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To behold is not necessarily to observe, and the power of comparing and combining is only to be obtained by education. It is much to be regretted that habits of exact observation are not cultivated in our schools; to this deficiency may be traced much of the fallacious reasoning, the false philosophy which prevails.
As quoted in Inaugural Address, Edward C.C. Stanford, 'Glasgow Philosophical Meeting' (8 Dec 1873), The Chemical News and Journal of Physical Science (2 Jan 1874), 7.
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To trace the series of these revolutions, to explain their causes, and thus to connect together all the indications of change that are found in the mineral kingdom, is the proper object of a THEORY OF THE EARTH.
Illustrations of the Huttonian Theory of the Earth (1802), 2.
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Watch the stars, and from them learn. To the Master’s honor all must turn, each in its track, without a sound, forever tracing Newton’s ground.
…...
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We can trace the development of a nervous system, and correlate with it the parallel phenomena of sensation and thought. We see with undoubting certainty that they go hand in hand. But we try to soar in a vacuum the moment we seek to comprehend the connexion between them … Man the object is separated by an impassable gulf from man the subject.
In 'Address Delivered Before The British Association Assembled at Belfast' (19 Aug 1874), in Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 194-195.
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What terrible questions we are learning to ask! The former men believed in magic, by which temples, cities, and men were swallowed up, and all trace of them gone. We are coming on the secret of a magic which sweeps out of men's minds all vestige of theism and beliefs which they and their fathers held and were framed upon.
In 'Illusions', The Atlantic Monthly (Nov 1858), 1, 60.
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When we trace the history of psychology we are led into a labyrinth of fanciful opinions, contradictions, and absurdities intermixed with some truths.
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 35.
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When you do something, you should burn yourself completely, like a good bonfire, leaving no trace of yourself.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 180
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Why it is that animals, instead of developing in a simple and straightforward way, undergo in the course of their growth a series of complicated changes, during which they often acquire organs which have no function, and which, after remaining visible for a short time, disappear without leaving a trace ... To the Darwinian, the explanation of such facts is obvious. The stage when the tadpole breathes by gills is a repetition of the stage when the ancestors of the frog had not advanced in the scale of development beyond a fish.
In The Works of Francis Maitland Balfour (1885), Vol. 1, 702.
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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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