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Home > Category Index for Science Quotations > Category Index E > Category: Extension

Extension Quotes (59 quotes)

... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself … A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.
'Operational Definition and Analogy in Physical Theories', British Journal for the Philosophy of Science (Feb 1952), 2, No. 8, 291.
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Un jour, en l'année 1666, Newton, retiré à la campagne, et voyant tomber des fruits d’un arbre, à ce que m'a conté sa nièce, (Mme Conduit) se laissa aller à une méditation profonde sur la cause qui entraîne ainsi tous les corps dans une ligne qui, si elle était prolongée, passerait à peu près par le centre de la Terre.
One day in the year 1666 Newton had gone to the country, and seeing the fall of an apple, [as his niece (Mme Conduit) told me,] let himself be led into a deep meditation on the cause which thus draws every object along a line whose extension would pass almost through the center of the Earth.
Original French from Éléments de Philosophie de Newton, Part 1, Chap. 3, in Oeuvres Completes de Voltaire (1785), Vol. 31, 175. Translation as given in an epigraph in Charles W. Misner, Kip S. Thorn and John Archibald Wheeler, Gravitation (1970, 1973), 47. An alternate translation is: “One day in the year 1666, Newton went into the country, and seeing fruit fall from a tree (as his niece, Madame Conduit, has informed me), entered into a profound train of thought as to the causes which could lead to such a drawing together or attraction.” As given in Robert Chambers (ed.), The Book of Days: A Miscellany of Popular Antiquities in Connection with the Calendar (1888), Vol. 2, 757. (Note: Voltaire originally published his Éléments in 1738, but Webmaster could not find the above quote in it.)
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A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown.
Autobiographical Notes (1946), 33. Quoted in Gerald Holton and Yehuda Elkana, Albert Einstein: Historical and Cultural Perspectives (1997), 227.
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A tool is but the extension of a man's hand, and a machine is but a complex tool. He that invents a machine augments the power of a man and the well being of mankind.
In Proverbs from Plymouth Pulpit (1887), 44. It appears as one of the quotations featured in one of the hallways of the first floor of the U.S. Capitols House wing, which are known as the Cox Corridors, after Allyn Cox, the artist who decorated them.
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According to my derivative hypothesis, a change takes place first in the structure of the animal, and this, when sufficiently advanced, may lead to modifications of habits… . “Derivation” holds that every species changes, in time, by virtue of inherent tendencies thereto. “Natural Selection” holds that no such change can take place without the influence of altered external circumstances educing or selecting such change… . The hypothesis of “natural selection” totters on the extension of a conjectural condition, explanatory of extinction to the majority of organisms, and not known or observed to apply to the origin of any species.
In On the Anatomy of Vertebrates (1868), Vol. 3, 808.
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All of today’s DNA, strung through all the cells of the earth, is simply an extension and elaboration of [the] first molecule.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1979), 27.
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Both religion and science must preserve their autonomy and their distinctiveness. Religion is not founded on science nor is science an extension of religion. Each should possess its own principles, its pattern of procedures, its diversities of interpretation and its own conclusions.
In Letter (1 Jun 1988) to Father George V. Coyne, Director of the Vatican Observatory. On vatican.va website.
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Colour, Figure, Motion, Extension and the like, considered only so many Sensations in the Mind, are perfectly known, there being nothing in them which is not perceived. But if they are looked on as notes or Images, referred to Things or Archetypes existing without the Mind, then are we involved all in Scepticism.
A Treatise Concerning the Principles of Human Knowledge [first published 1710], (1734), 109.
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Conservation is getting nowhere because it is incompatible with our Abrahamic concept of land. We abuse land because we regard it as a commodity belonging to us. When we see land as a community to which we belong, we may begin to use it with love and respect. There is no other way for land to survive the impact of mechanized man, nor for us to reap from it the esthetic harvest it is capable, under science, of contributing to culture. That land is a community is the basic concept of ecology, but that land is to be loved and respected is an extension of ethics. That land yields a cultural harvest is a fact long known, but latterly often forgotten.
A Sand County Almanac, and Sketches Here and There (1949), viii-ix.
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Disease is largely a removable evil. It continues to afflict humanity, not only because of incomplete knowledge of its causes and lack of individual and public hygiene, but also because it is extensively fostered by harsh economic and industrial conditions and by wretched housing in congested communities. ... The reduction of the death rate is the principal statistical expression and index of human social progress. It means the saving and lengthening of lives of thousands of citizens, the extension of the vigorous working period well into old age, and the prevention of inefficiency, misery, and suffering. These advances can be made by organized social effort. Public health is purchasable. (1911)
Quoted in Evelynn Maxine Hammonds, Childhood's Deadly Scourge: The Campaign to Control Diphtheria in New York City, 1880-1930(1999), 221.
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Experimental science can be thought of as an … extension of common sense.
In Science and Common Sense (1951), 32.
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Extremely hazardous is the desire to explain everything, and to supply whatever appears a gap in history—for in this propensity lies the first cause and germ of all those violent and arbitrary hypotheses which perplex and pervert the science of history far more than the open avowal of our ignorance, or the uncertainty of our knowledge: hypotheses which give an oblique direction, or an exaggerated and false extension, to a view of the subject originally not incorrect.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 12.
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Give me extension and motion, and I will construct the Universe.
As quoted, without citation, in Morris Kline, Mathematics in Western Culture (1964), 106. Webmaster has not yet located this in a primary source. Can you help?
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Hitherto the conception of chemical transmission at nerve endings and neuronal synapses, originating in Loewi’s discovery, and with the extension that the work of my colleagues has been able to give to it, can claim one practical result, in the specific, though alas only short, alleviation of the condition of myasthenia gravis, by eserine and its synthetic analogues.
'Some recent extensions of the chemical transmission of the effects of nerve impulses', Nobel Lecture, 12 December 1936. In Nobel Lectures: Physiology or Medicine 1922-1941 (1965), 412-3.
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I am further inclined to think, that when our views are sufficiently extended, to enable us to reason with precision concerning the proportions of elementary atoms, we shall find the arithmetical relation alone will not be sufficient to explain their mutual action, and that we shall be obliged to acquire a geometric conception of their relative arrangement in all three dimensions of solid extension.
Paper. Read to the Royal Society (28 Jan 1808), in 'On Super-acid and Sub-acid salts', Philosophical Transactions of the Royal Society of London, (1808), 98, 101.
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I am the most travelled of all my contemporaries; I have extended my field of enquiry wider than anybody else, I have seen more countries and climes, and have heard more speeches of learned men. No one has surpassed me in the composition of lines, according to demonstration, not even the Egyptian knotters of ropes, or geometers.
In Alan L. Mackay, A Dictionary of Scientific Quotations (1992, 1994), 71.
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I believe as a matter of faith that the extension of space travel to the limits of the solar system will probably be accomplished in several decades, perhaps before the end of the century. Pluto is 4000 million miles from the sun. The required minimum launching velocity is about 10 miles per second and the transit time is 46 years. Thus we would have to make the velocity considerably higher to make the trip interesting to man. Travel to the stars is dependent on radically new discoveries in science and technology. The nearest star is 25 million million miles way and requires a travel time of more than four years at the speed of light. Prof. Dr. Ing. E. Sanger has speculated that velocities comparable with the speed of light might be attained in the next century, but such extrapolation of current technology is probably not very reliable.
In Popular Mechanics (Sep 1961), 262.
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I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.
Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.
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I never got tired of watching the radar echo from an aircraft as it first appeared as a tiny blip in the noise on the cathode-ray tube, and then grew slowly into a big deflection as the aircraft came nearer. This strange new power to “see” things at great distances, through clouds or darkness, was a magical extension of our senses. It gave me the same thrill that I felt in the early days of radio when I first heard a voice coming out of a horn...
In Boffin: A Personal Story of the Early Days of Radar, Radio Astronomy and Quantum Optics (1991), 9.
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I was just going to say, when I was interrupted, that one of the many ways of classifying minds is under the heads of arithmetical and algebraical intellects. All economical and practical wisdom is an extension or variation of the following arithmetical formula: 2+2=4. Every philosophical proposition has the more general character of the expression a+b=c. We are mere operatives, empirics, and egotists, until we learn to think in letters instead of figures.
The Autocrat of the Breakfast Table (1858), 1.
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If it is true as Whewell says, that the essence of the triumphs of Science and its progress consists in that it enables us to consider evident and necessary, views which our ancestors held to be unintelligible and were unable to comprehend, then the extension of the number concept to include the irrational, and we will at once add, the imaginary, is the greatest forward step which pure mathematics has ever taken.
In Theorie der Complexen Zahlensysteme (1867), 60. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 281. From the original German, “Wenn es wahr ist, dass, wie Whewell meint, das Wesen der Triumphe der Wissenschaft und ihres Fortschrittes darin besteht, dass wir veranlasst werden, Ansichten, welche unsere Vorfahren für unbegreiflich hielten und unfähig waren zu begreifen, für evident und nothwendig zu halten, so war die Erweiterung des Zahlenbegriffes auf das Irrationale, und wollen wir sogleich hinzufügen, das Imaginäre, der grösste Fortschritt, den die reine Mathematik jemals gemacht hat.”
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In short, the greatest contribution to real security that science can make is through the extension of the scientific method to the social sciences and a solution of the problem of complete avoidance of war.
In "Science and Security", Science (25 Jun 1948), 107, 665. Written while Director of the U.S. National Bureau of Standards.
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In the animal world we have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life: understood, of course, in its wide Darwinian sense—not as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress. The mutual protection which is obtained in this case, the possibility of attaining old age and of accumulating experience, the higher intellectual development, and the further growth of sociable habits, secure the maintenance of the species, its extension, and its further progressive evolution. The unsociable species, on the contrary, are doomed to decay.
Mutual Aid: A Factor of Evolution (1902), 293.
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It is now widely realized that nearly all the “classical” problems of molecular biology have either been solved or will be solved in the next decade. The entry of large numbers of American and other biochemists into the field will ensure that all the chemical details of replication and transcription will be elucidated. Because of this, I have long felt that the future of molecular biology lies in the extension of research to other fields of biology, notably development and the nervous system.
Letter to Max Perua, 5 June 1963. Quoted in William B. Wood (ed.), The Nematode Caenorhabditis Elegans (1988), x-xi.
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It was on the 25th November 1740 that I cut the first polyp. I put the two parts in a flat glass, which only contained water to the height of four to five lignes. It was thus easy for me to observe these portions of the polyp with a fairly powerful lens.
I shall indicate farther on the precautions I took in making my experiments on these cut polyps and the technique I adopted to cut them. It will suffice to say here that I cut the polyp concerned transversely, a little nearer the anterior than the posterior end. The first part was thus a little shorter than the second.
The instant that I cut the polyp, the two parts contracted so that at first they only appeared like two little grains of green matter at the bottom of the glass in which I put them—for green, as I have already said, is the colour of the first polyps that I possessed. The two parts expanded on the same day on which I separated them. They were very easy to distinguish from one another. The first had its anterior end adorned with the fine threads that serve the polyp as legs and arms, which the second had none.
The extensions of the first part was not the only sign of life that it gave on the same day that it was separated from the other. I saw it move its arms; and the next day, the first time I came to observe it, I found that it had changed its position; and shortly afterwards I saw it take a step. The second part was extended as on the previous day and in the same place. I shook the glass a little to see if it were still alive. This movement made it contract, from which I judged that it was alive. Shortly afterwards it extended again. On the following days I .’ saw the same thing.
Mémoires, pour servir à l'histoire d'un genre de polyps d'eau douce à bras en forme de cornes (1744), 7-16. Trans. John R. Baker, in Abraham Trembley of Geneva: Scientist and Philosopher 1710-1784 (1952), 31.
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It... [can] be easily shown:
1. That all present mountains did not exist from the beginning of things.
2. That there is no growing of mountains.
3. That the rocks or mountains have nothing in common with the bones of animals except a certain resemblance in hardness, since they agree in neither matter nor manner of production, nor in composition, nor in function, if one may be permitted to affirm aught about a subject otherwise so little known as are the functions of things.
4. That the extension of crests of mountains, or chains, as some prefer to call them, along the lines of certain definite zones of the earth, accords with neither reason nor experience.
5. That mountains can be overthrown, and fields carried over from one side of a high road across to the other; that peaks of mountains can be raised and lowered, that the earth can be opened and closed again, and that other things of this kind occur which those who in their reading of history wish to escape the name of credulous, consider myths.
The Prodromus of Nicolaus Steno's Dissertation Concerning a Solid Body enclosed by Process of Nature within a Solid (1669), trans. J. G. Winter (1916), 232-4.
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Mars was surprising in its way but not flabbergasting; it was a disappointment not to find evidences of life, and there was some sadness in the pictures sent back to earth from the Mars Lander, that lonely long-legged apparatus poking about with its jointed arm, picking up sample after sample of the barren Mars soil, looking for any flicker of life and finding none; the only sign of life on Mars was the Lander itself, an extension of the human mind all the way from earth to Mars, totally alone.
In Late Night Thoughts on Listening to Mahler’s Ninth Symphony (1984), 22.
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Mathematics is the science of the functional laws and transformations which enable us to convert figured extension and rated motion into number.
In 'The Departments of Mathematics, and their Mutual Relations', Journal of Speculative Philosophy (Apr 1871), 5, No. 2, 170.
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Nobody knows more than a tiny fragment of science well enough to judge its validity and value at first hand. For the rest he has to rely on views accepted at second hand on the authority of a community of people accredited as scientists. But this accrediting depends in its turn on a complex organization. For each member of the community can judge at first hand only a small number of his fellow members, and yet eventually each is accredited by all. What happens is that each recognizes as scientists a number of others by whom he is recognized as such in return, and these relations form chains which transmit these mutual recognitions at second hand through the whole community. This is how each member becomes directly or indirectly accredited by all. The system extends into the past. Its members recognize the same set of persons as their masters and derive from this allegiance a common tradition, of which each carries on a particular strand.
Personal Knowledge (1958), 163.
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Now it came to me: … the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation. … This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.
In Paul Arthur Schilpp, 'Autobiographical Notes', Albert Einstein: Philosopher-Scientist (1949), 65-67.
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Once a molecule is asymmetric, its extension proceeds also in an asymmetrical sense. This concept completely eliminates the difference between natural and artificial synthesis. The advance of science has removed the last chemical hiding place for the once so highly esteemed vis vitalis.
‘Synthesen in der Zuckergruppe', Berichte der deutschen Chemischen Gesellschaft, 1894, 27, 3189.
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Our ultimate analysis of space leads us not to a “here” and a “there,” but to an extension such as that which relates “here” and “there.” To put the conclusion rather crudely—space is not a lot of points close together; it is a lot of distances interlocked.
The Mathematical Theory of Relativity (1923), 10.
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Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions.
In 'Future Prospects', On the Economy of Machinery and Manufactures (1st ed., 1832), chap. 32, 277-278.
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Science is in a literal sense constructive of new facts. It has no fixed body of facts passively awaiting explanation, for successful theories allow the construction of new instruments—electron microscopes and deep space probes—and the exploration of phenomena that were beyond description—the behavior of transistors, recombinant DNA, and elementary particles, for example. This is a key point in the progressive nature of science—not only are there more elegant or accurate analyses of phenomena already known, but there is also extension of the range of phenomena that exist to be described and explained.
Co-author with Michael A. Arbib, English-born professor of computer science and biomedical engineering (1940-)
Michael A. Arbib and Mary B. Hesse, The Construction of Reality (1986), 8.
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Science is not a substitute for common sense, but an extension of it.
'The Scope and Language of Science' (1954), reprinted in The British Journal for the Philosophy of Science (1957), 8, 2.
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Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined. Its validity is of the same order as that of ordinary perception; memory, and understanding. Its test is found, like theirs, in actual intuition, which sometimes consists in perception and sometimes in intent. The flight of science is merely longer from perception to perception, and its deduction more accurate of meaning from meaning and purpose from purpose. It generates in the mind, for each vulgar observation, a whole brood of suggestions, hypotheses, and inferences. The sciences bestow, as is right and fitting, infinite pains upon that experience which in their absence would drift by unchallenged or misunderstood. They take note, infer, and prophesy. They compare prophesy with event, and altogether they supply—so intent are they on reality—every imaginable background and extension for the present dream.
The Life of Reason, or the Phases of Human Progress (1954), 393.
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See, thro' this air, this ocean, and this earth,
All matter quick, and bursting into birth.
Above, how high progressive life may go!
Around, how wide! how deep extend below!
Vast chain of being, which from God began,
Natures ethereal, human, angel, man,
Beast, bird, fish, insect! what no eye can see,
No glass can reach! from Infinite to thee,
From thee to Nothing—On superior pow'rs
Were we to press, inferior might on ours:
Or in the full creation leave a void,
Where, one step broken, the great scale's destroy'd:
From Nature's chain whatever link you strike,
Tenth or ten thousandth, breaks the chain alike.
'An Essay on Man' (1733-4), Epistle I. In John Butt (ed.), The Poems of Alexander Pope (1965), 513.
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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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Technology, while adding daily to our physical ease, throws daily another loop of fine wire around our souls. It contributes hugely to our mobility, which we must not confuse with freedom. The extensions of our senses, which we find so fascinating, are no
My Faith in Democratic Capitalism, in Fortune (Oct 1955).
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The American Cancer Society's position on the question of a possible cause-effect relationship between cigarette smoking and lung cancer is:
1. The evidence to date justifies suspicion that cigarette smoking does, to a degree as yet undetermined, increase the likelihood of developing cancer of the lung.
2. That available evidence does not constitute irrefutable proof that cigarette smoking is wholly or chiefly or partly responsible for lung cancer.
3. That the evidence at hand calls for the extension of statistical and laboratory studies designed to confirm or deny a causual relationship between cigarette smoking and lung cancer.
4. That the society is committed to furthering such intensified investigation as its resources will permit.
Conclusions of statement after a meeting of the ACS board of directors in San Francisco (17 Mar 1954). Quoted in 'Tobacco Industry Denies Cancer Tie'. New York Times (14 Apr 1954), 51.
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The establishment of the periodic law may truly be said to mark a line in chemical science, and we anticipate that its application and and extension will be fraught With the most important consequences. It reminds us how important above all things is the correct determination of the fundamental constants of our science—the atomic weights of the elements, about which in many cases great uncertainty prevails; it is much to be desired that this may not long remain the case. It also affords the strongest encouragement to the chemist to persevere in the search for new elements.
In The Encyclopaedia Britannica: Ninth Edition (1877), Vol. 5, 714.
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The great object of all knowledge is to enlarge and purify the soul, to fill the mind with noble contemplations, to furnish a refined pleasure, and to lead our feeble reason from the works of nature up to its great Author and Sustainer. Considering this as the ultimate end of science, no branch of it can surely claim precedence of Astronomy. No other science furnishes such a palpable embodiment of the abstractions which lie at the foundation of our intellectual system; the great ideas of time, and space, and extension, and magnitude, and number, and motion, and power. How grand the conception of the ages on ages required for several of the secular equations of the solar system; of distances from which the light of a fixed star would not reach us in twenty millions of years, of magnitudes compared with which the earth is but a foot-ball; of starry hosts—suns like our own—numberless as the sands on the shore; of worlds and systems shooting through the infinite spaces.
Oration at Inauguration of the Dudley Astronomical Observatory, Albany (28 Jul 1856). Text published as The Uses of Astronomy (1856), 36.
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The greater is the circle of light, the greater is the boundary of the darkness by which it is confined. But, notwithstanding this, the more light get, the more thankful we ought to be, for by this means we have the greater range for satisfactory contemplation. time the bounds of light will be still farther extended; and from the infinity of the divine nature, and the divine works, we may promise ourselves an endless progress in our investigation them: a prospect truly sublime and glorious.
Experiments and Observations with a Continuation of the Observations on Air (1781), Vol. 2, ix.
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The institutional goal of science is the extension of certified knowledge. The technical methods employed toward this end provide the relevant definition of knowledge: empirically confirmed and logically consistent predictions. The institutional imperatives (mores) derive from the goal and the methods. The entire structure of technical and moral norms implements the final objective. The technical norm of empirical evidence, adequate, valid and reliable, is a prerequisite for sustained true prediction; the technical norm of logical consistency, a prerequisite for systematic and valid prediction. The mores of science possess a methodologic rationale but they are binding, not only because they are procedurally efficient, but because they are believed right and good. They are moral as well as technical prescriptions. Four sets of institutional imperatives–universalism, communism, disinterestedness, organized scepticism–comprise the ethos of modern science.
Social Theory and Social Structure (1957), 552-3.
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The invention of what we may call primary or fundamental notation has been but little indebted to analogy, evidently owing to the small extent of ideas in which comparison can be made useful. But at the same time analogy should be attended to, even if for no other reason than that, by making the invention of notation an art, the exertion of individual caprice ceases to be allowable. Nothing is more easy than the invention of notation, and nothing of worse example and consequence than the confusion of mathematical expressions by unknown symbols. If new notation be advisable, permanently or temporarily, it should carry with it some mark of distinction from that which is already in use, unless it be a demonstrable extension of the latter.
In 'Calculus of Functions', Encyclopaedia of Pure Mathematics (1847), Addition to Article 26, 388.
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The known is finite, the unknown infinite; intellectually we stand on an islet in the midst of an illimitable ocean of inexplicability. Our business in every generation is to reclaim a little more land, to add something to the extent and the solidity of our possessions. And even a cursory glance at the history of the biological sciences during the last quarter of a century is sufficient to justify the assertion, that the most potent instrument for the extension of the realm of natural knowledge which has come into men's hands, since the publication of Newton's ‘Principia’, is Darwin's ‘Origin of Species.’
From concluding remarks to a chapter by Thomas Huxley, 'On the Reception of the ‘Origin of Species’', the last chapter in Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin (1887), Vol. 1, 557.
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The Mathematician deals with two properties of objects only, number and extension, and all the inductions he wants have been formed and finished ages ago. He is now occupied with nothing but deduction and verification.
In 'On the Educational Value of the Natural History Sciences', Lay Sermons, Addresses and Reviews (1872), 87.
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The moment after, I began to respire 20 quarts of unmingled nitrous oxide. A thrilling, extending from the chest to the extremities, was almost immediately produced. I felt a sense of tangible extension highly pleasurable in every limb; my visible impressions were dazzling, and apparently magnified, I heard distinctly every sound in the room and was perfectly aware of my situation. By degrees, as the pleasurable sensations increased, I last all connection with external things; trains of vivid visible images rapidly passed through my mind, and were connected with words in such a manner, as to produce perceptions perfectly novel. I existed in a world of newly connected and newly modified ideas. I theorised—I imagined that I made discoveries. When I was awakened from this semi-delirious trance by Dr. Kinglake, who took the bag from my mouth, indignation and pride were the first feelings produced by the sight of the persons about me. My emotions were enthusiastic and sublime; and for a minute I walked round the room, perfectly regardless of what was said to me. As I recovered my former state of mind, I felt an inclination to communicate the discoveries I had made during the experiment. I endeavoured to recall the ideas, they were feeble and indistinct; one collection of terms, however, presented itself: and with the most intense belief and prophetic manner, I exclaimed to Dr Kinglake, 'Nothing exists but thoughts!—the universe is composed of impressions, ideas, pleasures and pains!'
Researches, Chemical and Philosophical (1800), in J. Davy (ed.), The Collected Works of Sir Humphry Davy (1839-40), Vol 3, 289-90.
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The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.
In A Treatise on Projections (1880), Introduction, xi. Published as United States Coast and Geodetic Survey, Treasury Department Document, No. 61.
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The transition from a paradigm in crisis to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field's most elementary theoretical generalizations as well as many of its paradigm methods and applications. During the transition period there will be a large but never complete overlap between the problems that can be solved by the old and by the new paradigm. But there will also be a decisive difference in the modes of solution. When the transition is complete, the profession will have changed its view of the field, its methods, and its goals.
The Structure of Scientific Revolutions (1962), 84-5.
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Their specific effect on the glucosides might thus be explained by assuming that the intimate contact between the molecules necessary for the release of the chemical reaction is possible only with similar geometrical configurations. To give an illustration I will say that enzyme and glucoside must fit together like lock and key in order to be able to exercise a chemical action on each other. This concept has undoubtedly gained in probability and value for stereochemical research, after the phenomenon itself was transferred from the biological to the purely chemical field. It is an extension of the theory of asymmetry without being a direct consequence of it: for the conviction that the geometrical structure of the molecule even for optical isomers exercises such a great influence on the chemical affinities, in my opinion could only be gained by new actual observations.
'Einfluss der Configuration auf die wirkung der Enzyme', Berichte der deutschen Chemischen Gesellschaft, 1894, 27, 2985-93. Trans. B. Holmstedt and G. Liljestrand (eds.) Readings in Pharmacology (1963), 251.
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Thus one becomes entangled in contradictions if one speaks of the probable position of the electron without considering the experiment used to determine it ... It must also be emphasized that the statistical character of the relation depends on the fact that the influence of the measuring device is treated in a different manner than the interaction of the various parts of the system on one another. This last interaction also causes changes in the direction of the vector representing the system in the Hilbert space, but these are completely determined. If one were to treat the measuring device as a part of the system—which would necessitate an extension of the Hilbert space—then the changes considered above as indeterminate would appear determinate. But no use could be made of this determinateness unless our observation of the measuring device were free of indeterminateness. For these observations, however, the same considerations are valid as those given above, and we should be forced, for example, to include our own eyes as part of the system, and so on. The chain of cause and effect could be quantitatively verified only if the whole universe were considered as a single system—but then physics has vanished, and only a mathematical scheme remains. The partition of the world into observing and observed system prevents a sharp formulation of the law of cause and effect. (The observing system need not always be a human being; it may also be an inanimate apparatus, such as a photographic plate.)
The Physical Principles of the Quantum Theory, trans. Carl Eckart and Frank C. Hoyt (1949), 58.
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To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
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We need another and a wiser and perhaps a more mystical concept of animals. Remote from universal nature, and living by complicated artifice, man in civilization surveys the creature through the glass of his knowledge and sees thereby a feather magnified and the whole image in distortion. We patronize them for their incompleteness, for their tragic fate of having taken form so far below ourselves. And therein we err, and greatly err. For the animal shall not be measured by man. In a world older and more complete than ours they move finished and complete, gifted with extensions of the senses we have lost or never attained, living by voices we shall never hear. They are not brethren, they are not underlings; they are other nations, caught with ourselves in the net of life and time, fellow prisoners of the splendour and travail of the earth.
The Outermost House (1928), 25.
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When not protected by law, by popular favor or superstition, or by other special circumstances, [birds] yield very readily to the influences of civilization, and, though the first operations of the settler are favorable to the increase of many species, the great extension of rural and of mechanical industry is, in a variety of ways, destructive even to tribes not directly warred upon by man.
In Man and Nature, (1864), 93-93.
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When physiologists revealed the existence and functions of hormones they not only gave increased opportunities for the activities of biochemists but in particular gave a new charter to biochemical thought, and with the discovery of vitamins that charter was extended.
'Biological Thought and Chemical Thought: A Plea for Unification', Linacre Lecture, Cambridge (6 May 1938), published in Lancet (1938),2, 1201.
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When, in an experiment, all known causes being allowed for, there remain certain unexplained effects (excessively slight it may be), these must be carefully investigated, and every conceivable variation of arrangement of apparatus, etc., tried ; until, if possible, we manage so to exaggerate the residual phenomenon as to be able to detect its cause. It is here, perhaps, that in the present state of science we may most reasonably look for extensions of our knowledge
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, 306.
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With the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out how thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 94-95. It is reprinted in Jeremy Gray, The Hilbert Challenge (2000), 282.
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[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
In Examination of Sir William Hamilton's Philosophy (1878), 607.
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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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