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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 D > Category: Distance

Distance Quotes (24 quotes)

A game is on, at the other end of this infinite distance, and heads or tails will turn up. What will you wager? According to reason you cannot leave either; according to reason you cannot leave either undone... Yes, but wager you must; there is no option, you have embarked on it. So which will you have. Come. Since you must choose, let us see what concerns you least. You have two things to lose: truth and good, and two things to stake: your reason and your will, your knowledge and your happiness. And your nature has two things to shun: error and misery. Your reason does not suffer by your choosing one more than the other, for you must choose. That is one point cleared. But your happiness? Let us weigh gain and loss in calling heads that God is. Reckon these two chances: if you win, you win all; if you lose, you lose naught. Then do not hesitate, wager that He is.
Pensées (1670), Section I, aphorism 223. In H. F. Stewart (ed.), Pascal's Pensées (1950), 117-119.
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A poet is, after all, a sort of scientist, but engaged in a qualitative science in which nothing is measurable. He lives with data that cannot be numbered, and his experiments can be done only once. The information in a poem is, by definition, not reproducible. ... He becomes an equivalent of scientist, in the act of examining and sorting the things popping in [to his head], finding the marks of remote similarity, points of distant relationship, tiny irregularities that indicate that this one is really the same as that one over there only more important. Gauging the fit, he can meticulously place pieces of the universe together, in geometric configurations that are as beautiful and balanced as crystals.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1995), 107.
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Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance.
Letter to William Huggins (13 Oct 1868). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 1862-1873, 451-2.
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But in the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another; and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule, therefore, throughout the universe, bears impressed on it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the double royal cubit of the Temple of Karnac ... the exact quantity of each molecule to all others of same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article and precludes the idea of its being external and self-existent.
'Molecules', 1873. In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 375-6.
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By such deductions the law of gravitation is rendered probable, that every particle attracts every other particle with a force which varies inversely as the square of the distance. The law thus suggested is assumed to be universally true.
In Isaac Newton and Percival Frost (ed.) Newton's Principia: Sections I, II, III (1863), 217.
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Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.
Science and Method (1908), trans. Francis Maitland (1914), 254-5.
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Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.
Science and Method (1908), trans. Francis Maitland (1914), 254-5.
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His mind illumined the Past and the Future and wrought greatly for the present. By his genius distant lands converse and men sail unafraid upon the deep.
Epitaph
Inscription on the tomb of Reginald and Helen Fessenden in Bermuda. In Frederick Seitz, The Cosmic Inventor: Reginald Aubrey Fessenden (1866-1932) (1999), 61, being Transactions of the American Philosophical Society, Held at Philadelphia For Promoting Useful Knowledge, Vol. 86, Pt. 6.
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I think that the event which, more than anything else, led me to the search for ways of making more powerful radio telescopes, was the recognition, in 1952, that the intense source in the constellation of Cygnus was a distant galaxy—1000 million light years away. This discovery showed that some galaxies were capable of producing radio emission about a million times more intense than that from our own Galaxy or the Andromeda nebula, and the mechanisms responsible were quite unknown. ... [T]he possibilities were so exciting even in 1952 that my colleagues and I set about the task of designing instruments capable of extending the observations to weaker and weaker sources, and of exploring their internal structure.
From Nobel Lecture (12 Dec 1974). In Stig Lundqvist (ed.), Nobel Lectures, Physics 1971-1980 (1992), 187.
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If the atoms in [a] decimetre cube of lead were all put into a chain side by side the same distance apart as they are in the normal lead, the strings of atoms so formed would reach over six million million miles.
In Lecture (1936) on 'Forty Years of Atomic Theory', collected in Needham and Pagel (eds.) in Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 99.
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In 1684 Dr Halley came to visit him at Cambridge, after they had been some time together, the Dr asked him what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it. Sr Isaac replied immediately that it would be an Ellipsis, the Doctor struck with joy & amazement asked him how he knew it, why saith he I have calculated it, whereupon Dr Halley asked him for his calculation without any farther delay. Sr Isaac looked among his papers but could not find it, but he promised him to renew it, & then to send it him.
[Recollecting Newton's account of the meeting after which Halley prompted Newton to write The Principia. When asking Newton this question, Halley was aware, without revealing it to Newton that Robert Hooke had made this hypothesis of plantary motion a decade earlier.]
Quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), 403.
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Just as the spectroscope opened up a new astronomy by enabling the astronomer to determine some of the constituents of which distant stars are composed, so the seismograph, recording the unfelt motion of distant earthquakes, enables us to see into the earth and determine its nature with as great a certainty, up to a certain point, as if we could drive a tunnel through it and take samples of the matter passed through.
'The Constitution of the Interior of the Earth, as Revealed by Earthquakes', Quarterly Journal of the Geological Society (1906), 62, 456.
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Magnitude may be compared to the power output in kilowatts of a [radio] broadcasting station; local intensity, on the Mercalli or similar scale, is then comparable to the signal strength noted on a receiver at a given locality. Intensity, like signal strength, will generally fall off with distance from the source; it will also depend on local conditions at the point of observation, and to some extent on the conditions along the path from source to that point.
From interview in the Earthquake Information Bulletin (Jul-Aug 1971), 3, No. 4, as abridged in article on USGS website.
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Our knowledge of stars and interstellar matter must be based primarily on the electromagnetic radiation which reaches us. Nature has thoughtfully provided us with a universe in which radiant energy of almost all wave lengths travels in straight lines over enormous distances with usually rather negligible absorption.
In 'Flying Telescopes', Bulletin of the Atomic Scientists (May 1961), Vol. 17, No. 5, 191.
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Pauling was shocked by the freedom with which the X-ray crystallographers of the time, including particularly Astbury, played with the intimate chemical structure of their models. They seemed to think that if the atoms were arranged in the right order and about the right distance apart, that was all that mattered, that no further restrictions need to be put on them.
Quoted by John Law in 'The Case of X-ray Protein Crystallography', collected in Gerard Lemaine (ed.), Perspectives on the Emergence of Scientific Disciplines, 1976, 140.
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Scripture and Nature agree in this, that all things were covered with water; how and when this aspect began, and how long it lasted, Nature says not, Scripture relates. That there was a watery fluid, however, at a time when animals and plants were not yet to be found, and that the fluid covered all things, is proved by the strata of the higher mountains, free from all heterogeneous material. And the form of these strata bears witness to the presence of a fluid, while the substance bears witness to the absence of heterogeneous bodies. But the similarity of matter and form in the strata of mountains which are different and distant from each other, proves that the fluid was universal.
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), 263-4.
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So numerous are the objects which meet our view in the heavens, that we cannot imagine a point of space where some light would not strike the eye;—innumerable stars, thousands of double and multiple systems, clusters in one blaze with their tens of thousands of stars, and the nebulae amazing us by the strangeness of their forms and the incomprehensibility of their nature, till at last, from the limit of our senses, even these thin and airy phantoms vanish in the distance.
On the Connexion of the Physical Sciences (1858), 420.
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The mountains too, at a distance, appear airy masses and smooth, but seen near at hand they are rough.
Diogenes Laertius, trans. Charles Duke Yonge, The Lives and Opinions of Eminent Philosophers (1901), 411.
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The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Physical astronomy, the branch of knowledge that does the greatest honor to the human mind, gives us an idea, albeit imperfect, of what such an intelligence would be. The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. Man owes that advantage to the power of the instrument he employs, and to the small number of relations that it embraces in its calculations. But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability.
'Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards' (1773, published 1776). In Oeuvres complètes de Laplace, 14 Vols. (1843-1912), Vol. 8, 144-5, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 26.
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The universe seems to me infinitely strange and foreign. At such a moment I gaze upon it with a mixture of anguish and euphoria; separate from the universe, as though placed at a certain distance outside it; I look and I see pictures, creatures that move in a kind of timeless time and spaceless space, emitting sounds that are a kind of language I no longer understand or ever register.
‘Interviews: Brief Notes for Radio’, Notes and Counter-Notes: Writings on the Theatre (1964), 136.
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Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. B. Cohen and Anne Whitman (1999), General Scholium, 943.
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We may produce at will, from a sending station. an electrical effect in any particular region of the globe; we may determine the relative position or course of a moving object, such as a vessel at sea, the distance traversed by the same, or its speed.
'The Problem of Increasing Human Energy', The Century (Jun 1900), 211. Collected in The Century (1900), Vol. 60, 209.
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Were the succession of stars endless, then the background of the sky would present us an uniform luminosity, like that displayed by the Galaxy—since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.
'Eureka: An Essay on the Material and Spiritual Universe' (1848), in W. H. Auden (ed.), Edgar Allan Poe: Selected Prose, Poetry, and Eureka (1950), 557.
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When autumn returns with its long anticipated holidays, and preparations are made for a scamper in some distant locality, hammer and notebook will not occupy much room in the portmanteau, and will certainly be found most entertaining company.
In The Story of a Boulder: or, Gleanings from the Note-book of a Field Geologist (1858), viii.
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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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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
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
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton

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