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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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Home > Category Index for Science Quotations > Category Index I > Category: Inexhaustible

Inexhaustible Quotes (26 quotes)

A mind which has once imbibed a taste for scientific enquiry, and has learnt the habit of applying its principles readily to the cases which occur, has within itself an inexhaustible source of pure and exciting contemplations.
In Dionysius Lardner (ed.), Cabinet Cyclopaedia, Vol 1, Preliminary Discourse on the Study of Natural Philosophy (1831), 14-15.
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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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As soon as we got rid of the backroom attitude and brought our apparatus fully into the Department with an inexhaustible supply of living patients with fascinating clinical problems, we were able to get ahead really fast. Any new technique becomes more attractive if its clinical usefulness can be demonstrated without harm, indignity or discomfort to the patient... Anyone who is satisfied with his diagnostic ability and with his surgical results is unlikely to contribute much to the launching of a new medical science. He should first be consumed with a divine discontent with things as they are. It greatly helps, of course, to have the right idea at the right time, and quite good ideas may come, Archimedes fashion, in one's bath..
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By far the most important books for geology students were the quarries and clay pits, the cliffs and creek beds, the road and railroad cuts in woods and fields. Our words and letters were the imprints of plants and animals in stone, the minerals and crystals, and our vast, inexhaustible, incorruptible, and infallible library was nature itself.
In Hans Cloos, Ernst Cloos (ed.) and Curt Dietz (ed.), Conversation With the Earth (1953, 1959), 28, as translated by E.B. Garside from the original German edition, Gespräch mit der Erde (1947).
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For you teach very clearly by your behaviour how slowly and how meagerly our senses proceed in the investigation of ever inexhaustible nature.
Elettricismo artificiale (1772), vii-viii, trans. in Antonio Pace, Franklin and Italy (1958), 58.
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Gödel proved that the world of pure mathematics is inexhaustible; no finite set of axioms and rules of inference can ever encompass the whole of mathematics; given any finite set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. I hope that an analogous Situation exists in the physical world. If my view of the future is correct, it means that the world of physics and astronomy is also inexhaustible; no matter how far we go into the future, there will always be new things happening, new information coming in, new worlds to explore, a constantly expanding domain of life, consciousness, and memory.
From Lecture 1, 'Philosophy', in a series of four James Arthur Lectures, 'Lectures on Time and its Mysteries' at New York University (Autumn 1978). Printed in 'Time Without End: Physics and Biology in an Open Universe', Reviews of Modern Physics (Jul 1979), 51, 449.
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Guido was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always itself, would in any case have lost its charm, while the rudiments of algebra continued to grow and blossom in his mind with an unfailing luxuriance. Every day he made the discovery of something which seemed to him exquisitely beautiful; the new toy was inexhaustible in its potentialities.
In Young Archimedes: And Other Stories (1924), 299. The fictional character, Guido, is a seven year old boy. Methylated spirit is an alcohol fuel.
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He said, “Americans look upon water as an inexhaustible resource. It’s not, if you’re mining it. Arizona is mining groundwater.”
Assembling California
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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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Nothing is rich but the inexhaustible wealth of nature. She shows us only surfaces, but she is a million fathoms deep.
In 'Resources', Letters and Social Aims (1875, 1894), 113.
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One is constantly reminded of the infinite lavishness and fertility of Nature—inexhaustible abundance amid what seems enormous waste. And yet when we look into any of her operations that lie within reach of our minds, we learn that no particle of her material is wasted or worn out. It is eternally flowing from use to use, beauty to yet higher beauty; and we soon cease to lament waste and death, and rather rejoice and exult in the imperishable, unspendable wealth of the universe.
John Muir
In My First Summer in the Sierra (1911), 325. Based on Muir's original journals and sketches of his 1869 stay in the Sierra.
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Optimism is a good characteristic, but if carried to an excess, it becomes foolishness. We are prone to speak of the resources of this country as inexhaustible; this is not so.
Seventh Annual Message to Congress, 3 Dec, 1907. In In Presidential Addresses and State Papers (1910), Vol. 12, 1541.
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Oxigen [oxygen], as you well know, is my hero as well as my foe, and being not only strong but inexhaustible in strategies and full of tricks, I was obliged to call up all my forces to lay hold of him, and make the subtle Being my prisoner.
Letter to Michael Faraday (11 Dec 1860), The Letters of Faraday and Schoenbein, 1836-1862 (1899), 340.
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Science too proceeds by lantern-flashes; it explores nature’s inexhaustible mosaic piece by piece. Too often the wick lacks oil; the glass panes of the lantern may not be clean. No matter: his work is not in vain who first recognizes and shows to others one speck of the vast unknown.
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Sir W. Ramsay has striven to show that radium is in process of transformation, that it contains a store of energy enormous but not inexhaustible. The transformation of radium then would produce a million times more heat than all known transformations; radium would wear itself out in 1,250 years; this is quite short, and you see that we are at least certain to have this point settled some hundreds of years from now. While waiting, our doubts remain.
In La Valeur de la Science (1904), 199, as translated by George Bruce Halsted, in The Value of Science (1907), 105.
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The forms of art are inexhaustible; but all lead by the same road of aesthetic emotion to the same world of aesthetic ecstasy.
In Art (1913), 37.
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The idea that our natural resources were inexhaustible still obtained, and there was as yet no real knowledge of their extent and condition. The relation of the conservation of natural resources to the problems of National welfare and National efficiency had not yet dawned on the public mind. The reclamation of arid public lands in the West was still a matter for private enterprise alone; and our magnificent river system, with its superb possibilities for public usefulness, was dealt with by the National Government not as a unit, but as a disconnected series of pork-barrel problems, whose only real interest was in their effect on the re-election or defeat of a Congressman here and there —a theory which, I regret to say, still obtains.
The Works of Theodore Roosevelt. Vol. 20: Theodore Roosevelt, An Autobiography (1926), 386.
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The longing to behold this pre-established harmony [of phenomena and theoretical principles] is the source of the inexhaustible patience and perseverance with which Planck has devoted himself ... The state of mind which enables a man to do work of this kind is akin to that of the religious worshiper or the lover; the daily effort comes from no deliberate intention or program, but straight from the heart.
Address (1918) for Max Planck's 60th birthday, at Physical Society, Berlin, 'Principles of Research' in Essays in Science (1934), 4-5.
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The physicist is like someone who’s watching people playing chess and, after watching a few games, he may have worked out what the moves in the game are. But understanding the rules is just a trivial preliminary on the long route from being a novice to being a grand master. So even if we understand all the laws of physics, then exploring their consequences in the everyday world where complex structures can exist is a far more daunting task, and that’s an inexhaustible one I'm sure.
In Lewis Wolpert and Alison Richards, A Passion For Science (1988), 37.
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Time, inexhaustible and ever accumulating his efficacy, can undoubtedly do much for the theorist in geology; but Force, whose limits we cannot measure, and whose nature we cannot fathom, is also a power never to be slighted: and to call in the one to protect us from the other, is equally presumptuous, to whichever of the two our superstition leans. To invoke Time, with ten thousand earthquakes, to overturn and set on edge a mountain-chain, should the phenomena indicate the change to have been sudden and not successive, would be ill excused by pleading the obligation of first appealing to known causes.
In History of the Inductive Sciences (1857), Vol. 3, 513-514.
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Two impressions remaining, after a life of scientific research:
1. The inexhaustible oddity of nature.
2. The capacity of the human system for recovery.
Unverified. Found as an epigraph, without citation, in Boris A Kupershmidt, The Variational Principles of Dynamics (1992).
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We are like tenant farmers chopping down the fence around our house for fuel when we should be using Natures inexhaustible sources of energy — sun, wind and tide. ... I'd put my money on the sun and solar energy. What a source of power! I hope we don't have to wait until oil and coal run out before we tackle that.
Edison in conversation Henry Ford and Harvey Firestone (1931), quoted as a recollection of the author, in James Newton, Uncommon Friends: Life with Thomas Edison, Henry Ford, Harvey Firestone, Alexis Carrel & Charles Lindbergh (1987), 31. The quote is not cited from a print source. However, in the introduction the author said he “kept a diary in which I noted times and places, key phrases, and vivid impressions.” He also “relied on publications by and about my friends, which jogged my memory.” Webmaster has found no earlier record of this quote, and thus suggests the author may have the gist of what Edison said, but is not quoting the exact words uttered by Edison, although quote marks are used to state what Edison said.
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We nuclear people have made a Faustian bargain with society. On the one hand, we offer … an inexhaustible source of energy … But the price that we demand of society for this magical energy source is both a vigilance and a longevity of our social institutions that we are quite unaccustomed to.
In Social Institutions and Nuclear Energy (1972), 33.
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What is the use of this history, what the use of all this minute research? I well know that it will not produce a fall in the price of pepper, a rise in that of crates of rotten cabbages, or other serious events of this kind, which cause fleets to be manned and set people face to face intent upon one another's extermination. The insect does not aim at so much glory. It confines itself to showing us life in the inexhaustible variety of its manifestations; it helps us to decipher in some small measure the obscurest book of all, the book of ourselves.
Introducing the natural history and his study of the insect Minotaurus typhoeus. In Jean-Henri Fabre and Alexander Teixeira de Mattos (trans.), The Life and Love of the Insect (1918), 128.
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What more pleasing prospect can be opened to our view than the boundless field of nature? not only comprehending the inhabitants of earth, sea, and air; but earth, sea and air themselves—presenting an inexhaustible fund for amusing and useful enquiry.
From Introduction to a Course of Lectures on Natural History: Delivered in the University of Pennsylvania, Nov. 16, 1799 (1800), 6.
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When I came home not a single acre of Government, state, or private timberland was under systematic forest management anywhere on the most richly timbered of all continents. … When the Gay Nineties began, the common word for our forests was 'inexhaustible.' To waste timber was a virtue and not a crime. There would always be plenty of timber. … The lumbermen … regarded forest devastation as normal and second growth as a delusion of fools. … And as for sustained yield, no such idea had ever entered their heads. The few friends the forest had were spoken of, when they were spoken of at all, as impractical theorists, fanatics, or ‘denudatics,’ more or less touched in the head. What talk there was about forest protection was no more to the average American that the buzzing of a mosquito, and just about as irritating.
In Breaking New Ground (1947, 1998), 27.
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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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Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
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Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
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Rene Descartes
Francis Crick
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Francis Bacon
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- 10 -
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