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Home > Category Index for Science Quotations > Category Index S > Category: Scope

Scope Quotes (45 quotes)

A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.
Science and the Common Understanding (1954), 53-4.
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As Karl Marx once noted: “Hegel remarks somewhere that all great, world-historical facts and personages occur, as it were, twice. He forgot to add: the first time as tragedy, the second as farce.” William Jennings Bryan and the Scopes trial was a tragedy. The creationists and intelligent design theorists are a farce.
In '75 Years and Still No Peace'. Humanist (Sep 2000)
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Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.
In Proceedings of London Royal Society (1895), 58, 11-12.
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Coolidge is a better example of evolution than either Bryan or Darrow, for he knows when not to talk, which is the biggest asset the monkey possesses over the human.
[Referring to the Scopes trial, with Darrow defending a teacher being prosecuted for teaching evolution in the state of Tennessee.]
'Rogers Thesaurus'. Saturday Review (25 Aug 1962). In Will Rogers' Weekly Articles (1981), Vol. 2, 66.
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Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer. This was true of electron theory—perhaps some readers will remember a book called The Electrical Theory of the Universe by de Tunzelman. It is true of general relativity theory with its belief that we can formulate a mathematical scheme that will extrapolate to all past and future time and the unfathomed depths of space. It has been true of wave mechanics, with its first enthusiastic claim a brief ten years ago that no problem had successfully resisted its attack provided the attack was properly made, and now the disillusionment of age when confronted by the problems of the proton and the neutron. When will we learn that logic, mathematics, physical theory, are all only inventions for formulating in compact and manageable form what we already know, like all inventions do not achieve complete success in accomplishing what they were designed to do, much less complete success in fields beyond the scope of the original design, and that our only justification for hoping to penetrate at all into the unknown with these inventions is our past experience that sometimes we have been fortunate enough to be able to push on a short distance by acquired momentum.
The Nature of Physical Theory (1936), 136.
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He leads a new crusade, his bald head glistening... One somehow pities him, despite his so palpable imbecilities... But let no one, laughing at him, underestimate the magic that lies in his black, malignant eye, his frayed but still eloquent voice. He can shake and inflame these poor ignoramuses as no other man among us...
[Describing William Jennings Bryan, orator, at the Scopes Monkey Trial.]
Henry Louis Mencken and S.T. Joshi (ed.), H.L. Mencken on Religion (2002), 18.
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I am not insensible to natural beauty, but my emotional joys center on the improbable yet sometimes wondrous works of that tiny and accidental evolutionary twig called Homo sapiens. And I find, among these works, nothing more noble than the history of our struggle to understand nature—a majestic entity of such vast spatial and temporal scope that she cannot care much for a little mammalian afterthought with a curious evolutionary invention, even if that invention has, for the first time in so me four billion years of life on earth, produced recursion as a creature reflects back upon its own production and evolution. Thus, I love nature primarily for the puzzles and intellectual delights that she offers to the first organ capable of such curious contemplation.
…...
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I believed that, instead of the multiplicity of rules that comprise logic, I would have enough in the following four, as long as I made a firm and steadfast resolution never to fail to observe them.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 16.
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I fear that the character of my knowledge is from year to year becoming more distinct and scientific; that, in exchange for vistas wide as heaven’s scope, I am being narrowed down to the field of the microscope. I see details, not wholes nor the shadow of the whole. I count some parts, and say, “I know.”
(19 Aug 1851). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: II: 1850-September 15, 1851 (1906), 406.
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I furnished the body that was needed to sit in the defendant's chair. [Explaining his role in the Scopes Monkey Trial.]
As quoted in Newsweek, Vol. 69, 94.
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I see nothing wrong ethically with the idea of correcting single gene defects [through genetic engineering]. But I am concerned about any other kind of intervention, for anything else would be an experiment, [which would] impose our will on future generations [and take unreasonable chances] with their welfare ... [Thus] such intervention is beyond the scope of consideration.
in The Second Creation: Dolly and the Age of Biological Control
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I think that the unity we can seek lies really in two things. One is that the knowledge which comes to us at such a terrifyingly, inhumanly rapid rate has some order in it. We are allowed to forget a great deal, as well as to learn. This order is never adequate. The mass of ununderstood things, which cannot be summarized, or wholly ordered, always grows greater; but a great deal does get understood.
The second is simply this: we can have each other to dinner. We ourselves, and with each other by our converse, can create, not an architecture of global scope, but an immense, intricate network of intimacy, illumination, and understanding. Everything cannot be connected with everything in the world we live in. Everything can be connected with anything.
Concluding paragraphs of 'The Growth of Science and the Structure of Culture', Daedalus (Winter 1958), 87, No. 1, 76.
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In particular, and most importantly, this is the reason why the scientific worldview contains of itself no ethical values, no esthetical values, not a word about our own ultimate scope or destination, and no God, if you please. Whence came I and whither go I?
…...
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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 has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have “collected data” that the mathematician is able to deduce the required generalisation. Thus a Maxwell followed Faraday and a Newton completed Kepler.
In Higher Mathematics for Students of Chemistry and Physics (1902), 3.
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It is a remarkable fact that the second law of thermodynamics has played in the history of science a fundamental role far beyond its original scope. Suffice it to mention Boltzmann’s work on kinetic theory, Planck’s discovery of quantum theory or Einstein’s theory of spontaneous emission, which were all based on the second law of thermodynamics.
From Nobel lecture, 'Time, Structure and Fluctuations', in Tore Frängsmyr and Sture Forsén (eds.), Nobel Lectures, Chemistry 1971-1980, (1993), 263.
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It is here [in mathematics] that the artist has the fullest scope of his imagination.
In The Dance of Life (1923), 138-139.
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It is reported of Margaret Fuller that she said she accepted the universe. “Gad, she'd better!” retorted Carlyle. Carlyle himself did not accept the universe in a very whole-hearted manner. Looking up at the midnight stars, he exclaimed: “A sad spectacle! If they be inhabited, what a scope for misery and folly; if they be na inhabited, what a waste of space!”
Opening paragraph of book of collected essays, Accepting the Universe (1920), 3. “‘I accept the universe’ is reported to have been a favorite utterance of our New England transcendentalist, Margaret Fuller…” was stated by William James in The Varieties of Religious Experience (1902), 41. James continues, “and when some one repeated this phrase to Thomas Carlyle, his sardonic comment is said to have been: ‘Gad! she'd better!’” Note that James does not here merge Carlyle's remark about the universe. Burroughs’ attribution of the “sad spectacle” quote is, so far, the earliest found by the Webmaster, who has not located it in a printed work by Carlisle himself. If you know a primary source, or earlier attribution, please contact Webmaster.
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Let no one mistake it for comedy, farcical though it may be in all its details. It serves notice on the country that Neanderthal man is organizing in these forlorn backwaters of the land, led by a fanatic, rid of sense and devoid of conscience.
{Commenting on the Scopes Monkey Trial, while reporting for the Baltimore Sun.]
In Michael Shermer, Why Darwin Matters (2006), 26.
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Let us suppose that an ichthyologist is exploring the life of the ocean. He casts a net into the water and brings up a fishy assortment. Surveying his catch, he proceeds in the usual manner of a scientist to systematise what it reveals. He arrives at two generalisations:
(1) No sea-creature is less than two inches long.
(2) All sea-creatures have gills.
These are both true of his catch, and he assumes tentatively that they will remain true however often he repeats it.
In applying this analogy, the catch stands for the body of knowledge which constitutes physical science, and the net for the sensory and intellectual equipment which we use in obtaining it. The casting of the net corresponds to observation; for knowledge which has not been or could not be obtained by observation is not admitted into physical science.
An onlooker may object that the first generalisation is wrong. “There are plenty of sea-creatures under two inches long, only your net is not adapted to catch them.” The icthyologist dismisses this objection contemptuously. “Anything uncatchable by my net is ipso facto outside the scope of icthyological knowledge. In short, what my net can't catch isn't fish.” Or—to translate the analogy—“If you are not simply guessing, you are claiming a knowledge of the physical universe discovered in some other way than by the methods of physical science, and admittedly unverifiable by such methods. You are a metaphysician. Bah!”
In 'Selective Subjectivism', The Philosophy of Physical Science (1938, 2012), 16.
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Paris ... On this side of the ocean it is difficult to understand the susceptibility of American citizens on the subject and precisely why they should so stubbornly cling to the biblical version. It is said in Genesis the first man came from mud and mud is not anything very clean. In any case if the Darwinian hypothesis should irritate any one it should only be the monkey. The monkey is an innocent animal—a vegetarian by birth. He never placed God on a cross, knows nothing of the art of war, does not practice lynch law and never dreams of assassinating his fellow beings. The day when science definitely recognizes him as the father of the human race the monkey will have no occasion to be proud of his descendants. That is why it must be concluded that the American Association which is prosecuting the teacher of evolution can be no other than the Society for Prevention of Cruelty to Animals.
[A cynical article in the French press on the Scopes Monkey Trial, whether it will decide “a monkey or Adam was the grandfather of Uncle Sam.”]
Newspaper
Article from a French daily newspaper on the day hearings at the Scopes Monkey Trial began, Paris Soir (13 Jul 1925), quoted in 'French Satirize the Case', New York Times (14 Jul 1925), 3.
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Perhaps the least inadequate description of the general scope of modern Pure Mathematics—I will not call it a definition—would be to say that it deals with form, in a very general sense of the term; this would include algebraic form, functional relationship, the relations of order in any ordered set of entities such as numbers, and the analysis of the peculiarities of form of groups of operations.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 287.
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Science is a field which grows continuously with ever expanding frontiers. Further, it is truly international in scope. … Science is a collaborative effort. The combined results of several people working together is often much more effective than could be that of an individual scientist working alone.
From his second Nobel Prize Banquet speech (10 Dec 1972). In Wilhelm Odelberg (ed.), Les Prix Nobel en 1972 (1973).
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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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Surely the claim of mathematics to take a place among the liberal arts must now be admitted as fully made good. Whether we look at the advances made in modern geometry, in modern integral calculus, or in modern algebra, in each of these three a free handling of the material employed is now possible, and an almost unlimited scope is left to the regulated play of fancy. It seems to me that the whole of aesthetic (so far as at present revealed) may be regarded as a scheme having four centres, which may be treated as the four apices of a tetrahedron, namely Epic, Music, Plastic, and Mathematic. There will be found a common plane to every three of these, outside of which lies the fourth; and through every two may be drawn a common axis opposite to the axis passing through the other two. So far is certain and demonstrable. I think it also possible that there is a centre of gravity to each set of three, and that the line joining each such centre with the outside apex will intersect in a common point the centre of gravity of the whole body of aesthetic; but what that centre is or must be I have not had time to think out.
In 'Proof of the Hitherto Undemonstrated Fundamental Theorem of Invariants', Collected Mathematical Papers (1909), Vol. 3, 123.
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The classification of facts and the formation of absolute judgments upon the basis of this classification—judgments independent of the idiosyncrasies of the individual mind—is peculiarly the scope and method of modern science.
From The Grammar of Science (1892), 7.
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The end of knowledge is power ... the scope of all speculation is the performing of some action or thing to be done.
De Corp, EW, i, I, 1, 6, 7. In Jean Hampton, Hobbes and the social contract tradition (1988), 46. Hampton indicates that this quote is 'after Bacon' and in a footnote, that 'Hobbes was Bacon's secretary as a young man and had philosophical discussions with him (Aubrey 1898, 331).'
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The history of this paper suggests that highly speculative investigations, especially by an unknown author, are best brought before the world through some other channel than a scientific society, which naturally hesitates to admit into its printed records matters of uncertain value. Perhaps one may go further and say that a young author who believes himself capable of great things would usually do well to secure the favourable recognition of the scientific world by work whose scope is limited and whose value is easily judged, before embarking upon higher flights.
'On the Physics of Media that are Composed of Free and Perfectly Elastic Molecules in a State of Motion', Philosophical Transactions (1892), 183, 560.
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The instinct to command others, in its primitive essence, is a carnivorous, altogether bestial and savage instinct. Under the influence of the mental development of man, it takes on a somewhat more ideal form and becomes somewhat ennobled, presenting itself as the instrument of reason and the devoted servant of that abstraction, or political fiction, which is called the public good. But in its essence it remains just as baneful, and it becomes even more so when, with the application of science, it extends its scope and intensifies the power of its action. If there is a devil in history, it is this power principle.
In Mikhail Aleksandrovich Bakunin, Grigorii Petrovich Maksimov, Max Nettlau, The political philosophy of Bakunin (1953), 248.
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The main steps of my argument may be summarized thus:
1. Organisms are highly coordinated structures.
2. Only certain avenues of change are compatible with their conditions of coordination.
3. The formative and selective action of these internal conditions is theoretically and empirically different from that of Darwinian selection.
4. Mutations in the mode of coordination of the genetic system lie outside the scope of the classical arguments purporting to show that natural selection is the only directive agency.
5. The coordinative conditions constitute a second directive agency.
In Internal Factors in Evolution (1965), 73.
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The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature. ... It is this sudden confrontation with the depth and scope of ignorance that represents the most significant contribution of twentieth-century science to the human intellect.
In Medusa and the Snail: More Notes of a Biology Watcher (1974, 1979), 58.
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The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature. Indeed, I regard this as the major discovery of the past hundred years of biology. It is, in its way, an illuminating piece of news. … It is this sudden confrontation with the depth and scope of ignorance that represents the most significant contribution of twentieth-century science to the human intellect.
Essay, 'The Hazards of Science', collected in The Medusa and the Snail: More Notes of a Biology Watcher (1979), 73.
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The only thing harder to understand than a law of statistical origin would be a law that is not of statistical origin, for then there would be no way for it—or its progenitor principles—to come into being. On the other hand, when we view each of the laws of physics—and no laws are more magnificent in scope or better tested—as at bottom statistical in character, then we are at last able to forego the idea of a law that endures from everlasting to everlasting.
In 'Law without Law' (1979), in John Archibald Wheeler and Wojciech Hubert Zurek (eds.), Quantum Theory and Measurement (1983), 203.
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The physicians surely are the natural advocates of the poor and the social problem largely falls within their scope.
Introductory article, 'The Aims of the Journal “Medical Reform”', in the first edition of Die medizinische Reform (10 Jul 1848). From the original in German, “Die Ärzte sind die natürlichen Anwälte der Armen und die sociale Frage fallt zu einem erheblichen Theil in ihre Jurisdiction.” As translated in Rudolf Virchow and L.J. Rather (ed.), Collected Essays on Public Health and Epidemiology (1985), Vol. 1, 4. Elsewhere seen translated as “Physicians are the natural attorneys of the poor, and the social problems should largely be solved by them,” or “The physicians are the natural attorneys of the poor, and social problems fall to a large extent within their jurisdiction.”
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The question of a possible physiological significance, in the resemblance between the action of choline esters and the effects of certain divisions of the involuntary nervous system, is one of great interest, but one for the discussion of which little evidence is available. Acetyl-choline is, of all the substances examined, the one whose action is most suggestive in this direction. The fact that its action surpasses even that of adrenaline, both in intensity and evanescence, when considered in conjunction with the fact that each of these two bases reproduces those effects of involuntary nerves which are absent from the action of the other, so that the two actions are in many directions at once complementary and antagonistic, gives plenty of scope for speculation.
In 'The Action of Certain Esters and Ethers of Choline, and Their Relation to Muscarine', The Journal of Pharmacology and Experimental Therapeutics, 1914-15, 6, 188.
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The scope of Medicine is so wide as to give exercise to all the faculties of the mind, and it borrows from the stores of almost every form of human knowledge—it is an epitome of science.
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), 4.
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The worth of a new idea is invariably determined, not by the degree of its intuitiveness—which incidentally, is to a major extent a matter of experience and habit—but by the scope and accuracy of the individual laws to the discovery of which it eventually leads.
In Scientific Autobiography and Other Papers (1968), 109-110.
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There is no reason why the history and philosophy of science should not be taught in such a way as to bring home to all pupils the grandeur of science and the scope of its discoveries.
New Perspectives in Physics (1962), 195.
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There is, it appears, a conspiracy of scientists afoot. Their purpose is to break down religion, propagate immorality, and so reduce mankind to the level of brutes. They are the sworn and sinister agents of Beelzebub, who yearns to conquer the world, and has his eye especially upon Tennessee.
[Report on the Scopes Monkey Trial.]
Baltimore Evening Sun (11 Jul 1925). In H.L. Mencken, S. T. Joshi (Ed.), H.L. Mencken on Religion (2002), 178.
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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When one considers how hard it is to write a computer program even approaching the intellectual scope of a good paper, and how much greater time and effort have to be put in to make it “almost” formally correct, it is preposterous to claim that mathematics as we practice it is anywhere near formally correct.
In 'On Proof and Progress in Mathematics', For the Learning of Mathematics (Feb 1995), 15, No. 1, 33. Reprinted from Bulletin of the American Mathematical Society (1994), 30, No. 2, 170-171.
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Where we reach the sphere of mathematics we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is just here that the artist has the fullest scope for his imagination. … We are in the imaginative sphere of art, and the mathematician is engaged in a work of creation which resembles music in its orderliness, … It is not surprising that the greatest mathematicians have again and again appealed to the arts in order to find some analogy to their own work. They have indeed found it in the most varied arts, in poetry, in painting, and in sculpture, although it would certainly seem that it is in music, the most abstract of all the arts, the art of number and time, that we find the closest analogy.
In The Dance of Life (1923), 138-139.
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Why may we not add Geology to the list of poetical sciences? Why shall not that science, which is the second science in eras and magnitudes, and the first, in affording scope for the imagination, be brought into favor with the Muses and afford themes for the Poet?
In 'The Poetry of Geology', The Indicator, 1849, 109.
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Words are to the Anthropologist what rolled pebbles are to the Geologist—Battered relics of past ages often containing within them indelible records capable of intelligible interpretion—and when we see what amount of change 2000 years has been able to produce in the languages of Greece & Italy or 1000 in those of Germany, France & Spain we naturally begin to ask how long a period must have lapsed since the Chinese, the Hebrew, the Delaware & the Malesass had a point in common with the German & Italian & each other.—Time! Time! Time!—we must not impugn the Scripture Chronology, but we must interpret it in accordance with whatever shall appear on fair enquiry to be the truth for there cannot be two truths. And really there is scope enough: for the lives of the Patriarchs may as reasonably be extended to 5000 or 50000 years apiece as the days of Creation to as many thousand millions of years.
Letter to Charles Lyell, 20 Feb 1836, In Walter F. Cannon, 'The Impact of Uniformitarianism', Proceedings of the American Philosophical Society, 1961, 105, 308.
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[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity.
In Ueber das Verhältnis der Naturwissenschaften zur Gesammtheit der Wissenschaft, Vorträge und Reden (1896), Bd. 1, 176. Also seen translated as “In mathematics we see the conscious logical activity of our mind in its purest and most perfect form; here is made manifest to us all the labor and the great care with which it progresses, the precision which is necessary to determine exactly the source of the established general theorems, and the difficulty with which we form and comprehend abstract conceptions; but we also learn here to have confidence in the certainty, breadth, and fruitfulness of such intellectual labor”, in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 20. From the original German, “Hier sehen wir die bewusste logische Thätigkeit unseres Geistes in ihrer reinsten und vollendetsten Form; wir können hier die ganze Mühe derselben kennen lernen, die grosse Vorsicht, mit der sie vorschreiten muss, die Genauigkeit, welche nöthig ist, um den Umfang der gewonnenen allgemeinen Sätze genau zu bestimmen, die Schwierigkeit, abstracte Begriffe zu bilden und zu verstehen; aber ebenso auch Vertrauen fassen lernen in die Sicherheit, Tragweite und Fruchtbarkeit solcher Gedankenarbeit.”
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 80 -
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- 70 -
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- 50 -
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- 40 -
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- 30 -
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