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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Scarcely Quotes (74 quotes)

1839—The fermentation satire
THE MYSTERY OF ALCOHOLIC FERMENTATION RESOLVED
(Preliminary Report by Letter) Schwindler
I am about to develop a new theory of wine fermentation … Depending on the weight, these seeds carry fermentation to completion somewhat less than as in the beginning, which is understandable … I shall develop a new theory of wine fermentation [showing] what simple means Nature employs in creating the most amazing phenomena. I owe it to the use of an excellent microscope designed by Pistorius.
When brewer’s yeast is mixed with water the microscope reveals that the yeast dissolves into endless small balls, which are scarcely 1/800th of a line in diameter … If these small balls are placed in sugar water, it can be seen that they consist of the eggs of animals. As they expand, they burst, and from them develop small creatures that multiply with unbelievable rapidity in a most unheard of way. The form of these animals differs from all of the 600 types described up until now. They possess the shape of a Beinsdorff still (without the cooling apparatus). The head of the tube is a sort of proboscis, the inside of which is filled with fine bristles 1/2000th of a line long. Teeth and eyes are not discernible; however, a stomach, intestinal canal, anus (a rose red dot), and organs for secretion of urine are plainly discernible. From the moment they are released from the egg one can see these animals swallow the sugar from the solution and pass it to the stomach. It is digested immediately, a process recognized easily by the resultant evacuation of excrements. In a word, these infusors eat sugar, evacuate ethyl alcohol from the intestinal canal, and carbon dioxide from the urinary organs. The bladder, in the filled state, has the form of a champagne bottle; when empty, it is a small button … As soon as the animals find no more sugar present, they eat each other up, which occurs through a peculiar manipulation; everything is digested down to the eggs which pass unchanged through the intestinal canal. Finally, one again fermentable yeast, namely the seed of the animals, which remain over.
In 'Das entriithselle Geheimiss der geisligen Giihrung', Annalen der Pharmacie und Chemie (1839), 29, 100-104; adapted from English translalion by Ralph E. Oesper, The Human Side of Scientists (1975), 203-205.
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A body of work such as Pasteur’s is inconceivable in our time: no man would be given a chance to create a whole science. Nowadays a path is scarcely opened up when the crowd begins to pour in.
Pensées d’un Biologiste (1939). Translated in The Substance of Man (1962), Chap. 6.
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A scientific writer can scarcely encounter anything more undesirable than, after completing a work, to have one of the foundations shaken. I became aware of this situation through a letter from Mr. Bertrand Russell as the printing of this volume neared completion.
In Epilog, Grundgestze der Arithmetic (1903), Vol. 2, 253. Russell wrote in 1901, just as Frege was about to publish Volume 2 of his last major work. English translation by Webmaster using Google translate and online dictionaries, from the original German: “Einem wissenschaftlichen Schriftsteller kann kaum etwas Unerwünschteres begegnen, als dass ihm nach Vollendung einer Arbeit eine der Grundlagen seines Baues erschüttert wird. In diese Lage wurde ich durch einen Brief des Herrn Bertrand Russell versetzt, als der Druck dieses Bandes sich seinem Ende näherte.” The translation in John E. Hopcroft, 'Turing Machines', Scientific American (May 1984), 250, No. 5, 95, gives: “A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.”
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A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the subatomic energy which, it is known exists abundantly in all matter; we sometimes dream that man will one day learn how to release it and use it for his service. The store is well nigh inexhaustible, if only it could be tapped. There is sufficient in the Sun to maintain its output of heat for 15 billion years.
Address to the British Association in Cardiff, (24 Aug 1920), in Observatory (1920), 43 353. Reprinted in Foreward to Arthur S. Eddington, The Internal Constitution of the Stars (1926, 1988), x.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.
In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.
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After having produced aquatic animals of all ranks and having caused extensive variations in them by the different environments provided by the waters, nature led them little by little to the habit of living in the air, first by the water's edge and afterwards on all the dry parts of the globe. These animals have in course of time been profoundly altered by such novel conditions; which so greatly influenced their habits and organs that the regular gradation which they should have exhibited in complexity of organisation is often scarcely recognisable.
Hydrogéologie (1802), trans. A. V. Carozzi (1964), 69-70.
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All things on the earth are the result of chemical combination. The operation by which the commingling of molecules and the interchange of atoms take place we can imitate in our laboratories; but in nature they proceed by slow degrees, and, in general, in our hands they are distinguished by suddenness of action. In nature chemical power is distributed over a long period of time, and the process of change is scarcely to be observed. By acts we concentrate chemical force, and expend it in producing a change which occupies but a few hours at most.
In chapter 'Chemical Forces', The Poetry of Science: Or, Studies of the Physical Phenomena of Nature (1848), 235-236. Charles Dicken used this quote, with his own sub-head of 'Relative Importance Of Time To Man And Nature', to conclude his review of the book, published in The Examiner (1848).
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As an antiquary of a new order, I have been obliged to learn the art of deciphering and restoring these remains, of discovering and bringing together, in their primitive arrangement, the scattered and mutilated fragments of which they are composed, of reproducing in all their original proportions and characters, the animals to which these fragments formerly belonged, and then of comparing them with those animals which still live on the surface of the earth; an art which is almost unknown, and which presupposes, what had scarcely been obtained before, an acquaintance with those laws which regulate the coexistence of the forms by which the different parts of organized being are distinguished.
'Preliminary discourse', to Recherches sur les Ossemens Fossiles (1812), trans. R. Kerr Essay on the Theory of the Earth (1813), 1-2.
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But if you have seen the soil of India with your own eyes and meditate on its nature - if you consider the rounded stones found in the earth however deeply you dig, stones that are huge near the mountains and where the rivers have a violent current; stones that are of smaller size at greater distance from the mountains, and where the streams flow more slowly; stones that appear pulverised in the shape of sand where the streams begin to stagnate near their mouths and near the sea - if you consider all this, you could scarcely help thinking that India has once been a sea which by degrees has been filled up by the alluvium of the streams.
Alberuni's India, trans. E. C. Sachau (1888), Vol. 1, 198.
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Eventually, we reach … the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial.
In Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202. The lecture series was delivered at Yale University in Fall 1935. Part of a longer quote on this page that begins: “The explorations of space…”.
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Facts may belong to the past history of mankind, to the social statistics of our great cities, to the atmosphere of the most distant stars, to the digestive organs of a worm, or to the life of a scarcely visible bacillus. It is not the facts themselves which form science, but the method in which they are dealt with.
From The Grammar of Science (1892), 15.
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Generations to come, it may be, will scarcely believe that such a one as this ever in flesh and blood walked upon this earth.
…...
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Given one has before oneself a strong, healthy, youth rich in spirited blood and a powerless, weak, cachectic old man scarcely capable of breathing. If now the physician wishes to practise the rejuvenating art on the latter, he should make silver tubes which fit into each other: open then the artery of the healthy person and introduce one of the tubes into it and fasten it into the artery; thereupon he opens also the artery of the ill person...
[First detailed description of blood transfusion (1615)]
In N.S.R. Maluf, 'History of Blood Transfusion', Journal of the History of Medicine and Allied Sciences (1954), 9, No. 1, 59.
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I have never had any student or pupil under me to aid me with assistance; but have always prepared and made my experiments with my own hands, working & thinking at the same time. I do not think I could work in company, or think aloud, or explain my thoughts at the time. Sometimes I and my assistant have been in the Laboratory for hours & days together, he preparing some lecture apparatus or cleaning up, & scarcely a word has passed between us; — all this being a consequence of the solitary & isolated system of investigation; in contradistinction to that pursued by a Professor with his aids & pupils as in your Universities.
Letter to C. Ransteed, 16 Dec 1857. In L. Pearce Williams (ed.), The Selected Correspondence of Michael Faraday (1971), Vol. 2, 888.
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I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the “Law of Frequency of Error.” The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshaled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.
In Natural Inheritance (1894), 66.
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I need scarcely say that the beginning and maintenance of life on earth is absolutely and infinitely beyond the range of sound speculation in dynamical science.
In lecture, 'The Sun's Heat' delivered to the Friday Evening Discourse in Physical Science at the Royal Institution in London. Collected in Popular Lectures and Addresses (1889), Vol. 1, 415.
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I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
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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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I well know what a spendidly great difference there is [between] a man and a bestia when I look at them from a point of view of morality. Man is the animal which the Creator has seen fit to honor with such a magnificent mind and has condescended to adopt as his favorite and for which he has prepared a nobler life; indeed, sent out for its salvation his only son; but all this belongs to another forum; it behooves me like a cobbler to stick to my last, in my own workshop, and as a naturalist to consider man and his body, for I know scarcely one feature by which man can be distinguished from apes, if it be not that all the apes have a gap between their fangs and their other teeth, which will be shown by the results of further investigation.
T. Fredbärj (ed.), Menniskans Cousiner (Valda Avhandlingar av Carl von Linné nr, 21) (1955), 4. Trans. Gunnar Broberg, 'Linnaeus's Classification of Man', in Tore Frängsmyr (ed.), Linnaeus: The Man and his Work (1983), 167.
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I would clarify that by ‘animal’ I understand a being that has feeling and that is capable of exercising life functions through a principle called soul; that the soul uses the body's organs, which are true machines, by virtue of its being the principal cause of the action of each of the machine's parts; and that although the placement that these parts have with respect to one another does scarcely anything else through the soul's mediation than what it does in pure machines, the entire machine nonetheless needs to be activated and guided by the soul in the same way as an organ, which, although capable of rendering different sounds through the placement of the parts of which it is composed, nonetheless never does so except through the guidance of the organist.
'La Mechanique des Animaux', in Oeuvres Diverses de Physique et de Mechanique (1721), Vol. 1, 329. Quoted in Jacques Roger, Keith R. Benson (ed.), Robert Ellrich (trans.), The Life Sciences in Eighteenth-Century French Thought, (1997), 273-4.
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If we survey the mathematical works of Sylvester, we recognize indeed a considerable abundance, but in contradistinction to Cayley—not a versatility toward separate fields, but, with few exceptions—a confinement to arithmetic-algebraic branches. …
The concept of Function of a continuous variable, the fundamental concept of modern mathematics, plays no role, is indeed scarcely mentioned in the entire work of Sylvester—Sylvester was combinatorist [combinatoriker].
In Mathematische Annalen (1898), Bd.50, 134-135. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 173.
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In all works on Natural History, we constantly find details of the marvellous adaptation of animals to their food, their habits, and the localities in which they are found. But naturalists are now beginning to look beyond this, and to see that there must be some other principle regulating the infinitely varied forms of animal life. It must strike every one, that the numbers of birds and insects of different groups having scarcely any resemblance to each other, which yet feed on the same food and inhabit the same localities, cannot have been so differently constructed and adorned for that purpose alone. Thus the goat-suckers, the swallows, the tyrant fly-catchers, and the jacamars, all use the same kind ‘Of food, and procure it in the same manner: they all capture insects on the wing, yet how entirely different is the structure and the whole appearance of these birds!
In A Narrative of Travels on the Amazon and Rio Negro (1853), 83-84.
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In assessing Audubon, whose firm grip on the popular imagination has scarcely lessened since 1826, we must as historians of science seriously ask who would remember him if he had not been an artist of great imagination and flair. ... The chances seem to be very poor that had he not been an artist, he would be an unlikely candidate for a dictionary of scientific biography, if remembered to science at all.
In Charles Coulston Gillespie (ed.), Dictionary of Scientific Biography (1972), Vol. 1, 331.
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In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science, whatever the matter may be.
Often seen quoted in a condensed form: If you cannot measure it, then it is not science.
From lecture to the Institution of Civil Engineers, London (3 May 1883), 'Electrical Units of Measurement', Popular Lectures and Addresses (1889), Vol. 1, 80-81.
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In spite of what moralists say, the, animals are scarcely less wicked or less unhappy than we are ourselves. The arrogance of the strong, the servility of the weak, low rapacity, ephemeral pleasure purchased by great effort, death preceded by long suffering, all belong to the animals as they do to men.
Recueil des Éloges Historiques 1819-27, Vol. 1, 91.
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In the course of centuries the naïve self-love of men has had to submit to two major blows at the hands of science. The first was when they learnt that our earth was not the centre of the universe but only a tiny fragment of a cosmic system of scarcely imaginable vastness... the second blow fell when biological research destroyed man's supposedly privileged place in creation and proved his descent from the animal kingdom and his ineradicable animal nature… But human megalomania will have suffered its third and most wounding blow from the psychological research of the present time which seeks to prove to the ego that it is not even master in its own house, but must content itself with scanty information of what is going on unconsciously in its mind.
Introductory Lectures on Psychoanalyis (1916), in James Strachey (ed.), The Standard Edition of the Complete Psychological Works of Sigmund Freud (1963), Vol. 16, 284-5.
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In the whole of geophysics there is probably hardly another law of such clarity and reliability as this—that there are two preferential levels for the world’s surface which occur in alternation side by side and are represented by the continents and the ocean floors, respectively. It is therefore very surprising that scarcely anyone has tried to explain this law.
In The Origins of Continents and Oceans (4th ed. 1929), trans. John Biram (1966), 37.
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It can hardly be pressed forcibly enough on the attention of the student of nature, that there is scarcely any natural phenomenon which can be fully and completely explained, in all its circumstances, without a union of several, perhaps of all, the sciences.
Quoted in John Lubbock, The Pleasures of Life (Appleton, 1887), 182.
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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 most interesting to observe into how small a field the whole of the mysteries of nature thus ultimately resolve themselves. The inorganic has one final comprehensive law, GRAVITATION. The organic, the other great department of mundane things, rests in like manner on one law, and that is,—DEVELOPMENT. Nor may even these be after all twain, but only branches of one still more comprehensive law, the expression of that unity which man's wit can scarcely separate from Deity itself.
Vestiges of the Natural History of Creation (1844), 360.
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It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
Letter to Farkas Wolfgang Bolyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
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It must ... be admitted that very simple relations ... exist between the volumes of gaseous substances and the numbers of simple or compound molecules which form them. The first hypothesis to present itself in this connection, and apparently even the only admissible one, is the supposition that the number of integral molecules in any gases is always the same for equal volumes, or always proportional to the volumes. Indeed, if we were to suppose that the number of molecules contained in a given volume were different for different gases, it would scarcely be possible to conceive that the law regulating the distance of molecules could give in all cases relations so simple as those which the facts just detailed compel us to acknowledge between the volume and the number of molecules.
'Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in which they enter into these Compounds', Journal de Physique, 1811, 73, 58-76. In Foundations of the Molecular Theory; Alembic Club Reprints, Number 4 (1923), 28-9.
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It need scarcely be pointed out that with such a mechanism complete isolation of portion of a species should result relatively rapidly in specific differentiation, and one that is not necessarily adaptive. The effective inter­group competition leading to adaptive advance may be between species rather than races. Such isolation is doubtless usually geographic in character at the outset but may be clinched by the development of hybrid sterility. The usual difference of the chromosome complements of related species puts the importance of chromosome aberration as an evolutionary process beyond question, but, as I see it, this importance is not in the character differences which they bring (slight in balanced types), but rather in leading to the sterility of hybrids and thus making permanent the isolation of two groups.
How far do the observations of actual species and their subdivisions conform to this picture? This is naturally too large a subject for more than a few suggestions.
That evolution involves non-adaptive differentiation to a large extent at the subspecies and even the species level is indicated by the kinds of differences by which such groups are actually distinguished by systematics. It is only at the subfamily and family levels that clear-cut adaptive differences become the rule. The principal evolutionary mechanism in the origin of species must thus be an essentially nonadaptive one.
In Proceedings of the Sixth International Congress of Genetics: Ithaca, New York, 1932 (1932) Vol. 1, 363-364.
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It needs scarcely be pointed out that in placing Mathematics at the head of Positive Philosophy, we are only extending the application of the principle which has governed our whole Classification. We are simply carrying back our principle to its first manifestation. Geometrical and Mechanical phenomena are the most general, the most simple, the most abstract of all,— the most irreducible to others, the most independent of them; serving, in fact, as a basis to all others. It follows that the study of them is an indispensable preliminary to that of all others. Therefore must Mathematics hold the first place in the hierarchy of the sciences, and be the point of departure of all Education whether general or special.
In Auguste Comte and Harriet Martineau (trans.), The Positive Philosophy (1858), Introduction, Chap. 2, 50.
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Just now nuclear physicists are writing a great deal about hypothetical particles called neutrinos supposed to account for certain peculiar facts observed in β-ray disintegration. We can perhaps best describe the neutrinos as little bits of spin-energy that have got detached. I am not much impressed by the neutrino theory. In an ordinary way I might say that I do not believe in neutrinos… But I have to reflect that a physicist may be an artist, and you never know where you are with artists. My old-fashioned kind of disbelief in neutrinos is scarcely enough. Dare I say that experimental physicists will not have sufficient ingenuity to make neutrinos? Whatever I may think, I am not going to be lured into a wager against the skill of experimenters under the impression that it is a wager against the truth of a theory. If they succeed in making neutrinos, perhaps even in developing industrial applications of them, I suppose I shall have to believe—though I may feel that they have not been playing quite fair.
From Tarner Lecture, 'Discovery or Manufacture?' (1938), in The Philosophy of Physical Science (1939, 2012), 112.
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Life, therefore, has been often disturbed on this earth by terrible events—calamities which, at their commencement, have perhaps moved and overturned to a great depth the entire outer crust of the globe, but which, since these first commotions, have uniformly acted at a less depth and less generally. Numberless living beings have been the victims of these catastrophes; some have been destroyed by sudden inundations, others have been laid dry in consequence of the bottom of the seas being instantaneously elevated. Their races even have become extinct, and have left no memorial of them except some small fragments which the naturalist can scarcely recognise.
'Preliminary discourse', to Recherches sur les Ossemens Fossiles (1812), trans. R. Kerr Essay on the Theory of the Earth (1813), 16-7.
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Mathematical studies … when combined, as they now generally are, with a taste for physical science, enlarge infinitely our views of the wisdom and power displayed in the universe. The very intimate connexion indeed, which, since the date of the Newtonian philosophy, has existed between the different branches of mathematical and physical knowledge, renders such a character as that of a mere mathematician a very rare and scarcely possible occurrence.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 3, 184.
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Medicine is essentially a learned profession. Its literature is ancient, and connects it with the most learned periods of antiquity; and its terminology continues to be Greek or Latin. You cannot name a part of the body, and scarcely a disease, without the use of a classical term. Every structure bears upon it the impress of learning, and is a silent appeal to the student to cultivate an acquaintance with the sources from which the nomenclature of his profession is derived.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 11.
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Most American citizens think that life without the telephone is scarcely worth living. The American public telephone system is therefore enormous. Moreover the system belongs to an organization, the Bell companies, which can both control it and make the equipment needed. There is no surer way of getting efficient functional design than having equipment designed by an organization which is going to have to use it. Humans who would have to live with their own mistakes tend to think twice and to make fewer mistakes.
In 'Musical Acoustics Today', New Scientist (1 Nov 1962), 16 No. 311, 256.
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No place affords a more striking conviction of the vanity of human hopes than a publick library; for who can see the wall crouded on every side by mighty volumes, the works of laborious meditation, and accurate inquiry, now scarcely known but by the catalogue, and preserved only to encrease the pomp of learning, without considering how many hours have been wasted in vain endeavours, how often imagination has anticipated the praises of futurity, how many statues have risen to the eye of vanity, how many ideal converts have elevated zeal, how often wit has exulted in the eternal infamy of his antagonists, and dogmatism has delighted in the gradual advances of his authority, the immutability of his decrees, and the perpetuity of his power.
Non unquam dedit
Documenta fors majora, quam fragili loco
Starent superbi.

Seneca, Troades, II, 4-6
Insulting chance ne'er call'd with louder voice,
On swelling mortals to be proud no more.
Of the innumerable authors whose performances are thus treasured up in magnificent obscurity, most are forgotten, because they never deserved to be remembered, and owed the honours which they have once obtained, not to judgment or to genius, to labour or to art, but to the prejudice of faction, the stratagem of intrigue, or the servility of adulation.
Nothing is more common than to find men whose works are now totally neglected, mentioned with praises by their contemporaries, as the oracles of their age, and the legislators of science. Curiosity is naturally excited, their volumes after long enquiry are found, but seldom reward the labour of the search. Every period of time has produced these bubbles of artificial fame, which are kept up a while by the breath of fashion and then break at once and are annihilated. The learned often bewail the loss of ancient writers whose characters have survived their works; but perhaps if we could now retrieve them we should find them only the Granvilles, Montagus, Stepneys, and Sheffields of their time, and wonder by what infatuation or caprice they could be raised to notice.
It cannot, however, be denied, that many have sunk into oblivion, whom it were unjust to number with this despicable class. Various kinds of literary fame seem destined to various measures of duration. Some spread into exuberance with a very speedy growth, but soon wither and decay; some rise more slowly, but last long. Parnassus has its flowers of transient fragrance as well as its oaks of towering height, and its laurels of eternal verdure.
The Rambler, Number 106, 23 Mar 1751. In W. J. Bate and Albrecht B. Strauss (eds.), The Rambler (1969), Vol. 2, 200-1.
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Nobody since Newton has been able to use geometrical methods to the same extent for the like purposes; and as we read the Principia we feel as when we are in an ancient armoury where the weapons are of gigantic size; and as we look at them we marvel what manner of man he was who could use as a weapon what we can scarcely lift as a burthen.
From Speech delivered at the Dejeuner, after the Inauguration of the statue of Isaac Newton at Grantham. Collected in Edmund Fillingham King, A biographical sketch of Sir Isaac Newton (1858), 105.
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Nothing, however, is more common than energy in money-making, quite independent of any higher object than its accumulation. A man who devotes himself to this pursuit, body and soul, can scarcely fail to become rich. Very little brains will do; spend less than you earn; add guinea to guinea; scrape and save; and the pile of gold will gradually rise.
In Self-help: With Illustrations of Character and Conduct (1859, 1861), 301-302.
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Now this circumscribed power, which we have scarcely examined, scarcely studied, this power to whose actions we nearly always attribute an intention and a goal, this power, finally, that always does necessarily the same things in the same circumstances and nevertheless does so many and such admirable ones, is what we call 'nature' .
Histoire Naturelle des Animaux sans Vertèbres (1815), Vol. 1, 312, trans. M. H. Shank and quoted in Madeleine Barthélemy-Madaule, Lamarck the Mythical Precursor: A Study of the Relations between Science and Ideology (1982), 28-9.
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On one occasion, when he was giving a dinner to some friends at the university, he left the table to get them a bottle of wine; but, on his way to the cellar, he fell into reflection, forgot his errand and his company, went to his chamber, put on his surplice, and proceeded to the chapel. Sometimes he would go into the street half dressed, and on discovering his condition, run back in great haste, much abashed. Often, while strolling in his garden, he would suddenly stop, and then run rapidly to his room, and begin to write, standing, on the first piece of paper that presented itself. Intending to dine in the public hall, he would go out in a brown study, take the wrong turn, walk a while, and then return to his room, having totally forgotten the dinner. Once having dismounted from his horse to lead him up a hill, the horse slipped his head out of the bridle; but Newton, oblivious, never discovered it till, on reaching a tollgate at the top of the hill, he turned to remount and perceived that the bridle which he held in his hand had no horse attached to it. His secretary records that his forgetfulness of his dinner was an excellent thing for his old housekeeper, who “sometimes found both dinner and supper scarcely tasted of, which the old woman has very pleasantly and mumpingly gone away with”. On getting out of bed in the morning, he has been discovered to sit on his bedside for hours without dressing himself, utterly absorbed in thought.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 257.
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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Professor Tyndall once said the finest inspiration he ever received was from an old man who could scarcely read. This man acted as his servant. Each morning the old man would knock on the door of the scientist and call, “Arise, Sir: it is near seven o'clock and you have great work to do today.”
A Thousand & One Epigrams: Selected from the Writings of Elbert Hubbard (1911), 72.
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Religious creeds are a great obstacle to any full sympathy between the outlook of the scientist and the outlook which religion is so often supposed to require … The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our own pet theory happened to be included, or if the list were brought up to date every few years. We should say that the students cannot possibly realise the intention of scientific training if they are taught to look on these results as things to be recited and subscribed to. Science may fall short of its ideal, and although the peril scarcely takes this extreme form, it is not always easy, particularly in popular science, to maintain our stand against creed and dogma.
Swarthmore Lecture (1929), Science and the Unseen World (1929), 54-56.
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Scarcely any attempt is entirely a failure; scarcely any theory, the result of steady thought, is altogether false; no tempting form of Error is without some latent charm derived from Truth.
In 'Lecture 7', Lectures on the History of Moral Philosophy in England (1852), 101.
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Scarcely anyone who comprehends this theory can escape its magic.
Quoted, without citation, in Norman K. Glendenning, Our Place in the Universe (2007), 107. Webmaster has not found any other source for this quote, and cautions doubt about its authenticity. If you know a primary source, please contact Webmaster.
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Science in England is not a profession: its cultivators are scarcely recognised even as a class. Our language itself contains no single term by which their occupation can be expressed. We borrow a foreign word [Savant] from another country whose high ambition it is to advance science, and whose deeper policy, in accord with more generous feelings, gives to the intellectual labourer reward and honour, in return for services which crown the nation with imperishable renown, and ultimately enrich the human race.
The Exposition of 1851: Or the Views of Industry, Science and Government of England (1851), 171.
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Scientific knowledge scarcely exists amongst the higher classes of society. The discussion in the Houses of Lords or of Commons, which arise on the occurrence of any subjects connected with science, sufficiently prove this fact…
In Reflections on the Decline of Science in England (1830), 8.
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Sheppey hath long been noted for producing large quantities of Sheep (whence probably its name is derived) as well as Corn; and exhibits to the Curious Naturalist a most desirable Spot, by affording many rare Plants, and more especially in the of its Northern Cliffs, so great a Quantity and Variety of Fossils, both native and extraneous are scarcely to be paralleled. These Cliffs length about six miles; Minster, Shurland and Warden are the Manors to which they appertain, the more elevated parts whereof reach about thirds of their extension, and are at the very highest of them not less than fifty yards perpendicular height above the Beach and Shore.
Quoted in Augustus A. Daly, History of the Isle of Sheppey (1975), 247.
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Skepticism is a useful tool of the inquisitive mind, but it is scarcely a method of investigation.
(1928). As quoted, without source, in James P. Vanyo, 'The Legal System: Can it be Analyzed to Suit the Scientist?', Jurimetric Journal (Winter 1973), 14, No. 2, 106.
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Such is the character of mathematics in its profounder depths and in its higher and remoter zones that it is well nigh impossible to convey to one who has not devoted years to its exploration a just impression of the scope and magnitude of the existing body of the science. An imagination formed by other disciplines and accustomed to the interests of another field may scarcely receive suddenly an apocalyptic vision of that infinite interior world. But how amazing and how edifying were such a revelation, if it only could be made.
In Lectures on Science, Philosophy and Art (1908), 6.
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Superstring theories provide a framework in which the force of gravity may be united with the other three forces in nature: the weak, electromagnetic and strong forces. Recent progress has shown that the most promising superstring theories follow from a single theory. For the last generation, physicists have studied five string theories and one close cousin. Recently it has become clear that these five or six theories are different limiting cases of one theory which, though still scarcely understood, is the candidate for superunification of the forces of nature.
His synopsis of lecture, University of Maryland Distinguished Lecture Series (2 Mar 1998), on web page.
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The Animal and Vegetable Kingdoms are to nearly join’d, that if you will take the lowest of one, and the highest of the other, there will scarce be perceived any great difference between them.
In An Essay Concerning Humane Understanding (1689, 1706, 5th ed.), 381.
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The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.
Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 350.
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The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors, so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.
…...
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The explorations of space end on a note of uncertainty. And necessarily so. … We know our immediate neighborhood rather intimately. With increasing distance our knowledge fades, and fades rapidly. Eventually, we reach the dim boundary—the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial. The search will continue. Not until the empirical resources are exhausted, need we pass on to the dreamy realms of speculation.
From conclusion of The Silliman Memorial Lectures Series delivered at Yale University (Fall 1935). Collected in The Realm of the Nebulae: The Silliman Memorial Lectures Series (1936), 201-202.
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The great basic thought that the world is not to be comprehended as a complex of ready-made things, but as a complex of processes, in which the things apparently stable no less than their mind-images in our heads, the concepts, go through an uninterrupted change of coming into being and passing away, in which, in spite of all seeming accidents and of all temporary retrogression, a progressive development asserts itself in the end—this great fundamental thought has, especially since the time of Hegel, so thoroughly permeated ordinary consciousness that in this generality it is scarcely ever contradicted.
Ludwig Feuerbach and the Outcome of Classical German Philosophy (1886). C. P. Dutt (ed.) (1934), 54.
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The large collection of problems which our modern Cambridge books supply will be found to be almost an exclusive peculiarity of these books; such collections scarcely exist in foreign treatises on mathematics, nor even in English treatises of an earlier date. This fact shows, I think, that a knowledge of mathematics may be gained without the perpetual working of examples. … Do not trouble yourselves with the examples, make it your main business, I might almost say your exclusive business, to understand the text of your author.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 74.
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The means by which I preserve my own health are, temperance, early rising, and spunging the body every morning with cold water, a practice I have pursued for thirty years ; and though I go from this heated theatre into the squares of the Hospital, in the severest winter nights, with merely silk stockings on my legs, yet I scarcely ever have a cold...
'Lecture 3, Treatment of Inflammation', The Lectures of Sir Astley Cooper (1825), Vol. 1, 58.Lectures on surgery, Lect. 3.
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The only sure foundations of medicine are, an intimate knowledge of the human body, and observation on the effects of medicinal substances on that. The anatomical and clinical schools, therefore, are those in which the young physician should be formed. If he enters with innocence that of the theory of medicine, it is scarcely possible he should come out untainted with error. His mind must be strong indeed, if, rising above juvenile credulity, it can maintain a wise infidelity against the authority of his instructors, and the bewitching delusions of their theories.
In letter to Caspar Wistar (21 Jun 1807), collected in Thomas Jefferson Randolph (ed.), Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson (1829), Vol. 4, 93.
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The operations of the universe are unlimited, and in the great book of nature, man has scarcely read more than the title page or the preface.
Address (2 Jun 1874) at the Laying of the Cornerstone of the American Museum of Natural History, in Fifth and Sixth Annual Reports of the American Museum of Natural History (1 Dec 1874), 49.
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The work … was … so blinding that I could scarcely see afterwards, and the difficulty was increased by the fact that my microscope was almost worn out, the screws being rusted with sweat from my hands and forehead, and my only remaining eye-piece being cracked… Fortunately invaluable oil-imraersion object-glass remained good.
From 'Researches on Malaria', Journal of the Raoyal Army Medical Corps (May 1905), 4, No. 5, 549.
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Then if the first argument remains secure (for nobody will produce a neater one, than the length of the periodic time is a measure of the size of the spheres), the order of the orbits follows this sequence, beginning from the highest: The first and highest of all is the sphere of the fixed stars, which contains itself and all things, and is therefore motionless. It is the location of the universe, to which the motion and position of all the remaining stars is referred. For though some consider that it also changes in some respect, we shall assign another cause for its appearing to do so in our deduction of the Earth's motion. There follows Saturn, the first of the wandering stars, which completes its circuit in thirty years. After it comes Jupiter which moves in a twelve-year long revolution. Next is Mars, which goes round biennially. An annual revolution holds the fourth place, in which as we have said is contained the Earth along with the lunar sphere which is like an epicycle. In fifth place Venus returns every nine months. Lastly, Mercury holds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun. For who in this most beautiful of temples would put this lamp in any other or better place than the one from which it can illuminate everything at the same time? Aptly indeed is he named by some the lantern of the universe, by others the mind, by others the ruler. Trismegistus called him the visible God, Sophocles' Electra, the watcher over all things. Thus indeed the Sun as if seated on a royal throne governs his household of Stars as they circle around him. Earth also is by no means cheated of the Moon's attendance, but as Aristotle says in his book On Animals the Moon has the closest affinity with the Earth. Meanwhile the Earth conceives from the Sun, and is made pregnant with annual offspring. We find, then, in this arrangement the marvellous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultation by the Sun and re-appearance. Indeed Mars in particular at the time when it is visible throughout the night seems to equal Jupiter in size, though marked out by its reddish colour; yet it is scarcely distinguishable among stars of the second magnitude, though recognized by those who track it with careful attention. All these phenomena proceed from the same course, which lies in the motion of the Earth. But the fact that none of these phenomena appears in the fixed stars shows their immense elevation, which makes even the circle of their annual motion, or apparent motion, vanish from our eyes.
'Book One. Chapter X. The Order of the Heavenly Spheres', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 49-51.
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These facts shaw that mitosis is due to the co-ordinate play of an extremely complex system of forces which are as yet scarcely comprehended. Its purpose is, however, as obvious as its physiological explanation is difficult. It is the end of mitosis to divide every part of the chromatin of the mother-cell equally between the daughter-nuclei. All the other operations are tributary to this. We may therefore regard the mitotic figure as essentially an apparatus for the distribution of the hereditary substance, and in this sense as the especial instrument of inheritance.
The Cell in Development and Inheritance (1896), 86.
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We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.
'On Physical Lines of Force' (1862). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 500.
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We should scarcely be excused in concluding this essay without calling the reader's attention to the beneficent and wise laws established by the author of nature to provide for the various exigencies of the sublunary creation, and to make the several parts dependent upon each other, so as to form one well-regulated system or whole.
'Experiments and Observations to Determine whether the Quantity of Rain and Dew is Equal to the Quantity of Water carried off by the Rivers and Raised by Evaporation', Memoirs Manchester Literary and Philosophical Society, 1803, 5, part 2, 372.
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What has been done is little—scarcely a beginning; yet it is much in comparison with the total blank of a century past. And our knowledge will, we are easily persuaded, appear in turn the merest ignorance to those who come after us. Yet it is not to be despised, since by it we reach up groping to touch the hem of the garment of the Most High.
In A Popular History of Astronomy During the Nineteenth Century (1893), 528. Also quoted in Carl Sagan, Broca's Brain (1986), 240.
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Whilst I am writing to a Philosopher and a Friend, I can scarcely forget that I am also writing to the greatest Statesman of the present, or perhaps of any century, who spread the happy contagion of Liberty among his countrymen.
Letter to Benjamin Franklin, 29 May 1787. Quoted In Desmond King-Hele (ed.), The Letters of Erasmus Darwin (1981), 166.
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[A crowd] thinks in images, and the image itself calls up a series of other images, having no logical connection with the first … A crowd scarcely distinguishes between the subjective and the objective. It accepts as real the images invoked in its mind, though they most often have only a very distant relation with the observed facts. * * * Crowds being only capable of thinking in images are only to be impressed by images. It is only images that terrify or attract them and become motives of action.
From Psychologie des Foules (1895), 29 & 56. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap 2, 22 & last sentence, 55. Original French text: “[La foule] pense par images, et l’image évoquée en évoque elle-même une série d’autres n’ayant aucun lien logique avec la première. … La foule ne sépare guère le subjectif de l’objectif. Elle admet comme réelles les images évoquées dans son esprit, et qui le plus souvent n’ont qu’une parenté lointaine avec le fait observé. * * * Les foules, ne pouvant penser que par images,ne se laissent impressionner que par des images. Seules les images les terrifient ou les séduisent, et deviennent des mobiles d’action.”
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[I can] scarcely write upon mathematics or mathematicians. Oh for words to express my abomination of the science.
Lamenting mathematics whilst an undergraduate at Cambridge, 1818.
Quoted in John Gascoigne, Cambridge in the Age of Enlightenment (1989), 272.
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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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